Afterthought on afterimages: Green flashes and green lights

Some experiments are fun and not painstaking. Here is one from my student days ...

by Michael H. Brill, Datacolor

Afterimages from bright lights are usually undesired and hardly ever helpful, but they can tell you something about the visual system. Here’s an experiment you can try at home, that shows a remarkable interaction of your two eyes during an afterimage. You will need a strong pen-light overlaid by a green filter, a strong, directed white light (such as a 500-watt fiber-optic projector), a magnifying glass lens, half a ping-pong ball (placed over the right eye), and a white wall under artificial light (incandescent will do). The problem, as you do the experiment, is to explain the afterimage effect.

First of all, hold the green pen-light at arm’s length and flash it into your left eye. Then look away at the white wall. The long-lasting dark (negative) afterimage will look magenta at first and then turn bluish purple. This happens whether or not your right eye is open. Closing the left eye or dimming the light on the white paper makes the afterimage turn bright green (positive).

Now repeat, but when you look at the wall with your left eye, shine the projector into your right eye through the half ping-pong ball, producing a uniform field that won’t distract you from the left-eye’s afterimage. I think you will see the afterimage in the left eye flash bright green for a second and then return to a dark purple appearance. By the way, the projector should be about 3 feet away from your right eye, and you should look at it only through the ping-pong ball.

As long as the negative afterimage persists, the green flash can be elicited repeatedly by turning the projector light on and off. The flash is the same color as the light occasioning the afterimage (in this case green). The green flash cannot be attributed to stray light entering the left eye from the light producing the uniform field on the right eye: More light in the left eye just makes the afterimage appear darker and more purple. On the contrary, the flash effect is similar to the polarity reversal that happens when light is dimmed in the left eye.

So why is this happening, and how can you prove it?

Give up? Well, it seems that when you turn on the light in the right eye, the right-hand iris contracts, and that causes the left-hand iris to contract as well. That dims the light from the white wall by decreasing the pupil diameter. (This effect will be strongest in young people who still have some action in their irises.)

How can I show this? Repeat the above experiment, instead of looking at the white wall, look at a distant white light source through the magnifying glass. Position the lens so its near focal point is in the plane of the pupil, sends light through the middle of the pupil without being affected by the iris. You’ll know you have the right distance when the image of the light source floods your whole retina. Now turn on the projector to the right eye, and lo! The green flash will not appear.

It might appear that you need about eight arms to do this, so it is not as casual an experiment as I have misled you to believe. But it is not quantitatively demanding, and I published it for a small audience at MIT without incident [1]. As of this year, you can read any of the progress reports on the Web. It costs no money, and the complete obscurity of this unrefereed publication is balanced by its refreshing availability to all, without passing a toll gate. Academic freedom has turned inside out, and we have found an unexpected place where the green light is flashing.

M. H. Brill, Binocular afterimage effect, MIT Research Lab. of Electronics Progress Report, PR 120, pp. 168-169 (1978). http://dspace.mit.edu/bitstream/handle/1721.1/56698/RLE_PR_120_XXVI.pdf?sequence=1.

Thoughts on Annotated Webliography and its Relatives

[ Once in a while it is good to revisit an old idea we decided not to pursue, to see what has emerged instead…MHB]

Ten years ago the ISCC approved a Project Committee to establish an Annotated Webliography of Color. The goal was to point to excellent Web sources of color information. The scope was daunting: Criteria to select a website for annotation/citation, a first selection of websites for citation, rules for updating the resulting Annotated Webliography, and transition of the effort to a standing committee that (ever vigilant) would update the webliography.

As the chair, I started to compile a list of websites, and several people added to it. But soon enthusiasm waned. Also, some URLs on the list began to fail. I resigned as committee chair in 2002 because the Web medium seemed too transitory to justify ever-vigilant ISCC checking. Ironically, the Project Committee description is fossilized at http://www.iscc.org/functions/pc.php#proj53. If nothing else, it proves we were among the first to coin the term “webliography”!

Where has the Web gone since 2002? Aside from installing more toll gates so you have to pay for information (in my opinion a bad thing), it has moved in two directions, attempts at objective truth (often consensus-driven, exemplified by Wikipedia) and undisguised opinion (blogs). The goal of our Webliography was more like Wikipedia’s model. I will now discuss two excellent websites as examples and try to classify them. My classification doesn’t follow ISCC interest-group stereotypes.

First consider Jill Morton’s “Color Matters”. It addresses artists and designers, but there are also stories relating to color science. My favorite from “Color Matters” is about a red-tailed hawk named Windwalker who, from a perch on the author’s arm, removed and discarded all the strawberries from her strawberry short cake, presumably because “Windwalker had never seen me eat anything as bloody red as the meat that he himself consumes on a daily basis. He was using a delightful combination of memory, loyalty and his ability to discern colors to intelligently correct a situation that in his mind was not normal.”

Is “Color Matters” more like Wikipedia or more like a blog? Most of its content makes it more like Wikipedia, even though it has a small, carefully labeled blog section and a forum called “Color Tales.” Outside these sections, I don’t see much editorializing, but lots of information gathering. In one way it is not like Wikipedia: Its structure makes it hard to locate particular material. If you want to find the article on Windwalker, it’s best to type “Color Matters” “Windwalker” into Google.

Now consider the “Mostly Color Channel”---which I abbreviate as MCC. MCC is the vision of Giordano Beretta (an innovator in color printing technology), but with contributions by Nathan Moroney and three others. MCC cross-references to many sites, including CIE activity reports, the ISCC historical translations and Hue Angles. But it offers much more, including videos, slide presentations, historical essays and blog entries---a huge amount of work! One of the historical essays quotes a letter to Science from toymaker Milton Bradley describing a telephone-controlled color wheel to “telephone a color”---an 1892 ancestor of Ralph Stanziola’s VCS-10! There’s also a video showing a display comprising a 3D swarm of individually controllable lights. Among the blog entries, Giordano offers book reviews---some in Italian. Try his review of Snakes in Suits on for size!

The site originated under the auspices of Hewlett-Packard, but now is independent of HP and represents the untrammeled opinions of its authors. You will see lots of color technology, as well as cultural artifacts that involve color. But also you will see intellectual tangents and corners of knowledge---interspersed with passionate editorials. The site is not organized for easy access to targeted information, but if you just click on anything you will be fascinated, as I was. (Again, Google will help you find a particular item.)

I think MCC is the Whole Earth Catalog of color---but with no price-tags. Interestingly, Steve Jobs called the Whole Earth Catalog the forerunner of the World-Wide Web---a sort of “Google in paperback form”. I disagree, because unlike Google, the Whole Earth Catalog purveyed a vision---to enable people to develop a self-sustainable lifestyle.

MCC also has a vision, conveyed in the footer of Giordano’s blog: “The Internet is an amalgam of forms blurred under epistemological pressures. In Søren Kierkegaard’s words, under this flat shower of leveled information, where everybody is interested in everything and nothing is too trivial or too important, people just accumulate information and postpone decisions indefinitely, i.e., nobody takes action and nobody is responsible for truth — there is no mastery, just gossip. He called this the æsthetic sphere of existence, exhorting us to evolve to the ethical sphere, where we do not just accumulate information but take action and make commitments. Blogs are instruments to overcome flatness by creating opportunities for vertical activities. In this sense this blog is a view from my window — a collection of tidbits I judged relevant to computational color science and in general to the promotion of scientific excellence in areas of strategic importance for the future of research, economy and society.”

That’s a hard act to follow, Giordano. Bravo!

Notes from the NPA: New platonic solids, new visions of Doppler shift

Michael H. Brill
[Here are some notes from a most unconventional convention. Perhaps they will make the ISCC blog light up… …MHB]

The Natural Philosophy Alliance is even more diverse than the ISCC. Its members--- artists, lawyers, physicians, chemists, physicists and mathematicians---all give voice via their own expertise to challenge current scientific theories. They agree with each other less often than ISCC members. (Yes, that’s possible.) I attended their meeting (NPA17) [1] in Long Beach, CA the week after ISCC met in Princeton. Two NPA nuggets might intrigue ISCC members: a geometrical shape with interesting optical properties, and a thought experiment to clarify the Doppler effect.

Artist Michael R. Evans [2] dubs the “atom” out of which he builds his creations the Trion-Re’. Realizable in paper or clear acrylic plastic, the Trion-Re’ looks like a shortened weaving-shuttle. You can make one by cutting out the 60°-arc-limited parts in the figure below. Assemble the parts so A is preserved, the three B vertices coincide, edge 1 meets 1’, 2 meets 2’, and 3 meets 3’. [Exercise for the reader: Is this construction mathematically possible or must it be forced? See “Trion Re’dux” below.]


On a mathematical note, the Trion-Re’ has the minimum number of faces (F), vertices (V) and edges (E) that satisfies Euler’s formula V + F - E = 2 for polyhedra. Although the Trion-Re’s faces are not flat when assembled, given the above construction they start out flat and are never stretched (i.e., have zero Gaussian curvature).

Another NPA nugget was Physicist Francisco J. Műller’s paper [3] asking, if we think we understand Doppler red-shifts of light, then how do shifts of non-light happen (e.g, for a Fraunhofer absorption line incurred by an interstellar cloud)? Let a stationary Earth E look at a star S (possibly receding) through a cloud C (possibly receding). Say the recession red-shifts 656 nm to 670 nm. (I will speak of shift rather than scaling because the wavelengths here are not very different from each other.) There are three cases.

Case I: If S and C recede together from E, then the S’s spectrum and C’s absorption line are red-shifted together (the latter to 670 nm). C receives 656 nm light from S with no Doppler shift (because C and S are not in relative motion). The cloud absorber stops that radiation, and the rest of the light is passed Doppler-free. The lengthening path from C to E then shifts the entire spectrum including the absorption line.

Case II: If S recedes while C and E are stationary, then S’s spectrum is red-shifted but not C’s absorption line. Now C is in the same frame as E. S’s light is already red-shifted upon reaching C, and in particular 642 nm light is shifted to 656 nm and is stopped by the absorber. The absorption is at 656nm, but the rest of the spectrum is shifted 14 nm higher.

Case III: If S is stationary relative to E and C recedes, then C’s absorption line is red-shifted but S’s spectrum is not. Light received through C outside C’s absorption band has no interaction with C. For these wavelengths, the cloud does not exist, so S and E are static and have a vacant path between them—incurring no Doppler shift. But light emitted at 670 nm is blocked by C (at 656 nm), and that line is Doppler-shifted back to 670 nm due to the recession C from E.

Műller and I seem to agree on the results of these three cases, but whereas I model Doppler shifts based on how the whole optical path stretches in time [4], Műller has a different view. I thought this problem would be interesting for ISCC thinkers. In a sense the assumptions are simpler than the ones we take for granted in color science. At first I saw the cloud as a filter, but Műller correctly noted that even a transparent filter interacts with the light at all wavelengths, unlike in parts of the Doppler example.

Oh, by the way, much is said in NPA about Einstein’s relativity theories, and I added to that this year [5]. Back to normal stuff next issue!


1. http://conf17.worldnpa.org/ and click Abstracts to read any paper.
2. M. R. Evans, The geometry of light, Proc Nat. Philos.Alliance, 7, 149-153 (2010).
3. F. J. Műller, The Doppler effect of absorption spectral lines in moving astronomic bodies (How can it happen?) Proc Nat. Philos.Alliance, 7, 336-342 (2010).
4. M. H. Brill, Doppler effect: surprises from the time domain, J. Nanophotonics 4, 041520 (4 Feb 2010).
5. M. H. Brill, Cochetkov’s speeding bola---yet another entanglement for special relativity, Proc Nat. Philos.Alliance, 7, 62-63 (2010).

P. S. Trion Re’dux

My Trion Re’ puzzle (above) has several levels of answer---so I won’t wait for the next issue to clue you in. Can the three flat leaves be rolled up into a 3D convex figure with three-fold symmetry about the axis AB? Yes, but….

Examined along the AB axis, any cross-section of the Trion Re’ is an equilateral triangle, and the triangles are all centered on the axis and have the same orientation. Any progression of triangle sizes (as a function of position on the AB axis) is enforced by the shape of the unrolled leaf (whether or not limited by 60° arcs). Since the corresponding triangle sides are straight and parallel, each face rolls and unrolls between 3D and flat. So the answer to my puzzle is “Yes.”

A this point, it bothered me that the lining-up of the triangles implies that the edges of the Trion-Re’ are plane curves in 3D. They are also plane curves when unrolled flat. So how do you roll a planar 60° arc out of its plane so it becomes again a plane curve? I was able to show this is not possible if you use a circular cylinder as a “curling iron”. But I still don’t know the cross-sectional shape of the cylinder that makes it work. Maybe some ISCC geometer can find it.

Then I heard from artist Michael Evans (through physicist Greg Volk): The faces of the acrylic Trion Re’ are not Gaussian-flat, but are closer to being parts of spheres! So we have two distinct constructions, folks, the paper-folding one (with its neat math problem) and the acryllic one (with its neat optical property). They may be “artistically equivalent,” a matter to be decided by Interest Group 3!

The Peculiar Distribution of Last Color Names

Michael H. Brill and Karen E. Linder

This column might seem an excuse for a tangent on mathematics, but be patient---the color-related topic will re-appear…MHB]

Here’s a color-related experiment you can do with the phone book: Record the number of people whose last names are colors. The distribution is far from uniform. The 2010 Residential White Pages for Princeton/Suburban-Trenton NJ shows the following incidence of last names that are color names: Brown (555), White (228), Green (154), Gray (73) [Grey (3)], Black (47), Blue (14). As a check on the geographic specificity of this result, we tried Marquis Who’s Who in the World 2001 and got a similar ranking: Brown (140), White (51), Green (30), Black (25), Gray (23) [Grey (2)], Blue (4). Neither source has any last names Red, Orange, Yellow, Indigo, Violet, We didn’t try any other color names. Why does this regularity exist? Mathematicians have taken such observations as points of departure for century-long theorizing. For example, in 1881, Simon Newcomb [1] noted, “that the ten digits do not occur with equal frequency must be evident to any one making use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first digit is oftener 1 than any other digit, and the frequency diminishes up to 9.” Benford rediscovered the tendency (henceforth called Benford’s law) in 1938. Others [2] have given theoretical explanations, and it is discussed in the context of the mathematics of fractals [3].

The probability of first digit d works out to log₁₀(1 + 1/d), which summed over d gives 1. Proof of plausibility: Require the probability density function of a continuous number to be scale-invariant [constant in log₁₀(x)]; note that implies a/x is the density function in x; note the integral of a/x diverges, so consider first only over one decade, from 10^m to 10^m+1\, and then realize the numbers don’t change when 1 decade is expanded to n decades. Over one decade of x (10^m to 10^m+1), the probability density is f(x) = 1/x, and the probability of first digit d is log₁₀(d+1) – log₁₀(d) = log₁₀(1 + 1/d); Finally, realize that, although starting or stopping in the middle of a decade produces an artifact, the artifact gets vanishingly small when the number of decades n gets larger and larger. Another view of this argument and its limitations appears in [4].

You can confirm Newcomb’s observation by an experiment with a phone book: Tally the first digits of street-address numbers, and observe that Newcomb, Raimi, et al. were right. You can stop after one or two pages…

By the way, Benford’s law is not just a curiosity, but is now used in detecting fraudulent random-guess data in income tax returns and other financial reports (http://www.rexswain.com/benford.html, and also [5]).

A related effect is called Zipf’s law (http://en.wikipedia.org/wiki/Zipf's_law), which has the same form in a variety of venues: The most frequent word in a natural language occurs about twice as often as the second-most-frequent word, about three times as often as the third-most-frequent word, etc. The same kind of relationship applies to the populations of cities in a country versus their population ranking.

Can such roots be found in the peculiar distribution of last color names? The last-color-name distribution is similar to Zipf’s law, but the decrease is too steep. Have we forgotten some common last-color-names that would fill in the gaps? Perhaps a cross-cultural study (e.g., performed by previous authors of this column) might fill in some of the gaps or give a key insight. We hope any such insights might find happier uses than detecting tax evasion.

1. S. Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math., 4, 39-40 (1881).
2. R. A. Raimi, The peculiar distribution of first significant digits, Sci. Amer. 221, 109-120 (December, 1969).
3. B. Mandelbrot, Fractals: Form, Chance, and Dimension, W. H. Freeman, 1977.
4. http://mathworld.wolfram.com/BenfordsLaw.html
5. T. P. Hill. "The First-Digit Phenomenon", American Scientist< 86, p. 358 (July-August 1998).

Disk Color Mixture and Beyond

Don Hall, Former President of Applied Color Systems, Inc. (ACS) and ACS-Datacolor

[Rotating a disk for fun, knowledge, dizziness, and profit. This month we’ll hear from Don Hall, who has engaged in all of the above and even patented some of it. Don starts by reviewing a recent paper by Rolf Kuehni, and then reaches farther… - MHB]

Rolf Kuehni [1] recently published a comprehensive and well researched paper on the historic use of a modified child’s toy, a spinning top, to investigate the mysteries of color.

Kuehni starts with Ptolemy’s second-century, first-recorded, observation that a fusion of color occurs when a spinning multi-colored potter’s wheel reaches a certain speed. Eight hundred years later Alhazen, a Persian natural scientist, made a similar observation. After another 700 years, experimenters tried to understand why disk mixtures don’t ‘properly’ correlate with pigment mixtures. After this was understood, disk color mixture found practical use. In 1763, Antonio Scopoli, an Austrian physician and natural scientist, used disk mixture in classifying insect colors. Two years later, Chevalier D’Arcy, a physicist, measured the persistence of a rotating visual image using a glowing piece of coal. He needed at least eight revolutions per second for the image to fuse. (See [2] for more on the time resolution of vision.)

Over the next hundred years, Kuehni continues, disk-mixture studies revealed “accidental colors”, afterimages and complementary colors. During this period attention gradually shifted to empirically based color order systems.In 1810, the artist Philipp Otto Runge proposed such a system but had difficulty correlating Newton’s colors with pigment mixtures and decided to experiment with disk mixtures. In the process he lightness-matched the chromatic segments against the black & white segments.

Several years later, in 1855, James C. Maxwell reported using the famous disk-mixture device of his own design to advance color theory. By 1860 he switched from a spinning
disk to a visual colorimeter to match spectral colors with spectral primaries. A few years later O. N. Rood used disk mixture to reconstruct or “correct” Maxwell’s diagram.

In 1900 A.H. Munsell patented his Color Sphere which, when spun, produced neutral grays of decreasing Value from the top to bottom of the sphere. Later Munsell used disk mixture to create the color panels that populated his 3D Color Tree. In subsequent years the Munsell Company offered his color chips in a circular form with a center hole and slitted radius for mounting on a spinning disk device.

By the 1920’s and 30’s, visual photometers, tristimulus colorimeters and spectrometers obviated the need for spinning-disk mixture. However, as Kuehni reports, there was one final gasp for that old technology. In 1977, Applied Color Systems Inc. (Princeton, NJ) began to develop an instrument for measuring color materials that were not readily measured on a reflectance spectrophotometer because of texture, pattern, size or geometry. After nearly two years of unsuccessfully exploring color CRT and color projection systems, Ralph Stanziola, ACS’s Executive Vice President and Technical Director, decided to take a page out of the past, to the amazement of his associates, by developing a “Maxwell Disc” connected to a computer to match colors. Although the Visual Color Simulator (VCS-10) took three years to develop, it was technically successful as a visual color measuring input device for computer color matching and also as an accurate color simulator that could rapidly transmit visually simulated colors to remote locations. As Kuehni correctly points out, it may have worked well but it was too expensive to be widely accepted.

During the development of the VCS-10, some visual anomalies were encountered, particularly during start-up while the color disk pack accelerated to the flicker-fusion rate. Some observers complained of nausea and vertigo, and others saw different colors in their peripheral vision. To avoid these perturbations, the power to the controlled illumination lamps was not activated until the rotation was fast enough for flicker fusion.

The effect we were avoiding by turning the lamps off is related to a much weaker disk-color effect that is not properly disk color mixture (and which Kuehni doesn’t mention). Produced in 1894 by toy maker C.E. Benham, the “Artificial Spectrum Top” [3] was a disk that was one half black and the other half a white background overprinted with four areas having a series of three concentric black arcs arranged in a step-wise fashion. When this disk was spun below the flicker-fusion rate, concentric circles of weak colors appeared. When rotated the opposite way the illusionary colors reversed order.

Benham’s top is still a subject of scientific investigation [4, 5] and disk color mixture may be a matter for history. Nevertheless, I still have a Swiss Made “Optischer Farbmischer” [www.swissmade.com] on my desk as a reminder of the pleasure of working with Ralph Stanziola on the VCS-10 and in a sense reliving some experiences of the scientific pioneers that Kuehni documents so well.

REFERENCES:
1. Kuehni, RG. A brief history of disk color mixture, Col. Res. Appl. 35, 110-121 (2010).
2. Morgan Eye Center, Univ. of Utah, Temporal Resolution http://webvision.med.utah.edu/temporal.html
3. Benham C.E. The artificial spectrum top, Nature 51, 113-114 (1894).
4. LeRohellec J, Vienot, F. Interaction of luminance and spectral adaptation upon Benham subjective colors, Col. Res. Appl. 26, S174-S179 (2001).
5. Kenyon,G, Hill, D, et al. A theory of the Benham top based on center-surround interactions in the parvocellular pathway, Neural Networks 17, 773-786 (2004).

Engineering, Insanity, and 999 Years of Optics

Michael H. Brill, Datacolor

We’re not quite at the millennium mark for Alhazen’s Book of Optics. It brings to mind a story of how Alhazen got started in his “second career” that should inspire us all…

A recent Scientific American article [1] prefaced the results of a photo contest by noting that we are approaching the millennial anniversary (2011) of Persian scientist Ibn al-Haytham’s (Alhazen’s) starting to write his Book of Optics. The article used Alhazen’s discovery of the properties of a magnifying glass as a segue to the wonders of photography through microscopes---and hence to the contest.

Quite apart from the science, one story of that beginning [2, 3, but not 4] has a message to us today. As a civil servant at age 45, Alhazen was called to Egypt by Al-Hakim bi-Amr Allah, the sixth ruler of the Fatimid caliphate, to regulate the flood waters of the Nile. At first Alhazen envisioned a dam where the Aswan now stands, but upon reconnoitering on the south border of Egypt, saw no way to bring that plan to fruition. Quickly realizing his inability, he retired from engineering. In that regime a “severance package” likely would mean your head cut off in a basket. To save his life, Alhazen feigned insanity, and was forthwith held in house arrest from 1011 until al-Hakim died in 1021. Under house arrest, he immediately began his Book of Optics, and thereafter generated many scientific works for the rest of his life (i.e., through 1039).

In the Book of Optics one finds the first modern scientific treatment of optics and vision. Alhazen methodically investigated the magnifying properties of a lens, and also its property as a “burning glass” when focusing the sun’s radiation. He also was the first to project an entire image from outdoors onto a screen indoors through a small hole, and thereby to demonstrate and explain the action of a camera obscura. He had a theory of the Moon illusion (one of many such theories that still mark our landscape). He might have attributed the focusing aspect of a glass lens to the function of the lens of the eye, but the lens’s inversion of the image (which is not evident in vision) was a stumbling block in those days.

One could go on: In the remaining decades of his life, Alhazen contributed to many more areas of science. A geometry problem named after him has stimulated recent publications, and his challenge to Ptolemy’s cosmology was a fitting precursor of the Copernican revolution. Alhazen also described the modern scientific method (usually credited to Francis Bacon). He even noted that a prism splits light into colored components that have different refrangibility---a creditable forerunner of Newton’s work more than 600 years later.

So what encouragement can we take from the example of Alhazen? When confronted by mid-life requirements to reinvent ourselves, we can remember Alhazen’s “retirement” from engineering. Even after a good career goes awry, even after ten years of putative insanity, it is possible to propagate 1000 years of heritage in one’s chosen field.

REFERENCES:

1. G. Stix, “Illuminating the Lilliputian: 10 Bioscapes Photo Contest winners revealed,” Scientific American, Dec. 2009.

2. Alhazen, Wikipedia.

3. Lorch, Richard (2008), "Ibn al-Haytham", Encyclopædia Britannica.

4. Roshdi Rashed, “A polymath in the 10th century”, Science 297, p. 773 (2002).