What one would expect from this arrangement is a reproduction of the original scene in various shades of white, ink and red because of the red filter in front of one of the projectors. Surprisingly, what Land saw on the screen was reproduction of most of the colors of the original scene. Although the colors were dull, they were there, notwithstanding the fact that Land was projecting two black-and-white slides.

For more than 20 years Land and John J. McCann and their colleagues have endeavored to explain how the human visual system (the eye and the visual cortex) perceives the subtle differences of shading in what is viewed. Land described the original work in this magazine in 1959 [see "Experiments in Color Vision," by Edwin H. Land; SCIENTIFIC AMERICAN, May, 1959]. The two decades of experimentation since then have yielded a deeper understanding of the color process, as can be gathered from Land's more recent article [see "The Retinex Theory of Color Vision," by Edwin H. Land; SCIENTIFIC AMERICAN, December, 1977].

Robert Szabo, a student at Cleveland State University, not long ago repeated Land's procedure of making black-and-white transparencies through color filters and then projecting the transparencies superposed on a screen with a single color filter. Although the results are not as sharply colored as Land's earlier results apparently were, they are easy for an amateur photographer to obtain and they do show essentially what Land saw. On occasion Land has photographed still lifes of fruits and other such objects and at other times he has employed a complex array of colored papers that he calls a "Mondrian." Szabo chose to photograph a fairly new color chart, the ColorChecker, produced by Macbeth, a division of the Kollmorgen Corporation. The chart is apparently becoming a standard reference in all kinds of color photography because of the spectral design of the squares arranged on it. Each square is designed to closely mimic a natural color a photographer might encounter. For example, one square has a blue that closely matches a typical blue sky not only in the dominant blue but also throughout the visible spectrum.

An advantage in photographing a standard reference is that one can at any time compare the reference with the projected images. A still-life scene does not have such permanence, particularly if it includes fruit. Another advantage is that one's results might be more easily conveyed to another person if both of them employ the standard reference. The Mondrian array does not lend itself to that flexibility.

The ColorChecker may also present a disadvantage: the results of the experiment may be partly affected by the colors surrounding a particular square in the projected display. With the random array of the Mondrian's small sections, each of which has various colors and is surrounded in a variety of ways, the influence of surrounding colors can be avoided.

When Szabo photographed the color chart, he mounted his camera on a sturdy stand and triggered it remotely so that he could avoid jarring it. Two tungsten floodlights were aimed at an angle of about 45 degrees to the tabletop on which the chart was laid. Instead of high-quality color filters Szabo chose less expensive but still good filters that are available from the Edmund Scientific Company (6982 Edscorp Building, Barrington, N.J. 08007). The filters come in a booklet of 44. Each filter is five by eight inches, a convenient size for photographing and projecting. A booklet is also available from the company to show the spectral-transmission characteristics of the filters.

The best type of film is thought to be Polaroid's black-and-white transparency film because it responds to light fairly evenly across the visible spectrum. Szabo decided to try the relatively inexpensive Pan-X black-and-white film. With a Kodak direct-positive processing kit he was able to develop and mount his own slides. As he photographed the color chart he first set his camera at the correct exposure (f-stop and exposure speed) for the lighting conditions and then bracketed those values by photographing the chart at other nearby exposures. In order to be able to compare the slides later he carefully recorded the exposure data for each frame. Two carousel slide projectors served for projecting the slides on a conventional screen. The lights for both the projection and the photographing should both be good white lights, matched reasonably closely in their color composition.

The slide made through the filter that passes primarily the longer wavelengths is called the long record. The other slide, made with the filter that passes primarily the shorter wavelengths, is the short record. In following Land's experiments Szabo made a great many trials, employing a variety of filters and projection methods. Some of his results are given in the table in Figure 6.

In the simplest kind of trial there was a short and a long record; when a filter was included in the projection, it was the filter for the long record in front of the projector holding the long record. For example, in one trial the long record was made through the Edmund filter 821, which transmits primarily in the red. The short record was made through filter 856, which transmits mainly in the blue. What Szabo then had were two black-and-white slides that had been individually photographed through filters transmitting at opposite ends of the visible spectrum. The slides provided no readily apparent color information, and even if they had embodied a color code of some kind, it would presumably not have included green and yellow because neither of the filters transmitted the green and yellow wavelengths well.

When Szabo projected the slides, he put filter 821 in front of the projector holding the long record. On superposing the two projected images he found a reproduction of the ColorChecker that showed not only red but also some blue. yellow and green (but no purple).

The slides Szabo projected had been photographed at the proper exposures for the illumination provided by his floodlights. When he checked the slides he had made at somewhat longer and shorter exposures, he generally found that the projected image had about the same color characteristics, provided the slide had not been too strongly overexposed or underexposed. Land had said that the intensity level of the projectors was not critical. Whatever color coding the black-and-white slides showed did not depend critically on the brightness of the light. Szabo and I checked that result by mounting two crossed polarizing sheets in front of one of the projectors. By adjusting the angle between the polarizing axes of the sheets we could vary the brightness of the image cast on the screen by the projector. The brightness was not critical to the projection of the colors we saw.

In another trial Szabo used for the short record a slide made through filter 817 and for the long record the slide made earlier through filter 821. Filter 817 transmits more in the orange than 821. Again the long-record filter 821 was placed in front of the long-record projector. The projected superpositioning was quite faint and showed mainly pink. The transmission characteristics of the two filters were apparently too similar to give rise to a full spectrum in the projection. If the same filter had been used for photographing both slides, no colors would have been produced except the ones provided by a filter placed in front of one of the projectors.

The first article by Land in this magazine included a graph with which one can predict which colors will not appear in the projected images. For example. Szabo projected his slides made through filter 821 (which has a peak transmission at wavelengths between 650 and 700 nanometers) and filter 856 (which has a peak transmission at about 475 nanometers). The corresponding point on the graph lies in a region labeled "No purple." Szabo indeed saw no purple.

In one region on the graph; running along the diagonal, the long and short records are too nearly the same to produce colors in the projected image. Szabo's filters 817 and 821 apparently corresponded to a point near the diagonal. An unmarked region below the diagonal corresponds to a situation where the filter for the long record serves in the projection of the short record and vice versa. Both Szabo and I found it amusing to hold the long-record filter in front of the long-record projector and then move it in front of the short-record projector to get a color reversal.

Szabo also tried projecting with the short-record filter in front of the short-record projector and with no filter in front of the long-record projector. The colors were usually not as good. For example, he photographed through filter 858 (which transmits blue green) and filter 863 (which transmits more in the blue): the projected image consisted of browns, blues and blue greens.

In addition Szabo tried stacking the filters, that is, using two or more at the same time in order to narrow the band pass of wavelengths being transmitted. In one trial he stacked filters 861. 863 and 866 to eliminate any light from being transmitted in the range from 550 to 700 nanometers, which corresponds to yellow, red and some green. He made the long record with filter 821 and projected the slides with that filter in front of the long-record slide. Szabo found no yellow in the projection, but the other colors were present.

In one series Szabo photographed the long record through a stack (filters 874 and 877) to give a narrow band pass centered near 500 nanometers. The short record was photographed through filter 866, which transmits more in the blue with a transmission peak at 450 nanometers. When he put the long-record filters in front of the long-record slide, he got blues and greens. When instead he placed the short-record filter in front of the long record, he got blues and a dull yellow (a color reversal, since the "wrong" filter was in front of the long record). Out of curiosity he then put those filters aside and placed in front of he long-record slide still another filter, 807, which transmits in a broad band ranging from 525 nanometers through 775 nanometers. Although the projection filter was not the proper one, some dull color did emerge in the projection.

Land said in his first article that the colors will emerge even if the short record is made without a filter. Szabo combined such an unfiltered slide in an unfiltered projection with some of his long-record slides. When the long-record filter was placed in front of the long-record projector, dull colors appeared on the screen.

Why do any of the slide combinations show colors in their superposed projection? The complete explanation is still not known, but Land and his colleagues have narrowed the search considerably in the past two decades. In a complex scene color is not assigned to a particular area according to the color theory in which the three visual pigments in the human retina serve as three separate photometers. Since the absorption curves of the pigments peak at 440, 535 and 565 nanometers, the photometers are said to be sensitive to different areas of the visual spectrum and to span between them the entire visual spectrum. The theory holds that when the energy falling on the retina at, say, 565 nanometers is greater than that at the other peaks, the observer perceives the area viewed as being reddish. Conversely, a preponderance of energy at 440 nanometers yields a perception of blue.

Such was the textbook explanation for a long time, at least in simple discussions of color theory. Then Land demonstrated that color was independent of the energy flux into the eye at any particular wavelength. For example, in one experiment he caused the energy from two areas to be the same at the three absorption peaks. According to simple color theory, the two areas should then appear to be the same color. When the areas were viewed as part of the complex Mondrian array, however, an observer would discover, for example, that one area was green and the other was red. Hence the energy fluxes in themselves were not the source of the color information being processed by the observer.

In a complex scene color is assigned as a result of two main processes. First the visual system compares the energies at the three absorption peaks (the receptors for the short, middle and long wavelengths) and in effect assigns a triplet of numbers accordingly. Color has not yet been determined. Next the visual system compares that area with other areas in the scene, assigning to each area its own triplet of numbers. Finally the system can begin to assign color after comparing the triplets from a large number of areas. For example, if a triplet from a particular area is high in the long wavelengths, somewhat lower in the middle wavelengths and lower still in the short wavelengths, it will be assigned a reddish color.

In the first of the experiments I have described Szabo photographed the color chart through a red filter and then separately through a blue filter. The long record showed black-and-white shadings according to the reflectance of the various squares in the red wavelengths. Red areas appeared light in the slide, orange areas a bit less light and blue areas relatively dark. In the short record the situation was reversed: blue areas appeared light, orange areas darker and red areas darkest. These relative shadings code the color information that can be scanned and decoded by an observer.

When the long record was projected with the same red filter, the projected scene was the same (to the limits of the accuracy of the film and the whiteness of the projection lamp) as the one transmitted through the filter in the photography. Blue areas were projected dark, orange areas less dark and red areas light. The color available in the light areas was, of course, only pink or red. When that projector was turned off and the short record was then projected with no filter in front of it, the projected image showed a range of dark and light regions reflecting what had been transmitted through the blue filter. This time the projection had only shades of dark gray, light gray and white light, but they recorded the degree of blue light coming from each of the squares on the color chart.

When both projectors are turned on and the images are superposed, why do you see colors other than just pink and red? First consider a square you will see as red. In the superposed images the square is light in the long wavelengths, not as light in the middle wavelength and relatively dark in the short wave lengths. Why? Because the long record is providing relatively bright light in the long wavelengths and the short record is providing relatively little light in the short wavelengths. In a sense the visual system computes the ratios of lightness in each of the wavelength regions and assigns to the square a triplet of numbers according to the ratios.

Now consider a square that is blue in the projection. The long record is providing little of the long-wavelength light to the square, whereas the short record is providing relatively bright light Again the visual system compares the lightness at the short, middle and long wavelengths and assigns a triplet of numbers. The color blue is not yet assigned, because the observer's visual system has not yet understood what the particular triplet of numbers means as to color.

The process is repeated for every square seen in the projection, apparently automatically and without necessarily sweeping the eyes over the images. Every square is assigned a certain triplet of numbers according to how light it is in the short, middle and long wavelengths. Then the triplets are compared. A square with a triplet indicating that it is light in equal amounts in all three wavelength regions is assigned white. Another square with a triplet indicating less light in the middle wavelengths and still less in the short wavelengths is assigned red. A third square, which in comparison with the white square has less light in the middle wavelengths and still less in the long wavelengths, is assigned blue. A square that is light in the middle wavelengths, a bit dimmer in the long wavelengths and still darker in the short wavelengths may be assigned yellow. And so it goes until as much color as it is possible to interpret from the projection has been assigned.

Suppose the chart had no reference white square. Would the process of assigning colors be destroyed? No. The triplets would still be assigned to each square and then compared. Since red light is being projected from the long record, it can act as a reference point. For example, a triplet that is relatively deficient in the long wavelengths, less deficient in the middle wavelengths and stronger in the short wavelengths could be assigned blue in comparison with the red square. The experiment works better (in the sense that the colors are more easily distinguished) if the filters employed in the photography have distinctly separate band passes. Then the light and dark shadings of the slides are more distinguishable.

The explanation of color assignment have presented here is only a brief summary of a much richer model developed by Land and McCann and their colleagues. You should read their articles to get a better explanation. Since Szabo's experiments are inexpensive and fairly easy to do, you might want to try some of them yourself.

I have received quite a bit of mail about the stereoscope and stereoscopic pictures, which I described in my December column. Apparently many people are making their own stereoscope photographs and slides. One organization, the National Stereoscopic Association, offers a bimonthly journal, Stereo World, to its members, some 800 strong. (If you are interested, write to John Weller, P.O. Box 14801, Columbus, Ohio 43214.) The members buy, sell and make samples of stereoscopic photography.

Some readers suggested that I mention two points about making your own stereoscope photographs. First, a stereoscopic pair in which the second exposure is made by rotating the camera has less depth than one in which the second exposure is made by displacing the camera to the side. Second, one should not think that putting a pair of identical photographs in the stereoscope can achieve the same effect as putting in a true stereoscopic pair. With both kinds of pair the eye can utilize depth clues relating to the size of objects and the converging geometry of things, but with identical photographs depth clues from the convergence of the eyes are of course not available.

An apparently controversial subject is whether displacing the camera more than the interocular distance between photographs gives rise to exaggerated depth in the stereoscopic pair. One reader, Philip R. Pennington of Portland, Ore., said he had never seen such exaggeration even in stereoscopic pairs made several miles apart. Other readers said they regularly make use of the depth distortion offered by wide base lines, particularly in aerial photography designed to enhance the contour variations of the ground.

Some of the most beautiful samples of stereoscopic pictures that I have received came from James Raymond of Fairbanks, Alaska, who photographed Mount McKinley with a base line of about 2,000 feet while flying in an airplane. An amazing stereoscopic pair came from Ralph C. Eagle of the University of Pennsylvania School of Medicine. They were micrographs made with the scanning electron microscope, showing cancer cells in a specimen of the human iris. The specimen had been rotated by seven degrees between exposures, and depth is readily apparent.

In discussing the colors in soap films in my column for last September I briefly described the problem of laying a thin film on a surface that has a higher refractive index than the film. A good way to accomplish the feat has been sent to me by A. A. Fote of the Aerospace Corporation in Los Angeles. In order to investigate the behavior of lubricating oils under space conditions he prepares thin oil films on polished metal surfaces. When the films are sufficiently thin, they display interference colors similar to the ones seen on many soap films.

Fote mixes a solution of Apiezon Coil with heptane so that the oil makes up from 20 to 40 percent of the total volume. The solution is poured into a container that has a controlled leak at the bottom, and the flat metal piece to be coated is suspended vertically inside the container. As the solution drains from the bottom a thin layer remains on the metal. Since the heptane evaporates almost immediately, the film is oil only. The thickness of the oil film can be controlled somewhat by changing the concentration of the oil in the solution and the rate at which the solution leaks out. Thinner film layers result from lower concentrations and slower drainage.

At Fote's suggestion I replaced the Apiezon C with ordinary mineral oil, which is also soluble in heptane. For the bath I set up a funnel to drain into a beaker through a hose that was partly closed by a clamp of the screw type. I poured the solution into the funnel and controlled the rate of drainage by adjusting the clamp. Then I suspended a small, flat piece of metal in the solution. As the solution drained, the piece of metal was coated with a layer of mineral oil. To form a film with a uniform thickness you must be sure the solution drains at a constant rate. To that end I worked with a funnel that had vertical sides at the top, and I kept my piece of metal in the upper section.

The relative indexes of refraction of the film and the metal govern the colors one sees in thin oil films and whether with ultrathin films one sees a white film or a dark one. Some metals have a high index of refraction (steel about 2.5); others have lower values (copper about .6 and silver about .2). When an oil is applied as a layer on a surface that has an index of refraction higher than that of the oil, ultrathin layers are transparent and show no colors. If white light is shined on the layer, white light is reflected to the observer. On the other hand, when the oil has the larger index of refraction, an ultrathin film is dark.

Somewhat thicker films give interference bands and a variety of colors. You have probably noticed such colors on metal cookware. When the metal surfaces of pots and pans oxidize, the thin oxide layer acts as the thin film and contributes colors created by the interference of light.

The first metals I tried in my oil bath gave no interference colors, although I could see the oil films clearly. Fote explained that my metals were probably not sufficiently polished to make interference possible. At least three factors are involved. First, thinner layers (thin enough for perceptible interference) may be more likely on a highly smooth metal surface. Second, a rough metal surface will destroy the coherence of the light waves that is necessary for interference. Third, with a rough surface the thickness of the film layer will vary so rapidly from point to point that the interference colors will wash out into a perceived whiteness.

To understand the second factor one must follow the path of a light ray in the film. A ray incident on a film splits into two rays: one that is reflected immediately and another that passes through the film and is reflected off the back of it. If the back surface, lying next to the metal, is rough, the ray will not be reflected outward in the same direction as the ray reflected from the front surface. The waves in the rays therefore cannot interfere. If a metal surface is to show interference colors in an oil film covering it, the surface should be polished so brightly that you can see your reflection in it. I obtained clear, beautiful colors with a stainless-steel kitchen knife. The colors included pink, blue and green, with some areas of yellow and brown. The thinner the film was, the wider these bands were, as is the case with soap films.

It seems to be more difficult to predict the colors with these oil films than it is with soap films because the intensity of the reflection of light from metal surfaces varies considerably with wavelength and with angle of reflection. For a highly polished metal the reflection from the back surface of the film is so much stronger than the reflection from the front surface that the interference colors are lost in the white glare from the back reflection. The glare appears to be particularly strong when the incident light is approximately perpendicular to the film.

When I first dipped a piece of metal in the oil bath (before I began the drainage), a film climbed about .5 centimeter up the metal surface. After a while the film formed "tears" that ran back down the metal. On my kitchen knife I could see interference colors in the film except where the thicker drops descended. The climbing film and the formation of drops have been noted in other circumstances since about 1850, when the effect was observed in glasses of wine. Usually the climbing is attributed to the fact that fluid is being pulled upward by unequal surface tensions in the vertical film, an effect named after Carlo Marangoni.

Readers interested in the structures and colors of soap films might want to look into an excellent book, The Science of Soap Films and Soap Bubbles, by Cyril Isenberg, recently published by Tieto Ltd., 5 Elton Road, Clevedon, Avon, K England.

Bibliography

INTERFERENCE COLOR. Hiroshi Kubota in Progress in Optics: Vol. 1, edited by E. Wolf. North-Holland Publishing Company, 1961.

LIGHTNESS AND RETINEX THEORY. Edwin H. Land and John J. McCann in Journal of the Optical Society of America, Vol. 61, No. 1, pages 1-11; January, 1971.

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