IF YOU PRESS YOUR FOREFINGER GENTLY against your closed eyelid for a minute or less, you will probably start to see phosphenes: shapes and colors that march and swirl across your darkened field of view. Phosphenes can also appear in flickering light, in darkness and when you accidentally bump your head. You may also be able to see them simply by tightly closing your eyes. I first noticed them as a child when I cried with my face buried in a pillow. Phosphenes were among the many subjects investigated a century ago by Hermann von Helmholtz. I shall review here a few of the experiments he described in his Treatise on Physiological Optics. I shall also discuss some recent experiments reported by Christopher W. Tyler of the Smith-Kettlewell Institute of Visual Sciences in San Francisco. In reviewing these studies I have been stimulated to experiment with phosphenes myself, and I shall report some of my observations. Your observations will be of interest too, because not all people see the same types of phosphenes. Let me strongly warn you, however, against hurting yourself. If pressing your eyes hurts, stop. Even if it does not hurt, do not press for more than a minute. Do not stare into bright lights. If your eyes hurt when you look toward a bright light with your eyelids closed, abandon the experiment. Nothing you can learn about phosphenes is worth the slightest harm to your eyes. Helmholtz described some of the observations of phosphenes made by earlier workers, notably Johannes Purkinje in 1819. Helmholtz also made observations of his own. He pointed out that when a steady pressure is applied to a spot on the eye, a continuous phosphene appears at the opposite side of the visual field. For example, pressing a closed eye near the temple gives rise to a distinct phosphene toward the nose. The phosphene has a bright center surrounded by a dark ring and a bright outer ring. When Helmholtz looked to the left with his right eye closed, the phosphene became less bright. He could not quite make the phosphene overlap his foveal vision. (The fovea is the tiny area of the retina where the packing of cones is densest. When you look directly at something, its image falls on the fovea.) In one experiment Helmholtz stared at his nose with his right eye and held a sheet of white paper in front of his face. The paper served as a diffuse and evenly illuminated surface. He pressed against his right eyelid near the temple, being careful to have his finger about halfway up the eyeball. The phosphene, which appeared on the nose side of his field of view, consisted of a dark spot surrounded by a bright curved band. To the right of the band were thin dark stripes. At the point of view corresponding to the fovea was a dull gray area. Farther to the right, at the region corresponding to the point where the optic nerve enters the retina, was another indistinct dark spot. When Helmholtz did the experiment again with a dark background instead of the illuminated paper, the disposition of the phosphene images was similar but the bright and dark regions were interchanged. The sensation of a phosphene in the foveal vision was absent. In repeating the experiments I illuminated my field of view with the diffuse screen of a slide sorter. I closed my left eye and kept my right one open. It was easy to create a phosphene on the nose side of my visual field with a light touch against my right eyelid near the temple. The phosphene appeared to be purple or dark blue. I could not readily identify as much structure as Helmholtz described. At the foveal area in my field of view was a small gray spot surrounded by a brighter region. Off to the right was a gray area shaped somewhat like an arrowhead pointing toward the foveal region. All these features were easier for me to see if I periodically varied the pressure on my eyelid. As I did so the nasal phosphene and the bright spot at the foveal region oscillated horizontally and out of phase with each other. With a prolonged and heavier pressure on a closed eye the phosphene display can be far more complex. Colors and forms float kaleidoscopically across the field of view; the images are bright, colored and constantly changing. Purkinje wrote that the "background generally consisted of fine quadrangles in regular array, on which there were either stars with eight rays, or dark or bright rhombs with vertical and horizontal diagonals. and the patterns were surrounded by alternately bright and dark bands." Helmholtz saw less regularity. He likened the displays to fine leaves or mossy surfaces. Sometimes complex mazes appeared. Often bright blue or red sparks flashed across the display. Even when he released the pressure, still keeping his eye closed, the display continued for a while. If he opened his eye after releasing the pressure, he was first unable to see anything. Then the brighter objects in his visual field became brilliant. Superposed on these objects he still saw parts of the phosphene display, but now the bright and dark regions were reversed. Eventually his vision returned to normal. Several experimenters had reported seeing an image of the circulatory network in the retina when they pressed a finger against a closed eye. Helmholtz, apparently unable to repeat the observation, was skeptical that the retinal network was involved. Nevertheless, some people do see it. W. A. Nagel, who wrote footnotes to Helmholtz' Treatise. noted that he could easily see "a dense network of bright lines on a dark ground" when he kept an eye shut for at least 20 minutes. Pressure was not necessary. Once the lines appeared he could distinguish a flickering in them, presumably because of the pulsation of blood through the retinal capillaries. When I press fairly hard on my eye, my vision blurs and the foveal region in the visual field becomes alive with pulsating pathways. I am probably disturbing the circulation of blood in the fovea. As a result I am seeing a pulsating image that reveals the circulatory network there. The retinal network lies in front of the photoreceptors and thus shadows part of the retina, but the shadows are normally ignored by the brain because they are constant. You consciously perceive only scenes that change, either because the objects move or because your eyes scan the scene. If the circulation through the network is disturbed, an indistinct outline of the network can be seen. Phosphenes can also be seen if the eyes are turned quickly to one side. If the background is dark, the images appear as bright spots or rings around the position of the blind spot in the field of view. The appearance of the phosphenes is not *e same for both eyes. The eye that turns toward the nose "sees" a duller phosphene than the eye that is turned toward the temple. If the background is bright, the spots are dark. This type of phosphene has been attributed to stretching or compression of-the optic nerve. When the eyes are turned quickly to the side, the nerve bundle in one eye is compressed and the bundle in the other eye is stretched. The resulting phosphene is momentary. Some observers see its shapes as rings or partial rings centered on the area of the blind spot. Purkinje described concentric bright bands toward the center of the visual field. With one eye turned strongly toward the nose, the display was continuous. For Helmholtz the display was brief even when an eye was turned strongly. Phosphenes can also appear when the eye suddenly changes its accommodation, or distance of focus, but they are not as apparent as the others I have described. Helmholtz suggested focusing on an object just outside a window and switching after a few minutes to a distant object. As the eye accommodates to the distant view a small bright border can be seen around the field of view. The sudden relaxation of the muscles of the eye apparently causes pressure variations that generate the phosphenes. Purkinje could also create the luminous border when he suddenly released pressure on his eye, but Helmholtz was unable to repeat the observation. Of all the phosphene images described by Helmholtz the strangest are the ones that appear to a person who sits for a while in total darkness. These displays, which have been called the "prisoner's cinema," require no pressure on the eyes. Phosphenes can appear whenever there is an absence of variation in the visual field. The situation can be total darkness or continuous brightness (such as a snowstorm). Helmholtz saw the darkness images as interfering waves that blended together. The waves moved slowly compared with some of the other displays. Helmholtz was able to demonstrate that the wave motion was synchronous with his breathing. The general background of the waves was never totally dark. He saw small luminous areas that appeared and disappeared with each breath. I see this type of phosphene when I spend the night in a cave during a spelunking trip. After I put out my lights to prepare for sleep the darkness is absolute. In 10 minutes or so, however, I see vague splotches of light. With no reference lights to guide me the phosphenes seem to be real lights just beyond my reach. Tyler recently published new observations on phosphenes. His paper is listed in the bibliography for this issue. When someone strongly converges his eyes, as in staring at the tip of his nose with his eyes crossed, two types of phosphenes can appear. If the convergence is rapid, you can see two large rings that momentarily surround the area of the blind spot. They are the rings seen by Purkinje during a rapid rotation of both his eyes. Since the rings appear when both eyes are turned toward the nose, they must be caused by a stretching of the Optic nerve. Another type of phosphene materializes if the convergence is done in front of a uniform light source and is strong and continuous. In the center of the field of view is a red dumbbell. Some observers report red disks rather than an entire dumbbell. Stresses from the convergence are responsible for the phosphene, but apparently external light is also required. The light could reach the retina either by passing through the pupil or by passing around the eyeball through the sclera, the white exterior layer of the eyeball. A simple check reveals the path of the light. If the fingers are placed on the nose side of each closed eyelid, the phosphene disappears, whereas if the fingers are placed on the temple side, the phosphene is unaltered. The light participating in the phosphene image therefore comes into the visual system through the pupil. The phosphene appears even if one eye is covered. Many different phosphenes can be created by pressing the palms against the closed eyes for about a minute. Tyler has classified the displays according to where the image is likely to be created in the visual pathway. With a mild pressure the display consists of colored swirls, which are probably caused by the decrease of oxygen in the retina as the pressure inhibits the flow of blood. The effect may be produced at the depth of the photoreceptors (the rods and the cones) or somewhere closer to the surface of the retina, as at the ganglion cells. Sometimes the fovea is surrounded by a blue ring or halo. Neither the structure nor the color is understood. With a bit more pressure that is then released you might see the retinal circulation pattern. The variation of pressure on the retina causes a variation in the flow of blood through the network. If as a result the nerve activity near the vessels is different from the nerve activity farther away, the outline of the vessel system might materialize. With still deeper pressure and its release you might see the circulatory network in the choroid coating between the retina and the sclera. This system, which appears as red on a black background, may show up best just as the pressure is released and the blood again flows through the network. This is one of the few ways the choroidal circulatory system can be observed directly. Two types of stationary point arrays can also be seen with deep pressure. Sometimes both are seen together. In one of them yellow points are randomly strewn across a dark background. In the other bright violet points appear on a darker background. The yellow points are of uniform size but the violet points become larger toward the periphery of the field of view. The arrays can be seen with either eye and do not require deep pressure on both eyes. Tyler argues that since the blood circulation has already been stopped by the pressure, these point arrays are probably produced somewhere farther along in the visual pathway than the photoreceptor level. When both eyes receive such deep pressure, the observer can see several complex displays. One possibility is a regular cellular grid resembling either a chessboard or an array of triangles. Another possibility is a similar cellular structure on a finer scale. Sometimes both structures can be observed, one superposed on the other. A few blank areas that Tyler likens to blank television screens are sometimes included. Since these complex displays require deep pressure and binocular viewing, they are probably produced relatively far up in the visual pathway. Tyler suggests they originate in the visual cortex, but where or how they are created is not understood. Some elements of the visual system seem to be designed to recognize lines, but as yet no elements are known that recognize squares, hexagons or any of the other geometric patterns seen in the phosphenes. If the pressure on the eyes did set off line-recognizing elements at random, one would expect to see a random array of lines rather than geometric patterns in phosphenes. Somewhere in the visual process, below the conscious level, there may be elements that respond to certain periodicities and shapes. In a rough analysis of the geometric phosphenes one might guess that such elements are being excited by the deep pressure on both eyes. Part of the fascination of a repetitively flashing stroboscopic lamp at a discotheque may lie in the phosphenes that result, even when the eyelids are closed. A light flashing at rates of between t0 and 30 hertz can induce vivid geometric arrays filled with strong colors. (My use of "phosphene" here may be inappropriate. Although the patterns one can see in some flickering lights are similar to the phosphene images arising from deep pressure on the eyes, I am not certain the effects are the same. Nevertheless, I shall make the assumption here that they are.) In recent studies with flickering lights observers viewed a screen lighted from the rear. A rotating wheel intersected and chopped the light falling on the screen, thereby producing a flickering but featureless illuminated surface. At a rate of about 30 hertz at least two types of structure could be perceived. One type consisted of squares laid out somewhat like a chessboard, the other of hexagons. Both lasted for five seconds or so before fading into another pattern or into an uninterpretable field. With the hexagon display the observers could distinguish a fine-scale array that was surrounded by an array of larger hexagons. These are only a few of the possible patterns one can see in a flickering light. At lower frequencies, near two hertz, the flickering may at most produce swirling gray-and-white regions. At higher frequencies (60 hertz or more) the flickering becomes less apparent as the individual pulses of light fuse to give a perception of continuous illumination on the screen. For most observers the colored geometric patterns become evident when the frequency is between 10 and 30 hertz. The patterns are believed to appear only if both eyes receive the flickering light. The need for binocular vision implies that the patterns are created farther along in the visual pathway than the eye, otherwise one eye would suffice. Perhaps the patterns are generated in the visual cortex, where complex shapes are perceived. The frequency of the flickering presumably matches some frequency or periodicity in the visual process there, and the brain is fooled into seeing the patterns. I first tried to see these phosphenes by the simple expedient of holding my hands in front of my face with the palms toward me and the little fingers touching. Behind my hands was an incandescent lamp. With my eyes closed I continuously separated and rejoined my hands to create a flickering effect. I found that I got more light if I lifted my eyebrows. I was careful not to look directly at the lamp with my eyes open because the result would be a strong afterimage when I closed my eyes for the demonstration. When I interrupted the light from the lamp at a frequency of about eight hertz, my field of view broke up into strikingly clear red and black squares, resembling a chessboard. The squares were aligned along diagonals that crossed the center of my field of view. The creation of this pattern called for a fairly strong light; the lamp was a 100-watt one, and I was about 10 centimeters from it. I could not see the squares when I moved to a greater distance. What I saw instead were globular blue phosphenes in the lower half of my field of view. The change may be due to the decreased illumination. The intensity must exceed a certain threshold in order to produce geometric patterns. Next I worked with a stroboscope. Its output was relatively bright and the frequency of the flash could be varied from one hertz up. I was careful not to look at the flashing light with my eyes open, not only to avoid afterimages but also to avoid damaging my eyes. (Some people are adversely affected by flashing bright lights. Do not do these experiments if you are thus affected.) In my first trials I covered my left eye and faced the strobe with my right eye closed. As I increased the flash frequency from a starting level of one hertz I began to see a vortex that seemed to be in the foveal area of my view. At a frequency of a few hertz vague radial lines stretched from the vortex, but otherwise the field was featureless. At about six hertz I saw what resembled a venetian blind. The foveal vortex was still there, but it was now brighter. With another small increase in frequency thin waves appeared, each one centered on the foveal region. The background was spotted. At a frequency of about 11 hertz chaotic bright places spotted the field. Dull colors appeared at the foveal region, which began to show vigorous pulsations. At 12 hertz the entire field pulsated with bright yellows and other colors that were duller. The field to the right of the foveal region formed an arrowhead that pointed to the fovea. Now I covered my right eye so that neither eye received light. The field of view broke up into a cellular mosaic that reminded me of a tortoiseshell. When the afterimage faded, I again uncovered my closed right eye, and the field again developed vivid colors and rapid pulsations. Thin capillary waves formed and disappeared. At the same frequency I covered my right eye and exposed my left eye, which I kept closed. The field consisted of petals in brilliant reds and yellows. Then I suddenly exposed both closed eyes. The center was again bright and the petals were still brilliant, but soon the display formed into checkerboards of red, yellow and blue. The sight was unnerving. It actually made me dizzy; I had to hold on to the chair to steady myself. The displays formed, dissolved, expanded and shrank all in full color. When I tilted my head forward, the structures seemed to broaden. With my head tilted upward a white horizon appeared across the bottom of my field of view. Presumably it was caused by a leakage of light between my closed eyelids. Above the white band were the colored designs. At higher frequencies the field became progressively less interesting until at about 40 hertz I saw only a bright, featureless background. At one point I faced away from the stroboscope, waited for a few minutes and then opened my eyes so that I could see my desk. White sheets of paper and Styrofoam cups were illuminated by the flashing light. On these objects I saw swirling designs similar to the ones I had seen while I was facing the stroboscope, but they now lacked color. When I faced the flashing light, any sensations of ordered arrays of polygons were certainly more noticeable with both of 15 INPUT "MO,DA:"; MO,DA: IF MO < 3 THEN MO = MO + 12

20 DA = DA + INT (30.6 * MO - 32.4): Z = 279.5 + DA * 360/365.25 : M = 57 + .9856 * DA

25 LO = Z + 1.915 * SIN (M * RPD) + .02 * SIN (2 * M * RPD)

30 X = SIN (LO * RPD) * .398 : D = ATN( X/ SQR(1 -X*X) ) : DECL = D /

PD : PRINT "DECL ="; DECL

35 Y = COS (LO * RPD) / COS (D) : RA = ATN (SQR (1- Y*Y) /Y) : IF RA #60; 0 THEN RA = RA + 3.14159

40 IF X < 0 THEN RA = -RA

45 ET = RA - Z * RPD : ET = ET * 4 /RPD

50 IF ET < -720 THEN ET = ET + 1440: GO TO 50

55 ET = ET/4

85 T = -5

90 FOR K = -10 TO 10 : C = (K * 7.5 - DL - ET) * RPD: B = TAN (C)

Charles Kluepfel's modifications of the computer program for the analemmic sundial 10 CLS : RPD = .01745 : L = 35.0 * RPD : DL = 1.8 : H = 1.0

15 INPUT "MO,DA:"; MO,DA: IF MO < 3 THEN MO = MO + 12

20 DA = DA + INT (30.6 * MO - 32.4): Z = 279.5 + DA * 360/365.25 : M = 57 + .9856 * DA

25 LO = Z + 1.915 * SIN (M * RPD) + .02 * SIN (2 * M * RPD)

30 X = SIN (LO * RPD) * .398 : D = ATN(X/ SQR(1 - X*X) ) : DECL = D / RPD : PRINT "DECL ="; DECL

35 Y = COS (LO * RPD) / COS (D) : RA = ATN (SQR (1-Y*Y) / Y) : IF RA #60; 0 THEN RA = RA + 3.14159

40 IF X < 0 THEN RA = -RA

45 ET = RA - Z * RPD : ET = ET * 4/RPD

50 IF ET < -720 THEN ET = ET + 1440: GO TO 50

55 ET = ET/4

60 PRINT "DL="; DL, "EQ TIME ="; ET, "TOTAL ANGLE ="; DL + ET

70 PRINT " ": PRINT "TIME(HRS)", "DIST(METERS)"

80 X = TAN (L) : F = 1 / COS (L) : G = X + 1 / X : W = 1 / SIN (L) 85 T = -5

90 FOR K = -10 TO 10 : C = (K * 7.5 - DL - ET) * RPD : B = TAN (C)

100 E = SQR ( (B * F) ^ 2 + G ^ 2) / G : J = 1/ (E * X)

110 A = ATN ( (G * E - J) / SQR (W ^ 2 - J ^ 2) )

120 Z = TAN (A - D) / TAN (A) : DIST = H * (Z - 1) * (G * E - J)

130 PRINT T, DIST : T = T + .5 : NEXT K : END

The entire program with Kluepfel's revisions my closed eyes illuminated. Occasionally, however, the petals or tortoiseshell features could be seen when only one eye was exposed or when one eye was exposed and then suddenly covered. The tortoiseshell pattern, sometimes with a swirling visible in each of its cells, does not seem to require flickering light, just bright light. I can occasionally see the pattern when I face (with closed eyes) a bright incandescent lamp. I have also seen it in my dentist's bright working light. (I will do anything to take my mind off what she is doing.) Much more could be done to classify phosphenes and track down their causes. You can watch for the displays when you are under physical strain. You might also want to try some of the experiments with pressure and flashing lights. If you do so, remember that if any of the maneuvers start to hurt your eyes, you should stop them immediately. Many people have written to me about two errors I made last December in my description of the analemmic sundial designed by C. K. Sloan. In explaining how to lay out the degree marks on the equinoctial line I incorrectly implied that the separation between the marks was a constant along the line. The illustrations were correct but I erred in the text. To find where the marks should be made, calculate the distance of a mark from the noon radial line. That distance is equal to the height of the gnomon multiplied by the secant of the dial's latitude and the tangent of the mark's hour angle. Suppose you want to place the mark for one degree past 1:00. Each passage of an hour represents 15 degrees. The mark is therefore 16 degrees past the noon radial line. Change this number to radians and then plug it into the tangent in the foregoing formula. You now have the distance between the noon radial line and the mark to be made on the equinoctial line. I also erred in explaining how the corrections for the longitude and for the equation of time are taken into account. I stated that once you have calculated the uncorrected position of the shadow point all you have to do is rotate the position either left or right around the ecliptic point to get the number of degrees for the correction. What I forgot is that you must also adjust the length of the shadow. For example, if you calculate the position of the shadow point for 3:00 and then rotate it a few degrees to the left for the correction, you also must make the shadow somewhat shorter. One easy way to make the correction is to calculate the uncorrected positions of the shadow point for each hour of the day. Lightly draw a curved line through the positions. Now make your corrections. Take the shadow position for, say, 3:00 and correct it for the longitude and the equation of time by sliding it the proper number of degrees along the lightly drawn line. If you are supposed to move it two degrees to the left, go to the left by two of the degree marks you have made on the equinoctial line and mark the shadow point on the lightly drawn curved line. Charles Kluepfel of New York sent plans by which the correction can be done with the computer program I presented in December. He also sent additional program lines by which the computer automatically calculates the equation of time and the declination for any day of the year. These lines, which are shown in the table above, are intended for Level II Basic for a Radio Shack TRS-80, but probably only slight changes are needed for other versions of the Basic language. Add these lines to my program. (Some of them replace lines in my program.) Also remove from the end of line 70 of my original program ,A$. When you run the program now, it will ask you for the date in which you are interested. For June 1 you would enter 6,1. The program then computes the equation of time, the declination and the distance (from the equinoctial line) for the shadow point after it has been corrected for the longitude and the equation of time. All you have left to do is make the angular correction for the longitude and the equation of time. Bibliography SUBJECTIVE PATTERNS ELICITED BY LIGHT FLICKER. Rockefeller S. L. Young, Robert E. Cole, Michael Gamble and Martin D. Rayner in Vision Research, Vol.15, No. 11, pages 1291-1293; November, 1975. SUBJECTIVE PATTERNS IN A FLICKERING FIELD: BINOCULAR VS. MONOCULAR OBSERVATION. Arnulf Remole in Journal of the Optical Society of America, Vol. 63, No. 6, pages 745-748; June, 1978. SOME NEW ENTOPTIC PHENOMENA. Christopher W. Tyler in Vision Research, Vol. 18, No. 12, pages 1633-1639; December, 1978. Suppliers and Organizations The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds. The Society for Amateur Scientists

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