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


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


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


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

schematic eye(2)

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