Vision ECE6397, Lecture 1

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ECE 6304 Visual System Physiology,
Computation, and Methods
Prof. Valery Kalatsky Dept. of Electrical
Computer Engineering University of Houston
Lectures 5, 6 The Eye
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The Eye
The eye can be compared to a TV camera
attached to an automatically tracking
tripod a machine that is self-focusing,
adjusts automatically for light intensity,
has a self-cleaning lens, and feeds into a
computer with parallel-processing capabilities
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Iris
The colored part of the eye is called the iris. 
It controls light levels inside the eye similar
to the aperture on a camera (the f-stop).  The
round opening in the center of the iris is called
the pupil.  The iris is embedded with tiny
muscles that dilate (widen) and constrict
(narrow) the pupil size.
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Pupil
The pupil is the black, circular opening in the
center of the iris.  It opens and closes in
order to regulate the amount of light entering
the eyeball.  The pupil size is controlled by
the dilator and sphincter muscles of the iris.
Range of pupil diameters 1 8 mm
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Cornea
The cornea is the transparent, dome-shaped window
covering the front of the eye. It is a
powerful refracting surface, providing 2/3 of the
eye's focusing power. Index of refraction 1.376.
Optical power 43 diopters. There are no blood
vessels in the cornea, it is normally clear and
has a shiny surface.  The cornea is extremely
sensitive - there are more nerve endings in the
cornea than anywhere else in the body The adult
cornea is only about 1/2 millimeter thick and
has a diameter of about 12 mm
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Lens
The purpose of the lens is to focus light onto
the back of the eye.  Optical power 20 diopters
(relaxed). Whole eye 60. Change in power due to
accommodation 8. Index of refraction 1.39 1.41
(high in center, low at edges) The lens is about
5 mm wide and has a diameter of about 9 mm for
an adult human The lens is encased in a
capsular-like bag and suspended within the eye
by tiny ligaments called zonules. 
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Ciliary Body
The ciliary body lies just behind the iris.  The
lens is suspended inside the eye by the zonular
fibers.     Functions Production of aqueous
humor, the clear fluid that fills the front of
the eye.  Control of accommodation by changing
the shape of the crystalline lens.  When the
ciliary body contracts, the zonules relax. 
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Accommodation
When the ciliary body contracts, the zonules
relax.  This allows the lens to thicken,
increasing the eye's ability to focus up
close.  When looking at a distant object, the
ciliary body relaxes, causing the zonules to
contract.  The lens becomes thinner, adjusting
the eye's focus for distance vision.  
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Sclera Choroid
The sclera, commonly known as "the white of the
eye," is the tough, opaque tissue that serves as
the eye's protective outer coat.
The choroid lies between the retina and sclera. 
It is composed of layers of blood vessels that
nourish the back of the eye.
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Vitreous
The vitreous is a thick, transparent substance
that fills the center of the eye. It is
composed mainly of water and comprises about 2/3
of the eye's volume, giving it form and shape.
Index of refraction 1.33 The viscous properties
of the vitreous allow the eye to return to its
normal shape if compressed.
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Retina
The retina is a very thin layer of tissue that
lines the inner part of the eye.  It is
responsible for capturing the light rays that
enter the eye.  Much like the film's role in
photography.  These light impulses are then
sent to the brain for processing, via the optic
nerve.
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Macula Fovea
The macula is located roughly in the center of
the retina, temporal to the optic nerve.  It is
a small and highly sensitive part of the retina
responsible for detailed central vision.  The
fovea is the very center of the macula. In
humans, the fovea takes up 2 of the retinal
area but accounts for 33 of all ganglion cells.
The macula allows us to appreciate detail and
perform tasks that require central vision such
reading.
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Optic Nerve
The optic nerve transmits electrical impulses
from the retina to the brain.   It connects to
the back of the eye near the macula.   The
visible portion of the optic nerve is called the
optic disc. The retina's sensory receptor cells
of retina are absent from the optic nerve. 
Because of this, everyone has a normal blind
spot.  This is not normally noticeable because
the vision of both eyes overlaps
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Conjunctiva
The conjunctiva is the thin, transparent tissue
that covers the outer surface of the eye.  It
begins at the outer edge of the cornea, covers
the visible part of the eye, and lines the
inside of the eyelids.  It is nourished by tiny
blood vessels that are nearly invisible to the
naked eye.
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Extraocular Muscles
The six tiny muscles that surround the eye and
control its movements are known as the
extraocular muscles.  The primary function of
the four rectus muscles is to control the eye's
movements from left to right and up and down. 
The two oblique muscles move the eye rotate
the eyes inward and outward. All six muscles
work in unison to move the eye.  As one
contracts, the opposing muscle relaxes, creating
smooth movements.  In addition to the muscles
of one eye working together in a coordinated
effort, the muscles of both eyes work in unison
so that the eyes are always aligned.
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Optics
A lens is a device for either concentrating or
diverging light, usually formed from a piece of
shaped glass
Lenses are classified by the curvature of these
two surfaces
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Converging Lens
If the lens is biconvex or plano-convex, a
collimated or parallel beam of light passing
along the lens axis and through the lens will be
converged (or focused) to a spot on the axis, at
a certain distance behind the lens (known as the
focal length). In this case, the lens is called
a positive or converging lens
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Diverging Lens
If the lens is biconcave or plano-concave, a
collimated beam of light passing through the
lens is diverged (spread) the lens is thus
called a negative or diverging lens. The beam
after passing through the lens appears to be
emanating from a particular point on the axis in
front of the lens. The distance from this point
to the lens is also known as the focal length,
although it is negative with respect to the focal
length of a converging lens.
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Focal Length
The focal length f is positive for converging
lenses, negative for diverging lenses, and
infinite for meniscus lenses. The value 1/f is
known as the power of the lens, and so meniscus
lenses are said to have zero power.
Lensmakers equation Lens power is measured
in dioptres, which have units of inverse meters
(m-1). Lenses are also reciprocal i.e. they
have the same focal length when light travels
from the front to the back as when light goes
from the back to the front (although other
properties of the lens, such as the aberration
are not necessarily the same in both directions).
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Imaging Properties
The thin lens formula
If an object is placed at a distance S1 along the
axis in front of a positive lens of focal length
f, a screen placed at a distance S2 behind the
lens will have an image of the object projected
onto it, as long as S1 gt f. Real Image
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Imaging Properties
If S1 lt f, S2 becomes negative, and the image is
apparently positioned on the same side of the
lens as the object. Although this kind of
image, known as a virtual image, cannot be
projected on a screen, an observer looking
through the lens will see the image in its
apparent calculated position. A magnifying
glass creates this kind of image.
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Imaging Properties
The formulas above may also be used for negative
(diverging) lens by using a negative focal
length (f), but for these lenses only virtual
images can be formed
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Magnification
M is the magnification factor if Mgt1, the
image is larger than the object. Notice the
sign convention here shows that, if M is
negative, as it is for real images, the image is
upside-down with respect to the object. For
virtual images, M is positive and the image is
upright. In the special case that S1 8, we have
S2 f and M -f / 8 0. This corresponds to a
collimated beam being focused to a single spot
at the focal point. The size of the image in
this case is not actually zero, since
diffraction effects place a lower limit on the
size of the image
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Multiple Lenses
Lenses may be combined to form more complex
optical systems. The simplest case is when
lenses are placed in contact if the lenses of
focal lengths f1 and f2 are "thin", the combined
focal length F of the lenses can be calculated
from
Since 1/f is the power of a lens, it can be seen
that the powers of thin lenses in contact are
additive
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Image Formation
Note detector is in medium nv 1.33 Lens
equation becomes
f1 - object focal length (front focal point) f2
- image focal length (back focal point)
Physical Distance from the lens to the
retina Effective
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Accommodation
Far point
Near point
Objective distance
Focal length
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Optical Power of the Eye
Lensmakers equation
For cornea R2 0 and f2 n f1
n 1.38, R1 8 mm f2 29 mm or 1/f2 34
diopters
For eye f2 22 mm or 1/f2 45 dopters
For lens 11 dopters
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Aberrations
Spherical aberration is caused because spherical
surfaces are not the ideal shape with which to
make a lens, but they are by far the simplest
shape to which glass can be ground and polished
and so are often used. Spherical aberration
causes beams parallel to but away from the lens
axis to be focused in a slightly different place
than beams close to the axis. This manifests
itself as a blurring of the image. Lenses in
which closer-to-ideal, non-spherical surfaces are
used are called aspheric lenses, which are
complex to make and often extremely expensive
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Chromatic Aberrations
Chromatic aberration is caused by the dispersion
of the lens material, the variation of its
refractive index n with the wavelength of light.
Since from the formulae above f is dependent on
n, if follows that different wavelengths of
light will be focused to different positions.
Chromatic aberration of a lens is seen as
fringes of color around the image.
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Chromatic Aberrations
It can be minimized by using an achromatic
doublet (or achromat) in which two materials
with differing dispersion are bonded together to
form a single lens. This reduces the amount of
chromatic aberration over a certain range of
wavelengths, though it does not produce perfect
correction
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Eye Capability
Resolution is diffraction limited for small pupil
sizes Limited by the aberrations of the optics
for large pupil sizes Optimal size is about 2-3
mm d 2mm, q 0.003 rad 0.017 deg 1 arc
min Corresponds to about 5 micron on retina
Dynamic range 10-14 to 10-6 W 8 order of
magnitude Sunlight 250 W/m2 Max power 10-3 W
for 1mm pupil Instantaneous range lower by 5
orders
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Eye related problems
Farsightedness. If the eyeball is too short or
the lens too flat or inflexible, the light rays
entering the eye particularly those from
nearby objects will not be brought to a focus
by the time they strike the retina. Eyeglasses
with convex lenses can correct the problem.
Farsightedness is called hypermetropia. Nearsigh
tedness. If the eyeball is too long or the lens
too spherical, the image of distant objects is
brought to a focus in front of the retina and is
out of focus again before the light strikes the
retina. Nearby objects can be seen more easily.
Eyeglasses with concave lenses correct this
problem by diverging the light rays before they
enter the eye. Nearsightedness is called myopia.
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Eye related problems
Cataracts One or both lenses often become cloudy
as one ages. When a cataract seriously
interferes with seeing, the cloudy lens is
easily removed and a plastic one substituted.
The entire process can be done in a few minutes
as an outpatient under local anesthesia With
age, everyone develops a condition known as
presbyopia.  This occurs as the ciliary body
muscle and lens gradually lose elasticity,
causing difficulty reading.
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