Download - Schematic eye(2)
Schematic eyeNAZIRSALAH.K
Bsc . OPTOMETRYAL-RAYHAN COLLAGE OF OPTOMETRY
KONDOTTY
a, anterior surface of cornea
b, posterior surface of cornea
c, anterior cortex
d, anterior core
e, posterior cortex
f, posterior core
V, anterior pole of the eye
g, posterior poles of the eye
line jh, visual axis
Optical system of the eye
Perfectly aligned optical system Paraxial rays
◦ Rays close to axis◦ Small angle of incidence
No spherical aberration◦ Pupil size 2mm
Approximations
Perfectly centered optical system
Paraxial ray approximation
Spherical aberration
cornea + tear layer - separates air from aqueous humor
Lens - separates aqueous from vitreous humor Rays refracted first (most) at the first surface of the
cornea - large difference in index of refraction at the air-to-cornea interface
Second surface of the cornea has negative power Cornea - over 70% of 64 diopters (D) of refractive
power of the unaccommodated eye lens supplies the remaining refractive power Accommodation - additional power is supplied by the
lens, which assumes a rounder form
Optics of eye
Europe until the Renaissance psychic spirit moved through a hollow optic nerve to the
retina and crystalline lens into the anterior chamber
projected out of the eyes as an emanation of rays that made objects in space visible
lens was the main receptor that created the visual sensation that traveled back as a visual spirit through the optic nerve to the brain
History
Alhazen (965–1039) – book of optics light emanated from luminous sources such
as the sun and was reflected from the object to the eye
an image was formed in the eye unsure of its precise nature because of
inadequate appreciation for the refractive properties of the ocular media
History
Eye worked like pin hole camera
Renaissance
Kepler (1571-1630) - role of the crystalline lens in the image-forming process
Points in space were imaged on the retina to form an inverted, real image caused by refraction by the cornea and lens
Proof by Scheiner (1573-1650) - removed part of the sclera and choroid from enucleated sheep eyes to reveal the back of the retina
Pointing the eye toward a bright object, he observed a small inverted image on the retina
1600s
Scheiner - cornea of the eye is convex mirror whose reflex image could provide a measure of the curvature of the cornea
a series of small glass marbles of various sizes from about 10 to 20 millimeters in diameter
Patient was seated opposite a bright window where the image of the crossbars could be observed
one marble and then another was inserted in the corner of the eye until at length one was found which gave a reflex image as nearly the same size as possible as that seen in the cornea
Inferred that the radius of curvature of the anterior surface of the cornea was at least nearly the same as that of the marble
Early attempts to understand optics
Invented ophthalmoscope refined ophthalmometer No accurate data on the crystalline lens Ophthalmophacometer by Tscherning -
separate Purkinje images of all refracting surfaces could be formed
depth of the anterior chamber and the curvatures of the anterior and posterior crystalline lens surfaces and the lens thickness calculated trigonometrically
Further …Helmholtz
refined the Helmholtz schematic eye invented the photokeratoscope to photograph
the corneally reflected image of a target consisting of concentric circles
Measurements of the spacing of circles in the image reveal whether the cornea is spherical, aspheric, or astigmatic
If the images are elliptic, the cornea is astigmatic, that is, toroidal
peripheral portions of the cornea could be investigated and its entire contour mapped
Gullstrand
six spherical refracting surfaces, two for the cornea and four for the crystalline lens
lens is seen as a central double convex core surrounded by a cortex that has a lower index of refraction
optical model of the eye
a, anterior surface of cornea
b, posterior surface of cornea
c, anterior cortex
d, anterior core
e, posterior cortex
f, posterior core
V, anterior pole of the eye
g, posterior poles of the eye
line jh, visual axis
Optical system of the eye
Light is assumed to travel from left to right Positive distances are measured from left to
right negative distances are measured from right
to left Object distances are measured from the
optical element to the object point Image distances are measured from the
optical element to the image point
TERMINOLOGY AND SIGN CONVENTION
the object distance from the lens to the object point is negative, that is, it is measured from right to left, and the image distance is positive.
Sign convention
Light diverging from the object point - negative vergence
spherical wavefronts grow larger as their radial distances from the source increase
curvature is the reciprocal of the radius of curvature
farther the wavefront is from the object, the smaller its curvature will be
Wavefront vergence in diopters equals the reciprocal of the radial distance in meters
VERGENCE
Vergence = 1/Distance in meters Light that is converging toward an image
has positive vergence Wavefronts become increasingly curved as
they approach the image point, and the vergence increases correspondingly
At distance of 4 meters, the vergence is ¼ = + 0.25 D 2 meters, the vergence is ½ = + 0.5 D
VERGENCE
paraxial characteristics of a complex optical system can be determined readily by reducing the system to six cardinal points◦ 2 focal points◦ 2 principal points◦ 2 nodal points
Cardinal points
When light from an infinitely distant source found to the left of an optical element strikes the element, the collimated paraxial rays will be converged to F‘◦ real image point for positive elements ◦ virtual image point for negative elements
Light originating from the first focal point F will be collimated by the optical element, forming an image at infinity
FOCAL POINTS
Positions of the first and second focal points formed by a positive thin lens in air and positive single refracting surface.
Positions of the first and second focal points formed by a negative thin lens in air and a negative single refracting surface.
plane defining the position of a thin lens that theoretically could replace the lens system
Principal points
pair of axial points in calculating image sizes An incident ray directed toward the first
nodal point will appear to emerge from the second nodal point with unchanged direction
points of unit angular magnification slope of the ray directed toward the first
nodal point is the same as the slope of the ray that appears to emerge from the second nodal point
Nodal points
principal and nodal points all coincide at the vertex of the lens
simple thin lens in a uniform medium
first and second nodal points coincide with the first and second principal points
object and image in a medium
Image in different medium
complex series of refracting surfaces that forms an image in vitreous of an object in air
All six cardinal points Schematic eye
The eye
Optical constants - indices
Positions
Gullstrand equation
P = equivalent refracting powerP1= refracting power of the first elementP2= refracting power of the second elementD= reduced distance
GULLSTRAND SCHEMATIC EYE
Catoptric images Dioptric images
Purkinje images
1 = corneal reflex◦ Brightest◦ virtual
2 = weak reflex◦ Virtual
3 = virtual◦ Depends on accommodation
4 = real◦ Depends on accommodation
Purkinje images
Refractive indices Radii of curvature Position of refractive elements
Calculations
n0 (air) = 1.00 n1 (cornea) = 1.376 n2 (aqueous) = 1.336 n3 (lens cortex) = 1.386 n4 (lens nucleus) = 1.406 n5 (vitreous) = 1.336
Refractive indices
r1 (cornea anterior surface) = +7.70 mm r2 (cornea posterior surface) = +6.80 mm r3 (lens anterior surface) = +10.00 mm r4 (lens nucleus anterior surface) = +7.91
mm r5 (lens nucleus posterior surface) = -5.76
mm r6 (lens posterior surface) = -6.00 mm
Radii of curvature
d1 (cornea anterior surface) = 0 mm d2 (cornea posterior surface) = +0.50 mm d3 (lens anterior surface) = +3.60 mm d4 (lens nucleus anterior surface) = +4.15
mm d5 (lens nucleus posterior surface) = +6.57
mm d6 (lens posterior surface) = +7.20 mm
Positions of refractive elements
power of anterior surface of cornea
power of posterior surface of cornea
Equivalent power of cornea
Reduced cornea thickness
Final power of cornea
Focal length of the cornea
first principal plane
second principal plane
first nodal point
second nodal point
power of the anterior cortex lens
power of anterior nucleus lens
Reduced distance of anterior lens cortex
Final refractive power of anterior lens cortex
Focal length of anterior cortex lens
Position of the 1. principal plane of lens cortex
Position of the 2. principal plane of lens cortex
Position of nodal points anterior lens cortex
power of posterior lens nucleus
power of posterior lens cortex
Reduced distance of posterior lens cortex
Final power of posterior lens cortex
Focal lengths of posterior lens cortex
Position of 1. principal plane of posterior lens cortex
Position of 2. principal plane of posterior lens cortex
Position of nodal points of posterior lens cortex
Equivalent power of lens (cortex + nucleus)
Reduced distance of lens
Refracting power of complete system of the eye
= +58.64D
Reduced the latitude of the eye
Position of the 1. Principal plane of eye
+1.35 mm
Position of 2. Principal plane of eye
+1.60 mm
1. focal length of the eye
-17.05 mm
2. focal length of the eye
+22.78 mm
Position of nodal points of eye
+7.08 mm
+7.46 mm
Position of the retinal fovea
+22.78 mm
Theoretical optical specification of an idealized eye, retaining average dimensions, omitting complications
Assumption - Refracting surfaces co-axial Real – lens is decentered and tilted P = +58.64D F1 = -17. 05 mm f2 = +22.78 mm H = +1.35 mm H’ = +1.60 mm N = +7.08 mm N’ = +7.46 mm
Schematic eye
HJ – Pupil E0 – pupil centre
Entrance and Exit pupils
Object – pupil Image formed by cornea Centre E
Entrance pupil
Object – Pupil Image formed by lens Centre – E’
Exit pupil
An incident pencil of rays directed towards and filling the entrance pupil would pass through the entire area of the real pupil, after refraction by the cornea, and on finally emerging into the vitreous body, limited by the exit pupil
A ray directed towards E passes through E’ after refraction
E and E’ are conjugate If a ray directed towards E makes an angle
u with the optic axis, the conjugate refracted ray will make an angle u’ where u’/u=0.82
Entrance and exit pupils
Entrance pupil ◦ 3 mm behind ant surface of cornea◦ 13% larger than real pupil
Exit pupil◦ Close behind real pupil◦ 4% larger
Entrance and exit pupils
The differences between the prediction of the paraxial ray method and the actual image are called aberrations.◦ Spherical aberration◦ Coma◦ Astigmatism◦ Chromatic aberration
Aberrations
optically homogeneous lens with spherical refracting surfaces would produce spherical aberration
Marginal rays have different focus
Spherical aberration
Positive spherical aberration - rays near the edge of the lens have an effective focal point that is closer to the lens than rays that strike the lens near the axis
Negative spherical aberration - rays near the edge of the lens have an effective focal point that is at a greater distance from the lens than rays that strike the lens near the axis
Positive and Negative
increases with the diameter of the lens minimized by limiting the opening of the
lens
In a lens
cornea is not spherical – steep at center, flat at periphery◦ Reduce spherical aberration
Lower index in the outer zones of the lens◦ Marginal rays refracted less
Constriction of the pupil ◦ Reduce spherical aberration
Countereffects in eye
During accommodation◦ curvatures of the lens become steeper◦ axial thickness increases◦ pupil constricts
Enable the eye to focus sharply near objects on the retina
Allows front surface of the lens to bulge in the center while keeping the periphery less curved
Control spherical aberration
Spherical aberration during accommodation
The differences between the prediction of the paraxial ray method and the actual image are called aberrations.◦ Spherical aberration◦ Coma◦ Astigmatism◦ Chromatic aberration
Aberrations
This aberration affects rays that come from an object that is not at the center of the lens.
magnification of a lens is different for marginal and paraxial rays
coma positive - the image of an object produced by off-axis rays is slightly larger than the image produced by paraxial rays
coma negative - the image produced by the off-axis rays is slightly smaller
Coma
several different images of different sizes all of which are in focus on the same screen
bright image formed by the paraxial rays and a series of smaller (or larger) images formed by the rays that hit the lens far away from the axis
like a comet – a clear image with a fuzzy tail oriented along the screen and composed of weaker images formed by the off-axis rays
Image in coma
The differences between the prediction of the paraxial ray method and the actual image are called aberrations.◦ Spherical aberration◦ Coma◦ Astigmatism◦ Chromatic aberration
Aberrations
off-axis effect When an object point is quite far off of the
central axis of the lens, the effective radius of curvature (and hence the effective focal length of the lens) in one direction is not the same as in a perpendicular direction.
produce a slight difference in the focal length for rays that are in the longitudinal plane of the lens and for rays that leave this plane
Astigmatism
A point on an off-axis object has two image points – one for the rays that strike the lens in the plane of the object and the central axis of the lens and another for rays that strike the lens perpendicular to this plane
At either of these two image points, the rays forming the other image are somewhat out of focus, and often form a small line segment
At intermediate points between the two image points the rays combine to form an image that sometimes looks like a small + sign.
Astigmatism
The differences between the prediction of the paraxial ray method and the actual image are called aberrations.◦ Spherical aberration◦ Coma◦ Astigmatism◦ Chromatic aberration
Aberrations
Combination of positive and negative lenses will have a net refractive power but their opposing dispersions will cancel
short wavelength light is refracted more strongly than long wavelength light
Resulting in chromatic aberration
Chromatic aberration
Eg: If light of wavelength 550 nm is in focus on
the retina, the image in ultraviolet light of wavelength 350 nm will be out of focus
lens acts as a filter transmit the visible spectrum but absorbs the near ultraviolet light of wavelengths shorter than 400 nm◦ Near ultraviolet increases chromatic aberration
sensitivity of the eye shifts toward the red end of the spectrum as the illumination is increased◦ rods - peak sensitivity at 500 nm (bluegreen)◦ cones - peak sensitivity 562 nm (yellowgreen)◦ Cones respond to long wavelength – less aberration
pigmentation of the macula lutea◦ Absorption of violet and blue regions
Countereffects