2. Photosensitivity
• Photosensitivity, for our purposes, refers to sensitivity to light
whose wavelength falls in the range of 400-700 nm.
• Upon absorption, which we will generally treat as the first
step towards vision, light behaves as though it were “quantal”
(consisting of discrete photons).
– Sir Isaac Newton advanced the theory that light was a stream of
particles in 1704!
• The number of photons that a source emits (or reflects) is
closely tied to its apparent brightness, but we shall see that the
relationship between brightness and number of photons is not
a simple one!
3. Characteristics of Light
• As it travels, it actually shows wave characteristics
(James Clerk Maxwell, 1873), and we characterize
it by its wavelength (distance between peaks of the
wave as it goes through one cycle).
• Wavelength is the principle determinant of the hue
of light, which is the perceptual characteristic
most like what people mean by the term “color.”
4. • 1 nm is a billionth of a meter.
• In normal eyes, 400 nm is seen as violet, 500 nm as blue-green, 600
nm as yellow, and 700 nm is seen as red.
• There is nothing inherently colored (hued) about wavelengths—hue is
entirely extracted by visual processing.
• The perception of color is not a simple function of wavelength (more
later).
5. Gross Anatomy of the Eye
Each eye is a spherical structure that is
20-25 mm in diameter.
The cornea is a bulge in the
sclera that is approximately 13
mm in diameter.
Aqueous Humor
Vitreous Humor
Blind spot
The gross anatomy of the eye is such that the retina covers more
than 270o of arc along the back surface.
6. • Behind the cornea is the aqueous humor, a fluid similar to
cerebro-spinal fluid.
• The iris is the colored membrane that surrounds the central
hole (the pupil).
– The color ranges from blue through black, and is controlled
genetically by mechanisms similar to the ones controlling skin
pigmentation.
– The size of the pupil is controlled by the light reflex, constricting
in bright light, dilating in dim light.
• It can vary in diameter by about a factor of 16, decreasing in size as
illumination increases (negative feedback).
• This has little to do with adaptation to light levels.
– Its major purpose is to decrease the size so that the optical imperfections near the
edge of the lens and cornea do not distort images (the center of the cornea and lens
are more refractive).
– In dim light, visual resolution is poorer due to optical imperfections at
the edges of the crystalline lens.
– As such, it is in the best interest of the visual system to minimize pupil
size.
– Pupil size is also determined by level of interest and arousal,
becoming larger under conditions of great interest.
8. The Cornea
• The cornea has a radius of curvature of about 8 mm,
and is the area where light enters the eye.
• The cornea is the first optical element of the eye,
serving as a simple lens that begins to gather light rays
and focus them on the other side (towards the retina).
– Because it bulges forward, it actually allows
reception of light from a region slightly behind the
observer.
9. • Most of the refraction takes place at the surface of
the cornea (43 diopters out of a potential total
power of 59 diopters for the combined cornea and
lens).
• This is evident from the great loss of power when
the eye is immersed in water when swimming.
– Since water and aqueous humour are so similar,
refraction does not occur at the interface of the
environment (water) and the cornea.
– The liquid aqueous humour nourishes the cornea and
lens, which have no blood supply.
• Light then passes through the aqueous humour to the lens.
• The light then travels through the jellylike vitreous
humour, which has an index of refraction close to that of
water, to the retina at the back of the eye.
10. • Most vertebrate eyes contain a crystalline
lens located behind the pupillary aperture.
– Its curvature is controlled by the ciliary
muscles, which cause it to bulge when
contracted, increasing the strength of the lens.
– The process of varying the refractive index of
the lens is referred to as accommodation, and is
crucial for objects occurring at different
distances (so that light is focused onto the
retina).
12. • Because directional information is carried by which
points on the retina are stimulated, the accuracy of
that directional information is limited by the extent to
which two independent points are focused as two
separate points on the retina.
• Optical systems operate by bending light beams
because of the differences in composition of the air
and the refracting medium.
– The refraction of light is due to a reduction in velocity as
the light passes through the lens (can be reduced by up to a
factor of three).
– While the velocity of light in a vacuum is not dependent
upon wavelength (186,000 miles per second), the reduction
in velocity as the medium changes is somewhat
wavelength-dependent (chromatic aberration).
13. • It is the property of all lenses that they take light emanating
from a point source, refract the beams, and form a single
point in the image plane.
• If we go to cases of multiple points it is easy to see that the
image is reversed on the image plane in comparison to the
object plane.
• This is best seen by looking only at rays passing through the
optical center within the lens:
S1
S2
I3
I2
S3 I1
Object Plane Image Plane
14. OA=Optical Axis; rays passing through it are not refracted
OA
do di
O
O
di do
As the object moves closer to the lens, the image moves further
away from the lens.
16. The Crystalline Lens
• The problem for the visual system is making sure that the image
plane corresponds to the retina, which is fixed at a distance of 22
mm behind the cornea.
• As the object is moved further away, the image is formed closer
to the lens; as the object is moved closer, the image is formed
further from the lens (the index of refraction must increase).
• The lens of the eye is is a gelatinous capsule that is held in place
behind the pupil by a complex web of suspensory ligaments
known as the Zonules of Zinn.
• The ligaments also are attached to the circular ciliary muscle.
– When viewing an object at a distance, the ciliary muscle relaxes. This causes the
Zonules of Zinn to become taut, which makes the lens flatter and thinner.
– When a near object is viewed, the ciliary muscle contracts. This causes the
Zonules of Zinn to slacken, which enables the lens to return to a more convex or
globular orientation.
17. • This is somewhat counter-intuitive. Usually, we associate muscle
contraction with parts of our bodies becoming taut and hard.
– However, in lens accommodation, the Zonules of Zinn slacken when the ciliary
muscles contract.
• The reason this happens is that the ciliary muscle is circular.
– When it is relaxed, the diameter of the circle is at its maximum, which means that
the Zonules of Zinn are pulled tight.
– Conversely, when the ciliary muscle contracts, the diameter of the circle becomes
smaller and the Zonules of Zinn relax.
– Thus, the ciliary muscles are responsible for the lens accommodation
response, controling the tension on the zonules which are attached to the
elastic lens capsule at one end and anchored to the ciliary body at the other
end.
– They function as a sphincter, easing tension on the zonules when
contracted (allowing the lens to bulge, increasing refraction) and making
the zonules taut when relaxed (flattening the lens, decreasing refraction).
18. Zonules of Zinn
Object moves
further away
Object moves
closer
19. • As such the lens is most refractive in a
when the zonules are in a relaxed state (with
the lens varying from 2-16 diopters).
• So, focusing at points closer than optical
infinity necessitates relaxation of the lens
(allowing it to bulge) because objects
brought closer are focused at a distance
further away from the lens (see the
expressions for focal lengths); without this
adjustment objects would be focused behind
the retina.
22. • Our ability to accommodate declines with age,
starting from about 8, and we lose about 1 diopter
of accommodation every 5 years up to age 30 (and
even more after age 30).
• By the time most people are between 40 and 50
years old, they find that their arms are too short
because they can no longer easily accommodate
the 2.5 diopters or so needed to see clearly at 40
cm.
– This condition is called presbyopia (meaning “old
sight”) because the lens becomes sclerotic (harder) and
the capsule that encircles the lens (enabling it to change
shape) loses its elasticity.
23. • The optical center of the combined cornea-lens
is about 17 mm in front of the retina
when the lens is relaxed (focus in the far-field)
and 14 mm when the refractive index
is greatest (focus in the near-field).
• The focal length (F) of a lens is formally
defined as, where do=distance
1 1 1
F do di
to object and di=distance to image.
• One could measure the focal length by
going to infinity and projecting an object, at
which point the image would be formed at
the focal length from the lens.
24. Measuring the Focal Length
• A somewhat more reasonable strategy is to
employ collimated light as the source.
• Collimated light sources emit parallel rays
of light, which is would would happen if the
object were at infinity.
do di=F
25. • For humans with a perfect optical apparatus,
the focal distance equals the distance
between the retina and the optical center (a
combination of the lens and cornea).
• As was stated earlier, the optical system
faces the difficulty of having a retina that is
only about 22 mm away, so it must refract
light strongly.
• Strength of lenses is typically measured in
1
diopters, where
1
diopter
• Stronger lenses have shorter focal lengths
and more diopters.
Focal Length inmeters
( )
26. • The cornea is the most refractive element,
providing about 43 diopters (1/43 = .02325 M =
23.25 mm), bringing the image to focus just
behind the retina if there were no lens.
• The minimum strength of the crystalline lens is 2
diopters, yielding a total of 45.
• Since 45 M-1=22.22 mm, this puts the image on
the retina for objects at optical infinity.
• As objects move closer the ciliary muscles
contract allowing more slack on the Zonules of
Zinn, causing the lens to bulge, producing a
greater refractive index (more diopters).
27. ; the lensmaker' s equation
Distance to Retina
0.0222 M
Cornea Only= 43
Minimum Lens 2.045045
1 1 1
o i F d d
Distance to Object (M) Total Diopters Lens Only
10 45.1450 2.1450
2 45.5450 2.5450
1 46.0450 3.0450
0.5 47.0450 4.0450
0.25 49.0450 6.0450
0.1 55.0450 12.0450
0.07 59.3308 16.3308
The closest object a young person can accommodate…..
28. • To focus a spot of light at optical infinity on the retina, the refractive power of the optical
components of the eye must be perfectly matched to the length of the eyeball.
– This perfect match, known as emmetropia.
• Refractive errors occur when the eyeball is too long or too short relative to the power of the
optical components.
• If the eyeball is too long for the optics (b), the image of a point will be focused in front of the
retina, and the spot will thus be seen as a blur rather than a spot of light.
– This condition is called myopia (or “nearsightedness”).
– Myopia can be corrected with negative (minus) lenses, which diverge the rays of starlight before they
enter the eye (c).
• If the eyeball is too short for the optics (d), the image of a point will be focused behind the
retina—a condition called hyperopia (or “farsightedness”).
– If the hyperopia is not too severe, a young hyperope can compensate by accommodating, and thereby
increasing the power of the eye.
– If accommodation fails to correct the hyperopia, the spot’s image will again be blurred.
– Hyperopia can be corrected with positive (plus) lenses, which converge the rays of starlight before
they enter the eye.
29. • When the cornea is not spherical, the result is astigmatism.
• With astigmatism, vertical lines might be focused slightly in front
of the retina, while horizontal lines are focused slightly behind it
(or vice versa).
• If you have a reasonable degree of uncorrected astigmatism, one or
more of the lines in above figure might appear to be out of focus,
while other lines appear sharp.
• Lenses that have two focal points (that is, lenses that provide
different amounts of focusing power in the horizontal and vertical
planes) can correct astigmatism.
30. Measuring the Quality of Lenses
• Optical quality is measured by the point spread
function of the eye or by the spatial modulation
transfer function (spatial MTF).
• Because of various optical aberrations, the
distribution of light from a point source will be
distributed over a Gaussian (bell shaped) region.
• The light from two nearby points in space will not
be two punctate spots on the retina but will instead
be two Normal distributions that overlap to
various extents, forming a single-peaked
distribution in image space when points in object
space get close together.
31. Point-spread functions
• Measurements of point-spread functions
were carried out by Westheimer and
Campbell, who looked at the retina with an
apparatus that works on the same principle
as an ophthalmoscope, whereby the amount
of light reflected from the retina is recorded
with a photocell out of the line of projection
from the light source.
32. Light that enters the
subjects eye is brought
into focus by the lens. A
small portion of this light
is reflected back out and
passes through the optics
of the eye for a second
time. On the return path,
the beam splitter, which is
nothing more than a
lightly silvered mirror,
reflects some of the light
and transmits the rest.
A portion of the
reflected light is
brought to focus on
one side of the
apparatus. Using a
very fine slit in the
measurement plane
with a photodetector
behind it, the reflected
light can be used to
infer the shape of the
retinal image.
33.
34. To the left are measurements taken
by Campbell and Gubisch as a
function of the pupil diameter (given
in mm). First (and most
importantly), note the increased
width as the pupil diameter
increases—when the pupil is wide
open, the image is blurred than when
the pupil is relatively constricted.
Notice that the measurements taken
when the pupil diameter is large are
less noisy—when the pupil is wide
open, more light enters and is
reflected, improving the quality of
the measurements. Note that the
optics of the eye have twice
distorted the distribution of light, so
some correction needs to be carried
out for the image on the back of the
retina to be inferred.
35.
36.
37. Spatial Modulation Transfer
Functons
• A mathematically equivalent and, in many ways,
more attractive approach to measuring the optical
degradations of the eye is to measure the Spatial
Modulation Transfer Function (MTF).
– An MTF is a measure of the extent to which different
spatial frequencies are passed by a given optical
system.
– For ordinary optical systems MTFs can be measured
directly by imaging spatial frequencies of some known
contrast, then measuring the contrast of the image with
a scanning photometer.
38. Contrast
L L
L L
max min
max min
Contrast
70
10
70
10
0.75
Contrast
50
30
50
30
0.25
Column 1: The grating at the bottom is half the amplitude/contrast of the grating at
the top.
Column 2: The grating at the bottom is twice the spatial frequency of the grating at
the top.
Column 3: The grating at the bottom is 90 degrees out of phase with respect to the
grating at the top.
39. Contrast
L L
L L
max min
max min
– If the optical system transmits perfectly, the contrast of
the image will be the same as the contrast of the
stimulus grating.
– When this has been done for the human visual system it
has been deduced that it passes no spatial frequencies in
excess of 60 c/deg. (Campbell and Gubisch, 1966).
– One approach measuring the MTF for the whole system
is to employ a psychophysical task in which the
participant adjusts the contrast of a grading until it can
just be discriminated from a uniform field with the
same average luminance.
40. • The inverse of contrast is plotted, so the
function is the contrast sensitivity function
(CSF).
Optics alone
41. Comparing the Contrast of the Image
and the Contrast of the Stimulus
• One varies the spatial frequency for gratings of
fixed contrast, comparing the contrast in the image
with the contrast in the stimulus (forming a ratio).
• Perfect optical systems will yield the same
contrast for the image as is in the stimulus at all
spatial frequencies—ours begins to attenuate
contrast at about 5-10 c/degree, yielding no image
contrast by 60 c/degree.
42. 1.0
0.1
0.01
ContrastImage/ContrastStimulus
No loss Attenuation of contrast
43. • Note that 60 c/degree corresponds to a cycle
width of 0.01667 degrees, a span of
appoximately 3 foveal cones (spaced at .008
degrees center to center).
• We need two receptors to encode a cycle
(the aliasing problem—see page 58 of the
text), so it appears that the upper cutoff is
consistent with the spacing of the cones.
• The optics happens to match the limits set
by cone spacing-it makes not sense to have
an optical system that would exceed the
quality limit set by the receptors (and vice-versa).
44. Exploratory Demonstration
Try Varying the Spatial Frequency (cycles per stimulus) and Contrast
of the Sample Sine-Wave Grating Presented Below
http://www.usd.edu/psyc301/CSFIntro.htm
45.
46. • Each rod outer segment contains the
photopigment rhodopsin, while there are three
different conopsins.
• Visual pigment molecules consist of a protein
(an opsin), the structure of which determines
which wavelengths of light they absorb, and a
chromophore, which captures light photons.
• The pigment rhodopson is found in the rods,
concentrated mainly in the stack of
membranous discs in the outer segment.
• Each cone has one of the other three pigments
(photopsins I, II, and III)—which respond to
long, medium, and short wavelengths,
respectively.
– All have the same 11-cis retinal as is found in
rhodopsin, but they have different opsins.
• In rod cells, the protein which binds to the
chromophore retinal is opsin, and the bound
complex of 11-cis-retinal plus opsin is known
as rhodopsin, or visual purple.
– Each photopigment molecule consists of two
components—a large protein opsin and the
chromophore retinal (derived from vitamin A).
• In mammalian cones, there are three
different conopsins (each with the same
11-cis-retinal).
Isomerization
47. • It appears that Na+ channels in the
receptor outer membrane are held open in
the dark by the phosphorylation of
membrane proteins by cGMP.
• Once a photon is absorbed, the
chromophore 11-cis-retinal to isomerized
to all-trans-retinal.
• This process, known as photoactivation,
initiates a biochemical cascade of events
eventually resulting in the closing of
channels in the cell membrane that
normally allow ions to flow into the rod
outer segment.
1. A G-protein is activated.
2. It then activates cyclic Guanosine
monophosphate phosphodiesterase (PDE).
3. PDE then hydrolyzes cGMP, reducing its
concentration.
4. This leads to the closing of Na+ channels in the
outer membrane, hyperpolarizing the receptor.
• When a single photon is absorbed, it is
estimated that 500 PDE molecules are
activated, and each PDE molecule can
inactivate many cGMP molecules.
– As such, there is an immense amplification
within the photoreceptor that provides great
sensitivity.
Isomerization
48. …..some of the intermediate steps in the
closing of Na+ channels during
photoactivation.
50. A log transform occurs at the
receptor level: the output of
receptors is proportional to the
logarithm of the input.
4
3
2
1
0
Output (Arbitrary Units)
1 10 100 1000 10000
Light Intensity
51. • A single photoisomerization
in the dark adapted state will
activate many PDE
molecules and will close
many Na+ channels.
• At higher background light
levels, there will be fewer
available PDE molecules, so
a greater number of
photoisomerizations will be
needed to close the same
number of Na+ channels.
• Since there are fewer open
Na+ channels at higher
background levels, it is also
true that activating a PDE
molecule is less likely to
have an impact since most
Na+ channels are already
closed.
52. Absorption Spectra
• The nature of the binding between the 11-
cis retinal and the different opsins
determines the probability with which
different wavelengths are absorbed.
53. Rhodopsin
S M L
The three cone types are named for where the peak of their sensitivity lies
on the spectrum. Thus, the cones that have a peak at about 440 nm are
known as short-wavelength cones (or S-Cones for short). The middle-wavelength
cones (M-Cones) peak at about 535 nm, and long-wavelength
cones (L-Cones) peak at about 565 nm. Do not be tempted to rename these
“blue,” “green,” and “red” cones, since color isn’t derived by examining a
single cone output (and the wavelengths do not generally match the color
names).
