tag:blogger.com,1999:blog-88509155458001240652024-03-06T01:39:26.064-05:00Hue AnglesDave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.comBlogger79125tag:blogger.com,1999:blog-8850915545800124065.post-56326899371101416502024-02-29T08:02:00.004-05:002024-02-29T08:05:18.569-05:00Blue Morphos Have a Cool Color<p style="text-align: center;"> <span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">Send contributions to <a href="mailto:mhbrill2001@gmail.com">mhbrill2001@gmail.com</a></span> </p><p style="text-align: left;">
</p><p class="MsoNormal"><a style="mso-comment-date: 20231226T1234; mso-comment-reference: JS_1;"><span style="mso-comment-continuation: 2;">Lately I’ve noticed a presence
that has accompanied me from room to room</span></a><span style="mso-comment-continuation: 2;"><span class="MsoCommentReference"><span style="font-size: 8pt;"><a class="msocomanchor" href="#_msocom_1" id="_anchor_1" name="_msoanchor_1"></a></span></span></span><span class="MsoCommentReference"><span style="font-size: 8pt;"><a class="msocomanchor" href="#_msocom_2" id="_anchor_2" name="_msoanchor_2"></a></span></span>,
fluttering over the pages I read and landing on a surprising number of them. This
presence is the blue morpho, a large butterfly (8-inch wingspan) that inhabits
Central and South America and is celebrated for its beautiful electric-blue
color. That color is structural: it is caused by the interaction of incident
light with the shape of a light-receiving surface, not by wavelength-dependent
light absorption by that surface.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I first encountered the blue morpho in Kai Kupferschmidt’s book,
<i>Blue: In Search of Nature’s Rarest Color</i>, which I reviewed in Issue 504 of
ISCC News. There I learned about a tricky problem that the butterfly appears to
have solved through natural selection. Interference patterns can lead to
brilliant structural colors, but the color you see generally depends on the
angles of illumination and viewing. As the viewing geometry changes, it is
difficult to preserve the color of the butterfly’s wing at all angles. Kupferschmidt
notes that scientists have only recently understood the angle-independence of
that color. The proof of their understanding was their effectiveness in imitating
the butterfly’s color and is the subject of several U.S. patents (see U.S.
Patent Nos. 11,428,854 and 11,200,583, and also Patent Application No. 20210018659).
The inventor is none other than Andrew Parker, who gave one of the ISCC presentations
on color and evolution last September, a month or so after I had encountered
Kupferschmidt’s book.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Parker’s solution is a multi-layer composite of scales similar
to the microscopic scales on the wings of the morpho butterfly. Normally, a set
of nearly identical features with even spacing would cause an interference
pattern. The trick inspired by the morpho butterfly is to add a constrained
randomness in the orientation of the scales. Besides being randomly oriented,
Parker’s scales are convex, and that convexity causes the incident light to diverge
into a variety of directions while keeping a sufficient intensity and wavelength
selectivity to stay electric blue. This convexity seems to be the main
mechanism of the solution: Parker designed his multi-layers so as to minimize
the effects of interference in the light scatter. To this end, he forced the
refractive index to have a smooth dependence on spatial position within the layer,
which encourages a ray-optic analysis. (This could be a big surprise to those
of us who assume that iridescence is a property intrinsic to a structural color---but
remember Newton’s prism can serve as a light-dispersing element.) You have seen
the ray-spreading behavior before, in the convex side mirrors on your car (“objects
in mirror are closer than they appear”). When you look at this mirror’s
reflection of a localized light source, it indeed seems farther away than a
flat-mirror reflection. The source retains its intensity but occupies less
visual angle and (in compensation) visibility in a wider range of scattering directions.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">At about the same time I learned of Parker’s invention, I
received my August issue of <i>Optics and Photonics News</i>, and there was our
blue friend again, now in the context of “Radiative cooling in living color.”
The research was done by Wanlin Wang et al. in Shenzhen University in China.
The primary research publication is W. Wang et al., Cooling colors below
ambient temperature, <a style="mso-comment-date: 20231220T1906; mso-comment-reference: MY_3;"><span style="mso-comment-continuation: 4;"><i>Optica</i>
<b>10</b></span></a><span style="mso-comment-continuation: 4;"><span class="MsoCommentReference"><span style="font-size: 8pt;"><a class="msocomanchor" href="#_msocom_3" id="_anchor_3" name="_msoanchor_3"></a></span></span></span><span class="MsoCommentReference"><span style="font-size: 8pt;"><a class="msocomanchor" href="#_msocom_4" id="_anchor_4" name="_msoanchor_4"></a></span></span>(2023), 1059-1068.</p>
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<p class="MsoNormal">As did Parker, the Chinese group claimed a blue-morpho-inspired
composite layer that achieves the viewing-angle insensitive blue color. For
angle diversity, they found that frosted glass provided a satisfactory solution.
But the Chinese group simultaneously strove for a different objective. Their angle-constant
blue layer also provides substantial radiative cooling-- up to 2 degrees C
lower than the ambient and better than using a white reflector. To achieve this
cooling performance, they adjusted the spectral properties of the layer over
all visible through mid-IR electromagnetic wavelengths. In particular, the
absorbed part of the incident solar radiation heats the surface and converts the
heat to black-body radiation with a mid-IR component that is much stronger than
the passive cooling emission that would otherwise be present in mid-IR. It
turns out that the Earth’s atmosphere is completely transparent to mid-IR radiation
(8000 to 13000 nm). Because of that transparency, radiation in the mid-IR
window promptly leaves the Earth and never returns. For us it might be a window
of escape from global warming. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Having read about the Shenzhen group’s radiative-cooling layer,
I tried to tie the design back to the morpho butterfly but found the analogy
wanting. It seemed to me that their device comprised two independent inventions---one
for angle-invariant color and one for radiative cooling---only the first of
which pertains to structural colors and thereby to the blue morpho. The main emphasis
of the <i>Optica</i> article was radiative cooling, which is not a property I’ve
ever seen attributed to the blue morpho. How, then, can one convincingly assert
that this research is related to the blue morpho? </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The plausibility seems to hinge on the choice between two
alternative words: “imitate” versus “inspire.”<span style="mso-spacerun: yes;">
</span>The Shenzhen group used both words to describe the connection. On one
hand, they <i>imitated</i> the structure of the blue morpho’s wing (presumably in
solving the color-versus-angle problem), but they were not imitating it anymore
when they were solving the cooling problem. On the other hand, they could have
been <i>inspired</i> by the blue morpho to do the entire project including the
cooling problem. Unlike an object of imitation, an object of inspiration does
not imply technical transfer to the project from the source of inspiration.
Imitation is hard, as implied by Yogi Berra: “If you can’t imitate him, don’t
copy him.” So, the blue morpho as inspiration is more inclusive (perhaps
all-inclusive: anything can be inspired by anything else).</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I tried to be tolerant of the looser connection implied by “inspired,”
but ultimately its all-inclusiveness turned me off and I remained unswayed. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Suddenly, the butterflies that were fluttering around me
disappeared.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The blue morpho is indeed a beautiful creature and a
wonderful muse. It’s not often I see a single actor participating in so many
shows at the same time. But the radiative-cooling show seems far-fetched for this
actor. I question the relevance, other than to say that the blue morpho has a
cool color. <br /></p>
<p class="MsoNormal"> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHBnGNqw_RXyf-vqVH5dYjboZBPuVY35XpGcUYLUAHFHb18ahQfFVPTFhD2fwk196YYhsGN_W59kBE3l4WkDa5RdJYkwl1uqUKXeBbW8z5VNkfgM1Kqb3I7XebZ4oB-S5GOPnZkKp245DrzTEP__nxnX8rhjxsnMKCk7LxIDiThQJknuAwTIUC0obgUaM/s520/520px-Blue_Morpho.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="345" data-original-width="520" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHBnGNqw_RXyf-vqVH5dYjboZBPuVY35XpGcUYLUAHFHb18ahQfFVPTFhD2fwk196YYhsGN_W59kBE3l4WkDa5RdJYkwl1uqUKXeBbW8z5VNkfgM1Kqb3I7XebZ4oB-S5GOPnZkKp245DrzTEP__nxnX8rhjxsnMKCk7LxIDiThQJknuAwTIUC0obgUaM/s320/520px-Blue_Morpho.jpg" width="320" /></a><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> <br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="mso-spacerun: yes;"> </span>Figure 1. Blue Morpho, Female, Dorsal view.</div>
<p class="MsoNormal" style="text-align: center;">Source: Wikipedia. Copyright <a href="https://creativecommons.org/licenses/by-sa/3.0/">https://creativecommons.org/licenses/by-sa/3.0/</a></p><p class="MsoNormal" style="text-align: center;"> </p><p class="MsoNormal" style="text-align: left;">Michael H. Brill <br /></p><p style="text-align: left;"><style id="dynCom" type="text/css"></style><style>@font-face
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-76579086934598731812023-11-01T09:20:00.015-04:002023-11-03T07:22:52.277-04:00Blue Book<p style="text-align: center;"> <span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">Send contributions to <a href="mailto:mhbrill2001@gmail.com">mhbrill2001@gmail.com</a></span> </p><p style="text-align: left;">
</p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"> </div><span style="font-family: times; font-size: medium;">After 12 years of waiting, I have found the answer to the
color-realism question I asked in a poem and kept on my Hue Angles blog site (<a href="https://hueangles.blogspot.com">https://hueangles.blogspot.com</a>): Does
color lie in the world or in the mind? <i>Answer:</i> “Blue is not out there,
and it is not inside us either. The radiant blue of a cornflower is a kind of collaboration
between us and the plant.” The origin of this quote is Kai Kupferschmidt’s book,
<i>Blue: In Search of Nature’s Rarest Color</i> [The Experiment, 2021], p. 7. Kupferschmidt
holds a degree in molecular biomedicine from the University of Bonn, writes for
<i>Science</i> magazine, and lives in Berlin. The pertinence of the sentence I
quote is in no way constrained by his restrictions of subject matter to the color
blue or to the reciprocal communication between humans and plants. I hope it
might quiet the din of debate between realists and subjectivists in philosophy.</span><p></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">Heartened by the author’s simple resolution of the realist
question in color, I backed away, for a moment, from the book—which a close
friend had just given to me. It is a small but physically dense 216 pages,
adorned on the inside with color layout (mostly blue) with full-page completely
blue separators between the chapters. The hard cover is entirely colored in
subtly different shades of blue (except for a peacock on the front), and even
the page edges are a dark blue. Receiving this object, I felt as if I were
receiving a mystical talisman like David Lynch’s blue key <a name="_Hlk144570762">in the movie <i>Mulholland Drive</i>.</a></span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium; mso-bookmark: _Hlk144570762;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">Hoping to understand this object better than I understand <i>Mulholland
Drive</i>, I thought, what’s the big deal about blue? Kupferschmidt made some
assertions about blue that seem to be oxymorons—that blue is ubiquitous (e.g.,
the blue sky) and rare (e.g., blue lobsters). Then I checked how many
Hue-Angles articles have “blue” in the title. The answer is four, not including
the present one. In comparison, green appears in three Hue-Angles titles, seven
colors appear in one or two titles, and no other color is mentioned at all. From
the example of Hue Angles itself, I was forced to acknowledge the plausibility
of Kupferschmidt’s assertions, even if they seem self-contradictory.</span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">So, I started to read. The five simply titled chapters are logical,
clear, and interesting. </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">STONES deals with the development of inorganic colorants,
including chemistry and historical connections. Kupferschmidt makes clear that
the search for the perfect blue led not only to Prussian blue as an artist’s
tool, but also to discovery of hydrocyanic acid—used to kill millions of people.
There is more than one side to the color blue.</span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">SEEING discusses the anatomy, physiology, and psychophysics
of color perception. The author covers a vast domain and makes the subject look
easy by his clear language and organization. For example, he explains the Blue
Dress by invoking color constancy. (I would have said “<i>failure </i>of color
constancy,” but that is a quibble.)</span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">PLANTS discusses color as a collaborative language to
communicate with animals (and with us). Also, the chapter emphasizes that most plants
have colors that are determined by molecular reactions to light, not by diffraction
off structures (as is more common for animals). The author observes that green
light is reflected from plants, and we see the light because it is available
and useless to the plants. From a plant’s point of view, the green part of the
spectrum is a “green gap.” But still in Kupferschmidt’s text, the color blue
predominates, from indigo to the coal-tar blues, from cornflowers to the
unattained grail of the blue rose. </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">SPEAKING emphasizes the cultural dependence of color-name
boundaries, as studied by Berlin and Kay. The chapter begins with William Gladstone
and ends with political correctness.</span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">ANIMALS talks about structural colors, and most of the examples
are birds. The chapter argues convincingly that the success of structural colors
lies in their invariance with respect to lighting/viewing geometry. This is
ensured if the precise diffractive structures are mixed with apparently random perturbations
that have a hidden regularity. We only recently came to understand this subtlety.<a href="#_ftn1" name="_ftnref1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[1]</span></span></span></span></a></span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">The book has two main themes. (1) blue is a special color;
and (2) one should give blue the attention, appreciation, and awe that it
deserves. Much of what the author finds special in the color blue is anecdotal
or otherwise not amenable to quantitative study; it certainly lacks a specific
point-by-point comparison of blue with other colors. Nonetheless, he has
devoted his non-working life to compiling an impressive array of historical and
scientific matter that will have wide appeal. He travelled far to acquire these
things.</span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">Early in the book, the author uses a cryptic comment to
command a reader’s thoughtful attention (much as does a Zen koan<a href="#_ftn2" name="_ftnref2" style="mso-footnote-id: ftn2;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[2]</span></span></span></span></a>), The
comment is this (p. 34): “It is […] no accident that accidents have played such
an important role in the history of color. The reason? So far it has been
nearly impossible to predict with any certainty what color a particular
substance will have without making it.” For example, the same process and raw
material can give rise to either ruby or emerald. The color can be considered
an accident. But the fact is that many such accidents happen in pigment
preparation; that fact by itself is no accident. It is the sensitivity of the
coloration mechanism to detailed orbital energies. The author applies similar
logic to explain the many years of exploration preceding the discovery of
Prussian blue and later blue pigments such as YInMn as late as 2009. The author
uses the device of non-accidental accidents to fortify his argument for the
specialness of blue.</span></p><p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">At the start of the SEEING chapter, Kupferschmidt delivers his
over-arching message through reference to a scene from the TV show <i>The
Simpsons</i>. Homer Simpson, after declaring himself “not easily impressed,” lets
his attention wander and exclaims, “Whoa! A blue car.”<span style="mso-spacerun: yes;"> </span>Although Kupferschmidt acknowledges the
humor, he muses that “even the sight of a blue car ought to amaze us” (p. 53). To
end the SEEING chapter, he echoes “Whoa! A blue sky.” The substitution of “sky”
for “car” recalls the opening lines of the book, recounting the Apollo 17
astronauts’ awe upon seeing the Earth from space. The ensuing photograph of the
Earth (called <i>The Blue Marble</i>) is famous and is often a point of
departure for a lecture warning us that we have a clear responsibility to save
our planet. Kupferschmidt does not give this lecture, but instead determines “to
look out into the world more often, as if I were seeing all its colors for the
first time, and to say to myself, ‘Whoa! A blue sky.’” (p. 82)</span></p><p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">Having solved one philosophical problem to my satisfaction,
Kupferschmidt’s book raises other questions: How can one sustain the enthusiasm
of seeing colors as if for the first time? Why is blue so special? </span></p><p class="MsoNormal"><span style="font-family: times; font-size: medium;"><br /></span></p>
<p class="MsoNormal"><span style="font-family: times; font-size: medium;">I see this book as a report of and homage to Kupferschmidt’s
personal spiritual journey in search of blue. For more about this journey,
please read the final section, HERE WAS BLUE. I won’t spoil it for you. I also
wish him well.</span></p><p class="MsoNormal"><span style="font-family: times; font-size: medium;"> </span></p><p class="MsoNormal">
</p><p class="MsoNormal"><span style="font-family: times; font-size: medium;">Michael H. Brill </span></p>
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<div style="mso-element: footnote-list; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgSQEJ0uNqKhhhZHWE8w70BxKdM0Pv92nlGdqMMhfUDQUO_HZZ2TgjrLxapTorTufv8kOr1cHJlp0umyIbp567GLw9qa-fgsCPDgyAxI6zu6BTzfFz7DxRLngGgyywsnpJ_K5BxxHxJst35FLp5U-oQf15-XijTYa54s_4rWkJ-exUaBXa7Dfy-k0KdYc/s4032/20230902_115332.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgSQEJ0uNqKhhhZHWE8w70BxKdM0Pv92nlGdqMMhfUDQUO_HZZ2TgjrLxapTorTufv8kOr1cHJlp0umyIbp567GLw9qa-fgsCPDgyAxI6zu6BTzfFz7DxRLngGgyywsnpJ_K5BxxHxJst35FLp5U-oQf15-XijTYa54s_4rWkJ-exUaBXa7Dfy-k0KdYc/w320-h240/20230902_115332.jpg" width="320" /> </a><br clear="all" /></div><div style="mso-element: footnote-list;">
<hr align="left" size="1" width="33%" />
<div id="ftn1" style="mso-element: footnote;">
<p class="MsoFootnoteText"><a href="#_ftnref1" name="_ftn1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="font-family: "Times New Roman",serif; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[1]</span></span></span></span></a> The
rainbow colors that we see when we look at a diffraction grating (like a CD)
are one type of simple structural color. But they are very sensitive to the
angles of lighting and viewing. Peacocks and Morphos butterflies pull some
three-dimensional tricks with their structural color so that the color is
constant over some range of angles. [John Seymour]</p>
</div>
<div id="ftn2" style="mso-element: footnote;">
<p class="MsoFootnoteText"><a href="#_ftnref2" name="_ftn2" style="mso-footnote-id: ftn2;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="font-family: "Times New Roman",serif; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[2]</span></span></span></span></a> A paradox
to be meditated upon that is used to train Zen Buddhist monks to abandon
ultimate dependence on reason and to force them into gaining sudden intuitive
enlightenment.</p>
<p class="MsoFootnoteText">“Koan.” <a href="https://www.merriam-webster.com/">Merriam-Webster.com</a>
Dictionary, Merriam-Webster, <a href="https://www.merriam-webster.com/">https://www.merriam-webster.com/</a></p>
<p class="MsoFootnoteText"> </p>
</div>
</div>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-58933218397887315672023-08-22T15:28:00.003-04:002023-09-03T06:08:18.649-04:00How to Stay Awake in Standards-Body Meetings<p style="text-align: center;">
<span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">Send contributions to <a href="mailto:mhbrill2001@gmail.com">mhbrill2001@gmail.com</a></span> </p><p style="text-align: left;"> </p><p style="text-align: left;">
</p><p class="MsoNormal">Having recently returned from Committee E12’s ASTM 125<sup>th</sup>
Anniversary Celebration in Conshohocken, PA, I examined the promotional button
that had been given to the attendees. It was plain and unassuming: black-and-white
printing of the logo, the occasion, and the catch phrase “helping our world
work better.”</p><p class="MsoNormal"> </p><p class="MsoNormal">“Can’t we jazz up this outreach?” I thought. Even our
current members find it hard to stay awake in some of our sessions.</p><p class="MsoNormal"> </p><p class="MsoNormal">I am the Vice Chair of Committee E12 (Color and Appearance).
Also, I am the Acting Chair. My friend Jack chairs three of E12’s thirteen technical
sub-committees. My friend Hugh does intensive work in all the sub-committees. We
are all aging out of the ASTM, leaving no successors. A ballot is upon us. No
wonder we are thinking about outreach.</p><p class="MsoNormal"> </p><p class="MsoNormal">On behalf of the ISCC News, Jodi Baker recently asked
several of us to write a progress report on the activities of E12. As a first
exercise, I found out that E12 originated five standards in the past ten years.
The standards themselves do not give the impression of a crescendo of purposeful
activity: Two of them pertain to retro-reflective materials, one is a
statistical algorithm, one is a color-difference formula, and one is a
well-used color-order system.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Such metrics as the number of standards per decade do not
get to the heart of ASTM’s progress, but Jodi’s question surely got to the
heart of our outreach problem.</p><p class="MsoNormal"><span style="mso-tab-count: 1;"> <br /></span></p><p class="MsoNormal"><span style="mso-tab-count: 1;"> </span>By its nature, standards bodies are difficult to glamorize.
A documentary standard represents a consensus between companies to combine
their products, say, by company A (making spectrophotometers) buying components
from company B (making lamps bought by company A to use in its spectrophotometers).
Smooth commerce requires compatible complementary functions. On the other hand,
too much collaboration begins to look like a monopoly, which is illegal. A delicate
balance must be struck between not enough consensus (e.g., railroad gauges don’t
match when they come from opposite sides of a country) and too much consensus
(monopoly). In general, a standard does not come close to the bleeding edge of
research because research is what distinguishes companies and grows their
profits. Research is usually a corporate secret.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Because standards are consensus documents and not news
reports, standards bodies are slow in their visible production, and color science
particularly shows this tendency.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Without glamor, how are we to sell standards-body membership
to our youthful successors? I think we must see standards bodies as a public
work, allowing parts of a product from different companies to be assembled according
to a public understanding. <span style="mso-spacerun: yes;"> </span>A documentary
standard represents an open covenant among companies who declare compliance with
the standard.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Keeping our standards in order requires vigilance, and that
is where younger people can make a substantial contribution. We need our
standards to be prescriptive (unambiguous in interpretation), current (not
obsolete), and driven into existence by commercial necessity (not by the pride
of authorship of a few individuals). Right now, ASTM and its volunteer members
are working hard to achieve this vigilance. Users and technical contacts of
each standard are continually reporting errors back to the originating
technical committee, who then revises the standard to correct the errors. That
measure improves the standard’s prescriptiveness. Each standard is reviewed for
revision or withdrawal every 5 years. That addresses the concern about
obsolescence. Finally, a standard announces no individual authorships (although
internally ASTM retains lists of contributors so periodic awards can be made). Anonymity
of authorship was intended to reduce the incentive of pride-of-authorship. (That
measure is not entirely effective, as Danny Rich humorously noted in an ISCC paper
from about 2010.)</p><p class="MsoNormal"> </p>
<p class="MsoNormal">So, how do you keep awake in a standards-body meeting? Do the
necessary job, knowing its general importance, (To fortify my resolve, I have
found it helpful to chew on coffee beans.) Also, get into lots of contentious
technical discussions at the meetings. I have learned a lot from such discussions
at ASTM.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">I invite you to get involved in ASTM activities (including
individual and organizational membership). Please go to
https://www.astm.org/get-involved/membership.html.</p><p class="MsoNormal"> </p><p class="MsoNormal">Michael H. Brill <br /></p>
<p class="MsoNormal"> </p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-47648705678079722292023-06-05T15:32:00.004-04:002023-06-06T01:49:51.304-04:00The Minefield of Color Ownership<p>
</p><p class="MsoNormal" style="margin-left: 1in; mso-layout-grid-align: none; text-autospace: none; text-indent: 0.5in;">
</p><p class="MsoNormal" style="margin-left: 1in; text-align: left; text-indent: 0.5in;">(Send contributions to <a href="mailto:mhbrill2001@gmail.com">mhbrill2001@gmail.com</a> ) <span style="mso-bidi-font-size: 10.0pt;"><br /></span></p><p class="MsoNormal" style="margin-left: 1in; text-align: left; text-indent: 0.5in;">
</p><p class="MsoNormal">When overseeing the intellectual-property process in a
company devoted to color, one regularly is asked whether a color can be “owned”
by dint of trademark or copyright. The stock answer is <i>no</i> for copyrights
and a qualified <i>yes</i> for trademarks. Whenever you select a color for a
product or its packaging (or a company’s logo), you must carefully avoid colors
that are already trademarked by one of your business competitors. It is a
matter of legal opinion whether a business is to be regarded as your competitor.
If so, then as far as your business is concerned, these colors are essentially
owned by the trademark-holders. If you use the trademark colors (in any of a
broad range of contexts), the owners are likely to sue you, which will surely
be expensive and also block the sale of your product until its color is changed
or until the court case is resolved. <br /></p>
<p class="MsoNormal">An article written a decade ago<a href="#_ftn1" name="_ftnref1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[1]</span></span></span></span></a> describes
several trademarked colors: John Deere green (or, more saliently, a specific
green and yellow), Target red, T-Mobile magenta, UPS brown, Tiffany blue, University
of Texas burnt-orange, University of North Carolina blue, Home Depot orange, Caterpillar
yellow, and 3M purple.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">The stock answer to our initial question is a bit too simple,
as we will now show. What follows might be considered too much information, but
we will proceed anyway.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">How do you know you have picked a safe color? As metrologists,
we naturally seek refuge in measured numbers. We’d like to define a quantified
color space (accompanied by an agreed-upon illuminant/observer for object colors
or a white point for emissive displays). Within that space, we’d like to know
where the property line is that delineates colors that are owned from colors
that are free to be used.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Surprisingly, however, color-trademark litigations proceed
with no quantitative evaluation, only the verdict of a jury in a courtroom
under available light and in the context decided by the lawyers. Even the system
of color names (often Pantone colors) has no rhyme or reason.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">It looks as if color space has turned into a minefield of ownership
(perhaps worthy of the double entendre “mine” field). One of us (HSF) has had personal
experience as an expert witness. Here are some details.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Only three things may be unqualifiedly trademarked in the
United States: a brand name, a logo or a slogan. Trademarking a color alone is available
<span style="mso-spacerun: yes;"> </span>only under very limited circumstances.
Colors that are functional (e.g., the color of a medicinal pill that is used to
identify the drug) or colors that are purely aesthetic are not trademark-eligible.
<span style="mso-spacerun: yes;"> </span>If a trademarked logo is colored, the color
or color combination is included as a property of the logo. Thus, a color may
become associated with the brand, as say Coca-Cola red or John Deere green.
That immediately raises the question as to what are the protected tolerances
around a logo-protected color? The answer is that there are no formal
guidelines. That will be decided by a jury who will be instructed to find an
interference if they think the intent of the color choice was to imitate the
trademarked logo in the consumer’s mind. Obviously, the farther you get from
the trademarked color, the better your chances. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">There is another way in which a color may become protected
by law. Although it is not registerable, a product’s “trade dress,” which is its
overall appearance including color, design and markings, may be claimed for
protection against others duplicating it. A good example is the Coke bottle. That
distinctive shape and the green glass constitute Coca-Cola’s trade dress.
Notice that no other cola company uses green glass. Yet almost all breweries
package at least part of their output in green glass. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">That raises another issue. Trademark protection applies only
to the product lines or industries in which they are granted. You are free to make
your product in John Deere green if your product is not a tractor or farm
machinery. What if you had a product that wasn’t a tractor or farm machinery
but could possibly be made by John Deere---say, a mailbox? You probably should
go to John Deere and license the green and yellow combination from them for
mailboxes. They will give you an exclusive for mailboxes in their green and
yellow, and farmers everywhere will rush to buy your box. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">Is there a common-law trademark? Yes, there is, but it applies
only locally. You can open a store called “Jones’s Grocery Store” and you can
choose the color and the typescript for placing over the front door. No one
else can use that logo, even if it is unregistered, but that’s going to protect
you only in your small town. Someone in the town down the road a bit, or
someone across town if the town is big enough, can use the same device with
impunity. Again, the criterion will be intent to imitate. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">Registration of a trademarked logo will, however, provide
nationwide coverage, and will imply an additional benefit. You will receive protection
from foreign goods that infringe your trademark from being imported. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">The minefield of the situation remains how close, or how far
away, does your color have to be from a registered trademark to be unassailable?
Pick a color that can’t be confused with the protected color or you might find
out the answer to this question the hard way. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">Given these circumstances, the idea that a color is “owned”
is defensible—no more fictitious than our deeming a condominium to be “owned” by
its occupant when its defining walls are not. Furthermore, the metaphor of a
minefield is not too extravagant.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Neither of the authors are lawyers, so the information
contained here is not to be taken as legal advice. The information is intended
to be a jumping-off point for further discussion within the ISCC.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Michael H. Brill and Hugh S. Fairman</p>
<div style="mso-element: footnote-list;"><br clear="all" />
<hr align="left" size="1" width="33%" />
<div id="ftn1" style="mso-element: footnote;">
<p class="MsoFootnoteText"><a href="#_ftnref1" name="_ftn1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span style="font-family: "Times New Roman",serif; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">[1]</span></span></span></span></a> A.
Tzatzev, Colors that are Trademarked, Business Insider (29 Sept, 2012) <span style="mso-spacerun: yes;"> </span><a href="https://www.businessinsider.com/colors-that-are-trademarked-2012-9"><span style="color: blue;">Colors That Are Trademarked (businessinsider.com)</span></a></p>
</div>
</div>
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<p><style>@font-face
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-29300487820536020342023-02-04T14:45:00.002-05:002023-02-04T19:19:06.339-05:00The Seven Pillars of SI Wisdom<p style="text-align: center;"> <span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">(send contributions to <a href="mailto:mhbrill2001@gmail.com">mhbrill2001@gmail.com</a>)</span></p><p>
</p><p class="MsoNormal">Early metrology is sometimes exemplified by the <i>King’s
foot</i>, a convention established in the 12<sup>th</sup> Century by Henry I of
England. The most obvious problem with the King’s foot was the need to recalibrate
when the regime changed.<span style="mso-spacerun: yes;"> </span>The underlying
problem was more subtle. Any anthropocentric metric—by which I mean a metric
based on human attributes or performance--- is both statistically and
conceptually more fragile than one based on universal constants of nature.</p>
<p class="MsoNormal" style="margin-left: 0.5in;"> </p>
<p class="MsoNormal">Nowadays (<a href="https://www.bipm.org/en/home">https://www.bipm.org/en/home</a>)
<span style="mso-spacerun: yes;"> </span>we start with seven precisely related constants
of nature and derive from them seven reference units which are said to be all
we’ll ever need. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>The constants are cesium hyperfine frequency
Δν<sub>Cs</sub> , Planck’s constant h, the speed of light in vacuum c,
the elementary charge e, Boltzmann’s constant k, Avogadro’s number N<sub>A</sub>
,<b><span face=""Arial",sans-serif" style="color: #202124;"> </span></b>and the
luminous efficacy of a defined visible radiation K. The basic units are mass
(kilogram), distance (meter), time (second), amount of matter (mole), electric
current (Ampere), temperature (kelvin degree), and luminous intensity (candela).
The whole system, called SI, comprises what we might call the <i>seven pillars
of SI wisdom</i>.<span style="mso-spacerun: yes;"> </span>The system seems to
have no anthropocentrism.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">But wait! The seventh constant and the seventh unit are not
like the others. This seventh pillar depends not only on humanity in general, but
on particular observers whose flicker sensitivity and brightness data the CIE aggregated
to define the 1924 luminous efficiency function V<a name="_Hlk121619835">(λ</a>)
in visible wavelength λ .</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The history of the candela in Wyszecki and Stiles (<i>Color
Science</i>, <i>2<sup>nd</sup> ed</i>, Wiley 1982; pp. 254-255) is quite
educational.<span style="mso-spacerun: yes;"> </span>Rather than use the whole
1924 <a name="_Hlk122081797">V(λ) </a>curve (which was to be obsoleted and
conditionalized a lot in the next century), standards bodies defined the
candela with only two human-related numbers: the peak wavelength (555 nm) of V(λ)
and the watt-to-lumen ratio (1/683).<span style="mso-spacerun: yes;"> </span>Interestingly,
the SI does not define the candela for any light other than monochromatic at 555
nm, so, for example, I cannot ask SI what the candela count is for a given wattage
of light at 460 nm.<span style="mso-spacerun: yes;"> </span>This illustrates that
any reduction of the candela’s dependence on human vision decreases the universality
of SI.</p>
<p class="MsoNormal"><a name="_Hlk122029780"> </a></p>
<span style="mso-bookmark: _Hlk122029780;"></span>
<p class="MsoNormal">The candela didn’t enter the SI system uncontested. <span style="mso-spacerun: yes;"> </span>A sign of the struggle was that for many years
the US National Bureau of Standards (NBS) divorced itself from all human
factors including metrology of vision and other senses.<span style="mso-spacerun: yes;"> </span>When NBS deflected responsibility for calibration
of color-measurement instruments, the need for such calibration was satisfied
by private companies such as Hemmendinger Color Lab.<span style="mso-spacerun: yes;"> </span>Fortunately, NBS (now NIST) takes on
metrology of a more human sort, so they’re helping to manage the seventh pillar.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">We’ve come a long way in the standardization of fundamental
constants and their units.<span style="mso-spacerun: yes;"> </span>But one of
the seven basic units of SI, the candela, is tied to a human-based
standard.<span style="mso-spacerun: yes;"> </span>Even in the newest refinement
of SI, a vestige of the King’s foot remains! </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">That the SI metrologists felt forced to include a human-vision
metric in one of its seven pillars reminds us of the importance of vision in
our understanding of the universe. A question to ponder: Of all the five
senses, why was vision salient?<span style="mso-spacerun: yes;"> </span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Michael H. Brill</p>
<p class="MsoNormal">Retired Color Scientist</p>
<p class="MsoNormal">mhbrill2001@gmail.com </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p><style>@font-face
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-65959694096290293482022-11-03T13:30:00.004-04:002022-11-03T13:30:55.949-04:00Erwin Schrödinger’s Math Error<p style="text-align: center;"> (
<span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a></span>
)
</p><p class="MsoNormal">In mid-August, an article from Los Alamos National Laboratory
(LANL) News was brought to my attention [1]. The title was provocative: “Math
error: A new study overturns 100-year-old understanding of color perception.” The
error—made by Erwin Sch<a name="_Hlk114500982">rö</a>dinger in 1920 but actually
going back to Bernhard Riemann in 1854—was to model color perception as a 3D curved
space (called a Riemannian space) in which distance along special curves,
called geodesics, represents perceived color difference. The article from LANL
News called it a math error—exhilarating to discover among the works of the
greats after more than a century. The article cited a research paper in the
Proceedings of the National Academy of Sciences (PNAS) and was based on work at
LANL [2]. The LANL authors were declaring that their work should inspire a paradigm
shift in color science.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I was curious enough to get the PNAS paper. Unsurprisingly, what
they called the “math error” was a counterfactual assumption and not a mistake
in the algebra. Further, LANL had not proposed an alternative model, and a
paradigm shift requires a new as well as an old paradigm. So there’s no paradigm
shift yet.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">To understand more requires a bit more about Riemannian
space. Picture the surface of a sphere. Draw a point on the sphere, and a little
circle around the point. On a Euclidean plane the ratio of the circumference to
the diameter of that circle would be π, but on the sphere it is less than π
(Figure 1), because the surface of the sphere is a Riemannian space of 2
dimensions. A geodesic between two points A and B on a sphere is the big circle
on the sphere that is in the plane containing the sphere’s center. The arc of shortest
distance <i>d</i>(AB) between A and B on the sphere is on that big circle
(Figure 2). </p><p class="MsoNormal" style="text-align: center;"><img alt="" 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" /> </p><p class="MsoNormal" style="text-align: center;">
</p><p class="MsoNormal" style="text-align: center;"><i>Figure 1 – The distance from a point to the circle, if
constrained to be on the sphere, is always greater than the straight-line distance
through the interior of the sphere</i>.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal" style="text-align: center;"><span style="mso-no-proof: yes;"><img alt="" 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" /></span></p>
<p class="MsoNormal" style="text-align: center;"><i>Figure 2 – The black arc shows the shortest path between
two points</i>. </p><p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
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</p><p class="MsoNormal">Given this background, here is the logic of the paper: <span style="mso-spacerun: yes;"> </span>In a Riemannian space, if 3 points A, B, C are
on a geodesic with B between A and C, then their distances <i>d</i> have additivity:
<i>d</i>(AB) + <i>d</i>(BC) = <i>d</i>(AC). To test this additivity, the
authors first assumed that the neutral colors comprise a geodesic in Riemannian
color space, Then they showed experimentally that, for widely separated neutral
colors, <i>d</i>(AB) + <i>d</i>(BC) is greater than <i>d</i>(AC). Therefore, colors
can’t form a Riemannian space. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The person who brought the LANL News article to my attention
wanted to know if the PNAS research paper would lead to a paradigm shift with
industrial color implications. A glance at the history of such errors is enough
to make a fair prediction.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Consider the basic laws of color matching—Grassmann’s laws. The
error there is in the assumption that matches are transitive: If A matches B
and B matches C, then A must match C. But in the real world, “A matches B” means
“A is within a just-noticeable color difference of B.” So Grassmann was wrong. Yet
the New York Stock Exchange was unaffected. In fact, I am not aware of any effect
on color-matching protocols.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Next, consider the Euclidean color space (a special case of
Riemannian in which the geodesics are straight lines and distance is the square
root of the sum of squares of coordinate differences). Euclidean color spaces
have existed for more than 150 years. The earliest may be Helmholtz’s color
space (which was Euclidean in log RGB coordinates). A typical one is CIELAB (in
nonlinear coordinates relative to XYZ). The latest may be DIN99o, the current
version of the German standard DIN99, which was published in 2018. Euclidean
spaces persist even though their incorrectness was noted by Ludwig Silberstein
in 1943 [3].</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">For CIELAB, the lack of perceptual uniformity was not
totally ignored. In response to the long-obvious fact that CIELAB’s Euclidean
distance doesn’t track color differences, the standards bodies detoured around
the impressive and difficult Riemannian alternative and took a new approach:
they built color-difference models using the underlying CIELAB coordinates, but
wrote color differences using creative combinations of CIELAB quantities. Examples
are CMC, CIE94, and CIE2000—all applicable for small color differences. (Large
color differences were left to a few adventurers.) But none of this activity could
be called a paradigm shift.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In view of these examples, let’s look at the history of
Riemannian color spaces that are not Euclidean. The earliest may be Schroedinger’s
in 1920 (missed being Euclidean by “<i>tha…at</i> much”), and the latest may be
in a September article <span style="color: #0d0d0d;">[4] which</span> describes
the post-CIELAB Riemannian choice as the road rarely taken. That observation in
itself denies Riemannian color space the status of “the current scientific
paradigm” as asserted in the PNAS paper. The vaunted paradigm shift, then, has
neither a “before” nor an “after” paradigm. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">And the LANL result has an ironic twist: Its principle of
diminishing returns teaches us that we should care less rather than more about
evaluating very large color differences, because large color differences matter
less than we had assumed. “Relax…it’s no big deal,” it says.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">So a paradigm shift is not imminent. But the buzz generated by
the LANL article might give The Dress a run for its money! </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><i>Thank you to John Seymour for creating the illustrations
for this article.</i></p>
<p class="MsoNormal"><span style="color: #0d0d0d;"> </span></p>
<p class="MsoNormal">[1] <a href="https://discover.lanl.gov/news/0810-color-perception">https://discover.lanl.gov/news/0810-color-perception</a>
.</p>
<p class="MsoNormal">[2] Bujack R, Teti E, Miller J, Caffrey EJ, and Turton TL, The
non-Riemannian nature of perceptual color space. Proc Nat Acad Sci, vol 119,
No. 18 (2022)</p>
<p class="MsoNormal">[3] Silberstein L, Investigations on the intrinsic
properties of the color domain. J Opt Soc Am 33 (1943), 385-418. </p>
<p class="MsoNormal"><span style="color: #0d0d0d;">[4] Candry P,<span style="mso-spacerun: yes;"> </span>De Visschere P, Neyts K. Line element for the
perception of color. Optics Express30(20) 36307-36331(2022).</span></p>
<p class="MsoNormal"><span style="color: #0d0d0d;"> </span></p>
<p class="MsoNormal"><span style="color: #0d0d0d;">Michael H. Brill</span></p>
<p class="MsoNormal"><span style="color: #0d0d0d;">Datacolor</span></p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-13772269611098740022022-08-30T18:47:00.005-04:002022-08-30T18:51:29.906-04:00Response to Hue Angles ISCC 498<p>
</p><p class="MsoNormal">In the <i>Hue Angles</i> column Spring 2022 issue of the
ISCC newsletter, Michael Brill offered a challenge for all his fellow chromo-historians:
<i>What is the oldest hack in color engineering?</i> Dr. Brill’s nomination was
the normalization of the tristimulus values against the illuminant.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">I accept his challenge, and submit not one, but two related
hacks, just to distinguish my entry from the hundreds of others who responded
to the challenge.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">I contend that the tristimulus functions are themselves a
hack, well, actually two hacks. And since you can’t normalize tristimulus
values <i>until you</i> <i>have</i> tristimulus values, I claim that my hacks
are slightly older than the normalization hack proposed by Dr. Brill. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">To explain my proposed hacks, I need to give some thrilling backstory.
There is a common misconception that the tristimulus functions (also referred
to as the <i>Standard Observer</i>) that we know and love were developed to
create color metrics that mimicked how we see color. Nope. Not true. There is
another common misconception that the tristimulus functions were the best guess
in 1931 as to the spectral response of the human eye. Sorry. That’s not true
either. The backstory will explain both of those misconceptions.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Color measurement in the 1920s was considerably different
than it is today. Today, we punch a button and a set of color coordinates comes
out. In the 1920s, measurements were performed by a device called a <i>tristimulus
light mixing colorimete</i>r<a href="#_ftn1" name="_ftnref1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span face=""Calibri",sans-serif" style="font-size: 11pt; line-height: 107%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">[1]</span></span></span></span></a>.
The user would meticulously adjust the intensities of a red light source, a green
light source, and a blue light source to match a sample. This was a time
consuming and painstaking task and the human being was an integral part of the
color measurement device. The settings of the three light sources were used as
a proxy for the measured value of the color [3].</p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGA78EFXKZ9nlO817HTrcKv--4IJpGRp3rvyoAKXM-RKS6Mxe-lz-5J2mOlf-RROvdziYGqXX6a5elJxAq4706uGmACrd9dcmh9HbEee8uA5TkVIJsRW4GKVlJQm6_Xz63CUlfV5LuaPfKy1j3wZRIkioVjeKgFI65UG2vqmSAqcE_1IHDxcyOTsbD/s1017/Screen%20Shot%202022-08-30%20at%206.41.40%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="463" data-original-width="1017" height="189" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGA78EFXKZ9nlO817HTrcKv--4IJpGRp3rvyoAKXM-RKS6Mxe-lz-5J2mOlf-RROvdziYGqXX6a5elJxAq4706uGmACrd9dcmh9HbEee8uA5TkVIJsRW4GKVlJQm6_Xz63CUlfV5LuaPfKy1j3wZRIkioVjeKgFI65UG2vqmSAqcE_1IHDxcyOTsbD/w414-h189/Screen%20Shot%202022-08-30%20at%206.41.40%20PM.png" width="414" /> </a></div><div class="separator" style="clear: both; text-align: center;">
<p align="center" class="MsoNormal" style="text-align: center;"><i>Conceptual drawing
of a tristimulus light mixing colorimeter</i></p>
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{page:WordSection1;}</style></p><div style="mso-element: footnote-list;"><p class="MsoNormal">The Such devices were difficult to use and had poor
reproducibility. Someone came up with the clever idea that a spectrophotometer
and gobs of arithmetic could be used to emulate a tristimulus colorimeter. I
will tentatively say that this person was Deane Judd. At the very least, he was
thinking about this in 1930 [4]. </p><p class="MsoNormal"> </p><p class="MsoNormal">The aforementioned “gobs of arithmetic” required the
creation of gobs of standardized data in the form of <i>color matching
functions</i>. These color matching functions answered the question of “how would
a hypothetical user adjust the hypothetical knobs of a hypothetical tristimulus
colorimeter to match (for example) 530 nm light?”</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Two scientists from England, John Guild and W. David Wright,
independently took on the task of creating said gobs of data with the help of a
total of 17 volunteers between them. Guild and Wright chose different versions
of red, green and blue light sources, so their color matching functions were
different. But once the correction was made for this difference, their data
agreed reasonably well. The averaged data was massaged a bit and standardized in
1931 by the committee that is now known as the CIE. They called it the Standard
Observer.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">The idea of using a spectrophotometer and gobs of arithmetic
to emulate a tristimulus colorimeter was clever. It was also ad hoc, that is,
it served as a quick fix to a problem that was at hand. But it did not address
the more general need for a way to emulate the human visual system. Hence, it
qualifies as a hack. </p><p class="MsoNormal"> </p>
<p class="MsoNormal">The committee now known as the CIE needed to decide which
tristimulus colorimeter to emulate. Virtually any choice of red, green and blue
lights would suffice. Golly gee, they could even substitute an exotic violet
for the blue or a subtle chartreuse for the green. They decided to go even
wilder and standardize on lights made from unobtanium<a href="#_ftn1" name="_ftnref1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span face=""Calibri",sans-serif" style="font-size: 11pt; line-height: 107%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">[2]</span></span></span></span></a>.
Good golly gosh and gee willickers, since it’s all just computation anyway, who
says the choice of standard stimuli for a standard tristimulus colorimeter even
has to be physically possible?!??!? </p><p class="MsoNormal"> </p>
<p class="MsoNormal">Being the wild and crazy guys they were, their choice of
lights for the primary lights emitted negative amounts of light at certain
wavelengths. Why? Their particular choice minimized the gobs of arithmetic
needed to determine the tristimulus values that stood as proxy for color
measurements. This is my second proposal for a primordial color engineering hack.
It was clever and solved an immediate problem – hand calculation of
colorimetric values. But once again, the bigger issue of emulating the eyeball
went by the wayside.</p><p class="MsoNormal"> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXMP9iS3ytJrnDN4vIZWS1NeF5H0kK8RIfyyfAEOntsRHdyHC2FB0b9jphd9R4ct5BRpQrOd63YP6uWWqrU3Wy4y8Bp5rs9Wry8oSHT87aItraEUyskmGkEIAp7TUt_PPlXUVtq1CUvblpBs0p8YnSUK8UwxjEqn7ZYtkPRrpe7W8EpnDvglersgNW/s706/Screen%20Shot%202022-08-30%20at%206.44.27%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="706" height="371" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXMP9iS3ytJrnDN4vIZWS1NeF5H0kK8RIfyyfAEOntsRHdyHC2FB0b9jphd9R4ct5BRpQrOd63YP6uWWqrU3Wy4y8Bp5rs9Wry8oSHT87aItraEUyskmGkEIAp7TUt_PPlXUVtq1CUvblpBs0p8YnSUK8UwxjEqn7ZYtkPRrpe7W8EpnDvglersgNW/w405-h371/Screen%20Shot%202022-08-30%20at%206.44.27%20PM.png" width="405" /></a></div>
<p></p><p align="center" class="MsoNormal" style="text-align: center;"><i>The tristimulus
functions [5]</i></p><p align="center" class="MsoNormal" style="text-align: center;"><i> </i></p>
<p class="MsoNormal">I propose Seymour’s Rule of Hackery: Every good hack has an
equal and opposite unforeseen consequence. As you would expect, there were
unforeseen consequences that the 1931 committee did not foresee when they decided
to emulate a long-since extinct color measuring device in a way that would save
precious microseconds of computing time on any cell phone. Tune in to the next
ISCC newsletter and you will see the unforeseen!</p><p class="MsoNormal"> </p><p class="MsoNormal">References: <br /></p>
<p class="MsoNormal">[1] Wyszecki G and Stiles WS, Color Science, 1st ed. New
York: Wiley, 1967, p. 279.</p>
<p class="MsoNormal">[2] Smith and Guild, The CIE colorimetric standards and
their use, Trans. Opt. Soc. 33, 102 (1931-32), p. 89</p>
<p class="MsoNormal">[3] Seymour, John, Why does the a* axis point toward magenta
instead of red?, Color Research and Application, 23 July, 2020</p>
<p class="MsoNormal">[4] Judd, Deane B., Reduction of Data on Mixture of Color
Stimuli, Bureau of Standards Journal of Research, Vol 4 (1930)</p>
<p class="MsoNormal">[5] Judd, Deane B., The 1931 I. C. I. Standard Observer and
Coordinate System for Colorimetry, JOSA Vol. 23, Oct. 1933</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><i><span style="background: white none repeat scroll 0% 0%; color: #222222; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">This article was written by <b>John
Seymour</b>, who has to his credit several earlier pieces in the ISCC News and
has (more famously) a blog at</span></i><span style="background: white none repeat scroll 0% 0%; color: #222222; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"> </span><a href="http://johnthemathguy.blogspot.com/" target="_blank"><span style="background: white none repeat scroll 0% 0%; color: #1155cc; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">johnthemathguy.blogspot.com</span></a><i><span style="background: white none repeat scroll 0% 0%; color: #222222; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">. Due to his immeasurable modesty, John has not signed his
name, but I reveal his identity here. MHB</span></i><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"></span></p>
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<div id="ftn1" style="mso-element: footnote;">
<p class="MsoFootnoteText"><a href="#_ftnref1" name="_ftn1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span face=""Calibri",sans-serif" style="font-size: 10pt; line-height: 107%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">[1]</span></span></span></span></a> <span style="font-size: 11pt;">Some of you may recognize the word <i>tristimulus.</i>
The prefix <i>tri</i>- means three, and <i>stimulus</i> refers to the three
flavors of lights in the device. A bit of foreshadowing for the perceptive
reader.</span></p><p class="MsoFootnoteText"><a href="https://www.blogger.com/#_ftnref1" name="_ftn1" style="mso-footnote-id: ftn1;" title=""><span class="MsoFootnoteReference"><span style="mso-special-character: footnote;"><span class="MsoFootnoteReference"><span face=""Calibri",sans-serif" style="font-size: 10pt; line-height: 107%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">[2]</span></span></span></span></a> “A
common observation about unobtainium is that it meets all requirements
perfectly, other than not actually existing.”</p>
<p class="MsoFootnoteText"><a href="https://www.techtarget.com/whatis/definition/unobtainium#:~:text=Unobtainium%20is%20a%20term%20used,other%20than%20not%20actually%20existing" target="_blank">https://www.techtarget.com/whatis/definition/unobtainium#:~:text=Unobtainium%20is%20a%20term%20used,other%20than%20not%20actually%20existing</a>.</p><p class="MsoFootnoteText"><span style="font-size: 11pt;"> </span></p>
</div>
</div>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-64605044336391781102022-05-17T17:28:00.020-04:002022-05-18T10:39:47.739-04:00The Oldest Hack in Color Engineering<p style="text-align: center;">
<span style="font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">(Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a></span>)</p><p class="MsoTitle" style="text-align: center;"> </p><p class="MsoTitle">
</p><p class="MsoNormal">When I was at MIT, I learned what it meant to call something
“a hack.” The term referred to a patch in software (or hardware) that was ad
hoc but clever and fixed a problem. There are many other definitions of “hack”
(the noun), but I don’t use those here. To me, “hack” is not necessarily
pejorative, but descriptive.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In color engineering there have been many hacks, originating
even before the term “color engineering” was popular. Two rather good ones are
Cal McCamy’s approximation for correlated color temperature of a light given its
chromaticity [1] and the CIELAB L* function as an approximate inversion of a
fifth-degree polynomial that characterized the Munsell Renotation System lightness
scale [2].</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Just for fun, I now ask you: What is the oldest hack in
color engineering? One could nominate Newton’s representation of color as a
closed circle. Newton must have been aware that the purples are not elementary
colors that he could see with his prisms. But Newton and others may have
adopted the circle as an instructive idealization, and that is not a hack.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">To get the ball rolling (I expect hundreds of reader responses),
I nominate <i>the object-color tristimulus value</i> (X, Y or Z, for any
illuminant and observer you like). This quantity is defined as a specific ratio
(see ASTM E-308, any edition). The numerator is the wavelength integral of the
product of illuminant power density, reflectance and color-matching function
(generally <span style="mso-no-proof: yes; mso-text-raise: -2.5pt; position: relative; top: 2.5pt;"></span>x-bar, <span style="mso-no-proof: yes; mso-text-raise: -2.5pt; position: relative; top: 2.5pt;"></span><span style="mso-spacerun: yes;">y-bar </span>or <span style="mso-no-proof: yes; mso-text-raise: -2.5pt; position: relative; top: 2.5pt;"></span>z-bar). The denominator is the
wavelength integral of the product of the illuminant power density and the
function <span style="mso-no-proof: yes; mso-text-raise: -2.5pt; position: relative; top: 2.5pt;"></span>y-bar. There’s also a factor of
100, but that doesn’t matter. <span style="font-size: 11pt;"></span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">What problem does this definition cleverly solve? In a
single stroke, it renders the object-color tristimulus value dimensionless and independent
of the absolute light intensity, as is its cousin – the emissive-mode tristimulus
value. (This latter fact emerges from the grounding of emissive-mode tristimulus
values on the emissive-mode color-matching experiments that underlie basic
colorimetry. In a short paper I just submitted to Color Research and
Application, I explain how the titration in a color match leads to cancelation
of all dimensions.) Creating the object-mode ratio makes the tristimulus values
from reflected lights appear comparable to the values from emitted lights and emissive
displays. Certainly color-matching equivalence classes of reflected lights are
not disturbed by the ratio. But, as many color-management experts have warned,
we should be careful in asserting exact colorimetric color reproduction between
emissive and reflective media. For one thing, only the reflective tristimulus
space has an unambiguous white point.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">How is the object-color tristimulus value a hack? It is ad
hoc, solves the units problem, and is clever enough to survive generations of
standards bodies like the ASTM and the CIE. The ad hoc quality manifests when
we observe that the object-color tristimulus values have a distinct and asymmetric
dependence on Y wrought by the denominator, yet that asymmetry was not based on
color matching (as should befit a true tristimulus value). Furthermore, as the
current object-color tristimulus value is a ratio between two spectrum integrals,
it will have a weird illuminant-invariance such as I have found for Von Kries
adapted tristimulus values [3] and band ratios [4]. If the illuminant is restricted
to a finite linear function space, changing its coefficients will not alter the
object-color tristimulus value if the reflectance is outside a forbidden function
subspace. There’s no room for such games in the emissive-mode tristimulus values.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">So that is why I consider the object-color tristimulus value
as a hack. My only remaining question is, how old is it? Wyszecki and Stiles
[5] point to the dawn of the 1931 CIE system of colorimetry. I have not investigated
further, but it’s entirely possible that this hack precedes not only the term “color
engineering,” but also the name “tristimulus value” itself. I’ll leave that subject
to serious historians in our ranks.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">[1] McCamy CS, Color Res Appl 17 (1992), 142-144 (with
erratum in Color Res Appl 18 (1993), 150. </p>
<p class="MsoNormal">[2] Newhall SM, Nickerson D and Judd DB, Final report of the
OSA subcommittee on spacing of the Munsell colors, J Opt Soc Am 33 (1943), 385-418.
</p>
<p class="MsoNormal">[3] Brill MH, Minimal Von-Kries illuminant invariance, Color
Res Appl 33 (2008), 320-323.</p>
<p class="MsoNormal">[4]<span style="font-family: Times; font-size: 11pt; mso-bidi-font-size: 10.0pt;"> </span>Brill MH, "Can color-space transformation
improve color computations other than von Kries?" in:<span style="mso-spacerun: yes;"> </span>Human Vision, Visual Processing, and Digital
Display IV, J. P. Allebach and B. E. Rogowitz, Editors, Proc. SPIE 1913,485-494
(1993).</p>
<p class="MsoNormal">[5] Wyszecki G and Stiles WS, Color Science, 1<sup>st</sup>
ed. New York: Wiley, 1967, p. 279.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Michael H. Brill </p>
<p class="MsoNormal">Datacolor</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-90055191776285303852022-03-02T06:44:00.004-05:002022-03-02T06:44:59.481-05:00My Big Win in Vegas!<p style="text-align: center;">
<span style="font-family: "Times New Roman",serif; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">(Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a></span>)</p><p>
</p><p class="MsoNormal">When I find myself in a casino, it’s always because of a
professional meeting. My reaction to these casino visits is perhaps predictable.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In 1979, I attended the Illuminating Engineering Society
meeting in Atlantic City. There I dropped a coin in a slot machine, and then
became so absorbed in a conversation with Bill Thornton that I was oblivious
when a red carpet was unrolled behind me and Sammy Davis, Jr. walked from one
end to the other. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In 1985, I attended the quadrennial AIC meeting in Monte
Carlo. There I sacrificed another coin to a one-armed bandit, and then became
so absorbed in a conversation with Claude Pelissier that I didn’t see the
sights all around me on the “topless” beach. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In 1992, a field trip after an Acoustical Society meeting in
Salt Lake City lodged me at an inexpensive casino/hotel in Mesquite, NV. A
somewhat larger sacrifice went to a slot machine there. I was so impressed by
the casino’s use of light and color to disorient patrons so they would gamble,
that I presented a summary of the ruse at an ISCC Interest Group III panel
discussion (see ISCC News Issue 340). Nobody told me what glamorous opportunity
I missed in Mesquite, but I must have missed something because I got lost on
the way back to my table from the restaurant salad bar due to the evil genius
of the casino architects.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">In 2005, I returned to Nevada, this time to an ASTM E12
meeting in Reno. By now my obligatory slot sacrifice swelled to five dollars. I’m
reasonably sure I didn’t miss any glamorous sights, and I was aware that, in
all my experiences with casinos, I hadn’t retrieved a penny from the slot
machines. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">But then, in September 2021, I visited Las Vegas and had my
Big Win. The meeting this time (American Urology Association) was not mine but
my partner Karen’s. After she made travel arrangements with me in tow, the AUA
thought it prudent to make the meeting virtual. Karen was determined not to change
our plans, so we checked into the Venetian, the conference hotel. (It was on
the opposite end of the price scale from the hotel I’d stayed at in Mesquite in
1992.) Karen attended the virtual meeting from our hotel room. To me it was a
bit eerie, like a s<a name="_Hlk87440054">é</a>ance with ghosts from an
alternate universe. Meanwhile, I explored the hotel/casino complex. True to my
experience in Mesquite, I became repeatedly lost on a grand scale. One small
but effective confusion was to call two of the three hotels in the complex “Venetian”
and “Venezia.” The architecture and a sinuous indoor canal spoke “Venice,” but
straight paths and right angles were rare, and the site map had little visual correspondence
to the site itself. Even employees of some of the concessions could not
describe how to get to other places under the same roof.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Later, we embarked on an evening tour on a double-decker bus,
and I had an opportunity to meet my obligatory slot machine. The tour guide
gave us an hour in the environs of the Golden Nugget Casino. Stepping inside, I
found that the only acceptable way to sit down for an hour was to gamble. Karen
slid a $20 bill into a machine, and we managed to keep busy for more than a half
hour. Her goal was to get as much run-time as possible out of that investment. She
found that strategy was great fun when she visited Las Vegas with her mother several
years earlier. When I slid my $20 bill into the same machine, I had a different
goal. After a while I had won almost ten dollars, whereupon I decided to cash
out. A little slip of paper appeared, and I grabbed it and asked the nearest
bystanders where I could find the cashier prior to the imminent departure of
our bus. Peering with cow-like eyes, they told me they didn’t know. How could
anyone gamble without a plan for even the first two minutes that would ensue if
they actually won? It was sad. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Out of time, I returned to the bus and read the paper slip
from the machine: <i>Void after 30 days</i>! I’d have to come back to the
Golden Nugget later in my trip. But I never did. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">So that was how I scored my Big Win in Vegas. Well, maybe a Bigger
Win was to have made the trip despite some significant health issues and with
the overarching Covid risk. Some people thought I was crazy to do it. Maybe it’s
good to indulge such craziness just once amid the larger-than-life habitués of
Vegas.</p><p class="MsoNormal"> </p>
<p class="MsoNormal">Michael H. Brill </p>
<p class="MsoNormal">Datacolor</p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-42969766904175188482021-11-04T08:53:00.002-04:002021-11-04T08:53:08.597-04:00If CIECAM is the answer, what was the question?<p class="MsoTitle"> (Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a> )</p><p class="MsoTitle"> </p><p class="MsoTitle">
</p><p class="MsoNormal">Imagine, while studying in preparation for his next life as
a color scientist, the ghost of Alex Trebek visits us in his former role and announces
his truly Final Jeopardy answer:</p>
<p class="MsoNormal">“CIECAM.” </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The contestants blink and Trebek explains:</p>
<p class="MsoNormal">“If CIECAM is the answer, what was the question?”</p>
<p class="MsoNormal">And the contestants answer:</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>Contestant 1</b>: “What model predicts symmetric color
matches?” WRONG: That was CIEXYZ.</p>
<p class="MsoNormal"><b>Contestant 2</b>: “What model predicts asymmetric color
matches?” WRONG: That was CIECAT.</p>
<p class="MsoNormal"><b>Contestant 3</b>: “What model predicts color difference?”
WRONG: That was CIECAM-UCS.</p>
<p class="MsoNormal"><b>Contestant 4</b>: “What<b> </b>model allows a
stimulus, in given viewing conditions, to be numerically described with
correlates of perceptual attributes such as brightness, lightness,
colorfulness, chroma, and hue?” [1] CORRECT: Although CIE’s color-appearance
models, CIECAMs, are not the only possible models.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>Contestant 2</b>: “That’s not fair! I’ve seen CIECAMs
tested by asymmetric matches, but never by the elusive ‘numerically described
perceptual attributes.’” </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>Contestant 3</b>: “Well, come to think of it, Luo et al. [2]
describe experiments to test people’s ability to use particular perceptual
attributes: ‘For the memory matching method, observers are first trained using
the Munsell colour order system (or some other suitable system) until they are
very familiar with these scales (i.e., Munsell Value, Chroma, and Hue) … In the
magnitude estimation method, observers are asked to make estimates of the
magnitudes of some perceptual attributes (e.g., lightness, colourfulness, and
hue). It is essential that each observer clearly understands the perceptual
attributes being scaled.’”</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>Contestant 2</b>: “It sounds as if those experiments tested
the memorability and amenability for scaling of particular coordinates of a
particular color-order system. They cannot make a statement about color appearance
independent of the color-order coordinates chosen for training the subjects. How
do you know one CAM is better than another if the subject’s training has such a
bias? And I understand the precision of these tests is pretty low. I still
think there is no match-free way to test a CAM—or for that matter, to use a CAM
for color management. Alex is wrong and we should have a recount.”</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><b>Trebek</b>: Well, it’s time for me to go now. This discussion
is turning into a quagmire, and it looks like real color-management systems
rely on asymmetric match predictions anyway. So let’s ask a professional
organization like the ISCC to sort it out. Meanwhile, I’ll have to tell my
game-show successor that the right question for CIECAM is “What color-management
model is not out of Jeopardy?”</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">[1] M. D. Fairchild and L. Reniff, A pictorial review of
color appearance models, 1997 SID/IS&T Color Imaging Conference, first paragraph
of Introduction.</p>
<p class="MsoNormal">[2] M. R. Luo et al., Quantifying colour appearance part I.
LUTCHI colour appearance data. Color Res Appl 16: 168-180 (1991).</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Michael H. Brill </p>
<p class="MsoNormal">Datacolor</p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-16021283816622326152021-08-17T17:45:00.002-04:002021-08-18T07:14:01.178-04:00Color-Coding the Pandemic<p> </p><p>Michael H. Brill, Datacolor</p><p>(Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a> )</p><p>Each of us has a different life story through the pandemic. My story does not include the uneasy “new normal” experienced by students in school. Part of the “new normal” requires students to attend school in staggered part-time schedules. How did kids react to this complication? In curiosity, I Googled my old high-school newspaper, the Brentwood Pow Wow. (Yes, the Native American name remains.) Immediately a web page appeared with an article for their April Fools’ edition: “Satire: Crayola Box Plan to Replace Original Tri-color Hybrid Plan;” author, Lilian Velasquez; dateline, 24 March 2021. This was going to be about color coding, about the resilience of young people, and maybe more.<br /></p><p>The school had seen fit to illuminate the monthly calendar with color-coded parts to clarify three alternative student schedules. That was the original Tri-color plan. Ms. Velasquez started with a calendar illustrating the Tri-color plan (using the first three entries on the list below), and then “sprinkled in” the rest: </p><p><b>Teal</b>: Fully remote students <br /><b>Gold</b>: Hybrid students attend school on Tuesday and Fridays, and alternating Wednesdays.<br /><b>Green</b>: Hybrid students attend school on Monday, Thursday, and alternating Wednesdays. <br /><b>Chocolate</b>: Attend school 9 times a year, on the first Monday of each month. <br /><b>Cherry</b>: Attend school every day for only 4 hours each day from 9 a.m. to 1 p.m. <br /><b>Magenta</b>: Attend school only on Fridays for 16 hours. <br /><b>Indigo</b>: Attend school on the weekends from 7 a.m. to 2 p.m. (Saturday and Sunday) <br /><b>Silver</b>: Attend school twice a month on the 7th and on the 21st.</p><p>Velasquez then showed a typical one-month calendar annotated with a delightfully confusing panoply of font colors: a scheme that might give new meaning to the term “drop-out colors.” It’s the kind of gentle extrapolation one expects from high-school students in an April Fools’ satire. I remember reading such extrapolations and writing them. The genre was grounded in acceptance of the normal. Now it is the “new normal.”</p><p>Before I went to Russia in 2008 to teach English as a Second Language (ESL), I heard that Russians would characteristically respond to a story of complaint and indignation by declaring, “It is normal.” My trip confirmed that assertion. I think that every time we reset the condition that we consider normal, we rewrite the past to conform. It is a coping mechanism, and it is helped along by writers.</p><p>In the same vein, Jorge Luis Borges said: “Every writer ‘creates’ his own precursors. His work modifies our conception of the past, as it will modify the future.” The better the writer, the more responsibility this incurs.</p><p>Still, the past is not easily erased. Brentwood High School retains Native American metaphors. Our media preserve other metaphors, as does our collective memory—sometimes unconsciously. Borges himself, with his quote, immortalizes his own present (and our recent past) by using “his” instead of “their” in describing a hypothetical writer.</p><p>It is a delicately balanced narrative into which Ms. Velasquez entered as she wrote extrapolating a color code for the “new normal.” She writes well, and her underlying optimism can encourage us all. I wish her the best as she extrapolates further—we hope from a better “new normal.”</p><p>And perhaps her new color code foretells a career as an artist or color scientist!<br /> </p><p>Michael H. Brill<br />BHS Class of 1965<br /></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-21797302839134816912021-05-10T15:01:00.001-04:002021-05-10T15:01:24.288-04:00Into Something Rich and Strange<p>
</p><p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">About 30 years ago [1]
I encountered aerial photographs that were captivating, rich and strange. The
photographs were acquired with a camera geometry similar to that of a flash-attached
pinhole camera. The light flashed, reflected off the surface of the Earth, and
then returned to the camera, all via straight-line paths. But such an image
didn’t look at all like it came from a pinhole camera. Most of the spatial
features were familiar, but long black shadows appeared between them. We don’t usually
see cast shadows in flash-attached-camera images, because any object producing
such a shadow hides it from sight. That’s why the contrasts are so low and
unappealing in photographs from an old-style flash camera. But the new image
broke that rule, exhibiting shadows as if they were cast by a setting sun in
the evening: a romantic image, as it were. </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">What were these
strange cameras? To answer the “what” question, I must first answer “why,” and
that will break the romantic thrall. In the last century, interest in viewing the
Earth from space was beset by the problem that most of the Earth is having a
cloudy day just now (for any now). To see through the clouds, you need to use
light with long wavelengths. Microwaves worked, and they became the basis of
imaging radar systems. </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">Could you make a
pinhole camera system with a microwave light source? No—you couldn’t focus the
beam or tell where it was coming from when it returned. The designers of this
camera had to give up on the conventional idea of capturing on a flat film the
direction of a viewed object on the Earth (called a <i>world point</i>). Instead,
they did a clever thing. They flashed a complicated microwave pulse (called a
chirp) in all directions, and then captured reflected returns. They sorted the light-intensity
returns according to their time delay from the source (proportional to the
range of the world point) and also according to their time scaling (proportional
to Doppler effect). Oh yes, I must mention that the new camera had to be moving
relative to the Earth, and its velocity had to be known, whereupon this second
piece of information became proportional to the cosine of the angle from the
vehicle direction and that of the world point. If you know the range of a world
point, then that locates it on a sphere centered on the camera. If you know the
vehicle direction, then you know the angle between the velocity and the
direction to the world point, and that places the world point on a cone with
its vertex at the camera. Knowing the world point’s range sphere and Doppler
cone means that you have identified a circle in space on which the world point
must lie. Such circles are called <i>projection circles</i>.</span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">Now let’s return to a
comparison of our new camera with a pinhole camera. If you look at a world point
along a line of sight through a pinhole camera, you can tell what line the
world point is on (identified by direction), but you can’t tell how far along
the line the world point resides. If you look at a world point for the new
camera, you know which projection circle the world point is on, but you can’t
tell which point on the circle is occupied by the world point. Somehow in this
imaging system, even though the light still travels in straight lines, the part
of the 3D world point location that is inaccessible on a 2D image is a circle
and not one of those straight lines. The romantic thrall has ended, but for me
the mathematical thrall has begun!</span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">The new camera, by
the way, is called a synthetic-aperture-radar (SAR) system [2]. And that brings
me to another comparison with a conventional camera. Instead of ending up in a
light-sensitive medium such as film, the SAR’s rays enter a localized receiver
and are mathematically sorted to provide the coordinate locations (range and
Doppler) in a mathematically defined structure called a synthetic aperture. That
plane does not correspond to a physical object, but is a mathematical structure
in 3D. It’s not so strange, really. That kind of structure is common in
holography, hence the term “quasi-holographic” that is used to describe the SAR
technology.</span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">Of course, you will need
to know how the conventional and new cameras work together to reconstruct the
three dimensions of a world point. The answer is: quite well. It </span>is common
[3] to solve for a 3D point using a camera image and a SAR image (see Fig. 1). The
process is similar to triangulation as used by pairs of conventional cameras. </p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal"><span style="mso-bidi-font-size: 10.0pt;">Now some of you may wonder
where the shadows enter all of this. </span>The straight-line light propagation
certainly leaves cast shadows, but these shadows occupy noticeable area in a
SAR image (e.g., search SAR image example). The pixels there are dark because
no light intensity is directed to them by the math algorithm. The SAR shadows are
called layover. It’s ho-hum and official. Yet somehow, I sense we are “into
something rich and strange,” to offer an Ariel perspective.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">This brings me to my final point. I don’t believe artists
have yet explored SAR technology as a medium for expression. So, following the
lead of Anish Kapoor as described by Carl Jennings’s essay in this issue, I hereby
deny anybody but me the right to use SAR in art. So there, IP attorneys!</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><i>Note: This essay is dedicated to Dr. Eamon B. Barrett, my
long-time friend and collaborator in imaging mathematics, who passed away March
30 after a long illness. MHB</i></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><u><span style="mso-tab-count: 4;"> </span></u></p>
<p class="MsoNormal"><span style="font-size: 10.0pt;">[1] Brill M, Triangulating from
optical and SAR images using direct linear transformations, <i>Photogram. Eng. &
Rem. Sensing</i> 53 (1987), 1097-1102.</span></p>
<p class="MsoNormal"><span style="font-size: 10.0pt;">[2] Ausherman, DA, et al., Developments
in radar imaging, <i>IEEE Trans. Aerospace & Electronic Sys</i>. AES-20
(1984), 363-400.</span></p>
<p class="MsoNormal"><span style="font-size: 10.0pt;">[3] Qiu C, Schmitt M, Ziu X, Towards
automatic SAR-optical stereogrammetry over urban areas using very high resolution
imagery. <i>ISPRS J Photogram & Remote Sens </i>138 (2018), 218-231.</span></p>
<p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"><span style="mso-bidi-font-size: 10.0pt;">Michael H. Brill</span></p>
<p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"><i><span style="mso-bidi-font-size: 10.0pt;">Datacolor</span></i></p>
<p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"><span style="mso-bidi-font-size: 10.0pt;"> </span></p>
<p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaNEuaNgL7F_CXLMVQ5LVBMEhexa4ScwrRCBY3FTNMRxXB_INz1uCIy2Y8ZEjD525UXGO_v-Ngxl5rUM3VjHYBy0vCF8zEYog6L1GjfdE6dIiEifrB60U-76MvcWLR4mEynilMGi5BtOE/" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="709" data-original-width="1241" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaNEuaNgL7F_CXLMVQ5LVBMEhexa4ScwrRCBY3FTNMRxXB_INz1uCIy2Y8ZEjD525UXGO_v-Ngxl5rUM3VjHYBy0vCF8zEYog6L1GjfdE6dIiEifrB60U-76MvcWLR4mEynilMGi5BtOE/w374-h213/SARfigure1.PNG" width="374" /> </a></div><div class="separator" style="clear: both; text-align: center;"> </div><p></p><p class="MsoNormal" style="mso-layout-grid-align: none; text-autospace: none;"><span style="mso-bidi-font-size: 10.0pt;">Fig. 1. Triangulation of a world point <b>X</b>
as the intersection of camera line-of-sight L and SAR projection circle C. The quantity
w<sub>2</sub> is the velocity of the SAR sensor, and image points <b>Y</b><sub>1</sub>
and <b>Y</b><sub>2</sub> are camera and SAR images of <b>X</b>. [adopted from
Ref. 1]</span></p>
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{page:WordSection1;}</style></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-34491247606497826342021-02-16T17:41:00.004-05:002021-02-16T17:41:50.964-05:00Ruminations on Eating Photons<p>Michael H. Brill, Datacolor</p><p>(Send contributions to <a href="mailto:mbrill@datacolor.com">mbrill@datacolor.com</a> )</p><p>Plants see photons.</p><p>People see photons.</p><p>Plants eat photons.</p><p>Do people eat photons? I suspect not. It would be too <i>light</i> a diet. </p><p>The above was my first reaction to Carl Jennings’s latest column, “Eating Color: Color Perception in Plants” [ISCC News # 492 (2020), pp. 5-8]. Carl wrote from the viewpoint of an artist who embodied the title metaphor in his works. I, of course, tend to pursue more technical implications—starting with a joke. And, unlike all the trite photon jokes I had seen on the Internet, this one seemed to have a serious teaching point.</p><p>Let’s start with the seeing of photons. The chemistry of vision involves amplifying a rather weak photon signal (weak because it must be divided up in space, time, and spectrum), and the agent of the amplification is the discharge of a battery. When the battery is discharged, it must be recharged (using a lot of metabolic energy) before it can be used again. (Sometimes, as with retinal rods, the battery gets discarded and replaced, not recharged.) Seeing, either by plants or by animals, involves treating the photon as a signal and amplifying that signal chemically. Any vision system, plant or animal, uses energy by combining oxygen with other elements; hence respiration is a prerequisite for seeing.</p><p>Now let’s proceed to the eating of photons. Photosynthesis also has a battery that is similar to vision’s battery, but the energy goes the other way. Not only the photo-active material, but the whole organism increases in mass and energy as a result of the incident photon energy. Carbon adds to the mass of the organism and oxygen is released. </p><p>I’ve just described the eating of photons by plants. Do animals eat photons in the same way? No, and I think the reason is that animals are not able to use the photons as a direct energy source. They have to eat in other ways, which are familiar to us. Photons are too <i>light</i> a diet to sustain animals directly. [One must note a small exception of this rule, the creation of Vitamin D via the Sun’s UV radiation on skin.]</p><p>I published a little about this subject in ISCC News # 427 (2007), p.7: “Power to the Pupil” (not a Hue Angles column). There my main focus was the creation of batteries using rather large amounts of visual pigment from animals, and also the design of solar cells using principles very similar to those used in certain cameras.</p><p>Some of you might complain at this point about my colloquialism of “seeing photons” in place of “information-processing an electromagnetic signal” and “eating photons” instead of “transmuting electromagnetic power into stored energy.” In anticipation of such a complaint, I can only say that less colloquial language might deny me immortality in the immense archives of photon jokes that persist ready for simple Internet search. Enjoy. </p><p>_______</p><p>[Note: I recently learned that Ronald Penrod passed away August 12, 2020 at the age of 80. Ron was a pioneer in digital colorant formulation. His color-science career (1965-1991) was at Uniroyal Inc. (previously U.S. Rubber), where he added commentary and software to Ray Winey’s original 1962 report on the colorant-formulation method. This contribution was discussed in Bill Longley’s Hue Angles essay, "Color Creeks Ray Winey has Found People Up" (<a href="http://hueangles.blogspot.com/2009/)">http://hueangles.blogspot.com/2009/)</a>. MHB]</p><div><br /></div><p></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-12247901793993926482020-10-26T13:10:00.000-04:002020-10-26T13:10:05.809-04:00The Revolving Door between Color Science and the English Department<p>Past <i>Hue Angles</i> columns have featured examples of career changes from color science to other areas. (See Issue #250 [2011] on <a href="https://hueangles.blogspot.com/2011/03/">Terry Benzschawel’s transition to Wall Street </a>quant and Issue #475 [2016] on <a href="https://hueangles.blogspot.com/2016/08/">Mike Stokes’s transition to data privacy</a>.) </p><p>In this article, I describe Suguru Ishizaki’s transition from color science to an English department. Such experiences can inspire hope for successful career transitions in the field of color science even in the current job crisis.</p><p>Ishizaki’s contribution to color science is heralded by his 1994 Color Imaging Conference paper [1], also extended in a successive paper [2]. He undertook the prodigious task of coloring sub-areas on a color-coded map or chart so that each sub-area, subject to spatial induction from its neighbors, would match an intended color in the key to the chart. The task is hard because every time you change a sub-area color, you must also change the neighboring areas to preserve all the color matches with the key. The process is iterative and multi-dimensional. To my knowledge, Ishizaki’s is the first and only attempt to capture and control such complicated and inter-dependent conditions for asymmetric matches. (Usually investigators look at only a center field as influenced by a single surround, and do not ask the matching question.)</p><p>Starting with this work (which led to his Ph.D. at the MIT Media Lab), Ishizaki built a career, alternately in academia and industry, based on a broader over-arching theme of human communication through design. He started at the Design School at Carnegie Mellon University (CMU), then worked at Qualcomm on early mobile applications, and ended up at CMU’s English Department, where he is now an Associate Professor. Dr. Ishizaki’s current research area is Technology-Enhanced Learning for writing and Computer-Assisted Rhetorical Analysis [3].</p><p>Several people I know started as English majors and ended up in color science. Bob Karpowicz, who became a product manager at Datacolor, had an undergraduate English major. Mike Tinker (who became an expert in color digital cinema at Sarnoff) started from a B.A. in English literature; then, as a graduate student in English, he wrote a computer program that recognized writers by their word patterns. That wasn’t accepted as a thesis topic, so Tinker pursued another topic to a Ph.D. in English with a minor in computer science. </p><p>And I myself was an undergraduate English major, though this is unacknowledged on my diploma due to a binary choice being given to me on graduation day. (How English departments have changed since then!)</p><p>But whereas in all these cases the door of the English department was marked “Exit,” Dr. Ishizaki found a door marked “Enter.” I hope someday that he returns to color science to continue the career he started and that nobody else can match. Or perhaps someone else will continue his pivotal work.</p><p>[1] Ishizaki, S. Adjusting simultaneous contrast for dynamic information display. Proceedings of IS&T and SID's Color Imaging Conference, Scottsdale, 1994: pp 137- 140. </p><p>[2] Ishizaki, S. Color adaptive graphics: what you see in your color palette isn’t what you get! CHI ’95: Conference Companion on Human Factors in Computing Systems. May 1995, pp. 300-301.</p><p>[3] <a href="https://design.cmu.edu/people/courtesy-appointment/suguru-ishizaki">https://design.cmu.edu/people/courtesy-appointment/suguru-ishizaki</a></p><p><br /></p><p><i>Michael H. Brill</i></p><p>Datacolor</p><div><br /></div>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-75481145788612607742020-08-24T07:24:00.002-04:002020-08-24T11:40:00.830-04:00Why Colors Show Up as Icons in Mathematics<p> <span face="" style="font-family: "times new roman", serif; font-size: 12pt;">In eerie resonance with Euclid’s definition of a point as “that which has no part,” J. Lettvin’s </span><i style="font-family: "times new roman", serif; font-size: 12pt;">Colors of Colored Things</i><span face="" style="font-family: "times new roman", serif; font-size: 12pt;"> begins with the following: “Judgment of color (including brightness) seems not to depend on extension [… Redness] is like nothing else but itself, it cannot be decomposed or described, but only exhibited; it is a </span><i style="font-family: "times new roman", serif; font-size: 12pt;">simple</i><span face="" style="font-family: "times new roman", serif; font-size: 12pt;">.” [1] </span><span face="" style="font-family: "times new roman", serif; font-size: 12pt;"> </span><span face="" style="font-family: "times new roman", serif; font-size: 12pt;">Lettvin goes on to discuss (in his unique way) the familiar complications of how vision transforms stimuli into color, but he retains the view that the judgment of color is a simple. I will now look at some implications of this idea.</span></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">Color as a simple is readily added to a geometrical object, and the color icons enrich the meaning. Examples range from traffic signals to the stylized footprints in an Arthur Murray dance studio. But mathematics offers some particularly interesting morsels. Three come to mind. One of these, the four-color map problem has been described in an earlier Hue Angles [2]. Another shows up in the title of Arthur Loeb’s book <i>Color and Symmetry</i> [3], in which permutations of color coding in a pattern enrich the geometric symmetries incurred by such operations as glides and reflections. Now I want to introduce you to a third, perhaps less familiar example, the road-coloring problem.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">The road-coloring problem involves a network with directed paths between pairs of vertices. Under some surprisingly general conditions, it is possible to color-code the paths so that, given a destination vertex, a single set of instructions in the form of a sequence of color choices will bring you from any source vertex to the same destination vertex. The Wikipedia article on the road-coloring problem sets the context: “In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from.” You start with a graph with numbered vertices and colored arrows between the vertices. The arrows are like one-way streets: the instructions (a sequence of path colors) assume you are always going in the direction of the arrow you’re on. To convince yourself that this behavior is possible, try the exercise based on the eight-vertex graph in Ref. [4]. <o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">The road-coloring problem started as a conjecture by Benjamin Weiss in 1970, but it took 38 years to prove. The proof came from Avraham Trahtman, a 63-year-old Israeli former security guard (who was a mathematician in his earlier life in the USSR) [5]. Trahtman [6] proved not only that the nominated graphs all had coloring sequences with the desired property, but also that one’s mathematical life can peak long after one’s teens and twenties.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">Encouraged by checking the eight-vertex graph in Ref. 4, I wondered if I could make a simpler graph with only three nodes that had the same property. In the figures I show here, three nodes support two possible solutions, but I had to allow the possibility of paths from a node to itself. <o:p></o:p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikJchCIcKzYRSusHMYlEmenhKzfB8o4W-ze8ETEtsCYu8_k_EheAYNzcxkwAKGtVbXshgBtmf8N5epSn1iuq8J1W5Ctpj24EKp_lOxatoiy6ixJTwo-fPzs09MyfN-dOL8Loz1sOwCWg0/s1084/Screen+Shot+2020-08-24+at+7.19.06+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1084" data-original-width="1002" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikJchCIcKzYRSusHMYlEmenhKzfB8o4W-ze8ETEtsCYu8_k_EheAYNzcxkwAKGtVbXshgBtmf8N5epSn1iuq8J1W5Ctpj24EKp_lOxatoiy6ixJTwo-fPzs09MyfN-dOL8Loz1sOwCWg0/w242-h262/Screen+Shot+2020-08-24+at+7.19.06+AM.png" width="242" /></a> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT0gawFi-dbZkdI_hZ3Et-9vC7NcOWlqCYeQAuso5GAVFvjKL8j83-bOE5mVbpifkSTtqh1VByUC3hyVCr5nu3L1PqwY6JSwVQx7n58DleicLJsLPFCf22Pjh5iSs7Jv8XvNX35VJBQI8/s964/Screen+Shot+2020-08-24+at+7.19.28+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="964" data-original-width="954" height="263" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT0gawFi-dbZkdI_hZ3Et-9vC7NcOWlqCYeQAuso5GAVFvjKL8j83-bOE5mVbpifkSTtqh1VByUC3hyVCr5nu3L1PqwY6JSwVQx7n58DleicLJsLPFCf22Pjh5iSs7Jv8XvNX35VJBQI8/w259-h263/Screen+Shot+2020-08-24+at+7.19.28+AM.png" width="259" /></a></div><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><br /></p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><div style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: left;"><span style="font-size: 12pt;">Drawing of two three-vertex road-coloring solutions (author, 2013).</span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">The medium is felt marker on flip-chart paper, photographed in a cool-white-fluorescent-lit office. </span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">Not surprisingly, the “red” looks very orange. My apologies, but I hope the idea is clear.</span></div></blockquote><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: left;"><br /></p><p class="MsoNormal" style="font-size: 12pt; margin: 0in 0in 0.0001pt;"><span style="font-family: "times new roman", serif;">In the case of my first graph, if you live at vertex 1, all you have to tell your visitor is “take the red arrow from where you are to the next vertex (in the direction indicated by the arrow), and that will be node 1. That’s what I mean by the instruction R</span><span style="font-family: wingdings;">→</span><span style="font-family: times new roman, serif;">1 from anywhere (i.e., from vertex 1, 2, or 3). Similarly, if you live at vertex 2, your instruction is “take the green path one step from wherever you are.” If you live at vertex 3, your instruction is “take the blue path.” Because the arrows are like one-way streets, you must always go in the direction of the arrow you choose. <o:p></o:p></span></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">In the second graph, there are still only three vertices, but the paths involve two steps and not just 1. Starting from vertex 1, 2, or 3, if you take two R steps, you end up at vertex 1. I denote that action as RR<span style="font-family: wingdings;">→</span><span style="font-size: 12pt;">1, etc. But notice that I use only two colors of path instead of three (as in my first graph). There is a tradeoff between the number of colors and the length of the instruction string. </span></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">What use is the road-coloring problem (now a theorem)? It serves very well in the theory of automata. To quote Weifu Wang [7], “When the automaton is running and encounters an error, and if the road coloring conjecture is true, the automaton can always follow a certain sequence and go back to the previous correct state, regardless of what error it encountered.” I think the “correct state” is the address of the person giving the instructions, and the “error state” is where the presumed visitor is when he gets instructions. It’s a little confusing to call the direction “back” when you’re proceeding forward along the arrows to get there. But synchronizing a move to an earlier known state seems the key to the application.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">One place <i>not</i> to use the road-coloring theorem is in an Arthur Murray dance studio. Imagine giving a color-sequence instruction set to a bunch of dancers and have them all pile on top of each other when they (synchronously) reach the home vertex.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><o:p> </o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[1] J. Y. Lettvin, MIT RLE QPR 87, 1967, p. 193, dspace.mit.edu/bitstream/handle/1721.1/55670/RLE _QPR_087_XIV.pdf <o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[2] M. H. Brill, <a href="http://hueangles.blogspot.com/2013/03/" style="color: #954f72;">http://hueangles.blogspot.com/2013/03/</a><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[3] A. Loeb, <i>Color and Symmetry</i>, Wiley, 1971.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[4] <a href="https://en.wikipedia.org/wiki/Road_coloring_theorem" style="color: #954f72;">https://en.wikipedia.org/wiki/Road_coloring_theorem</a><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[5] <a href="http://usatoday30.usatoday.com/tech/science/mathscience/2008-03-20-road-coloring-problem-solved_n.htm" style="color: #954f72;">http://usatoday30.usatoday.com/tech/science/mathscience/2008-03-20-road-coloring-problem-solved_n.htm</a><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[6] A. N. Trahtman, The Road Coloring Problem. <i><a href="https://en.wikipedia.org/wiki/Israel_Journal_of_Mathematics" style="color: #954f72;" title="Israel Journal of Mathematics">Israel Journal of Mathematics</a></i>, Vol. 172, 51–60, 2009<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">[7] W. Wang, The Road Coloring Problem. (2011). <a href="https://math.dartmouth.edu/~pw/M100W11/weifu.pdf" style="color: #954f72;">https://math.dartmouth.edu/~pw/M100W11/weifu.pdf</a><o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">.<o:p></o:p></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;"><i>Michael H. Brill<o:p></o:p></i></p><p class="MsoNormal" style="font-family: "times new roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">Datacolor<o:p></o:p></p>Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-17898319531919712062020-06-04T13:02:00.001-04:002020-06-04T13:02:14.055-04:00Color/BW Tropes in Cinema<div class="MsoNormal" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0.0001pt;">
Once again Carl Jennings has inspired a Hue Angles article from me. This time, Carl’s description of Olafur Eliasson’s black-and-white effect with narrowband light (<i>ISCC News</i>, Issue 489) reminded me of various color/black and white (BW) tropes in cinema. Whereas Tony Stanton’s Munsell 2018 presentation (<a href="http://www.iscc-archive.org/Munsell2018_Presentations/Stanton-Breakout-HistoryOfColorCinema.pdf" style="color: #954f72;"><span style="color: #0563c1;">http://www.iscc-archive.org/Munsell2018_Presentations/Stanton-Breakout-HistoryOfColorCinema.pdf</span></a>) is a more serious history that highlights the use of color/BW as part of the technological evolution, my essay here highlights some artistic uses of color/BW.<o:p></o:p></div>
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I’ll begin with the <i>Wizard of Oz</i> (1939), wherein the black and white (actually sepia-tone dyed black and white) Kansas shots give way to the dazzling color of Oz. The transition wasn’t trivial: “<span lang="EN" style="color: #222222;">A set was painted sepia tone and Bobie Koshay, Judy Garland's double was outfitted in a sepia dress and given a sepia make-up job. Koshay walks to the door and opens it, revealing the bursting color of Munchkinland beyond the doorframe. She steps out of the way of the shot and the camera glides through the door, followed by Judy Garland, revealed in her bright blue dress</span>.” [1]<o:p></o:p></div>
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A similar trope occurs in <i>Pleasantville</i> (1998), in which real-life characters are injected into a black-and-white 1950s sitcom. Within the sitcom, the characters (and objects) appear in black and white until they transcend the repression implied by the sitcom and find emotional spontaneity and “modernity” of viewpoint. I find the message is too preachy, but if for nothing else, the film is noteworthy in being claimed to be <span lang="EN">the first new feature film created by scanning and digitizing recorded film footage to remove or manipulate colors (<a href="https://en.wikipedia.org/wiki/Pleasantville_(film)" style="color: #954f72;">https://en.wikipedia.org/wiki/Pleasantville_(film)</a> </span>.<o:p></o:p></div>
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Certain resonances of Oz can be seen in Antonioni’s <i>Red Desert</i> (1964), wherein the entire movie has a ghastly blue-green cast (the color, not the actors), until a fantasy scene at the end that opens out to abundant color and lets the audience sigh in relief. That one is not a black-and-white trope, but a reduced-color trope that recalls the Oz transition, but on a more subtle level.<o:p></o:p></div>
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A more powerful recent trope appears in <i>Schindler’s List</i> (1993), which is filmed in black and white except for the Sabbath candles and a red coat worn by a young Jewish girl who is thereby individuated as a casualty of the Holocaust. The emotional effect was a coup by Spielberg. And it used digital techniques for color replacement five years before the vaunted “first” of <i>Pleasantville</i>.<o:p></o:p></div>
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Finally, I must mention the comedic send-up of <i>Psycho</i>’s (1960) shower scene in Mel Brooks’s <i>High Anxiety </i>(1977), which is entirely in color. A bell boy has not-so-pleasant words with a patron in a hotel. The patron (Brooks) wants his newspaper brought to him, and the bell boy waits until the patron is in the shower and then rips the curtain aside and hysterically stabs at him with the rolled-up newspaper. (“There’s your paper!”) The paper falls under the water, and the black ink dissolves—and swirls down the drain in a vortex exactly like the black and white rendered blood that flows down the drain in <i>Psycho</i>. Pan to the patron’s apparently dead face: “That kid gets no tip!” [see <a href="https://www.youtube.com/watch?v=__2HBkrrlp4" style="color: #954f72;">https://www.youtube.com/watch?v=__2HBkrrlp4</a>]<o:p></o:p></div>
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There’s no limit to what can be done with the tension between color, and black and white. If you pay attention, you can see BW/color tropes in many other places. My most recent encounter was with the BW world comprising Saul Goodman’s drab alternate identity in <i>Better Call Saul</i> (TV Series). In fact, our editors have experimented with BW/color tension in recent issues of <i>ISCC News</i>.<o:p></o:p></div>
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[1] D. Faraci, True movie magic: how the Wizard of Oz went from black & white to color, written 16 Sep 2013, <a href="https://birthmoviesdeath.com/2013/09/16/true-movie-magic-how-the-wizard-of-oz-went-from-black-white-to-color" style="color: #954f72;">https://birthmoviesdeath.com/2013/09/16/true-movie-magic-how-the-wizard-of-oz-went-from-black-white-to-color</a>, website accessed 27 Feb 2020.<o:p></o:p></div>
Dave Wyblehttp://www.blogger.com/profile/09623357167770566661noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-71150480262457598412020-02-24T15:56:00.000-05:002020-02-24T15:59:09.997-05:00The Virtual Image: Keeping It RealWhen recently asked to explain the operation of a magnifying glass, one of us (MHB) revisited an old conundrum from secondary school: the virtual image. When a viewed object is within the focal length of the lens, an image is formed that is not inverted relative to the viewed object. Far more mystifying, it is on the same side of the lens as the light source, not on the side to which actual light is conveyed. Yet we see virtual images all the time.<br />
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You can see the traditional picture of a virtual-image situation in the part of Fig. 1 that includes the “eyepiece” lens and everything to the left of it. The “object” is a short, downward-pointing black arrow. The “virtual image” is the longer, dashed black arrow at the far left. The base of the object and of the image lie on the axis of the lens. The point of the arrow in object and image are connected by two rays (dashed black lines delimiting a pink area). One of these rays passes through the center of the lens, and in the ideal (thin-lens) case this ray will be undeflected by the lens. The other ray starts out parallel to the lens axis, and is bent by the lens so it passes through the focal point (not shown) that is to the right of the lens. (A collection of such rays from the Sun could concentrate enough to cause a fire.) If the object had been to the left of the left-hand focal point of the lens, this bent axial ray would have intersected the undeflected ray so as to form a real image: inverted relative to the object, on the same side of the lens as the light propagates, and generally understandable. But when, as in Fig. 1, the object lies to the right of the left-hand focal point, the two rays diverge to the right of the lens, and instead, we are told, we have to backtrack both rays until they intersect on the left-hand side, and this intersection is part of the virtual image.<br />
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How can an image form that is coincident neither with the eye nor with the light that should be generating that image? Virtual or not, this deserves an explanation.<br />
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As optical engineers will tell you (if pressed), the virtual image is a way of expressing a geometric relationship without involving the actual eye. As soon as you include the eye in the explanation (see Fig. 1) the paradox is resolved. The rays that diverge as they pass to the right of the eyepiece are brought together in focus by the lens of the eye. Where these rays meet, one finds a real image on the retina. This image is shown in Fig. 1 as a white arrow. It is a real image, being where the light ends up, where vision takes over, and in an inverted configuration that the visual system interprets correctly. (That is a subject for another essay.) <br />
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The important thing to remember about the virtual image is that it is a shorthand to replace a fairly intricate relationship of the rays that form the real image if the explanation includes the eye. That relationship is only partially apparent in Fig. 1. One gets the false impression that the bent axial ray from the eyepiece lens becomes the undeflected ray of the eye’s lens, and vice versa. Actually, the bent axial ray from the eyepiece lens passes through the right-hand focal point of the eyepiece, which only accidentally happens to be near the center of the eye lens. <br />
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A clearer picture of the eye’s focusing of the diverging rays is shown in Fig. 2, a ray-tracing simulation. Here the optical elements are more stylized than in Fig. 1: the two lenses are red-tipped line segments, the object consists of a pair of radiating green dots, and rays from the dots proceed through both lenses and meet at the right-hand convergence points that depict the real image on the retina. The virtual image is too far to the left to be captured by the figure. We think that both Figs. 1 and 2 are needed to show how the eye acts in a virtual-image situation.<br />
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In short, experts know the virtual image and how to “keep it real.” Now you know too.<br />
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<em>Michael H. Brill and Nilesh Dhote</em><br />
Datacolor<br />
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Fig. 1. Drastically abbreviated depiction of a virtual image and the real counterpart that emerges when the eye is included. Please ignore the yellow region. The figure in context can be found at <a href="https://micro.magnet.fsu.edu/primer/anatomy/components.html">https://micro.magnet.fsu.edu/primer/anatomy/components.html</a>.<br />
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Fig. 2. Simulation of formation of a real image using two lenses. The divergence of the rays through the left-hand (eyepiece) lens is evident from the rays that proceed outside the lens aperture of the eye. (See <a href="https://ricktu288.github.io/ray-optics/simulator/">https://ricktu288.github.io/ray-optics/simulator/</a>.)<br />
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<br />MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-21527587539280180012019-11-15T13:13:00.000-05:002019-11-15T13:13:54.372-05:00Black to the Future Redux
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A bit more than a decade ago, Hue Angles presented an article called “Black to the Future” [1]. To further darken a black carbon surface, investigators in Rensselaer Polytechnic Institute and at Rice University roughened the surface by a carpet-like arrangement of carbon nanotubes (.01" long, 1/30,000 as wide) standing on their ends. The result was a surface with a reflectance as low as 0.045 percent (three times darker than any previous material) and a refractive index that could theoretically be as low as 1.01 [2]. We proposed possible uses for such a material in spectrophotometry: </div>
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1. Black surfaces for minimizing stray light in optical instruments</div>
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<br />2. Light traps for suppressing unwanted diffraction orders</div>
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<br />3. Gloss traps for removing specular reflection</div>
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<br />4. Black calibration standards</div>
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Now, after more than a decade, how well did our wish-list work out? Not well, at least for commercial applications. At the ISCC topical meeting on black and white, held that very same year, it became clear that the carbon nanotube technology was too delicate and too expensive for our purposes. But the technology evolved and improved anyway, and new uses were found.</div>
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Beginning in 2014, Surrey NanoSystems issued a product called Vantablack, which reflects 0.04 percent of UV, visible, and IR radiation. Vantablack had the same mechanical vulnerability as its predecessors, so it did not find many applications on Earth. However, in space the substance could be undisturbed, and starting in 2015 helped capture stray light to enhance spaceborne imagery (e.g., tracking stars) without a large payload penalty. Also, back on Earth, it achieved an effect that was coveted by artists: three-dimensional objects covered with Vantablack would appear to be flat surfaces because not enough light was reflected to reveal the 3D topography. BMW even painted a car with Vantablack. By 2017, a version of Vantablack (S-VIS) became available in a spray-on form. The reflectance was understandably not quite so low in this form: 0.2 percent. But the material still served its various functions. Although Vantablack is not commercially available, Surrey NanoSystems has licensed the product.</div>
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Now there is a material that is still blacker. It emerged from laboratories in Shanghai and at Massachusetts Institute of Technology[3], and has a reflectance of 0.004 percent. The discovery was accidental, during attempts to grow carbon nanotubes on aluminum foil. To avoid the formation of oxides between the nanotubes and the foil, the investigators soaked the foil in salt water and moved it into a small oven where the nanotubes could grow without oxygen interference.</div>
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A popular article by Brandon Specktor [4] describes two implications of the new black technology. There is a $2 million diamond on exhibit in the New York Stock Exchange that has been covered with the material and is invisible on a background of similar black material. Specktor speaks poetically of the black material “eating” the diamond and that it is a “veritable black hole.” Indeed, as he suggests, we may soon be able to see real black holes if the new black material is deployed to optical instruments in space. But I don’t expect to see signs with the words “Schwarzschild radius” on any photos, though we have seen cartoons of other human-created follies (such as Pluto bedecked with the sign “am too a planet.”) Enough about black holes…</div>
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In summary, the last ten years have brought a factor of 10 reflectance decrease in the blackest black. We’ve achieved a decade in a decade. Stay tuned for the next decade.</div>
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[1] M H Brill, A Ingleson, and C McLellan, Black to the future. <em>ISCC News</em> # 434 (2008), 3-4.</div>
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<br />[2] Z-P Yang, L. Ci, JA Bur, S-Y Lin, PM Ajayan, Experimental observation of an extremely dark material made by a low-density nanotube array. <em>Nano Letters</em> <strong>8</strong>, No. 2 (Feb. 2008), 446-451.</div>
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<br />[3] K Cui, B L Wardle, Breakdown of native oxide enables multifunctional, free-form carbon nanotube-metal hierarchical architectures. CS Appl. Mater. Interfaces 2019 XXXXXXXXXX-XXX:September 12, 2019; <a href="https://doi.org/10.1021/acsami.9b08290">https://doi.org/10.1021/acsami.9b08290</a> </div>
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<br />[4] B Specktor, There’s a new blackest material ever, and it’s eating a diamond as we speak. <em>Live Science,</em> Sept 16, 2019, <a href="https://www.livescience.com/blackest-black-devours-diamond">https://www.livescience.com/blackest-black-devours-diamond</a>.… </div>
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<br /><em>Michael H. Brill</em><br />Datacolor</div>
<span style="color: black; font-family: "Times New Roman",serif; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Arial Unicode MS"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Arial Unicode MS"; mso-fareast-language: EN-US;"></span>MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-68680348169660951962019-09-06T11:26:00.000-04:002019-09-06T11:26:44.633-04:00Reflection on “Dark Spectrum Part II”As a new experiment for ISCC News, my column in Issue 487 (reproduced here), together with that of Carl Jennings, comprise an interdisciplinary dialogue within a single issue.<br />
<br />In the course of writing “Dark Spectrum Part II” for the current ISCC issue, Carl Jennings asked me for comments. In response, I began to think about the optics of Newton’s vs. Goethe’s experiment. My thought process changed through the dialogue, especially as it related to Figure 3 of Carl’s essay. This Hue Angles summarizes the essentials of our email discussion, which seems to reveal some heretofore unremarked differences between the experiments of Newton and Goethe.<br />
<br />I started off with the idea that Newton’s prism experiment passes collimated (uni-directional) light from the Sun through a hole in a light-blocking shade (like a window shade), and through a prism. The prism disperses the sunlight into a spectrum according to the various refrangibilities of the wavelength components of the light. Then, in one version of the experiment, the dispersed spectrum hits a screen, and is reflected as a multicolored pattern to the observer. Collimation is necessary because light from two directions incident on the same point will provide different banding, and the bands from multiple directions will superimpose to wash out the pattern. I was convinced that collimation, being essential to Newton’s experiment, also figured in Goethe’s experiment. The only difference, I thought, was that Newton looked at a narrow beam through a hole or slit, and Goethe looked at a broad beam with narrow blocking elements that would cast shadows the prism would refract differently according to wavelength. Accordingly, I reacted as follows to Carl’s Figure 3 and its caption (see below for figure):<br />
<br /><strong>Mike:</strong> The caption of Figure 3 states: “A pair of scissors against a bright white winter sky in Munich, through two prisms simultaneously. (Source: author).” A bright white winter sky is about as non-collimated as you can get, and on the face of it this seems incompatible with the color bands in Figure 3. The only way to assure collimation is to position the prisms on the light path that includes the scissors and the eye. In that case, if the distance between the prisms is long enough, only light going nearly parallel in one direction through the first prism will intercept the second prism and hence get to the camera. <br />
<br /><strong>Carl:</strong> You discuss the color bands in the scissor image (Fig.3) as being incompatible with non-collimated light - but that is exactly the point - it happens when it shouldn't! None of the banding should happen, collimated or non-collimated, but the fact is it is there and is easily observable. Both prisms used in the photo were between the camera and the scissors, so no light was collimated. I found that two prisms made the banding more distinct, though it is observable with one, if you use a good prism.<br />
<br /><strong>Mike:</strong> I now think the paradox of color-banding with light from a white winter sky is not a paradox after all. Newton needed collimated light because Newton’s prism images the spectrum directly on a screen. In Goethe’s geometry, there is another element that must be in the optical train: a lens. A lens provides a point-to-point transfer from an object to an image (in respective object and image planes), whether or not the light is diffuse. The plane of Goethe’s shadowing components was the object plane, the lens was in his eye, and the image plane was his retina (or a tangent plane thereof). In your scissors example, the lens was that of the camera. Of course, the eye’s lens is implicit in all these demonstrations, but it is physically essential in Goethe’s experiment in which the eye looks directly at the diffuse light through the prism(s). Newton’s experiment does not have the eye looking directly at the light through the prism, and no lenses are needed between the slit and the screen, so collimation of the spectrum-separated light is essential.<br />
<br />In other words, a lens (be it eye or camera) is essential for the diffuse white sky light to show bands when it passes the scissors (which should be in the object plane of the camera lens). That role of the lens is essential to Goethe’s experiment. A lens is also part of Newton’s experiment because Newton used his eye to see the card-reflected spectrum, but the lens plays a different role here. It is a subtle point but should be understood.<br />
<br />Incidentally, Figure 3 suggests to me that, although a diffuse white sky exists in front of the camera, there must be very little light from behind the camera or there would be a white desaturating reflection from the front surface of the scissors.<br />
<br />The discreteness you have noted of the band colors---as opposed to their presence at all---is still a perceptual effect, as you have said before. I have no further thoughts on this matter now.<br />
<br /><strong>Carl:</strong> That is very interesting - I have never come across a description of boundary colors (even colorimetric ones, as in Koenderink or Bouma) that discuss the role of the lens. This is certainly a key feature to Goethe's phenomenological approach, but as far as I can tell does not exist in the literature.<br />One more question. Would sunlight passing through a hole in a window shade be already collimated? I ask because in Newton's own diagram of his experiment you can see that he has placed a lens in front of the prism, presumably to collimate the light. <br />
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<strong>Mike:</strong> Good question. The Sun is very far away (93 million miles), but it has a diameter of 0.864 million miles, which causes the Sun to subtend about half a degree of visual angle. The Sun’s rays depart from collimation by as much as ¼ degree. Collimation is almost—but not quite—completed without the lens, and Newton obviously sought to do better.<br />
<br /><em>Michael H. Brill <br />Datacolor</em><br />
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<span style="color: black; font-family: "Arial",sans-serif; font-size: 10pt; mso-fareast-font-family: "Times New Roman";">Figure 3. A pair of
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MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-89300469641248327812019-05-16T12:05:00.000-04:002019-05-16T12:05:28.771-04:00The Mathematics of Flower ArrangementI have just returned from the Philadelphia Flower Show. The theme was “flower power” and it featured music and visual references to the 1960s. Because I learned most of the math I know in the 1960s, I searched restlessly for something that would resonate with that memory. (Yes, contrary to popular belief, I both lived through the 1960s and remember them.) Eventually I found a curiously mathematical-sounding reference in a description of flower arrangements: the Hogarth curve. A spray of flowers was described as a Hogarth curve if the dominant elements comprised or suggested an s-shaped form. <br />
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To the consternation of my companion, I immediately searching for Hogarth curves on my phone. There was no mathematics--the curves had been used to describe the aesthetics in drawing, painting, and flower arrangement, and their name derived from the “line of beauty” extolled by William Hogarth in his 1753 book, <em>The Analysis of Beauty</em>. Hogarth was an 18th-century English painter and writer. He (and many subsequent flower arrangers) saw s-shaped curves as signifying liveliness and activity that cannot be found with straight lines or other curves. I found no mathematical or scientific discussion of Hogarth curves, so I will speculate on an interpretation now.<br />
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There is one special point on an s-shaped curve called the point of inflection. It is in the middle of the curve, and is the point where the curvature changes from negative to positive. In other words, it is a point of zero curvature. Imagine looking at an s-shaped curve drawn on a flat sheet of paper, and noting (with a very sharp pencil) the point of inflection. Now change your point of view (e.g., slant the paper away from you) and re-image the figure with a pinhole camera. Surprisingly, the point of inflection of the new image is exactly at the image of the point you noted with the pencil. The point of inflection is an invariant of the perspective projection.<br />
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This invariance is a mathematical property of projective geometry (which includes perspective). A projective transformation sends any straight line into another straight line. It is more general than a linear transformation because parallel lines when mapped may converge: the meeting point is called a vanishing point. When you look at an s-shaped curve, there is only one point of that curve whose neighborhood is a straight line, and that is the point of inflection. Three points on the curve can be made as collinear as desired by moving them closer and closer to the point of inflection. Since the neighborhood of the inflection point is a straight line segment, the segment will stay at the same part of the s-curve when that curve is projected to another planar image.<br />
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What does this have to do with Hogarth’s praise for s-shaped curves in art? It might be that the inflection point is anchoring a moving viewer to a distinct point in the picture, relative to which all else is swirling around. By being a view-independent feature, it may be an effect opposite to the elusive smile of the Mona Lisa, which (as explained by Margaret Livingstone at Munsell2018) is a low-spatial-frequency rendering that is noticeable only in peripheral vision, which sees with much lower resolution than our fovea (center of vision). <br />
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In any event, this tiny vestige of math in the middle of flower arrangements may allow me to revisit the 1960s with a sense of entitlement to its memories.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNn6TQoAflVKLa3Mnj0PlTRG00TX6YbmY6VAijPGlTfmw92Pa8jrM2NPLLo9789usiRQopLyvdboYSOg2Fs1Si109wSPQmGNBJimG6-0uMq7jBGBuBXcWQx_kq7u5AIGqA9Cdvrg6oQi8F/s1600/Hogarth.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="429" data-original-width="666" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNn6TQoAflVKLa3Mnj0PlTRG00TX6YbmY6VAijPGlTfmw92Pa8jrM2NPLLo9789usiRQopLyvdboYSOg2Fs1Si109wSPQmGNBJimG6-0uMq7jBGBuBXcWQx_kq7u5AIGqA9Cdvrg6oQi8F/s320/Hogarth.PNG" width="320" /></a></div>
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<br /><span style="font-size: x-small;">Figure Credit </span><a href="https://www.gardenontario.org/docs/2013_shs_flowershow_handbook.pdf"><span style="font-size: x-small;">https://www.gardenontario.org/docs/2013_shs_flowershow_handbook.pdf</span></a></div>
<br />Michael H. Brill<br /><em>Datacolor</em>MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-65357534936300856862018-11-27T15:58:00.000-05:002018-11-27T16:26:05.295-05:00Visualizing Four-Dimensional Colorimetry<br />
This essay is a return to the now-popular topic of tetrachromacy (four-color vision [1]), but with a geometric flavor that responds to a challenge by Jan Koenderink:<br />
<br />
“I hold the view that it is not possible to understand human color vision completely without having appreciated the tetrachromatic (or polychromatic of any order) embedding. I consider it to be somewhat of a scandal that the literature has so little to offer there.” [2, p. 200]<br />
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Since the publication of Koenderink’s book, as if on cue, researchers confirmed one example of a human tetrachromat [3,4]. So it is timely to start to answer Koenderink’s challenge, comparing trichromacy with tetrachromacy and including some observations that he himself made. <br />
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In three color dimensions (e.g., CIE space), it is common to project out one of the dimensions, to produce a 2D chromaticity space. The physical-light domain in this space is a planar region delimited by the spectrum locus and the line of purples: i.e., the familiar horseshoe diagram. Inside the diagram, let’s denote a white point W and an arbitrary color A. If you draw a line from A through W, any points encountered thereafter are complementary to A. If you draw the line in the other direction from W through A, you will eventually meet the spectrum locus or the line of purples. If the meeting is with the spectrum locus, the meeting point is called A’s dominant wavelength. If the meeting is with the line of purples, then A has no dominant wavelength.<br />
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In four color dimensions, the chromaticity domain has 3 dimensions—still accessible to our spatial visualization, perhaps with some difficulty. The spectrum locus is still a curve, but it is a space curve that spans all three chromaticity dimensions---like a bent wire hanger. Now imagine the wire hanger shrink-wrapped by a plastic sheet.* Every point within the shrink-wrap can represent a physical light. Now, as in CIE space, denote a white point W and an arbitrary point A within the shrink-wrap. Again you can draw a line between A and W. Extending on the W side, the points are legitimate complements of A: they add in certain proportions to give W. Because of the abundance of shrink-wrap area relative to wire-hanger area (theoretically zero), it will come as no surprise that the line will likely end at a shrink-wrap point and not at a wire-hanger point: light A probably has no spectral complement. Extending the line on the A side, one similarly encounters shrink wrap and not wire hanger. That denies the existence of a dominant wavelength for the vast majority of colors. The selection of possible outcomes is the same for 3D as for 4D colorimetry, but the odds for each outcome are staggeringly different.<br />
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You can also use the picture of wire hanger and shrink wrap in understanding the optimal color reflectances in tetrachromatic color spaces. <br />
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In trichromacy, it has been shown many times that the optimal reflectances (on the exterior of the object-color solid in tristimulus space) have values 1 or 0 at each wavelength, with at most two transitions between 0 and 1. To derive the number of transitions [5] one can notionally slice the chromaticity space with a line and define the optimal reflectance transitions as the points on the spectrum locus that were impinged by the slice. The optimality follows from the argument that 1’s inhabit all of the curve’s wavelengths on one side of the slicing line and 0’s occupy the other side---you can’t do better than that. In trichromatic space, by the way, the number of transitions is two, if the spectrum locus is convex (which it mostly is).<br />
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One can use the same trick in tetrachromatic space, but now one is slicing a 3D chromaticity space with a plane. The number of intersections of the slicing plane with the spectrum locus (wire hanger) is the number of 1-0 transition wavelengths. It now remains to find the tetrachromat’s analogue to convexity of the spectrum locus and use it to minimize the maximum number of crossovers. One could begin by asserting that the spectrum-locus curve must span the three dimensions of the chromaticity space, and posit as an axiom that no plane can cross the spectrum locus more than 3 times. <br />
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In performing this exercise, I am realizing that, whereas one can use either chromaticity or tristimulus space to visualize basic colorimetry for trichromats, the chromaticity domain is essential for visualizing tetrachromatic relations.<br />
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*I intend shrink-wrap as a metaphor for the boundary of the 3D convex hull of the spectrum locus. Real shrink-wrap will sometimes incur concavity, so my metaphor is imperfect.<br />
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[1] Jennings C. All the colors we cannot see: tetrachromacy in humans. ISCC News Issue 482 (Spring 2018), pp. 13-14.<br />
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[2] Koenderink J. Color for the Sciences. Cambridge, MA: MIT Press, 2010, Section 5.10.3. <br />
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[3] Jordan G, Deeb S, Bosten J, Mollon JD. The dimensionality of color vision in carriers of anomalous trichromacy. J of Vision 10 (2010), p. 12.<br />
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[4] Jameson KA, Winkler AD, Goldfarb K. Art, interpersonal comparisons of color experience, and potential tetrachromacy. Invited proceedings paper for the 2016 IS&T International Symposium on electronic Imaging (EI 2016). Technical session on Human Vision and Electronic Imaging.<br />
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[5] West G, Brill MH, Conditions under which Schrödinger object colors are optimal, J. Opt. Soc. Am. 73, 1223-1225 (1983).<br />
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Michael H. Brill <br />
DatacolorMHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-79409671731177530002018-08-30T13:01:00.000-04:002018-08-30T13:01:25.687-04:00The YouTube Theory of Colour VisionWhen writing for a general audience, vision scientists often refer to the long-, middle- and short-wavelength cone classes (L, M and S) as red, green and blue cones respectively. While this simplification may seem harmless it unfortunately has been the starting point for a cascade of misunderstandings about human colour vision. To begin with it reinforces the assumption that hues are properties residing in wavelengths of light, and then understandably leads to the assumption that the three cone types individually detect red, green and blue hues/wavelengths. Together these assumptions lead to the conclusion commonly encountered in discussions of colour vision on social media that we “only really see three colours”. In turn this conclusion has teamed up with the homunculus fallacy to spawn a model of colour vision in which the cone cells send hue signals directly to an observing brain. When the brain receives a combination of cone signals that could be produced by a “real” colour in the spectrum it “thinks it sees” that colour. This model bears little resemblance to current science but has achieved the status of orthodoxy on several online platforms.<br />
<br />Expositions of this model can be found in four YouTube videos recorded as having from nearly half a million to more than 18 million views: “This Is Not Yellow” (Michael Stevens, September 2012 [1]), “How We See Color” (Colm Kelleher, TED-Ed, January 2013 [2]), “Colour Mixing: The Mystery of Magenta” (Steve Mould, The Royal Institution of Great Britain, February 2013 [3]) and “Does This Look White to You?” (Dianna Cowern, October 2015 [4]). Kelleher’s version is typical: “There are three kinds of cone cells that roughly correspond to the colors red, green, and blue. When you see a color, each cone sends its own distinct signal to your brain. For example, suppose that yellow light, that is real yellow light, with a yellow frequency, is shining on your eye. You don't have a cone specifically for detecting yellow, but yellow is kind of close to green and also kind of close to red, so both the red and green cones get activated, and each sends a signal to your brain saying so.”<br />
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Based on the assumptions that hues reside in the wavelengths of the spectrum and that the function of colour vision is to detect these hues/wavelengths of monochromatic light, when we “think we see” yellow while looking at a mixture of long and middle wavelengths our brain is being “tricked” or ”lied to”; this mixture of wavelengths is only “fake yellow” [1]. <br />
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In each video the verbal explanation implies that the “red and green cones” respond most strongly to “red and green wavelengths” respectively, and that there is no cone responding most strongly to “yellow wavelengths”, even when an accompanying diagram shows correctly that the “real yellow” wavelength lies near the peak of the “red cone” response [1,4]. Stevens adds the additional misconception that bright yellow objects such as lemons reflect only “real yellow” wavelengths (they in fact reflect strongly most of the long and middle wavelengths of the spectrum). <br />
<br />Mould [4] adds the novel idea that when the brain receives a combination of “red cone” and “blue cone” signals that could not be produced by a single wavelength it “makes up” a colour, magenta. The view that magenta alone is a “made up colour”, which is now also popular on the internet, reflects the assumption that the spectral hues are not “made up” because they “exist” in the wavelengths of the spectrum.<br />
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The YouTube explanations make no explicit reference to cone opponency, the process by which the cone responses are compared with each other beginning in the retina (rather than proceeding directly to the brain). Nor do they mention the important higher-level process of hue opponency [5], by which perceptions of hue are generated in a yet poorly understood way as combinations of red/green and yellow/blue hue components. It is in fact difficult to see how the concept of hue opponency could be grafted without causing great confusion onto an explanation that already invokes red, green and blue signals arising at the level of the cones.<br />
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In explaining colour vision science, it is important to make it clear that hues do not reside in wavelengths of light and that at the level of cone responses and cone opponency our vision detects not hues but variations in the balance of the long-, middle- and short-wavelength components of light across the visual field. Hues should not enter the narrative until the higher-level stage of hue opponency, in which detected variations in the spectral composition of light and in the spectral reflectance of objects evoke red/green and yellow/blue hue-opponent perceptions. <br />
<br />1 <a href="https://www.youtube.com/watch?v=R3unPcJDbCc">https://www.youtube.com/watch?v=R3unPcJDbCc</a> <br />2 <a href="https://www.youtube.com/watch?v=l8_fZPHasdo">https://www.youtube.com/watch?v=l8_fZPHasdo</a>; <a href="https://ed.ted.com/lessons/how-we-see-color-colm-kelleher">https://ed.ted.com/lessons/how-we-see-color-colm-kelleher</a> <br />3 <a href="https://www.youtube.com/watch?v=iPPYGJjKVco">https://www.youtube.com/watch?v=iPPYGJjKVco</a> <br />4 <a href="https://www.youtube.com/watch?v=uNOKWoDtbSk">https://www.youtube.com/watch?v=uNOKWoDtbSk</a><br />5 Wuerger, S., & Xiao, K. (2015). Color Vision, Opponent Theory. In R. Luo (Ed.), <em>Encyclopedia of Color Science and Technology</em> (pp. 413-418). Springer. doi:10.1007/978-3-642-27851-8_92-1<br />
<br />David J. C. Briggs (<em>National Art School and Julian Ashton Art School, Sydney, Australia</em>) <br />Dr. David Briggs has taught courses in colour for painters for twenty years and is the author of the website <a href="http://www.huevaluechroma.com/">www.huevaluechroma.com</a>. A recording of his recent ISCC webinar “The New Anatomy of Colour” is available through the ISCC website (<a href="https://iscc.org/SeminarSeries">https://iscc.org/SeminarSeries</a>).<br />
MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-34230996547387261812018-04-27T14:11:00.001-04:002018-04-27T14:11:45.947-04:00Psychology and the Big Adventure of the Elastic Yardstick<em>A psychologist looks to color science to resolve old measurement quandaries.</em><br />
<br /> A news flash: psychology is hard if you don’t have the right tools. Psychology has a significant problem with measurement. Call its problem what you will: a crossing of ideas, a confluence of concepts, a tired old mistake, or even a methodological thought disorder (the last phrase is from Michell 1997, p. 374). Psychology has had a perennial problem with measurement since the mid-1800s (if not before) when Gustav Fechner announced his law to relate psychological qualities to physical magnitudes. The heart of the problem is that measurement in psychology is taken to be the same activity as quantitative measurement in physics. Measurement in physics involves knowing how to measure distances and knowing how to measure time, among other notions; it is clear that we cannot extend the same activities of measurement to psychology without some conceptual upheaval in our understanding of measurement. "It is as if I were to say, 'You surely know what "It’s 5 o’clock here" means; so you also know what "It’s 5 o’clock on the sun" means.' " (Wittgenstein, 1953/2009, § 350, p.118e) We do not, at least not without a lot more work and a few conventions about astrophysics. The one activity (in psychology) is just not the same as the other (in physics). More than that: it is <em>meaningless</em> to begin to describe how the two activities are the same or different, before we think harder about measurement and psychology.<br />
<br />One can begin in psychology by honoring Fechner and repealing his law, repeating a phrase from Stevens (1957). We are not rid of the problem of measurement in psychology merely by repealing Fechner’s law, though. Stevens himself caused as much trouble by introducing another procedure he called ‘magnitude estimation’: a procedure of attaching number words to stimulus magnitudes. The very act of attaching numbers to perceptible magnitudes was supposed to constitute measurement, somehow. One can’t just attach numbers to situations and expect the procedure to stand as measurement: such an attitude trivializes psychology in a parody of physics. “The proposition that <em>one conversation is ten times as boring as another</em> is neither true nor false, but is simply a string of words to which no sense may be attached.” (von Kries in Niall, 1995). Stevens only created trouble by introducing one more procedure unworthy of being called measurement. So let us honor Stevens and repeal his law of magnitude estimation in turn.<br />
<br />Is there hope left for measurement in psychology ? Measurement continues to be a problem all over psychology today, but hope remains. We do know what constitutes effective measurement. The formal or mathematical conditions for quantitative measurement are well-known (as in Krantz, Luce, Suppes, and Tversky, 1971). Problems of measurement do matter, if a coherent description of color space matters in colorimetry – as one example. What can be done to resolve issues of the application of measurement in psychology? We can begin by recognizing that measurement is something that may be possible in psychology, <em>or else it may fail to obtain</em>. There may be <em>no</em> measurement in most domains of psychology: we just do not know when measurement makes sense. <br /><br />
Quantitative structure is a contingent matter for colorimetry as it is for psychology generally – not a law at all, not by Fechner and not by Stevens and not by anyone. I venture to say the quantitative nature of color space has not been demonstrated in full: we still do not know if measurement works within colorimetry in the same way it does for other, physical magnitudes. In a profoundly ironic twist though, measurement in color space has a far <em>better</em> chance of working than the application of quantitative measurement in a geometry of ‘visual space’. Color theory has a better legacy: the pioneers of modern color theory were acutely aware of problems of measurement as they advanced the notion of color space, and a ‘line element’ for color space. In contrast my bet is that ordinary measurement is meaningless for visual shape, that is, under what has been called ‘the geometry of visual space’. But that conclusion follows from a long and abstract argument which I leave for another day (though see Suppes, 1991, p.48).<br />
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<em>References</em><br />
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Krantz, D.H., Luce, R.D., Suppes, P. & Tversky, A. (1971). <em> Foundations of measurement.</em> <em>vol.1</em>. Academic Press. <a href="https://doi.org/10.1016/b978-0-12-425403-9.50007-2">https://doi.org/10.1016/b978-0-12-425403-9.50007-2</a><br />
<br />Michell, J. (1997). Quantitative science and the definition of measurement in psychology. <em>British Journal of Psychology</em>, <strong>88</strong>(3), 355 – 383. <a href="https://doi.org/10.1111/j.2044-8295.1997.tb02641.x">https://doi.org/10.1111/j.2044-8295.1997.tb02641.x</a><br />
<br />Niall, K.K. (1995). Conventions of measurement in psychophysics: von Kries on the so-called psychophysical law. <em> Spatial Vision</em>,<strong> 9</strong>(3), 275 – 305. <a href="https://doi.org/10.1163/156856895x00016">https://doi.org/10.1163/156856895x00016</a><br />
<br />Stevens, S.S. (1957). On the psychophysical law. Psychological Review, 64(3), 153 – 181. <a href="https://doi.org/10.1037/h0046162">https://doi.org/10.1037/h0046162</a><br />
<br />Suppes, P. (1991). The principle of invariance with special reference to perception. In: J.-P. Doignon & J.-C. Falmagne, Eds. <em>Mathematical psychology: current developments</em>. New York: Springer, pp. 35 – 53. <a href="https://doi.org/10.1007/978-1-4613-9728-1_2">https://doi.org/10.1007/978-1-4613-9728-1_2</a><br />
<br />Wittgenstein, L. (1953). <em>Philosophical investigations / Philosophische Untersuchungen</em>. Revised 4th edition, 2009. Wiley-Blackwell.<br />
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<em>Keith K. Niall</em> <br />
Keith lives in Toronto, Canada. He is translator and editor of <em>Erwin Schrödinger’s Color Theory</em>, and he is looking forward to writing a book about vision in his own voice. His email address is <a href="mailto:Keith.Niall@drdc-rddc.gc.ca">Keith.Niall@drdc-rddc.gc.ca</a>. MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-45386071690162789082018-02-12T11:43:00.001-05:002018-02-12T11:47:53.426-05:00We'll Always Have Parrots<br />
<span style="color: black; font-size: 12pt;"><span style="font-family: Calibri;"><span style="font-family: Times, "Times New Roman", serif;">My significant other and I have two
parrots, an African grey and a yellow-naped Amazon. They are 24 years old and
very feisty--i.e., apt to bite fingers and toes. They will also be
around long after we have departed this Earth, for they live to be at least 55
or 60. So that is why I have said "we'll always have parrots"
in "parroty" of Rick in <em>Casablanca</em>.<o:p></o:p></span></span></span><br />
<span style="font-family: Times, "Times New Roman", serif;"></span><br />
<span style="color: black; font-size: 12pt;"><span style="font-family: Times, "Times New Roman", serif;">And the parrots will always have
colors: Yellow and green (with a white eye ring) for the Amazon, and various
lightnesses of gray and red for the African grey. But the colors may vary
according to the aqueous environment: A grey feather immersed in water will
stay grey but darken slightly. Orange, yellow, and red will also hold
their color in water. But green (and blue, I am told) will change. In
particular, green turns brown when immersed in water. Clearly
there are at least two mechanisms for the color:
diffraction/iridescence for colors that change on immersion in water (change
of refractive environment), and conventional pigment reflectance for
colors that don't change on exposure to water. For more on bird-feather color,
see </span></span><br />
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<a href="https://academy.allaboutbirds.org/how-birds-make-colorful-feathers/" previewremoved="true"><span style="color: blue; font-family: Times, "Times New Roman", serif;">https://academy.allaboutbirds.org/how-birds-make-colorful-feathers/</span></a><span style="font-family: Times, "Times New Roman", serif;">.</span></div>
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<span style="font-family: Times, "Times New Roman", serif;"> </span></div>
<span style="font-family: Times, "Times New Roman", serif;"></span><br />
<span style="color: black; font-size: 12pt;"><span style="font-family: Calibri;"><span style="font-family: Times, "Times New Roman", serif;">Many experiments are possible,
including immersion of the whole bird. Sometimes I imagine I understand
how Edgar Allan Poe could have been a bit freaked out by his raven because it
was likely to outlive him. But, as Ilsa heard at that immortal moment in
Casablanca, it is more likely that "we'll always have parrots."<o:p></o:p></span></span></span><br />
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<span style="color: black; font-size: 12pt;"><o:p><span style="font-family: "calibri";"><span style="color: black; font-family: "calibri" , sans-serif; font-size: 12pt;"></span> </span> </o:p></span><div class="separator" style="clear: both; text-align: center;">
<span style="color: black; font-size: 12pt;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJbNnU7VhF9Zy0OvOXo7PSgj2UTdr3XNL0Kou4vnSbjCn9psfr7RfxP6tFku_pq5YB_nkDErt_ahHKqF6lwyYK8s84GyDWAUPJj2AriW8wQ7LY7Um_ftcygu0lhiPPTN4oddh9p0dHiBWk/s1600/Alex_and_Poobah.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1600" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJbNnU7VhF9Zy0OvOXo7PSgj2UTdr3XNL0Kou4vnSbjCn9psfr7RfxP6tFku_pq5YB_nkDErt_ahHKqF6lwyYK8s84GyDWAUPJj2AriW8wQ7LY7Um_ftcygu0lhiPPTN4oddh9p0dHiBWk/s320/Alex_and_Poobah.jpg" width="320" /></a></span></div>
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<em>Left to right: Alex and Poobah</em></div>
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<span style="color: black; font-size: 12pt;"><span style="font-family: Calibri;"><span style="font-family: Times, "Times New Roman", serif;">Michael H. Brill<o:p></o:p></span></span></span><br />
<span style="color: black; font-family: Times, "Times New Roman", serif; font-size: 12pt;"><em>Datacolor</em></span>MHBrillhttp://www.blogger.com/profile/03026453201875220765noreply@blogger.com0tag:blogger.com,1999:blog-8850915545800124065.post-5924065993803162802017-11-21T12:25:00.000-05:002017-11-21T12:33:34.013-05:00The Medium Shrinks the Message: New 4-Color Optical Data StorageLast weekend I had a second encounter with a popular blurb about a new optical-data-storage technology originating at Case Western Reserve University (my <em>alma mater</em>). A polymer chemist, Emily Pentzer (and co-authors), discovered a way to combine a thermochromic and a photochromic chemical in a polymer film to make four possible colors depending on the stimulation. You can see the essence of the invention in the figure below [1]. The refereed-journal publication is [2]. <br />
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The promise of the invention is to enable a twofold shrinkage of data storage because you can extract two bits of information (four colors) where previous technologies had enabled only one bit (0 or 1) per storage location. The medium could be said to shrink the message.<br />
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The blurb’s description is a bit cryptic relative to the above goal, so I began a line of investigation that began with pure imagination and ended with obtaining the paper and discussing the matter with its main author.<br />
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From [1], I learned that the invention involves a polymer layer that contains two kinds of small molecules in low concentration. Call the two additives P (photochromic, actually o-nitrobenzyl ester of benzoic acid) and T (thermochromic, actually cyano-substituted oligo(<em>p</em>-phenylene vinylene)). When a layer containing P and T (which is tough enough to resist even abrasion by sandpaper) is exposed to no light, it is colorless (black). When that layer is exposed to UV, it fluoresces ultramarine. When the layer is exposed to heat (perhaps via IR), it fluoresces green. Finally, when the layer is exposed to both heat and uv, it fluoresces cyan. The colors appear in the figure below. <br />
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To me the text doesn’t describe an encoding system (to which information can be deposited and then retrieved at leisure). I imagined the following variation of the technology for writing and subsequent reading. Suppose the stimulation is always a mixture of heat and UV. If the layer contains neither T nor P, the color is black; if it contains T but not P, the color is green; if it contains P but not T, the color is blue; and if it contains both P and T, the color is light blue. In this explanation, the information is contained in whether P or T (or both or neither) is applied to the information-storage site. The stimulating radiation at the moment of retrieval is always the same, because we have no way of knowing in advance which information-laden color will be retrieved.<br />
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My departure from [1] was a bad guess, and in retrospect pasting together all those little P and T fragments would be very expensive. I was led to the original paper [2], whose abstract clarifies the mechanism for the write and read algorithms for numbers (0) to (3): “The as-prepared film is non-fluorescent (0), and can be written through a wooden or metal mask with thermal treatment (1), light treatment (2), or both (3), giving three different colours of fluorescence under UV irradiation.”<br />
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This explanation still left me wondering how UV can write on the mixture of polymers and yet stops perturbing the medium during the reading process. When you are “reading” the written medium with a UV beam, how do you ensure you don’t change symbol (1) into symbol (3) and symbol (0) into symbol (2)? In other words, how do you arrange for the medium to be write-once, read-many-times? Accordingly, I conducted a brief e-mail interview with Dr. Pentzer. Here was the essence of it:<br />
<em>Hue Angles</em>: “Am I correct in assuming that the light treatment is UV, and that UV spectrum peaks at 365 nm?”<br />
<em>Pentzer</em>: “Yes, we use a typical hand-held UV lamp like that used to visualize TLC plates.”<br />
<br />
<em>Hue Angles</em>: “Is the thermal treatment done with a beam of IR radiation, or do you deliver localized heat with another technology?”<br />
<br />
<em>Pentzer</em>: “We actually use a little heat pen. We are currently trying to start a collaboration with engineers/other scientists who can use an IR beam. We want to combine engineering approaches with our chemistry.”<br />
<br />
<em>Hue Angles</em>: “When you are reading the written medium with a UV beam, how do you ensure you don’t change symbol (1) into symbol (3) and symbol (0) into symbol (2)?”<br />
<br />
<em>Pentzer</em>: “It really depends on the strength of the UV source. With a hand-held lamp, we can read about 20 minutes before we start to have issues with visibility. So, if we pattern with a strong UV light source, we can read with a handheld lamp---no problem. We also have to ensure we don't expose the patterned films to sunlight for too long...so, it's really a game of reading it only when you need to.”<br />
<br />
I’m sure we’ll hear more about this new technology as it develops. With all my speculations gone, the medium will shrink the message still further.<br />
<br />
References:<br />
[1]. CWRU researchers find a chemical solution shrinks digital data storage, <a href="http://thedaily.case.edu/cwru-researchers-find-chemical-solution-shrinks-digital-data-storage/">http://thedaily.case.edu/cwru-researchers-find-chemical-solution-shrinks-digital-data-storage/</a> . July 5, 2017.<br />
[2] P. Wei, B. Li, A. de Leon, and E. Pentzer, Beyond binary: optical data storage with 0, 1, 2, and 3 in polymer films.<em> J. Mater. Chem. C</em>, 2017, 5, 5780-5786. <a href="http://pubs.rsc.org/en/content/articlelanding/2017/tc/c7tc00929a#!divAbstract">http://pubs.rsc.org/en/content/articlelanding/2017/tc/c7tc00929a#!divAbstract</a> <br />
<br />
Michael H. Brill <br />
<em>Datacolor</em><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFeQHkYtvXB7moSiDf3dZScwj29nOof3iuOl4tysPSwZi4OdKwaRnz_0igM3CnarcrNOF0kt0zPw_NuFZUNgURJrObcrTDFTc6YhyJBHe8I-sFfWQK3ObVRQKgKDs_0gkJOeOsWzXdl-bl/s1600/4_color_data_storage.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="724" data-original-width="1024" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFeQHkYtvXB7moSiDf3dZScwj29nOof3iuOl4tysPSwZi4OdKwaRnz_0igM3CnarcrNOF0kt0zPw_NuFZUNgURJrObcrTDFTc6YhyJBHe8I-sFfWQK3ObVRQKgKDs_0gkJOeOsWzXdl-bl/s400/4_color_data_storage.jpg" width="400" /></a></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;">Graphical summary of the new CWRU technology (copied from the website in Ref. 1)</span></div>
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