NickallsPulfrich curve


last updated: 20050619 
The Pulfrich effect is an optical illusion in which an object which is moving
in a plane parallel to the viewer's forehead seems to move out of that plane and
to approach (or recede from) the viewer. To achieve this illusion it is
necessary only to dim the light reaching one eye, by a filter. The illusion is
stereoscopic: it only occurs when using both eyes.
The classical way to demonstrate the effect is using a swinging pendulum.
The phenomenon is due to a unilateral increase in
visual latency, resulting from the decrease in retinal image intensity due to
the filter.
Now we try to catch the phenomenon in a mathematical equation:
Now imagine that a vertical rod, moving in a horizontal circle on a turntable,
is viewed horizontally from the side with a filter in front of one eye. It was Pulfrich
(1922) who described some of the illusions that are to be seen while the
turntable is slowing down. This slowing down makes studying of the phenomenon
very difficult, that's why Dick Nickalls chose to observe a situation
with constant angular velocity and a view from various distances.
He found the theoretical apparent curves of the rod, and verified them
experimentally ^{1)}, as function of:
 the latency as result of the filter
 the distance from the rod to the center of the turntable
 the distance between the two eyes
 the distance form the observer to the center of the turntable
These parameters are related as follows to the constants in the given
formula:
 2a is the latency angle (latency difference in seconds * angular velocity)
 2b is the distance between the eyes / distance from the rod to the center
of the turntable
 c is the distance between the observer and the center of the turntable /
distance from the rod to the center of the turntable
When varying the latency, and keeping the distances the same, the rod appears
to have the same (nearby) or the opposite (far away) rotation direction of the
turntable. In the transition situation the curve is an arc of a circle. Beneath
five situations are given with latency angle growing from right to left.
It has been found in astronomy that observers differ consistently in
observational measurements. Each observer has a socalled personal equation
factor, explained as differences in reaction time and visual illusion as the
Pulfrich effect.
This should mean that the magnitude of the Pulfrich effect is personal (should
this not be the case for all optical illusions?), and e.g. a function of age.
notes
1) RWD Nickalls: the rotating Pulfrich effect, and a new method
of determining visual latency differences, Vision Research, Vol 26, pp 367372,
1986.
While working on the Pulfrich experiments a generalized
conic theorem was found, to be read in the Mathematical Gazette (2000), vol.
84 (July), pp 232241. 2) More information to be found at Southern
Illinois University.
