Holger Merlitz
As early as during the 19th century, Herrmann von Helmholtz described
an experiment, in which a distorted checkerboard had to be observed from
a given distance to be perceived as being straight [1].
This observation may indicate the presence of a certain distortion
in human visual perception which somehow manages to compensate for the
checkerboard's distortion.
1. What is the meaning of distortion here?
Distortion commonly means that the positions of image points are shifted
in a systematic manner. Here, we only care for the special case of
radially symmetric distortion, in which the image points are dislocated in radial
direction with respect to the center. We then introduce the distortion
parameter 'k', which quantifies the amount of distortion.
A
B
C
D
Fig. 1: Checkerboard patterns with increasing amount of
distortion. From left to right: k=1 (undistorted), k = 0.7, k = 0.5, k=0.
Helmholtz used checkerboard C.
2. Is there indeed a distortion in human visual perception?
Helmholtz used a checkerboard of distortion k=0.5 (Fig. 1 C). In 2009,
a group of Dutch scientists refined his experiment by letting test
persons look at a large computer screen with a checkerboard of variable
distortion. From a well defined distance, they had to fixate their gaze
onto the center of the board and to tune the distortion until the
contours appeared straight to them [2]. The resulting distortion
values, as chosen by the test persons, are shown in Fig. 2:
Fig. 2: The curve 'Fixation' displays the statistical distribution
of the distortion values chosen by the test persons (modified figure
from [2]). The maximum is located at k=0.73 (red arrow), while Helmholtz's
suggestion k=0.5 (orange) is in the marginal region of the distribution.
The test persons selected different distortion values, yielding a rather
broad distribution with a maximum at k=0.73. This indicates that the
curvatures of the contours are perceived differently by individual
observers. Helmholtz's k=0.5 distortion has rarely been chosen.
If observers perceive a distorted checkerboard as a straight board,
then some sort of compensation must be taking place in the visual
perception, and since all boards with k<1 are having a pincushion
distortion, which bends straight
lines inwards, this visual compensation must act as a barrel distortion
which bends lines outwards.
3. Under which condition is the visual barrel distortion visible?
A barrel distortion of the visual field whould bend straight contours,
which cut through peripheral areas of the field of view, outwards.
Since the measured amounts of distortion (Fig. 2) are rather small,
and since objects far off the direction of view are perceived blurred,
such an effect remains invisible in daily life situations. If, however,
an image scrolls at sufficiently high speed in front of the eye, as is
the case when looking through a binocular (which has no own distortion)
while panning, then the barrel distortion makes itself felt as a
perceived curvature of the visual field, which is known as
the globe effect
[3]. Since the middle of the last century, most binoculars were thus
given a deliberate pincushion distortion to eliminate
the globe effect, which has been reported to induce motion sickness
and nausea with some observers.
4. Modern approach to the compensation of visual distortion in binoculars
In 1949, after in-depth discussions among the developers and the Scientific
Directorate, Zeiss decided to implement a pincushion distortion according
to k=0 (Fig. 1 D) to their binoculars, and most binocular makers worldwide
followed their approach [4]. This did indeed eliminate the globe effect,
but also led to a significant bending of straight edges in the image. As discussed
above, recent results based on human perception theory show that the
lower distortion of k=0.7 (Fig. 1 B) already suffices to compensate for the visual barrel
distortion that affects the average observer (Fig. 2). Figure 3
displays the corresponding distortion curves:
Fig. 3: The relative distortion stands for the percentage of
which the positions of the image points are shifted away from the
center of the field. The k=0.7 curve (red) most efficiently
compensates the visual barrel distortion as measuresd in experiments
(Fig. 2), whereas k=0.5 (Helmholtz, orange) and k=0 (Zeiss since 1949,
green) are actually overcompensating.
The most efficient compensation of visual barrel distortion is achieved
with the k=0.7 curve (red), which implements less than half of the amount
of pincushion distortion of the k=0 curve as initially suggested
by Zeiss. The observer thus enjoys an image of low pincushion distortion
and at the same time a compensation of the globe effect. To be avoided
are irregular distortion curves as the 'mustache'-distortion shown in Fig. 3,
since this is known to generate a
very unpleasant
panning behavior of the binocular.
5. The Zeiss SFL series is corrected according to the k=0.7 curve
Zeiss has now altered its strategy of eliminating the globe effect and
implements the insights from visual perception theory into its new
SFL series. These binoculars thus exhibit a smooth panning
behavior and at the same time a low residual pincushion
distortion:
6. What comes next?
The visual experiments of [2], as summarized in Fig. 2, were based on a rather
small number of 20 test persons and prone to errors, since the rigorous
fixation of the observer´s view to the center of the checkerboard could not
be enforced during the measurements. A far superior way to measure human visual distortion should
apply animated pictures, presented to the test persons via VR headsets. Since
the perceived curvature of a moving image is far easier to judge than a fine
bending of blurred contours far off the direction of view, the results can be expected
to be of higher accuracy and less prone to errors.
[1] H. von Helmholtz, Handbuch der physiologischen Optik, 2. Auflage Voss, Leipzig (1980)
[2] A.H.J. Oomes, J.J. Koenderink, A.J. Doorn, H. de Ridder, What are the uncurved lines in our visual field? A fresh look at Helmholtz's checkerboard, Perception 38, p. 1284 (2009)
[3] H. Merlitz, Distortion of binoculars
revisited: Does the sweet spot exist?, Journal of the Optical Society of America A 27, 50 (2010)
[4] A. Sonnefeld, Über die Verzeichnung bei optischen Instrumenten, die
in Verbindung mit dem blickenden Auge gebraucht werden, Deutsche Optische
Wochenschrift 13 (1949)
Back Home
Last updated: November 2024