Human Image Formation
•What is the quality of the optics
of the human eye?
•How can we measure it and
describe it empirically?
The Cornea and
Lens Focus the
Image on The
Retina
17 mm
CrossSection of
a Real Eye
Lens
Cornea
Retina
Optic disk
Iris
Optic nerve
Recovered Sight
(Fine, Wade, Wandell)
Primary visual cortex is
one-fourth the normal
size
Motion selective cortex is
the normal size
• Chemical accident at 3 yrs
• One eye lost; other cornea destroyed
• Blind from age 3 through 46
• Stem cell replacement in right eye for
both epithelium and stem cells
Corneal
epithelium
cells
Limbic stem
cells
Structure of the lens
Special cellular properties that permit the lens to stretch
The fibrous nature of the
lens is evident in lowmagnification scanning
Lens fibers (micrograph 2)
are mature cells that have
lost their organelles,
including nuclei, and are
packed with soluble
structural proteins called
crystallins. The agerelated decrease in the
ability of the lens to
accommodate for near
vision is, in part, related to
the accumulation of more
lens fibers, but it is due
primarily to decreased
elasticity of the capsule.
Socket and knob interdigitations
maintain lens organization
Mature lens fibers are tightly
packed and join with one
another via knob- and
socketlike associations (k,
micrograph 2). These
elaborate cell interdigitations
maintain the lens
organization during shape
changes associated with
accommodation. In addition,
close packing of cells
prevents excess light
scattering and facilitates
communication between
adjacent cells.
Things I don’t know and would like to
• What governs the development of optical power of the eye?
(Wiesel recent work)
• What are the material properties of the cornea and lens that
give them their refractive power?
• What happens to these materials when cataracts develop?
Light Passes Through The Retinal Cells And Is
Absorbed by the Rods and Cones
GCL
INL
ON
L
OS
Light enters
Inner
Outer
Light Scattered From From The Retina Is Used To
Estimate Optical Quality
(e.g., Campbell and Gubisch)
Measurements
Of Light
Reflected From
The Retina
(Linespread) At
Various Pupil
Diameters
The Linespread Function Is A Useful
Summary of Optical Quality
Analyzing slit position
Simple Lenses
and Many Other
Optical
Systems
Satisfy the
Linear System
Priniciple of
Homogeneity
Superposition
and Shiftinvariance Are
Different
Properties Of A
Linear System:
Linear Systems
Are Not Always
Shift-Invariant
Harmonic patterns are widely used in
vision science research
h( x)  M  Ma sin(2 fx)
 M (1  a sin(2 fx)), a  1
M = mean level, a = contrast, f = spatial frequency
Harmonics have a
special role in
shift-invariant
linear systems
because they pass
through only
slightly altered
sin(2 f x)
s sin(2 f x   )
s 2 sin(2 f x)
Every image can be described as the
weighted sum of harmonics
1
0.8
0.6
0.4
0.2
0
0
20
40
60
1
1
1
0.5
0.5
0.5
+…
0
-0.5
-1
+…
0
-0.5
-1
0
20
40
F=1
60
+…
0
-0.5
-1
0
20
F=6
40
60
0
20
F=9
40
60
Approximation by harmonics improves
as we add more harmonics together
1
0.8
0.6
0.4
0.2
0
0
20
40
60
Sum of the first N harmonics
1
1
1
1
1
1
0.5
0.5
0.5
0.5
0.5
0.5
0
0
0
20
40
3
60
0
0
20
40
6
60
0
0
20
40
12
60
0
0
20
24
40
60
0
0
20
40
48
60
0
20
40
64
60
We can use shiftinvariance and
harmonics to
correct for the
double pass
experiment
What they want to know
What they measured
sin(2 f x)
s sin(2 f x   )
s 2 sin(2 f x)
Campbell and
Gubisch:
analysis
3.0 mm
Diffraction
limit
3.8 mm
2.4 mm
4.9 mm
2.0 mm
5.8 mm
1.5mm
6.0 mm
Inferred linespread (Westheimer)
We can describe a system’s performance
with respect to its treatment of harmonics:
The Modulation Transfer Function (MTF)
Reduction of
the harmonic
amplitude
Theoretical
MTFs are
similar to the
data, but not
exact:
This is a 10%
Field
Relative amplitude
1
0.75
0.5
Ijspeert
0.25
Westheimer
0
10
20
30
Frequency (cpd)
40
50