Spatial Vision

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Spatial Vision
2. Optical, anatomical neural determinants of
visual acuity and contrast sensitivity.
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Mechanisms Limiting VA and CS
1. Optics 2. Sampling 3. Neural Summation
inhibition
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Optics PSFs and two-point resolution
Center of diffraction limited PSF has radius r
1.22 l/a Where a pupil diameter and l
wavelength in same units (mm, m, or mm)
Airys Disk
Combining Airys disk and Rayleighs criterion,
we find that two point resolution is 1.22l/a
radians, or approximately l/a. For a
diffraction-limited system, resolution is better
for short wavelengths and large pupils. For a
diffraction limited system two-point res
(1.22 0.000555 (18060)/ p)/a 2/amm arc min
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PSFs and resolution convolution (V663)
Image
If PSF radius is larger than detail to be
reolved, resolution is compromised.
PSF
Object



convolution
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Optics MTFs and grating resolution.
Describe image quality by ability of optics to
image gratings
Object
object
Image
image
Optical System
period
Spatial frequency 1/period
Input
Output
Optical Filter
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The modulation transfer function
Proportion of Modulation (contrast) Transferred
from Object to Image
Mod(out)

Mod(in)
Mod(out)
MTF
Mod(in)
Spatial Frequency (c/deg)
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Three standard MTFs
Perfect Optics
1.0
Diffraction Limited Optics
a/? (c/rad?
Real optics
0.0
Spatial Frequency (c/deg)
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Optics MTFs and grating resolution.
Diffraction limited system, high frequency
cut-off is a/l c/radian. Thus the smallest
grating period that can be imaged is l/a.
l/a
Just get some modulation in image
1.0
image
object
Remember Rayleighs criterion. Separate two
points by about l/a, and just get some modulation
in image
a/? (c/rad?
0.0
Spatial Frequency (c/deg)
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Diffraction-limited VA varies with
wavelength For a 1 mm pupil, and 555 nm light,
a/l 1/0.000555 c/radian 1/000555 x
p/180 c/degree 31 c/deg For 400 nm, a/ l 43
c/deg. For 700 nm, a/ l 25 c/deg
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Comparing MTFs from real eye optics to
diffraction limited MTFs.
Diffraction
8 mm pupil
for 665nm
Eyes
MTF
1
3
5
7.3
8
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Predicting VA for aberrated optics
MTF
1
Neural CSF (plotted as threshold contrast
minimum retinal contrast required for detection)
MTF or Maximum contrast in retinal image
B
A
VA
0
Spatial Frequency
Spatial Frequency range A optics can image
contrasts above neural threshold. Spatial
Frequency range B optics cannot image contrasts
above neural threshold.
VA Maximum SF for which optics can image
contrasts higher than neural threshold
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Effect of pupil size on VA
Aberration effect
2
MAR
Diffraction effect
1
1
2
3
4
5
6
7
8
Pupil Diameter (mm)
2-3 mm pupil is best
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Resolution Limited by neural sampling (see V648)
The photoreceptor array samples the continuous
optical mage, and the sampled image is then
re-sampled by subsequent neurons (bipolars,
ganglion cells etc.). See Notes from V648.
What are the consequences of sampling? How does
sampling limit our VA?
Image of the
monkey
peripheral retina
(Heinz Wassler,
1999).
cones
rods
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Neural Sampling
Optical Image on Retina
Neural Retina
Perception
Cortex
Continuous
Sampled
Continuous
Sampled
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20/20 vision is not universal!
Defocus
Light Level
20/200
20/200
Rod vision
logMAR
MAR
20/20
20/20
MARBlur Circle/4
Defocus (Diopters)
Log Retinal Illuminance (Trolands)
Eccentricity
Motion
20/200
20/200
Scotopic
logMAR
logMAR
Photopic
20/20
20/20
2 deg/sec
Retinal Eccentricity (degrees)
0
30
Log Retinal Image Velocity
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Contrast Sensitivity is not constant!
Light Level
Eccentricity
4deg
Mesopic
Foveal
Photopic
Scotopic
30deg
20/200
20/15
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Impact of sampling on spatial resolution
Helmholtz
Two point Resolution
Must have sample between images of two points in
order to know that there is a gap between the
stimuli.
Neural Response
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Sampling and periodic patterns.
Shannons sampling theorem basically same idea
as Helmholtz (need one sample between each line)
Notice that, at limit of just one sample between
each bright line of grating, there will be
exactly 2 samples per period of the grating.
S
In order to resolve a periodic pattern there must
be at least 2 samples per period. Therefore, if
we know the spacing between samples, we know the
maximum resolvable spatial frequency fmax
1/(2s), where s separation between samples.
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Undersampling and Aliases
Repetitive Grating Stimulus If there are less
than 2 samples per period of repetitive signal,
it will be undersampled by the array, and the
resulting output will be indistinguishable from a
lower frequency signal.
signal
alias
samples
For resolution sample separation(s) must be lt
period/2. For human fovea cones separated by 1/2
arc minute, thus minimum resolvable period is 1
minute, or 60 c/deg. Above 60 c/deg, see aliases
if these high frequencies existed in retinal
image.
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2-Dimensional Undersampling Misrepresents
Spatial Frequency and Orientation of Patterns
Example with less than 2 samples per period
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The eyes optics filters out all SF above Nyquist
limit in fovea, since foveal nyquist (60 c/deg)
is slightly higher than optical cut-off (about 50
c/deg). This is not so in the peripheral retina
where the optical cut-off is higher than the
nyquist limit, thus aliases can be seen.
Optical limit
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Effect of spatial summation on acuity
Schematic RF that sums photons uniformly over a
square retinal area.
Notice that when the grating period RF width,
the neuron is blind to the grating (does not
respond), but when the RF is smaller than the
grating period, the neuron increases and
decreases its response if aligned with the light
or dark bar of the grating.

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Psychophysical experiments to determine the
summation characteristics of the most sensitive
neurons.
e.g. Small stimuliltRF area
square mm
(1)
Resp
Resonsenumber of photons in the RF
RF
(2)
Resp
Notice that the number of photon/mm2
(illuminance) is twice as high in example 2 where
the area of the stimulus was halved, but the
total number of photons (I A) is the same (16
photons).
square mm
Threshold photons (IA) constant if stimulus
area lt RF area
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LA constant for small stimuli This is known
as RICCOSs Law of spatial summation. This law
ONLY holds if the stimulus is smaller than the
RF. Thus maximum stimulus size for which LA
constant determines the summation area of most
sensitive neurons.
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Example in which the stimulus is larger than the
RF
When the stimulus is halved in size and the
luminance doubled, the number of photons incident
on the RF doubles. In this example, to keep the
total number of photons absorbed by the RF
constant and thus the response of the neuron
constant, luminance, not luminance X area must be
held constant.
Transition from the small stimulus sizes that
show Riccos behavior (L x A K) to the LK
behavior provides a psychophysical measure of the
visual systems summation area, often called
Riccos Area.
Resp
Resp
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Riccos Area
luminance
luminance X area
Stimulus Area
Stimulus Area
Photopically, foveally
RA
diam 10
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Hyperacuity
Puzzle How can we detect a position change less
than one cone diamter? Cones 30 sec,
hyperacuity lt6 sec (record1 sec).
Cone RFs
Response changes after dot moves from one RF to
another
Scale problem with this conceptualization
image
object
Cannot create a retinal image smaller than cone RF
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Original Explanation for sub-pixel positional
accuracy Helmholtz (mean local sign)
Use interpolation (estimate themean location).
Cone RF (each one has a local sign)
Distribution of local signs
Line stimulus
mean
This model rejected when discovered that vernier
acuity for dotsvernier acuity for long lines
showing that there was no need to average local
sign along the line.
As long as there are enough samples, mean local
sign estimates will be more accurate than RF size.