resolution away from the fovea

[T3D Peter Abrahams <telscope@xxxxxxxxxx>]

Does anyone know how human visual resolution falls off with 
angle from the optic axis?  I wonder if it's a gentle curve 
or lumpy.....If it's lumpy, it could give some credence to Canon's
statement [in their "Lens Book" that 100mm is the lens that 
equals human vision e.g. central attention, most of our field of view 
is (outside our) awareness until we move our eyes to center on the object
of interest.]
======
Resolution falls off very sharply away from the fovea, but there are plenty
of complicating factors (lumpiness not being one of them).  Maybe a 100mm
lens with squishy elements that is connected to a supercomputer would be apt.

>From my old buddy MIL-HDBK-141 (1962), p4-9.  Resolving power decreases
with distance from the fovea, to 25% at 5 degrees and only 7% of foveal
resolution at 10 degrees from the fovea.  The accompanying graph shows a
smooth, steep, exponential curve.
None of my other sources will commit themselves in text to measurements of
this type.

In the OSA Handbook of Optics, 1995, v1, p25.27, is a graph of similar
measurements, but it is not presented in text form and is a most complex
diagram of contrast sensitivity as a function of spatial frequency, at
various degrees of arc from the fovea. 

Seeing & the Eye, G. Hugh Begbie, is a good, more popular level book, and
on p103 is an excellent graph (lifted from Ruch & Patton, Physiology &
Biophysics, 1965).  This shows that acuity is 20% of foveal levels at 10
degrees from the fovea, and 10% at 20 degrees.
=============
Some complicating factors:
The size of the pupil.  Diffraction at small pupils is apparently not a
problem, but spherical & chromatic aberration at larger pupils is a major
problem.
MTF cannot be directly measured because there are no quantifiable output
values  Campbell & Gubisch (1966), among others, projected a line source
into the eye, then captured the diffusely reflected image from the retina,
a double pass through the eye.  The image was scanned to obtain a
line-spread function, then a Fourier transform was applied, to obtain an
MTF that had to be corrected for the double passage.  This clearly showed
the aberrations accompanying larger pupils, and confirmed a rule that the
eye is diffraction limited with pupils of 2mm or less.
This experiment is described in Williams & Becklund, Optics, 1986. p355.
They outline other difficulties in determining the resolution of the eye.
The transformation of radiant flux density to nerve impulses is nonlinear;
the...processes of the retina are inhomogeneous,......[complications due
to] information processing ...in the retina & nerve fibers; and each
observers...unique background...& response patterns.  

Resolution is very dependent on illuminance.  At very low levels of light,
res is better when the image is away from the fovea (more rods, less
cones); but with daylight levels of light, res increases with illumination.
The Eye and Visual Optical Instruments, Smith & Atchison, 1997. p302: The
eye has greatest visual acuity at the fovea and decreases rapidly with
distance from the fovea....Acuity also depends upon light level and
increases with light level, reaching a maximum with ambient luminances of
about 1000 cd/m^2.  Optimum acuity values are for the correctly focussed
eye.  Any defocus will reduce the acuity....

Optical System Design, R. Kingslake, 1983, p172, acuity of vision varies
with the distance of the object,owing to changes in the shape of the
crystalline lens during accommodation.

The optics of the eye deliver an image to the fovea that is superior to the
image to the off axis area.  This does not appear to be the factor that
limits resolution. 
Discussing optical quality, not perceived resolution:
OSAs Handbook of Optics, 1995, v1, p24.25: optical performance tends to
decline steadily with field angle, due to the effects of ocular oblique
astigmatism, although it is relatively constant over the central +-15-20deg
of the visual field........peripheral...resolution thresholds are not
markedly improved when the degrading effects of the eyes optics are
bypassed......optical image quality must be in excess of the needs of the
neural sampling array.  Thus optical image degradation can play only a
minor role in setting the limits to peripheral performance.

_______________________________________
Peter Abrahams   telscope@xxxxxxxxxx
the history of the telescope, the microscope,
    and the prism binocular


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