LAST MONTH I DESCRIBED VISUAL illusions that can be seen in an array of random dots or in the "snow" on a television screen when the set is tuned to a channel on which no broadcast is being made. The visual system somehow organizes these random displays into coherent flows and patterns. How it does so is poorly understood.

Another kind of organization of the random noise on a television screen that has been investigated in recent years is better understood. If you watch the visual noise while one eye is covered with a very dark but not opaque filter, the snow may break up into two layers that move in opposite directions and appear to lie at different depths. One layer seems to be recessed in the screen. The snow of this layer flows from the covered eye toward the uncovered one. The other layer protrudes from the screen and has snow that drifts in the opposite direction. The drift speed across your field of view is from five to 10 degrees per second. Some observers have difficulty perceiving the illusion; many others detect more than two layers.

Some workers have classified the effect in the general category of the Pulfrich illusion, which I discussed in this department for March, 1978. In the most familiar presentation of the illusion a pendulum is made to swing across the observer's field of view. One of the observer's eyes is covered with a dark filter and the other eye is left uncovered. Under these conditions the pendulum appears to swing not in a straight line but in an ellipse. According to most hypotheses about the Pulfrich illusion, the dark filter delays the perception of the visual signal at the retina of the covered eye. As a result the uncovered eye sees the moving object in its true position and the other eye sees the object in the position it occupied a moment earlier. In order to make sense of the scene the observer considers the object to be either closer to or farther from him than it is. If it is moving from the covered eye toward the uncovered one, the mental convergence of the apparent rays places it farther from the observer than it is, if the motion is in the opposite direction the object seems to be closer than it is.

The snow on the television screen is not a real moving object, but apparently the same type of illusion can result if the screen is viewed with one eye covered by a dark filter. The effect was originally discussed by Christopher W. Tyler of the Smith-Kittlewell Institute of Visual Sciences and John Ross of the University of Western Australia. Recent work by Joseph J. Mezrich and Albert Rose of the Exxon Corporate Research Laboratories in Linden, N.J., has further clarified the effect. Still, like most other visual illusions, the effect is not understood in all its details.

Suppose a noise element appears on the screen. According to a current hypothesis, if it is the left eye that is covered with the filter, the right eye perceives the spot immediately and the left eye perceives it a short time later. Now suppose that just then a second spot appears slightly to the right of the place originally occupied by the first one, which has now faded from the screen. The right eye immediately sees the second spot, whereas the left eye is just then seeing the first one. To make sense of the situation the observer's visual system in effect causes the apparent light rays from the two spots to converge, so that the screen seems to have a single recessed spot. The same thing would happen if a third spot appeared as the second spot faded from the screen. If the sequence of spots is appropriate, they will appear to move to the right as single recessed spot. The illusion turns up repeatedly and frequently across the screen. Even though the pattern of spots is in fact random, an appropriate sequence gives the illusion of a sheet-of moving spots recessed in the screen.

Similarly one sees spots as protruding from the screen and moving to the left if the sequence of spots is such that each one appears slightly to the left of the preceding one. The delay of one eye's response creates confusion unless the observer believes the light rays from the two spots come from a single spot a little off the screen. Hence the random noise of white spots on the screen is organized into sheets that seem to be at different depths and to move in opposite directions. If the observer moves the filter to the other eye, the directions of flow of the two sheets are reversed.

Mezrich and Rose discovered several curious features of the apparent motion of random noise. When they varied the density of the noise spots on the screen, the apparent speed of the spots across the screen was affected weakly, but below a certain threshold of spot density the effect disappeared. With densities somewhat above the threshold only a recessed sheet of moving spots was seen. Both sheets could be seen when the spots were at the density found on a television set tuned to an unused channel. (Sometimes the set will need a normal adjustment of its controls.) The fact that the apparent speed of the spots was independent of their density, provided the density was above the threshold, gave Mezrich and Rose one of the clues by which they explained the illusion.

The illusion also depended on the angle the screen subtended in the observer's field of view. As that angle was decreased from a large starting value the threshold for the spot density increased. Apparently as the display of noise was increasingly limited to the center of the fovea (the depression on the retina where the photoreceptors are packed most densely) greater densities of the noise elements were needed to provide the illusion of depth. When the angle was reduced from 30 minutes to 15, the spot-density threshold required for the illusion jumped to a much higher value When the angle was reduced further, the illusion disappeared. These unexpected results provided another major clue to the nature of the illusion.

How do the two clues fit together? The apparent speed of the spots is fixed by a characteristic angle (somehow determined by the observer) divided by a characteristic time that is important in the observation. The characteristic time is probably the time, 1/60 second, in which a fluctuation in intensity on the screen can occur. The characteristic angle is not as easy to guess. Two factors must be considered.

One factor stems from work that has been done with stereopsis in random-dot displays. In these experiments an observer usually views two displays simultaneously, one with each eye. Either display seen alone appears to have a purely random distribution of dots, but when the two displays are viewed simultaneously and fused, the observer can perceive depth and structure. Experimenters have found that if depth is to be perceived, the centers of the protruded area and the recessed area must be separated by at least eight minutes of angle. Therefore the mentally fused displays must occupy at least 15 minutes of angle in the observer's field of view to give enough separation.

Here, then, is a number related to the lower limit of the angle a television screen should occupy in an observer's field of view if the random-noise elements are to be organized into sheets at different depths. The screen must occupy at least 15 minutes of angle. If it occupies more than 30 minutes, the observer can organize the noise elements fairly easily. If it occupies between 15 and 30 minutes, the organization is more difficult. Then the threshold of spot density has to be higher to ensure that enough spots are present to give areas of recession and protrusion separated by at least eight minutes of angle.

Another matter to consider is that the spots appear to move smoothly across the screen when actually they do not move at all. Why does the observer perceive movement when the only thing happening on the screen is that the light is fluctuating in intensity? Previous research has been done on the illusion of motion perceived when stimuli are sequential and slightly separated. You have seen the illusion when lights in a row are blinked one after another to give the impression that the entire row is moving. It is commonly seen in displays outside theaters and motels.

If two sequential spots on a television screen are to be perceived as a smooth flow of one bright spot, the spots must be separated by no more than about 15 minutes of angle. The smooth flow, which is termed both a cascade and "phi motion," will be seen only if the flow in one direction is distinguishable from the flow in the other. Lacking the distinction, the observer will not be able to sort out the random fluctuations to perceive the cascade effect. The dark filter over one eye gives rise to the distinction between directions of cascade flow because it forces the two apparent flows onto sheets at different depths.

The speed of the flows is therefore determined by the angle limitations set by the cascade illusion and the depth illusion; the speed is also governed by the minimum time in which fluctuations arise. The angle limitations require that the sequential spots be separated by no more than 15 minutes of angle. The depth illusion requires that the adjacent areas of protrusion and recession be separated by at least eight minutes. Thus when a recessed spot and a protruding . one cross each other, their initial separation must be at least eight minutes of angle, and their separation 1/60 second later must be at least eight minutes but no more than 15. Dividing an angle of between eight and 15 minutes by a time of 1/60 second gives an apparent speed for the spots of between eight and 15 degrees per second, which is consistent with the measurements made by Mezrich and Rose.

Recent work by David S. Falk of the University of Maryland and Robert Williams of the University of Bristol suggests that the spots are further organized after they have been assigned to a particular sheet. The observer first sees the spots appearing randomly on the television screen. Monocular vision assigns speeds to the apparent cascading of the spots to the left or the right. Binocular vision, with the response of one eye delayed by a filter, assigns depth to the spots according to the Pulfrich illusion. At this point the speed and depth should show a range.

Falk and Williams suggested that the observer further organizes the spots by comparing the speeds of different groups.

Patches that have smaller apparent speeds and are relatively far apart give the impression the noise on the screen is moving faster than the patches are. Patches that have larger apparent speeds and are relatively close to each other will instead give the impression the noise is moving slower than the patches seem to be. Falk and Williams therefore argue that visual processing after the stereoscopic assignment of depth is responsible for the molding of the spectrum of speeds and depths into the illusion of spots on a single sheet moving at an approximately constant and uniform speed. There is one such sheet in each direction, left and right.

An alternative to the Pulfrich model is "random spatial disparity." According to this hypothesis, pairs of random spots are chosen and every pair of spots are fused into a single spot that is assigned depth. The greatest depth is assigned to pairs of spots that are separated by about 15 minutes. Only then is motion assigned. If the pattern fluctuates in 1/60 second, the apparent speed of the spots is 15 degrees per second. Further experimentation will determine whether this hypothesis accounts for the illusion better than the Pulfrich model or some other one.

I repeated some of the experiments of several investigators by holding two crossed polarizing filters in front of one eye while watching the snow on my black-and-white television set. I had several variables to control. The brightness and contrast on the screen could be modified and the transmission through the filters could be adjusted. With partial transmission and with the controls for brightness and contrast set close to their normal position the illusion of two sheets of coherent spots was readily apparent. It was fainter or absent if I turned the brightness all the way down The screen then appeared to have a flat display of glowing water bugs skimming around on the glass, sometimes briefly forming geometric patterns. The illusion also disappeared when the transmission through the filters was very low, that is, when the polarizing axes of the filters were almost perpendicular. With no filters in place, of course, the illusion was absent.

I noted one important difference between what I saw and the illusion described in the research papers. Usually the spots I saw swirled coherently. When the crossed filters were in front of my left eye, the swirling was clockwise, and when the filters were in front of my right eye, the swirling was in the opposite direction. I do not fully understand why I saw swirling at all. Its appearance was not critically dependent on the television controls. It still appeared when I replaced the polarizing filters with colored cellophane; hence it did not depend on the polarization of the light.

My guess is that the swirling resulted when I organized the coherent flow after making a stereoscopic fusion of the screens seen by my eyes. This level of further organization is along the lines suggested by Falk and Williams. The cascade effect seen monocularly leads to the illusion of moving spots. The mechanism of the Pulfrich illusion made me assign distance to the moving spots. I then further interpreted the spots by narrowing the range of their apparent speeds, but in addition I organized the moving patches into a swirl. For example, when the filters were in front of my left eye, the top of the screen was dominated by the patches moving to the right and the bottom by the patches moving to the left. The result was an apparent clockwise swirling. The illusion was so convincing that when I concentrated on only one sheet of spots, they also seemed to swirl.

I noted two additional effects. With the filters in place I closed my eyes alternately so that I could view the screen monocularly and without stereoscopic fusion. The uncovered eye saw a random array of spots, as would be expected and as is normally seen in television snow when the observer views it binocularly. The covered eye saw a dimmer screen and therefore saw not random spots but waves moving randomly as the random spots were organized into cascades. The same type of cascade can be seen if the screen is viewed without filters when the intensity is lowered.

The second effect I noted is similar to one I described last month. When one views a screen of snow monocularly, the center of the field of view appears to boil in a frenzy of activity while the surrounding area is relatively calm. Observing with filters, I noted the same hyperactive area on the screen when I looked at the screen monocularly with either the covered eye or the uncovered one. When I looked with both eyes and saw sheets of spots moving to the left or the right, the hyperactive area disappeared. When the spots broke into swirls, however, they seemed to circle in the hyperactive area. I checked this impression by rapidly switching from monocular viewing (closing either eye and locating the hyperactive area) to binocular viewing (with the swirling present).

Mezrich and Rose did another experiment that I repeated in a slightly different version. They were able to break up the random spots into spotted vertical strips and blank vertical strips. These strips were always uniform in width, but the experimenters were able to adjust their number. When the strips were relatively wide, so that the screen contained few of them, the illusion of coherently moving spots lying on sheets developed independently within each strip. With narrow strips and therefore more of them the coherent motion was seen across all of them.

The transition between the two effects was made when the frequency of strips was between one cycle and two cycles per degree in the field of view. (One cycle consists of a spotted strip and a blank one.) When the screen had one cycle per degree, the patches of recessed and protruding spots were separated enough so that the Pulfrich illusion of depth could be seen. (Remember that the separation must be at least eight minutes of angle.) At a frequency of one cycle per degree a strip of spots is 30 minutes wide and so can have enough separation of the patches. The observer then sees the illusion of depth and coherent motion within the strip.

When the frequency is two cycles per degree, a strip of spots is only 15 minutes wide. The patches are less likely to have the required separation, so that the illusion of depth and coherent motion is also less likely. On the other hand, the strips of spots are then close enough for the required separation to develop between adjacent strips. The illusion of depth and coherent motion then appears but is evident across all the strips rather than in individual ones.

I was able to achieve the same results by taping strips of paper vertically to my television screen. Although I worked with various widths, all the strips were the same width in any one experiment. Each time I made the uncovered parts of the screen the same width as the strips. In all the experiments I tried to position my head exactly as before so that the screen always occupied the same angle of view. The transition from coherent motion in individual strips to coherent motion across all the strips was at approximately the same frequency of strips found by Mezrich and Rose.

Recently a completely different set of observations with a television set was sent to me by Dwight M. Brown, Jr., of Shreveport, La. Brown noted that when he held a comb or a grid in front of his set, moving the object sometimes made things appearing on the screen seem to move. The illusion probably results from a moiré effect between a periodic spacing in the picture and the periodic spacing of the comb or grid.

Brown's grid was a Ronchi filter that he made from two pieces of thin aluminum plate and some bifilar (two-thread) No. 32 wire. He punched a 1 1/8-inch hole in each plate and wrapped the wire around the plate. Both sides of the hole then had wire wrapped across them. Brown fastened the wire on the side of the metal with epoxy and cut the wire with a file to separate the two metal pieces. Next he removed every second wire and put tape over the cut ends of the remaining wire.

Brown also experimented with stroboscopic effects associated with the television screen. You may have already noted that a spinning object in front of an active screen can create such an effect. Years ago I noted that a flat top spun in front of a television screen would appear to be stationary or even to move counter to its true direction of spin. The television picture is created by the electron beam inside the picture tube's sweeping from left to right, line by line until the bottom of the screen is reached. As a result the intensity of the screen fluctuates periodically.

Suppose a top with a pattern of lines on its upper surface is set spinning in front of the screen. If it is spinning at the same rate as the intensity fluctuations on the screen are changing, the upper surface of the top will be illuminated each time the pattern is in the same orientation. Unless the illumination is swamped by the room light, an observer will constantly see the pattern in the same orientation and the top will appear to be stationary. If the top's rate of rotation is slightly higher than the rate at which it is illuminated by the screen, the pattern will appear to turn slowly in the same direction as the top. If the top's rate of rotation is slightly lower than the illumination rate, the pattern will be illuminated each time in an orientation it achieves slightly before its orientation in the previous illumination. Consequently the pattern will seem to be turning in the direction opposite to the spin of the top.

Brown was able to achieve a stroboscopic effect with the line sweep of the screen in a rather simple way. He swung a string in a circle in front of the screen. When he looked through the rotating string and at the screen, dark lines flicked across the screen and the string seemed to jump from one position to another.

Bibliography

STEREOPSIS BY BINOCULAR DELAY. John Ross in Nature, Vol. 248, No. 5446, pages 363-364; March 22,1974.

STEREOPSIS IN DYNAMIC VISUAL NOISE. C. William Tyler in Nature, Vol. 250, No. 5469, pages 781-782; August 30, 1974.

COHERENT MOTION AND STEREOPSIS IN DYNAMIC VISUAL NOISE. Joseph J. Mezrich and Albert Rose in Vision Research, Vol. 17, No. 8, pages 903910; 1977.

STEREO MOVEMENT FOR INNER OCULAR DELAY IN DYNAMIC VISUAL NOISE: A RANDOM SPATIAL DISPARITY HYPOTHESIS. C. W. Tyler in American Journal of Optometry and Physiological Optics, Vol. 54, No. 6, pages 374-386; 1977.

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