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EXPLAINING AN ILLUSION

?Seeing is believing? is an old proverb. After all what can you believe in, if you can?t believe even what you yourself have seen? Nevertheless, we often encounter situations when we really can?t believe what our eyes see. For example, a large number of people often seek an explanation regarding perception of rotating wheels and fans rotation. Some are curious to know why do the blades of a table-fan kept in a room lit with a tube-light, some times appear to be rotating in counter-clockwise direction while others have observed that sometimes all of a sudden the blades appear rotating very slowly. Still many others have sought an explanation to the observation that often in a movie or a television program the wheels of a vehicle; cart, Tonga or a car are seen moving in a direction opposite to the logically expected direction, that is clockwise for a vehicle moving from left to right.

Obviously, these are not very recent phenomena. People have been perplexed with such observation ever since the invention of cinema/TV or tube-light. However, most often we tend to ignore such innocuous observations. But if you have developed scientific temper you would like to know how these observations can be explained. Scientists usually refer to such phenomena as the Wagon Wheel Effect or Stroboscopic effect. Let me try to understand the explanation usually accepted for these illusions.

If you examine a film strip closely or view a video tape in slow motion, you can easily find out that the perceived motion on a cinema/TV screen is a result of projecting only a small segment of infinite array of images an event is actually made up of. Thus in cinema (or TV) the perception of motion is produced by projection of a sequence of about 24 images in a second which differ from each other only in the position of a particular object. We perceive this projection as a moving object because of a queer characteristic of our visual sensory system. If we perceive an image momentarily (say for a fraction of a second) and then the image is removed from our view, as well as no other image is presented in front of our eyes, then we continue to perceive the image for a fraction of second more. This phenomenon is known as persistence of vision and is responsible for our perceiving a projection of 24 closely related images in quick succession (within a second) as a continuous event without getting aware of the breaks in between.

Let us now analyze the above phenomena. Suppose we record with a movie/TV camera the rotary motion of a circular disc marked with only one radial line. What will be the result, if the disc rotates at a speed of 24 revolutions per second? Since the camera records an image after every 1/24^th of a second, all the images it will record will have the radial mark in the same position and when we see the projection of this recording, the wheel will appear stationary. Now, consider another situation: the wheel completes one revolution in say 1/25^th of a second. What will a movie/TV recording yield in this case? Now, every time the camera registers an image the radial mark will be in a position slightly ahead of the preceding frame. Thus when this movie/video is projected, the projection will give a visual impression of a disc revolving the right direction. On the other hand, when the disc complete one revolution in slightly longer than 1/24^th of a second (say 1/23 second) the movie recording will yield a sequence of images whose projection will yield a visual impression of a disc moving in the direction opposite to the actual direction of rotation of the disc in the recorded scene. This is so because successive recorded frames will have the radial mark in the slightly receded position as illustrated in the diagram.

The perception of direction of rotation of a wheel with a number of identical spokes (or marks) has an additional dimension. To perceive the direction of motion from a limited number of images (frames) the brain interpolates for the intermediate positions of the object or its parts. When there is only a single mark, as illustrated above case, the successive positions of the mark can be unambiguously interpreted for the direction of rotation. However, if the wheel has more than two identical marks (or spokes), as is the case with vehicle wheels, another factor has to be taken into account. Thus, if a wheel has ten spokes, a rotation of 10 degrees brings the wheel into an identical (and indistinguishable) position. But, if in the successive frames of a movie/TV recording, the wheel rotates by an angle of 8 degrees, the visual perception system has to decide whether to perceive the motion (in the actual direction) by perceiving that each spoke moves by 8 degrees in successive frames or in the backward direction by interpreting the positions of subsequent (identical) spokes. The rotary motion in the above case is perceived to be in the opposite direction. This is so because the visual impression conveyed by a particular sequence of frames of a movie is determined by the ?principle of proximity?. Our visual perception system perceives motion in such cases by assuming least possible displacement in subsequent images.

Consider now the case of movie/TV recording a scene, in which a vehicle is moving at a speed of say 36 km/h, that is, 10 m/s. At this speed if the circumference of the wheel is 2m the wheel of the vehicle makes 5 revolutions per second. If the wheel has 10 spokes placed symmetrically the frequency at which identical configurations of the wheel appear is 50 times per second. What will be the nature of images that will be recorded by the camera in this case? In one twenty forth (1/24) of a second, any particular spoke would have moved into a position slightly ahead of the next-to-next spoke. The wheel will therefore appear to move rather slowly in the right direction. If the speed of the wheel is exactly 4.8 rps it will appear totally stationary as it will whenever the speed: revolutions per second, is an exact multiple of 2.4. However if the speed is around 3.5 (or a multiple thereof) the wheel will appear to be rotating in the reverse direction.? At intermediate speeds, the wheel may indeed appear moving at a very low speed, as one can easily see in a particular TV advertisement of MRF tyres.

To explain the observations related to illusions in light emitted from a tube-light one has to know that a fluorescent lamp (a tube-light) is not a steady source of light energy it appears to be. It flickers with a frequency about 100 Hertz -- double the frequency of the AC electric supply ( 50 Hz in India). This is so because light in a fluorescent tube is produced due to alternate electric discharge from its two coils located at its ends. Thus light from a fluorescent lamp is not really steady, it is flickering with a frequency of about 100 Hz. Which means that our eyes really register only 100 images in a second, rest of the scene does not reach our brain because there are momentary instants when there is no light which can strike the retina of our eyes. A table-fan normally has four blades. Its frequency, that is, the number of times it has exactly indistinguishable configuration is therefore four times the number of revolutions it completes in a second. The maximum speed of a common table fan is around 1600 rpm (revolutions per minute), that is around 27 rps -- which means that the blades will appear to occupy the same position 110 times in a second, Thus when the fan is rotating at full speed it is possible that the image profile of its blade may give an illusion of rotation in the anti-clockwise direction (the blades of a normal table fan rotate clockwise). A normal ceiling fan on the other hand rotates with a speed not exceeding 800 rpm; thus, it is unlikely that we will experience a similar illusion in this case. However, when the tube gets weak after being used for a long tim or the frequency of the AC supply is very low (as may be the case with AC supply from an invertor) we may experience this illusion with ceiling fans also.

Thus, almost all similar observations are easily explained. To see a convincing demonstration one may visit your nearest car mechanic who tunes car engines of modern cars like Maruti. Invariably these mechanics have with them equipment known as a stroboscopic gun. It is used to adjust the timing of an automobile engine. It emits intermittent flashes of light, (whose frequency can be controlled in some models). If you aim the light flashes from such a ?gun? on a rotating wheel or fan, you can find out whether its frequency is equal to, greater or lesser than the frequency of rotation of the wheel/fan. When the two frequencies match, you will see a steady image profile of the wheel/fan, while if it is more or less you will see a flickering image profile which gives the impression that the wheel is rotating clockwise or anti-clockwise direction.

Many people also claim to have experienced similar illusions in broad daylight. Personally, the author could not observe any such phenomenon despite best efforts spread out over a week. Many scientists have tried to explain some instances of such an illusion by invoking induced vibratory motion of the eyeballs. A few years ago, a group of scientists, Dale Pervis et. al. of the Department of Neurobiology at Duke university USA, carried out a study of this phenomenon and published their results in Proceedings of National Academy of Sciences USA (Vol. 93, 99 3693-7 1996). They even monitored the eye movements while subjects observed reverse motion of wheels/drums with an infrared tracking system. This equipment allows detection of movements as small as half a degree of visual arc. During their experiments no discernible eye movements occurred. They asked volunteers, in their study, to view disks/drum, which were rotated at varying speed under a calibrated light, which did not flicker at all. They claim that illusions of reverse motion can indeed occur in non-flickering light, but unlike in stroboscopic light static spoke patterns cannot be visualized in continuous light. Also whereas stroboscopic conditions can generate a stable perception of reversed rotation, in continuous light the illusion always alternates with the perception of orthograde rotation. These scientists conclude ?the human visual system processes sequential episodes of information rather than continuous temporal flow.? In simple language, it means that we really do not see every moment of a phenomenon; we only sample it at regular intervals and extrapolate in between. But that is only a hypothesis; it still awaits further confirmation through experimental evidence.

To sum up, the three facets of vision ? the scene, the retinal image and the visual impression may not always have one to one relationship with each other. Just as the image captured by a camera on a photographic film depends on the parameters of the camera (its shutter speed, aperture etc.) and the photographic film used, so is the retinal image. The interpretation of the image by the brain to yield a visual impression depends on the inputs to the visual cortex from the memory. Once we are aware of these facets of our visual system, we are less likely to be puzzled about many illusions we come across often.

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