I cannot reproduce this
optical illusion on
E2, but the best example I can find on the
internet is at “
www.perceptionweb.com/perc1197/wachtler.html”. There are much better examples in
textbooks about
visual perception and related topics.
This illusion fools you into seeing alternating dark and light bars when in fact no such bars are present - the centres of the bars are actually of the same luminance. This illusion can be explained in terms of the retinal ganglion cells and their nature of detecting contrast at various spatial frequencies.
The ganglion cells’ sensitivity to contrast can be measured by presenting sinusoidal gratings of various sizes and measuring the responses of the ganglion cells. It has been found that we become more insensitive to contrast differences as the sinusoidal grating becomes smaller. This is because the spatial frequency of the grating is so small that the contrast differences cannot be discerned - in other words, the changes in contrast are so close together that they cannot be resolved. Sensitivity to contrast also reduces for low spatial frequency sinusoidal gratings as the change in contrast is so gradual that it is effectively a uniform block of luminance.
The “contrast sensitivity function” is a plot of contrast sensitivity versus spatial frequency. An example is below (scales are logarithmic):
|
S |
C E | * *
O N | * *
N S | * *
T I | * *
R T | * *
A I | * *
S V | *
T I | *
T | *
Y | *
|___________________________*______
Spatial Frequency
The Craik-O’Brien-Cornsweet illusion consists of gradual shading patterns ending in abrupt changes of contrast. A plot of light intensity (or
luminance) versus
spatial distance looks like this:
I |
N | *| |* *| |*
T | * | | * * | | *
E |* | | * * | | *
N |----|-----*-*-----|------*-*------|-----*-*-----|-----*---- spatial distance
S | | * * | | * * |
I | | * * | | * * |
T | |* *| |* *|
Y |
Herein lies the reason why we see this pattern as a series of dark and light bars.
Fourier analysis can break down the above “
waveform” into two components – a
sine wave and a
square wave:
I |
N | * * * *
T | * * * *
E | * * * *
N |-----*-------------*--------------*-------------*--------- spatial distance
S | * * * *
I | * * * *
T |* * * *
Y |
I |____ _______________ _____
N | | | | |
T | | | | |
E | | | | |
N |----|-------------|---------------|-------------|--------- spatial distance
S | | | | |
I | | | | |
T | |_____________| |_____________|
Y |
When these two
waves are combined, they
add or
subtract at each point. Just by looking you can see how their combination produces the same
intensity pattern of the Craik-O’Brien-Cornsweet illusion. Now the effects of the illusion can be explained.
The visual system uses the information from the ganglion cells to process the visual scene. The square wave component has a spatial frequency that is easily seen. Its sudden changes of contrast are easily detected by the ganglion cells. However, the slow, gradually changing, contrast pattern of the sine wave component is not easily detected by the ganglion cells. In fact, as there is no apparent change in intensity, such a contrast pattern is not even detected by the visual system. So, with the square wave detectable and the sine wave not, the Craik-O’Brein-Cornsweet illusion appears as a series of solid bars – in other words, it appears as the intensity pattern that would be obtained if the square wave was present alone.
The only physical difference between the Craik-O’Brein-Cornsweet illusion and a series of solid bars cannot be detected by the visual system, and so the two appear to be the same.