Copyright (c) 1960, Alfred Lit. Permission of the author and
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This explanation is adapted from Lit (1960) on target thickness. Please refer to that paper, posted elsewhere at this web site, for further information. Lit's (1949) classic, also posted at this web site, explains the geometry in full detail.

The stereoscopic effect with which the present experiment deals was first described and analyzed by Pulfrich in 1922. A target which is oscillating at eye level in a frontoparallel plane appears to rotate out of its plane of oscillation when a neutral or colored filter is placed in front of one of the observer's eyes.

The depth effect becomes noticeable at some threshold difference of binocular retinal illuminance and progressively increases as the difference of binocular retinal illuminance is increased.

Pulfrich (following a suggestion by Fertsch) accounted for these depth displacements in terms of a difference in the hypothesized visual latent periods of the two eyes. The visual latent period of each eye was assumed to be a reciprocal function of the prevailing level of retinal illuminance. Thus, the eye covered with the filter presumably "signals" a position of the oscillating target that lags behind the position signaled by the uncovered eye. Hence, at any given moment, synchronous binocular signals are provided by pairs of noncorresponding retinal points in the two eyes, and the magnitude of the stereoeffect theoretically depends on the amount of the retinal disparity produced as a consequence of the difference in the visual latent periods of the two eyes.

In Lit's work, the appearance of the targets to an observer, with the upper target in motion, would be as in this figure, or in this animation:

Consider the geometry, viewed from above, shown in in the next figure, of
a target that is oscillating in a frontoparallel plane with constant linear
velocity *V* for the central portion of its stroke.

The linear path of the target in its plane of oscillation is denoted by
*W _{1}W_{2}*. The distance

As indicated, the filter is placed in front of the left eye. The point
*P _{F}'* represents the far position in the vertical median plane at
which the oscillating target, at point

In accordance with the laws of binocular space discrimination, lines of sight
from each eye are drawn through the two respective points of target localization,
*P _{F}'* and

Thus, when the target is moving from left to right and appears to be located at
the far position *P _{F}'* towards which the eyes are converged, the
onset of stimulation for the right eye occurs when the target (at

The time taken for the target to move from *B* to *P _{LR}*
represents the magnitude of the visual latent period of the right eye, and the time
taken for the target to move from

Consequently, the time taken for the target to move from *A* to *B*
represents the difference, , in the
visual latent periods of the two eyes, based on the far position of target
localization, *P _{F}'*. It follows by the same reasoning that when
the target is moving from right to left and appears to be located at the near
position,

It can be readily seen from similar triangles in the diagram above that for
target localizations at *P _{N}'* and

where *X*=1/2 the distance from *A* to *B*, and *b*=1/2 the
distance between the centers of rotation of the two eyes.

For an oscillating target moving with constant linear velocity *V*, the
time taken for the target to pass through the distance *X* is given by the
formula

The time taken for the target to move from *A* to *B* (or *B* to
*A*) represents the difference, , in
the visual latent periods of the two eyes. Since =2*t*, we obtain from Eq. (2)

By substituting for *X* the respective expressions given in Eq. (1), we
finally obtain the following relationships between the experimentally determined
near and far displacements (*C _{N}* and

It should be noted from purely geometric considerations that, for any constant
difference of binocular retinal illuminance, the magnitude of the stereoscopic
effect as measured by *C _{N}* and

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The Pulfrich Effect, SIU-C. Last updated 2000-08-09