Many explanations have been given for the Zollner illusion: angle expansion theory, where a vertical line looks tilted due to the perceptual system increasing the angle between the vertical and cross-hatch lines; lateral inhibition, where different orientation receptors decrease the amount of firing in their neighboring cells preferring a slightly different orientation, thereby skewing the vertical line; and fatigue, where different orientation receptors decrease activity due to overexposure. A similar though slightly different illusion has been referred to as "the grating illusion" for lack of an established name. It is slightly different from the Zollner illusion in that because of a central white circle, the test line is separated from the background lines in a way that the traditional Zollner is not. David Shinar (1977) found that a combination of the Zollner illusion and the rod-and-frame illusion is additive or reductive depending upon angular orientation. R. Ian Horrell (1971) found that distortion in angle estimation was enhanced by a herring-bone background of different angular orientations, and this was caused by the interaction between the individual angles of the test angle with the herring-bone background. The grating illusion is a very powerful illusion that possibly is due to the same mechanism that causes the Zollner illusion, but research on it revealed no published experiment that tested its magnitude or provided implications and/or similarities to Zollner. This experiment is really based on two hypotheses. First, the grating illusion by its nature of keeping the test lines separate from the background oblique lines should not be as strong in magnitude as a test line superimposed upon oblique lines (employing similar mechanisms as Zollner, just with extremely long cross-hatches). This is the test for the effect of proximity on illusion magnitude. Second, using two test lines in both the grating illusion and the complementary Zollner pattern should produce illusion magnitudes slightly less than the single-line tests since a single line should be more easily influenced by what is around it than two lines with synchronized movement. This is the test for the effect of singularity.
Subjects
The subjects for this experiment were 11 Alma College undergraduate students (four males and seven females), some with previous experience with visual illusions, some without. Because one subject did not adjust Control #1 before pressing the key to continue, his data skewed the average and had to be removed. Thus, there are only ten sets of data for this experiment.
Apparatus and Stimuli
The apparatus used for this experiment was the Eye Lines software (Beagley, 1990). A computer with a monitor capable of tilting was used as well to eliminate the possibility of subjects basing true vertical on the lining up of pixels on the computer screen (stair-step effect). A piece of white posterboard with a circle 20 cm. in diameter cut in the middle served to eliminate the rod-and-frame illusion effect with the sides of the monitor. True vertical was determined with the tilted screen (124.4 degrees counterclockwise from the X axis) and programmed into the computer as the target adjusted value.
Four stimuli and two controls were programmed into the computer. The four stimuli each had oblique background lines in five different angular orientations: with true vertical equaling 90 degrees, background lines were 105 degrees, 120 degrees, 135 degrees, 150 degrees, and 165 degrees. Stimulus #1 was the grating illusion with one test line, Stimulus #2 was the grating illusion with two test lines moving together, Stimulus #3 was a single test line on the array of oblique lines, and Stimulus #4 was two test lines on the background of oblique lines (Please see Figures 1 through 4). Control #1 was simply a single test line the subject was required to make vertical on the white screen without the distraction of oblique background lines and Control #2 had the two test lines on a plain white screen. All lines were black and approximately 1 mm. wide. Spatial frequency was approximately 6 background lines per centimeter of the computer screen.
Please note: the angular orientations of the background lines in these figures
do not match those of the test stimuli because of the tilt of the monitor.
Figure 1 and Figure 2: Stimulus 1, grating illusion with 1 line, and Stimulus 2, grating illusion with 2 lines.
Figure 3 and Figure 4: Stimulus 3, Zollner illusion with 1 line, and Stimulus 4, Zollner illusion with 2 lines.
Procedure
Subjects were asked to sit approximately 50 cm. from the computer screen. The stimuli and controls were presented in random order, two times each for each angular orientation of the oblique lines. This makes the subject adjust for verticality in 44 different instances. Eye Lines and Statview do all the computing and display graphs of the data. Differences were computed between each stimulus and its corresponding control for each subject, making it easier to make comparisons between subjects and angles.
As can be seen in Figure 5, subjects did experience more distortion at 105 degrees and at 120 degrees. However, after 120 degrees, the amount of distortion experienced begins to level off. A clear difference is seen as well among the amounts of distortion of the four stimuli: Stimuli 3 and 4 (the Zollner pattern) show much more distortion when the background lines were close to vertical (namely 105 and 120 degrees) than Stimuli 1 and 2 (the Grating pattern). Also, Stimulus 1 (single test line) shows much more distortion than Stimulus 2 (double test line) throughout the different angular orientations. Stimulus 4 (double test line) shows a greater magnitude than Stimulus 3 (single test line) at the 105 degree level, but this relationship reverses three times through the different angular orientations. Comparing the compiled data of Stimuli 1 and 2 with the compiled data of Stimuli 3 and 4 at the 105 degree orientation yielded a probability of .0084, which is statistically significant. Comparing the two sets of stimuli for the 120 degree orientation yielded a probability of .0007, which is also statistically significant.
The results do support both the hypotheses. Stimuli 3 and 4 were distorted more than 1 and 2 because the test line actually came into contact with the oblique background lines. In addition, at the 120 degree orientation, Stimuli 1 and 3 show more distortion than Stimuli 2 and 4 because a single line is skewed more easily than two lines with synchronized movement.
The most likely reason for this distortion is angle expansion theory. If a line which is truly vertical is superimposed upon oblique background lines, the line appears to tilt slightly in the opposite direction to the orientation of the background lines (making the angles between the vertical line and background lines larger, or expanding). Therefore, subjects will adjust a line until it is actually past vertical, though they still perceive it as being vertical. Because the data displayed in Figure 5 are all positive, on average the subjects overadjusted the test lines by the magnitude on the Y scale (in degrees), indicating that the illusion was probably due to the angle expansion theory.
Although the calculations have yielded probabilities which are statistically significant, this experiment would have been better had more subjects participated. More research on this particular topic is definitely needed. Duplicating this experiment with more subjects should increase knowledge so that conclusions can be drawn about the nature of the grating illusion and any implications and/or similarities to Zollner. Apparently, the same processes that produce the Zollner illusion produce the grating illusion. Perhaps the angle expansion theory is a description of one, but it is not yet proven and more research should be directed to this end.
BEAGLEY, W.K. (1990). Eye Lines [computer program]. Alma, MI. Alma College.
HORRELL, R. I. (1971). The angle of intersection of contours as the determinant of a
geometric illusion. Perception and Psychophysics, 10, 208-210.
SHINAR, D. (1977). Additivity of cues in perception of verticality. Perceptual and Motor
Skills, 44, 1327-1332.