Re: Stars in Stereo

[John Roberts <roberts@xxxxxxxxxxxxxxxxx>]

>Date: Tue, 27 Feb 1996 17:50:09 -0600
>From: crowell@xxxxxxxxxxxxxxxxx (Jim Crowell)
>Subject: Re: Stars in Stereo

>On the other hand, you have the "hyperacuities", which give you
>much smaller numbers & generally involve detecting differences
>in position of two things that are simultaneously visible.
>Vernier acuity is one example of this.  Typically it's measured
>by taking a vertical line & shifting the bottom half of it
>slightly to one side or the other--making a kink in the line--&
>finding the smallest offset the subject can detect.

Vernier acuity is important for design of display devices - placement of
display elements has to be extremely precise to avoid visible discontinuities.

I think it would be fair to say that some of these hyperacuities are a function
of the processing capabilities of the brain - for instance in the case of
vernier acuity, the brain has considerable hardware dedicated to detecting
and determining the positions of edges and lines. The perceived position of
a line is a function of the input of many retinal receptors, which tends to
compensate for some of the optical limitations of the eye. (Not to imply that
there's any violation of theoretical limitations.)

>Stereoacuity's another example; you might measure it by
>presenting a subject with pairs of vertical lines in each eye
>with slightly different spacings between them--leading to a
>perceived difference in depth--& finding the smallest difference
>in spacing that can be detected.

I believe someone calculated a few years ago that the maximum human stereo
acuity would require a detection of difference in spacings which is not
too much different from the theoretical resolution of an optical device
with an aperture equal to the human interocular. As mentioned above, that
could be interpreted as an illustration of the brain's ability to combine
image information from the two eyes.

>Anyway, the basic idea is that in one case you're measuring how
>well you can see something that's really small--the optical
>quality of the system--& in the other case you're measuring how
>well you can localize two things that are clearly visible.

>Actually, I think the most important differences between these
>setttings & everyday life have to do with the displays
>themselves; very high contrasts, sharp edges, that sort of
>thing.

An excellent point. I've observed that it's harder to judge depth in subjects
with low contrast, for instance front-lit mist. Are you aware of any formulas 
or tables for "derating" of human visual or stereo acuity as a function of 
the contrast of the subject?

>Jim Crowell
>U.C. Berkeley School of Optometry

John R.


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