Human eye optics

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Human Eye Optics
SOLO HERMELIN
Updated: 16.01.10http://www.solohermelin.com

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Table of Content
SOLO Optics - Eye
Human Eye Introduction
Human Eye Structure
Retina
Rods and Cones
Facts and Figures concerning the human retina
Human Eye Optics
Introduction to Lenses and Geometrical Optics
Waves and Rays
Optical Aberration
Common Vision Defects and Their Correction
Aberrometers
Color Blindness
Microscope Optical Components- Introduction
Eyepieces (Oculars)
References
The Lens

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http://www.olympusmicro.com/primer/anatomy/introduction.html

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http://www.olympusmicro.com/primer/anatomy/numaperture.html

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The visual pathway: from the eyes to the brain’s visual cortex (adapted from Gray 1918)
Human Eye Structure

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Structure of the eye from Hecht, Optics
The human eye is able to detect from about 390 to
780 nanometers, defining the visual spectrum

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1=Iris The colored part of the eye located between the
Lens and Cornea. It regulates the entrance of the light.
2 = Cornea The transparent, blood-free tissue covering
the central front of the eye that initially refracts or bends
light rays as light enters the eye. Contact lenses are fitted
over the Cornea.
3 = Retina The innermost layer of the eye, a
neurological tissue, which receives light rays focused on
it by the Lens. This tissue contains receptor cells (Rods
and Cones) that send electrical impulses to the brain via
the optic nerve when the light rays are present.
4 = Rods The receptor cells which are sensitive to light
and are located in the Retina of the eye. They are
responsible for night vision, as non-color vision in low
level light.
5 = Cones The receptor cells which are sensitive to light
and are located in the Retina of the eye. They are
responsible for color vision.
6 = Lens The eye's natural Lens. Transparent, biconvex
intraocular tissue that helps bring rays of light to a focus
on the Retina.
7 = Pupil The opening at the center of the Iris of the eye.
It contracts in a high level of light and when the eye is
focused on a distant object.
Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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Human Eye Structure

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The vertebrate retina is a light sensitive tissue lining the inner surface of the eye. The optics of
the eye create an image of the visual world on the retina, which serves much the same
function as the film in a camera. Light striking the retina initiates a cascade of chemical and
electrical events that ultimately trigger nerve impulses. These are sent to various visual
centers of the brain through the fibers of the optic nerve.
In vertebrate embryonic development, the retina and
the optic nerve originate as outgrowths of the
developing brain, so the retina is considered part of
the central nervous system (CNS). It is the only part
of the CNS that can be imaged non-invasively in the
living organism.
Retina
The retina is a complex, layered structure with several layers of neurons interconnected by
synapses. The only neurons that are directly sensitive to light are the photoreceptor cells. These
are mainly of two types: the rods and cones. Rods function mainly in dim light and provide
black-and-white vision, while cones support daytime vision and the perception of colour. A
third, much rarer type of photoreceptor, the photosensitive ganglion cell, is important for
reflexive responses to bright daylight.
Neural signals from the rods and cones undergo complex processing by other neurons of
the retina. The output takes the form of action potentials in retinal ganglion cells whose
axons form the optic nerve. Several important features of visual perception can be traced
to the retinal encoding and processing of light.

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Retina
Anatomy of vertebrate retina
The vertebrate retina has ten distinct layers. From
innermost to outermost, they include:
1.Inner limiting membrane - Müller cell footplates
2.Nerve fiber layer
3.Ganglion cell layer - Layer that contains nuclei of
ganglion cells and gives rise to optic nerve fibers.
4.Inner plexiform layer
5.Inner nuclear layer contains bipolar cells
6.Outer plexiform layer - In the macular region, this
is known as the Fiber layer of Henle.
7.Outer nuclear layer
8.External limiting membrane - Layer that separates
the inner segment portions of the photoreceptors from
their cell nuclei.
9.Photoreceptor layer - Rods / Cones
10.Retinal pigment epithelium

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Retina
Retina's simplified axial organization. The
retina is a stack of several neuronal layers.
Light is concentrated from the eye and passes
across these layers (from left to right) to hit the
photoreceptors (right layer). This elicits
chemical transformation mediating a
propagation of signal to the bipolar and
horizontal cells (middle yellow layer). The signal
is then propagated to the amacrine and ganglion
cells. These neurons ultimately may produce
action potentials on their axons. This
spatiotemporal pattern of spikes determines the
raw input from the eyes to the brain. (Modified
from a drawing by Ramón y Cajal.)
In adult humans the entire retina is approximately
72% of a sphere about 22 mm in diameter. The
entire retina contains about 7 million cones and 75
to 150 million rods. An area of the retina is the optic
disc, sometimes known as "the blind spot" because
it lacks photoreceptors. It appears as an oval white
area of 3 mm². Temporal (in the direction of the
temples) to this disc is the macula. At its center is
the fovea, a pit that is most sensitive to light and is
responsible for our sharp central vision. Human
and non-human primates possess one fovea as
opposed to certain bird species such as hawks who
actually are bifoviate and dogs and cats who possess
no fovea but a central band known as the visual
streak. Around the fovea extends the central retina
for about 6 mm and then the peripheral retina. The
edge of the retina is defined by the ora serrata. The
length from one ora to the other (or macula), the
most sensitive area along the horizontal meridian is
about 3.2 mm.

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Retina
In section the retina is no more than 0.5 mm thick. It has three layers of nerve cells and two of
synapses, including the unique ribbon synapses. The optic nerve carries the ganglion cell axons to
the brain and the blood vessels that open into the retina. The ganglion cells lie innermost in the
retina while the photoreceptive cells lie outermost. Because of this counter-intuitive arrangement,
light must first pass through and around the ganglion cells and through the thickness of the retina,
(including its capillary vessels,not shown) before reaching the rods and cones. However it does not
pass through the epithelium or the choroid (both of which are opaque).
The white blood cells in the capillaries in front of the photoreceptors can be perceived as tiny bright
moving dots when looking into blue light. This is known as the blue field entopic phenomenon (or
Scheerer's phenomenon).
Between the ganglion cell layer and the rods and cones there are two layers of neuropils where
synaptic contacts are made. The neuropil layers are the outer plexiform layer and the inner
plexiform layer. In the outer the rods and cones connect to the vertically running bipolar cells,
and the horizontally oriented horizontal cells connect to ganglion cells.
The central retina is cone-dominated and the peripheral retina is rod-dominated. In total there are
about seven million cones and a hundred million rods. At the centre of the macula is the foveal pit
where the cones are smallest and in a hexagonal mosaic, the most efficient and highest density.
Below the pit the other retina layers are displaced, before building up along the foveal slope until
the rim of the fovea or parafovea which is the thickest portion of the retina. The macula has a
yellow pigmentation from screening pigments and is known as the macula lutea. The area directly
surrounding the fovea has the highest density of rods converging on single bipolars. Since the
cones have a much lesser power of merging signals, the fovea allows for the sharpest vision the eye
can attain.

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Left cross-section of human eye, Right cells in the human retina
(adapted from Gray 1918)

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Rods and Cones

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1.Rods
The vast majority of the cells on the retina
Panchromatic -- sensitive to wide range of wavelengths.
But not energy/color-discriminating within this range: Receptors translate all light to
same "signal" = amount of light.
Thus, delivers "shades of gray", like a high speed, black and white film.
The specific chemical that makes rods active is rhodopsin, a complex protein with a
40,000 amu atomic weight, which makes up as much as 35% of the cell dry weight.
Absorption curve of rhodopsin shown roughly by the curve
Absorption of the photon splits off a small, 264 amu
fragment (a chromophore) called retinaldehyde (a
derivative of Vitamin A), and instantaneously one of the
double bonds changes from a cis to a trans type bond.
Remainder of protein is called opsin.

SOLO Optics - Eye
1.Rods (continue – 1)
In a process not well understood, splitting of protein changes permeability of the neuron's
membrane to sodium ions, which changes the electrical potential of the cell.
Change in potential propagates through nerve cells to transmit message to brain.
Between 1 to 10 photons must be absorbed to "trigger" particular rod (similar to
photographic grains in film).
However, rods are bundled to a single nerve fiber, so act together.
Slowly (over 30 min timescale), the full rhodopsin molecule is regenerated.
Rods concentrated to outer part of retina.
Completely missing in the 0.3 mm diameter fovea centralis, in
center of yellow patch called the macula.
Note the image of the full moon on retina is only
0.2mm.
Night blindness occurs when there is damage to the
outer part of the retina.
Normal vision (left and right) and night blindness (middle),
from http://www.retina-international.org/nightbld.htm.

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2.Cones
About 5% of the retinal cells.
Probably work same way as rods, but contain slightly different iodopsin protein with the
retinaldehyde group.
As a group, provide sensitivity to colors.
Translate color sensation to brain.
From three different kinds we achieve color sensitivity.

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Rod / Cone Sensitivity

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The RED sensitivity for the R-cones
or the L-cones
Range from 410 to 690 nanometer
Peak 580 nm
Peak range from 558 to 580 nm
The GREEN sensitivity for the G-cones
or the M-cones
Range from 440 to 670 nm
Peak 540 nm
The BLUE sensitivity for the B-cones
or the S-cones
Range from 400 to 540 nanometer
Peak 440 nm
Three Types of Cones:
L, M, S

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Facts and Figures concerning the human retina
1.Size of the retina
32mm from ora to ora along the horizontal meridian (Van
Buren, 1963; Kolb, unpublished measurements). Area of the
human retina is 1094 square mm (Bernstein, personal
communication) calculated from the expectations that the
average dimension of the human eye is 22 mm from anterior to
posterior poles, and that 72% of the inside of the globe is retina
(Michels et al., 1990).
2.Size of optic nerve head or disc.
1.86x 1.75 mm
3.Degrees and distance in micometers.
One degree of visual angle is equal to 288 µm on the retina without correction for shrinkage
(Drasdo and Fowler (1974).
4.Foveal position.
11.8o
or or 3.4 mm temporal to the optic disk edge
5.Cross diameter of the macula.
3mm of intense pigmentation, surrounded by 1 mm wide zone of less pigmentation
(Polyak, 1941).

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Facts and Figures concerning the human retina (continue - 1)
6.Cross diameter of the central fovea from foveal rim to foveal rim.
1.5mm (Polyak, 1941)
1.2-1.5mm (Ahnelt and Kolb, unpublished data)
7.Cross diameter of central rod free area.
400-600µm (Polyak, 1941)
750µm (Hendrickson and Youdelis, 1984)
570µm (Yamada, 1969)
250µm (Ahnelt et al., 1987)
8.Vertical thickness of the fovea from ILM to ELM.
In the foveal pit 150 µm (Yamada, 1969)
foveal rim 300 µm
9.Length of foveal axons (Henle fibers).
150-300µm (Ahnelt and Pflug, 1986).

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10.Vertical thickness of the retina in different areas.
The vertical extent of the retina across the horizontal meridian at
different eccentricities is shown in Figure 3. This is taken from data
given by Sigelman and Ozanics (1982). The small black numbers
are the originals from Sigelman and Ozanics which were measured
in typical histological preparations where there is a great deal of
shrinkage. The figures in red are those recently measured by Ahnelt
(personal communication) in well fixed EM quality material where
there is little or no shrinkage. Hence the latter numbers are larger.
The numbers are in mm.

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11.Age when fovea is fully developed.
Not before 4 years of age (Hendrickson and Youdelis, 1984).
12.Highest density of cones at center of the fovea
(counted in a 50 x 50 µm square).
147,000/mm2
(Osterberg, 1935)
178,000-238,000/mm2
(Ahnelt et al., 1987)
96,900-281,000/mm2
mean161,900/mm2
(Curcio et al., 1987).
13.Total number of cones in fovea.
Approximately 200,000. There are 17,500 cones/degree2
.
Rod free area is approximately 1o
thus there are 17,500
cones in the central rod-free fovea.
14.Total number of cones in the retina.
6,400,000(Osterberg, 1935).
15.Total number of rods in the retina.
110,000,000to 125,000,000 (Osterberg, 1935).

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16.Rod distribution
Rods peak in density 18o
or 5mm out from the center of the
fovea in a ring around the fovea at 160,000 rods/mm2
. (Fig. 5)
No rods in central 200 µm.
Average 80-100,000 rods/mm2
Rod acuity peak is at 5.2o
or 1.5 mm from foveal center
where there are 100,000 rods/mm2
(Mariani et al.,1984).
17.Number of axons in the optic nerve.
564776-1,140,030(Bruesch and Arey, 1942)
800,000-1,000,000(Polyak, 1941)
1,200,000(Quigley et al., 1982; Balaszi et al., 1984).
18.Number of cones to ganglion cells in the fovea.
1cone to 2 ganglion cells out to about 2.2o
(Schein, 1988).
19.Number of cones/retinal pigment epithelial cell (RPE).
30cones/RPE in fovea (Rapaport et al., 1995).

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20.Number of rods/retinal epithelial cell (RPE).
In periphery 22 rods/RPE cell
In rod peak (4-5 mm from foveal center) 28 rods/RPE cell
(Rapaport et al.,1995).

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21.Number of neural and glial types in the retina.
The retina consists of many millions of cell types packed together in a
tightly knit network spread over the surface of the back of the eye fundus
as a thin film of tissue only 1/2 millimeter thick. The retina is like a
three layered cake with three layers containing cell bodies of neurons
and two filling layers where synapses betwen the neurons occur. There
are two basic kinds of photoreceptors, rods and cones. The cones are
further subdivided into two types (long and short wavelength sensitive)
in the majority of mammals, i.e. most mamals are dichromats and have
divariant color vision. In primates a third wavelength sensitive cone has
developed closely related to the long wavelength cone type but a little
more sensitive in the middle wavelength (i.e. green cone). Thus primates
including man are trichromats and have trivariant color vision. Many
reptiles, birds and fish have 4 or even 5 types of cone each sensitive to a
slightly different peak wavelength.
The second order neurons postsynaptic to the photorecepors in the first synaptic
(filling layer) (outer plexiform layer) are bipolar cells and horizontal cells. There
are 9 types of bipolar cell and 2 to 4 types of horizontal cell in species from
mammals to fish. The third order neurons are amacrine cells and ganglion cells
that synapse in the inner synaptic filling layer (inner plexiform layer). There are
two types of interplexiform cell stretching between both plexiform layers, in most
vertebrate retinas.There are approximately 22 types of amacrine cell and 20 types
of ganglion cell in the typical mammalian retina. There may be 30 or more
amacrine cell types in fish and reptilian retinas and 22 or so ganglion cell types.
The increased number of third order neurons is due to the greater information
processing taking place in the non mammalian retinas that in mammalian.

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22.Useful Units in Vision Science (Wandell, 1995).
Radiometric units represent a physical measurement e.g., radiance is measured in watts sr -1 m-2.
Calorimetric units adjust radiometric units for visual wavelength sensitivity e.g., luminance
is measured in candela per square meter, cd/m2.
Lux are units of illumination. Thus a light intensity of 1 candela produces an illumination of
1 lux at 1 meter.
Scotopic luminance units are proportional to the number of photons absorbed by rod
photoreceptors to give a criterion psychophysical result.
Photopic luminance units are proportional to a weighted sum of the photons absorbed by L- and
M-cones to give a criterion psychophysical result.
Typical ambient luminance levels (cd/m2):.
Starlight: 0.001
Moonlight: 0.1
Indoor lighting: 100
Sunlight: 10.000
Maximum intensity of common CRT monitors: 100
One Troland (Td) of retinal illumination is produced when an eye with a pupil size of 1 mm2
looks at a surface whose luminance is 1 cd/m2.
Lens focal length: f(meters); lens power= 1/f (diopters).

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23.Image formation (Wandell, 1995).
The eyes are 6 cm apart and halfway down the head.
Visual angle of common objects (degrees, deg)
The sun or moon = 0.5 deg
Thumbnail (at arm's length) = 1.5 deg
Fist (at arm's length) = 8-10 deg
Visual field (measured from central fixation)
Monocular: 160 deg (w) x 175 deg (h)
Binocular: 200 deg (w) x 135 deg (h)
Region of binocular overlap: 120 deg (w) x 135 deg (h)
Range of pupil diameters: 1-8 mm.
Refractive indices
Air: 1.000
Glass: 1.520
Water: 1.333
Cornea: 1.376

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23.Image formation (Wandell, 1995) (continue – 1).
Optical power (diopters).
Cornea: 43
Lens (relaxed): 20
Whole eye: 60
Change in power due to accomodation: 8
Axial chromatic aberration over the visible spectrum: 2 diopters.
Visible spectrum: 370-730 nanometers (nm)
Peak wavelength sensitivity:
Scotopic: 507 nm
Photopic: 555 nm
Spectral equilibrium hues:
Blue: 475 nm
Green: 500 nm
Yellow: 575 nm
No spectral equilibrium: red

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http://www.olympusmicro.com/primer/lightandcolor/lensesintro.html
Introduction to Lenses and Geometrical Optics

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http://www.olympusmicro.com/primer/anatomy/magnification.html
Magnification

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Image Formation on the Retina

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converging beam
=
spherical wavefront
parallel beam
=
plane wavefront
Image Plane
Ideal Optics
ideal wavefront
parallel beam
=
plane wavefront
Image Plane
Non-ideal Optics
defocused wavefront
ideal wavefrontparallel beam
=
plane wavefront
Image Plane
Non-ideal Optics
aberrated beam
=
iregular wavefront
diverging beam
=
spherical wavefront
aberrated beam
=
irregular wavefront
Image Plane
Non-ideal Optics
ideal wavefront
Optical Aberration

SOLO
converging beam
=
spherical wavefront
parallel beam
=
plane wavefront
Image Plane
Ideal Optics
P'
Optical Aberration
converging beam
=
spherical wavefront
Image Plane
Ideal Optics
diverging beam
=
spherical wavefront
P
P'
An Ideal Optical System can be defined by one of the three different and equivalent ways:
All the rays emerging from a point source P, situated at a finite or infinite distance
from the Optical System, will intersect at a common point P’, on the Image Plane.
3
All the rays emerging from a point source P will travel the same Optical Path to reach
the image point P’.
2
The wavefront of light, focused by the Optical System on the Image Plane, has a
perfectly spherical shape, with the center at the Image point P.
1
Ideal Optical System

SOLO
ideal wavefrontparallel beam
=
plane wavefront
Image Plane
Non-ideal Optics
aberrated beam
=
iregular wavefront
diverging beam
=
spherical wavefront
aberrated beam
=
irregular wavefront
Image Plane
Non-ideal Optics
ideal wavefront
Optical Aberration
Real Optical System
An Aberrated Optical System can be defined by one of the three different and equivalent
ways:
The rays emerging from a point source P, situated at a finite or infinite distance
from the Optical System, do not intersect at a common point P’, on the Image Plane.
3
The rays emerging from a point source P will not travel the same Optical Path to reach
the Image Plane
2
The wavefront of light, focused by the Optical System on the Image Plane, is not
spherical.
1

Optical Aberration W (x,y) is the path deviation between the distorted and reference
Wavefront.
SOLO Optical Aberration

Display of Optical Aberration W (x,y)
Rays Deviation3
Optical Path Length Difference2
wavefront shape W (x,y)1
Red circle denotes the pupile margin.
Arrows shows how each ray is deviated
as it emerges from the pupil plane.
Each of the vectors indicates the the
local slope of W (x,y).
The aberration W (x,y) is
represented in x,y plane by
color contours.
x
y
( )yxW ,
Wavefront
Error
x
y
( )yxW ,
Optical
Distance
Errors
x
y
Ray
Errors
The Wavefront error agrees with
Optical Path Length Difference,
But has opposite sign because a
long (short) optical path causes
phase retardation (advancement).
Aberration Type:
Negative vertical
coma
Reference

Display of Optical Aberration W (x,y)
Advanced phase <= Short optical
path
Retarded phase <= Long optical
path
Reference
Ectasia
x
y
Ray Errors
y
( )yxW ,
x
Optical Distance Errors
x
y
( )yxW ,
Wavefront Error

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Real Imaging Systems
Departures from the idealized conditions of Gaussian Optics in a real Optical System are
called Aberrations
Monochromatic Aberrations
Chromatic Aberrations
• Monochromatic Aberrations
Departures from the first order theory are embodied
in the five primary aberrations
1. Spherical Aberrations
2. Coma
3. Astigmatism
4. Field Curvature
5. Distortion
This classification was done in 1857
by Philipp Ludwig von Seidel (1821 – 1896)
• Chromatic Aberrations
1. Axial Chromatic Aberration
2. Lateral Chromatic Aberration
Optical Aberration

SOLO
Real Imaging Systems
Seidel Aberrations Distortions of the Wavefront
( ) θθθθ cos''cos'cos'';, 32222234
rhCrhCrhCrhCrChrW DiFCAsCoSp ++++=
Optical Aberration

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Common Optical Defects in Lens Systems (Aberrations)

SOLO Optics
Zernike’s Polynomials
In 1934 Frits Zernike introduces a complete set of orthonormal polynomials
to describe aberration of any complexity.
( ) ( ) ( ) ( )θρθρθρ
m
N
m
n
m
n
m
nN YRaZZ == ,,
,2,1
2
813
min =







 ++−
= N
N
Integern
( ) ( ) { }



−
=




 −++
−=
oddN
evenN
msign
Nnn
Integernm
1
1
4
212
min2
Each polynomial of the Zernike set is a product of
three terms.
where
( )



≠+
=+
=
012
01
mifn
mifn
a
m
n
( ) ( ) ( )
( )[ ] ( )[ ]
( )
sn
mn
s
s
m
n
smnsmns
sn
R 2
2/
0 !2/!2/!
!1 −
−
=
∑ −−−+
−−
= ρρ
( )





≠
≠
=
=
oddisNandmif
evenisNandmif
mif
Y
m
N
0sin
0cos
01
θ
θθ
radial index
meridional
index

SOLO Optics
Properties of Zernike’s Polynomials.
( ) ( )∑∑=
n m
m
n
m
n ZCW θρθρ ,,
W (ρ,θ) – Waveform Aberration
Cn
m
(ρ,θ) – Aberration coefficient (weight)
Zn
m
(ρ,θ) – Zernike basis function (mode)
( ){ } ( ) mallnallforZZMean
m
n
m
n 00,, >== θρθρ1
( ){ } mnallforZVariance
m
n ,1, =θρ2
3 Zernike’s Polynomials are mutually orthogonal, meaning that they are independent
of each other mathematically. The practical advantage of the orthogonality is that
we can determine the amount of defocus, or astimagtism, or any other Zernike mode
occurring in an aberration function without having to worry about the presence of
the other modes.
4 The aberration coefficients of a Zernike expansion are analogous to the Fourier
coefficients of a Fourier expansion.
( ){ } ( ) ( )[ ] ( )∑∑∑∑ =














−=
n m
m
n
n m
m
n
m
n
m
n CZZCMeanWVariance
2
2
,,, θρθρθρ
( ) ( )
( ) '
1
0
'
12
1
nn
m
n
m
n
n
dRR δρρρρ
+
=∫ ( ) '0
2
0
1'coscos mmmdmm δδπθθθ
π
+=∫

SOLO Optics
In 1934 Frits Zernike introduces a complete set of orthonormal polynomials
to describe aberration of any complexity.
Astigmatism
{ }4,4,,2 22
−− ayax
Coma1
{ }3,5,,2 2
−+ axaxρ
Coma2
{ }4,4,,2 2
−+ ayaxρ
Spherical&
Defocus
( ) { }3,5,,3.12 22
−+ aaρρ
36Zernikes
Geounyoung Yoon, “Aberration Theory”

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Astimagtism

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“Aberation Theory”
Geunyoung Yoon Ph.D.

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SOLO Optics - Eye FIGURE 127: Top left, optical power (in diopters)
of the two main elements of the human eye, cornea
and crystalline lens (number in brackets is
corresponding f.l. if imaging in air; for the eye as a
whole, assuming a single imaging element with
22.2mm f.l. effective in the aqueous medium).
Top right, a graph showing approximate size of the
aberrated blur relative to the diffraction blur (Airy
disc diameter). Absolute blur size is at the minimum
for ~2mm pupil diameter. For larger pupils, blur is
enlarged due to eye aberrations, and for smaller
pupils due to diffraction. At large pupil openings,
dominant aberration component is roughness, as
can be seen from the right-most diffraction pattern.
It shows what an actual pattern at 5mm pupil may
look like, not one appropriate to the ray spot.
Change in the nominal size of the blur is much less
pronounced than the change relative to the Airy
disc.
Ray spots show axial blur for F, e and C spectral
lines at 1mm, 2mm and 5mm pupil diameter
(SPEC'S) of the eye model used). Longitudinal
chromatism is nearly constant at about 0.3mm of
axial defocus between F and C; relative to the Airy
disc (black circle), transverse chromatism changes
with the square of the pupil diameter. Hence, it is at
the level of a 4" f/12 achromat for about 3mm pupil
diameter. Both, diffraction and aberrated blurs are
relatively large with respect to the cones (~2μ-10μ)
and rods (~2.5μ-5μ), so it is diffraction and
aberrations that determine retinal image quality.
http://www.telescope-optics.net/eye_aberrations.htm
Eye Aberration

Common Vision Defects
SOLO Optics - Eye

SOLO Optics - Eye
Correction of Common Vision DefectsCommon Vision Defects
Hyperopia (Farsightedness) Myopia (Nearsightedness( Astigmatism

SOLO OPTICS
Aberrometers
A number of technical and practical parameters that may be useful in choosing an
aberrometer for daily clinical practice.
The main focus is on wavefront measurements, rather than on their possible
application in refractive surgery. The aberrometers under study are the following:
1.Visual Function Analyzer (VFA; Tracey): based on
ray tracing; can be used with the EyeSys Vista corneal topographer.
2.OPD-scan (ARK 10000; Nidek): based on automatic retinoscopy; provides
integrated corneal topography and wavefront measurement in 1 device.
3.Zywave (Bausch & Lomb): a Hartmann-Shack system that can be combined
with the Orbscan corneal topography system.
4.WASCA (Carl Zeiss Meditec): a high-resolution Hartmann-Shack system.
5.MultiSpot 250-AD Hartmann-Shack sensor: a custom-made Hartmann-Shack
system, engineered by the Laboratory of Adaptive Optics at Moscow State
University, that includes an adaptive mirror to compensate for accommodation
6.Allegretto Wave Analyzer (WaveLight): an objective Tscherning device

SOLO OPTICS
Aberrometers
Figure 1. The principles of the wavefront
sensors:
Top: Skew ray.
Center Left: Ray tracing.
Center Right: Hartmann-Shack.
Bottom Left: Automatic retinoscope.
Bottom Right: Tscherning.
Single-head arrows indicate direction
of movement for beams.
Figure 2. Reproductions of the fixation targets for the
patient: A: VFA.B: OPD-scan. C: Zywave. D: WASCA.
E: MultiSpot. F: Allegretto.

SOLO
OPTICSAberrometers
Johannes Hartmann
1865-1936
In 1920, an astrophysicist named Johannes Hartmann devised
a method of measuring the ray aberration of mirrors and lenses.
He wanted to isolate rays of light so that they could be traced and any
imperfection in the mirror could be seen. The Harman Test consist on
using metal disk in which regulary spaced holes had been drilled.
The disk or screen was then placed over the mirror that was to be tested
and a photographic plate was placed near the focus of the mirror. When
exposed to light, a perfect mirror will produce an image of regulary
spaced dots. If the mirror does not produce regularly spaced dots, the
irregularities, or aberrations, of the mirror can be determined.
Figure 1. Optical schematic for an early
Hartmann test.
Schematic from Santa Barbara Instruments Group (SBIG)
software for analysis of Hartmann tests.
1920

SOLO OPTICS
Optical schematic for first Shack-Hartmann sensor.
Around 1971 , Dr. Roland Shack and Dr. Ben Platt advanced the concept replacing
the screen with a sensor based on an array of tiny lenselets. Today, this sensor is known
as the Hartmann - Shack sensor. Hartmann – Shack sensors are used in a variety of
industries: military, astronomy, ophthalmogy.
Schematic showing Shack-Hartmann CCD output.
Schematic of Shack-Hartmann data analysis process.
Hartmann - Shack Aberrometer
Roland Shack
1971

SOLO OPTICS
Lenslet array made by Heptagon
for ESO. The array has 40 x 40
lenslets, each 500 μm (0.5 mm) in
size.
Part of lenslet array made by WaveFront Sciences.
Each lens is 144 μm in diameter.

SOLO OPTICS
Recent image from Adaptive
Optics Associates (AOA) shows
the optical set-up used to test
the first Shack-Hartmann
sensor.
Upper left) Array of images
formed by the lens array from a
single wavefront.
Upper right) Graphical
representation of the wavefront
tilt vectors.
Lower left) Zernike polynomial
terms fit to the measured data.
Lower right) 3-D plot of the
measured wavefront.

Color TheorySOLO
Color Blindness
Normal Color Vision Red-Blind/Protanopia Green-Blind/Deuteranopia
Blue-Blind/Tritanopia
Blue-Weak/Tritanomaly
Red-Weak/Protanomaly Green-Weak/Deuteranomaly
Monochromacy/Achromatopsia Blue Cone Monochromacy

SOLO Color Theory 1917
Shinobu Ishihara
(1879--1963)
Shinobu Ishihara created the Ishihara Color Test to detect
Color Blindness.
The Ishihara Color Blindness test – named after a
Japanese Professor at the University of Tokyo – is the most
well known tool to test for red-green color blindness. Mr
Ishihara developed this test almost 100 years ago. It was
first published in 1917 and is used since then to check if
someone is suffering from protanopia or deuteranopia, the
two different kinds of red-green color vision deficiencies.
A collection of 38 plates filled with colored dots build the
base of this test. The dots are colored in different shades of
a color and a number or a line is hidden inside with
different shades of an other color. But enough theory, take
the color blindness test by Mr Ishihara yourself and be
surprised (or not) of the result.
A plate from the Ishihara Test for color
blindness. Can you see the number 74? However,
whether you see the number or not, don’t take
this as a final indication: it is only one plate of
many plates in the full test and the colors on
your computer screen might not be exactly right.
A plate from the Ishihara Test for color blindness. Can
you see the number 12?

Color TheorySOLO
Color Blindness

Color TheorySOLO
Color Blindness
Types of colour vision
deficiency
Males Females
Overall ~ 8 % ~ 5%
Anomalous trichromasy
protanomaly 1%< / FONT> 0.01%
deutanomaly 5% 0.4%
tritanomaly rare rare
Dichromasy
protanopia 1% 0.01%
deuteranopia 1.5% 0.01%
tritanopia 0.008% 0.008%
Monochromasy
rod monochromasy rare rare
cone monochromasy rare rare
atypical monochromasy very rare very rare
Prevalence of congenital colour deficiencies

94
SOLO OPTICS
http://www.olympusmicro.com/primer/anatomy/components.html
Microscope Optical Components
- Introduction

95
SOLO OPTICS
Microscope Optical Components - Introduction

96
SOLO OPTICS
http://www.olympusmicro.com/primer/anatomy/bx51cutaway.html

97
SOLO OPTICS
http://www.olympusmicro.com/primer/anatomy/bh2cutaway.html

98
SOLO OPTICS
http://www.brayebrookobservatory.org/BrayObsWebSite/HOMEPAGE/PageMill_Resources/PUBLICATIONS/treediag.jpg

99
SOLO OPTICS
http://www.brayebrookobservatory
.org/BrayObsWebSite/BOOKS/EV
OLUTIONofEYEPIECES.pdf

SOLO OPTICS
Eyepieces (Oculars)

102
SOLO OPTICS
Numerical Aperture (NA) = n (sinμ)

103
SOLO
References
OPTICS
1. Waldman, G., Wootton, J., “Electro-Optical Systems Performance Modeling”,
Artech House, Boston, London, 1993
2. Wolfe, W.L., Zissis, G.J., “The Infrared Handbook”, IRIA Center,
Environmental Research Institute of Michigan, Office of Naval Research, 1978
3. “The Infrared & Electro-Optical Systems Handbook”, Vol. 1-7
4. Spiro, I.J., Schlessinger, M., “The Infrared Technology Fundamentals”,
Marcel Dekker, Inc., 1989
http://www.cs.bgu.ac.il/~icbv07/LectureNotes/ICBV-Lecture-Notes-12-Sensing-2
-The-Human-Eye-1SPP.pdf
Austin Roorda, PhD, “Optics Waveform”, University of Houston, College of Optometry

104
SOLO
References
Foundation of Geometrical Optics
[3] E.Hecht, A. Zajac, “Optics ”, 3th
Ed., Addison Wesley Publishing Company, 1997,
[4] M.V. Klein, T.E. Furtak, “Optics ”, 2nd
Ed., John Wiley & Sons, 1986

105
SOLO
References
[1] M. Born, E. Wolf, “Principle of Optics – Electromagnetic Theory of Propagation,
Interference and Diffraction of Light”, 6th
Ed., Pergamon Press, 1980,
[2] C.C. Davis, “Laser and Electro-Optics”, Cambridge University Press, 1996,
OPTICS

January 5, 2015 106
SOLO
Technion
Israeli Institute of Technology
1964 – 1968 BSc EE
1968 – 1971 MSc EE
Israeli Air Force
1970 – 1974
RAFAEL
Israeli Armament Development Authority
1974 – 2013
Stanford University
1983 – 1986 PhD AA

Human eye optics

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