Thick Lenses/Multiple Lens Systems. What we’ll do today ► Thick lens theory Concepts Cardinal points explained ► Schematic eyes Exact Reduced.

Thick Lenses/Multiple Lens Thick Lenses/Multiple Lens SystemsSystems

What we’ll do todayWhat we’ll do today

► Thick lens theoryThick lens theory ConceptsConcepts Cardinal points Cardinal points

explainedexplained

► Schematic eyesSchematic eyes ExactExact ReducedReduced Construction of Construction of

retinal imagesretinal images

► Catoptric imagesCatoptric images► Angle KappaAngle Kappa► Accommodation Accommodation

and AC/A ratioand AC/A ratio

Thick Lens TheoryThick Lens Theory

►A lens is not thin if the CT is sufficient A lens is not thin if the CT is sufficient to change the powerto change the power

►The eye is a moderately complex thick The eye is a moderately complex thick lens system lens system Focusing power depends on curved Focusing power depends on curved

surfaces, each separated by media of surfaces, each separated by media of different indices of refractiondifferent indices of refraction

Thick Lens TheoryThick Lens Theory Element by Element ImagingElement by Element Imaging►Use previously developed thin lens Use previously developed thin lens

imaging techniques for imaging techniques for each refracting each refracting surfacesurface. . Use the image of one lens as the object of Use the image of one lens as the object of

the next lensthe next lens Each refracting surface is an element of Each refracting surface is an element of

the system. the system. The medium between the elements is the The medium between the elements is the

index of the lens systemindex of the lens system

Imaging of multiple lens Imaging of multiple lens systems- element by elementsystems- element by element

RO

RI

n1 n2 n3

VO

RO

VI

E1 E2E3

Thick Lens PowerThick Lens Power

►F=FF=F11+F+F22- (t/n)F- (t/n)F11FF22

► If the n1=n3, then f=f’If the n1=n3, then f=f’ In In EnglishEnglish, this means that the focal , this means that the focal

lengths on either side of the lens will be lengths on either side of the lens will be the same if the index of refraction is the the same if the index of refraction is the same on both sides of the lens.same on both sides of the lens.

The Effect of Thickness on The Effect of Thickness on PowerPower

► When thickness is 0, When thickness is 0, the F=F1+F2the F=F1+F2

► If both surfaces are the If both surfaces are the same sign, increasing same sign, increasing the thickness makes the thickness makes the net equivalent the net equivalent power more negativepower more negative

► If one is negative and If one is negative and one is positive, then one is positive, then increasing CT makes increasing CT makes

the lens more negativethe lens more negative..

ProblemProblem

► Lens system has 2 thin lenses, +15D and -3D with CT of 17cm. An object is Lens system has 2 thin lenses, +15D and -3D with CT of 17cm. An object is placed 1m in front of the first lens. Where is the final image?placed 1m in front of the first lens. Where is the final image?

► Knowns FKnowns F11=+15D, F=+15D, F22=-3D, t=17cm, obj dist l=-3D, t=17cm, obj dist l11=-1m,=-1m,

► Unknown image dist l’Unknown image dist l’► Equations L’=F+L, L=n/l and L’=n’/l’Equations L’=F+L, L=n/l and L’=n’/l’

RO

+15 -3n1 n2 n3

100cm=l117mm

RO

+15 -3n1 n2 n3

100cm=l117cm

Incident vergence L1=n1/l1=1.00/-1.00=-1.0DEmergent vergence L’=L1+F1=-1.00+15=14DImage position l’=n2/L1=1/14=.0714m=7.14cm

7.14 -9.86

Incident vergence L2=n2/l2=1.00/-.0986=-10.14DEmergent vergence L2’=L2+F2=-10.14+(-3)=-13.14DImage position l’2=n3/L2=1/-13.14=.0761= -7.61cm

7.61

Lens systems:Lens systems: Size and Orientation Size and Orientation

► Product of Lateral Magnification of each Product of Lateral Magnification of each object/image object/image

► Note that you cannot predict Note that you cannot predict orientation of final imagesorientation of final images

► LM system= (LM1)(LM2)(LM3)….LM system= (LM1)(LM2)(LM3)….

► Recall LM=h’/hRecall LM=h’/h► LM=nl’/n’l LM=nl’/n’l

Lateral Mag of Lens SystemsLateral Mag of Lens Systems

►So, if you have the following lensesSo, if you have the following lenses

8x 7x 2x

Total mag is (8)(7)(2) =112X

ProblemProblem



explainedexplained



► Practical Practical applications of thick applications of thick lenses and lenses and schematic eyesschematic eyes

► Accommodation Accommodation and AC/A ratioand AC/A ratio

► Catoptric imagesCatoptric images

Cardinal PointsCardinal Points

► In thick lenses, not valid to assume that In thick lenses, not valid to assume that focal lengths are measured from the center focal lengths are measured from the center of lensof lens

► Convenient reference positions for all optical Convenient reference positions for all optical systemssystems Principal planesPrincipal planes Principal pointsPrincipal points Nodal points Nodal points

► They exist in thin lenses, but all coincide They exist in thin lenses, but all coincide with the axial position of the lens.with the axial position of the lens.

Some defintionsSome defintions

►Neutralizing (front vertex) power: Neutralizing (front vertex) power: Incident vergence on front of lens that Incident vergence on front of lens that yields image at infinityyields image at infinity

►Back Vertex Power: Emergent Back Vertex Power: Emergent vergence from back surface of lens for vergence from back surface of lens for object at infinity. Used in refraction and object at infinity. Used in refraction and lens prescriptions. lens prescriptions.

►Effective Power: shows what the power Effective Power: shows what the power is from the other surfaceis from the other surface

Cardinal Points: Locating H/H’Cardinal Points: Locating H/H’Principal PlanesPrincipal Planes

H’= emergent ray extended backward

H=incident ray extended forward

f

H

F’

f’

H’

Front vertex power Back vertex power

Bending a Thick LensBending a Thick Lens

►Changing the Changing the formform of the lens does not of the lens does not change the separation between the change the separation between the two planes, but it does change the two planes, but it does change the location of H/H’location of H/H’

► In the concave or convex lenses, the H In the concave or convex lenses, the H usually falls within the lensusually falls within the lens

►A meniscus lens shifts H/H’ towards A meniscus lens shifts H/H’ towards the more curved surface. the more curved surface.

Movement of H with lens Movement of H with lens shapeshape

H (principal plane) moves toward the most curved surface

Cardinal Points: Principal Cardinal Points: Principal PlanesPlanes

► Rays enter and Rays enter and leave H/H’ at the leave H/H’ at the same height, a same height, a property called property called unitary linear unitary linear magnificationmagnification

► H/H’ are H/H’ are conjugateconjugate, , meaning the optical meaning the optical image of each otherimage of each other

These planes can replace all other optical elements

H H’

Cardinal Points: Principal Cardinal Points: Principal PlanesPlanes

► CP are the reference planes- all object and CP are the reference planes- all object and image distances are measured relative to image distances are measured relative to themthem

► Primary and secondary focal points also Primary and secondary focal points also measured relative to the principal planesmeasured relative to the principal planes We usually measure from the back of a lens We usually measure from the back of a lens

(effective power/ vertex power)(effective power/ vertex power)

H H’

Cardinal Points: Principal Planes

F

F’

FH and H’F’ will be equal IF the media composing the object and image spacesIs the same refractive index. If it is not, the focal length will be longer on the side with the higher index

n n’

Cardinal Points: Cardinal Points: Principal Principal PointsPoints

► Where the principal plane intersects the optic axisWhere the principal plane intersects the optic axis..► They are a conjugate pair (object and image of each They are a conjugate pair (object and image of each

other)other)► In the eye, P and P’ are separated by 0.3mmIn the eye, P and P’ are separated by 0.3mm

P P’

Cardinal Points: Cardinal Points: Nodal PointsNodal Points

►The place where the chief ray passes The place where the chief ray passes undeviated through the lens (also true undeviated through the lens (also true for thin lenses) for thin lenses)

N N’

Cardinal Points: Cardinal Points: Nodal PointsNodal Points

►As long as n=n’, nodal point is at the As long as n=n’, nodal point is at the same location as principal point and same location as principal point and N’ is in the same place as P’N’ is in the same place as P’

► If n does not = n’ (like the eye) then If n does not = n’ (like the eye) then both N and N’ are NOT coincident with both N and N’ are NOT coincident with P and P’P and P’ They will shift in the direction of the They will shift in the direction of the

greater indexgreater index

Nodal PointsNodal PointsAny ray striking N will leave N’ with an identical inclination to the axis (Unitary Angular Magnification).

N N’

Optical CenterOptical Center

►The place where an undeviated ray The place where an undeviated ray crosses the optic axis. crosses the optic axis.

► In reality the nodal points represent In reality the nodal points represent the apparent position of the optical the apparent position of the optical center center

oN

N’

Thick Minus LensesThick Minus Lenses

AVFL PVFL

f’ f

F’F

H‘H

The lensometer usesBack vertex power becauseIt is relevant. Back vertex Power IS NOT vertex distance

Note that the AVFL and The PVFL may not be equal

Thick Plus LensesThick Plus Lenses

H H’

f f’

F F’

AVFL PVFL

Convex Meniscus Lens

Equivalent power (true)

Back or front surface power

TopicsTopics► Thick lens theoryThick lens theory

Cardinal points Cardinal points explainedexplained



► Angle KappaAngle Kappa► Catoptric imagesCatoptric images

Schematic EyesSchematic Eyes

►Refractive componentsRefractive components Corneal powerCorneal power Anterior chamber depth (n, aqueous)Anterior chamber depth (n, aqueous) Lens powerLens power Axial length of eye Axial length of eye N, vitreousN, vitreous Powers determined by radii of curvature Powers determined by radii of curvature

and nand n

Schematic Eyes- Schematic Eyes- Gullstrand’s Gullstrand’s ExactExact

► Unique in that it:Unique in that it: specifies n and radii specifies n and radii

for both the nucleus for both the nucleus and cortex of the lensand cortex of the lens

represents the cornea represents the cornea with both front and with both front and back surfacesback surfaces

Provides values for Provides values for the accommodative the accommodative and relaxed stateand relaxed state

F F’

-15.70 +24.38

Principal planes

Nodal points

Simplified Gullstrand ModelSimplified Gullstrand Model

► Lens has just one pair Lens has just one pair of refracting surfaces of refracting surfaces and a single indexand a single index

► Cornea is a single Cornea is a single refracting surfacerefracting surface

Principal planes

Nodal points

14.99

23.90

F F’

n=1.336 for aqueous, vitreousn=1.413 lensr, cornea= 7.80 (43.25D)r, ant/post lens=10.0 (33.50) ,8.0 (42.12)AC depth, lens thickness 3.6mm

Reduced Eye- simplestReduced Eye- simplest

F F’

n=4/3

17mm 24mm

N

All refraction takes placeAt the front surface of the cornea

7mm

Schematic EyeSchematic Eye

►The cornea is so powerful because of The cornea is so powerful because of the change in index of refraction the change in index of refraction between air and the tear filmbetween air and the tear film

n (air) =1.0

n=1.376

n=1.336

n=1.406

n (water) =1.336

F=n’-n/r

ProblemProblem

►Recall that Recall that F=n’-n/rF=n’-n/r

►So, what is the power of the cornea of So, what is the power of the cornea of 7.5mm radius in air?7.5mm radius in air?

►F=1.376-1.0/7.5 = F=1.376-1.0/7.5 = 50.D50.D►What is the power in water?What is the power in water?►F= 1.376-1.336/7.5 = F= 1.376-1.336/7.5 = 5.3D5.3D

Schematic Eyes- Construction of Schematic Eyes- Construction of Retinal ImagesRetinal Images

Fa

FrN

h

Because the light subtends the same angle at the nodal point and Fa, we can say that retinal image size is

related to the angle of incidence! Thus, h=tan(fa) So, as an object approaches, it appears larger b/c the angle is greater.

fa

VISUAL ANGLE

Finding the Retinal Image Finding the Retinal Image SizeSize

►Use similar triangles to solve these Use similar triangles to solve these problemsproblems

17mmH’ object

H’retinal imagex

ProblemProblem



explainedexplained



► Catoptric imagesCatoptric images► Angle KappaAngle Kappa

Catoptric (Purkinje) ImagesCatoptric (Purkinje) Images

►Each refracting element of the eye is Each refracting element of the eye is really also a mirror, as some of the really also a mirror, as some of the light is reflected back at youlight is reflected back at you Front corneal surfaceFront corneal surface Back corneal surfaceBack corneal surface Front lens surfaceFront lens surface Back lens surfaceBack lens surface

Catoptric (Purkinje) ImagesCatoptric (Purkinje) Images

1 3

2

4

These are the apparent positions

These are the actual positions

They are different b/c the light is refracted upon exiting the eye

So what???So what???

►These images have been used clinically:These images have been used clinically: Hirschberg reflexHirschberg reflex, , keratometrykeratometry use image 1 use image 1 Changes in the shape of the lens during Changes in the shape of the lens during

accommodation accommodation can be gleaned by can be gleaned by comparing the positions of images 3 and 4comparing the positions of images 3 and 4

Eye tracking systems Eye tracking systems use the 4use the 4thth purkinje purkinje imageimage

Refractive procedures- Refractive procedures- do you center on the do you center on the reflex or the pupil center? What about angle reflex or the pupil center? What about angle kappa? Where does best result occur?kappa? Where does best result occur?



explainedexplained



► Catoptric imagesCatoptric images► Angle Kappa Angle Kappa

(lambda)(lambda)

Angle KappaAngle Kappa

►The optical components of the eye are The optical components of the eye are not coincident with the line of sight, but not coincident with the line of sight, but are along an optical axis temporal to itare along an optical axis temporal to it

►The pupil is not usually centered on the The pupil is not usually centered on the optical axis of the eyeoptical axis of the eye Pupillary axisPupillary axis: imaginary line normal to the : imaginary line normal to the

cornea and containing the center of the cornea and containing the center of the pupilpupil

Line of sight- Line of sight- not anatomical. Noted not anatomical. Noted relative to the pupillary axisrelative to the pupillary axis


► Route of LOS through pupil located by Route of LOS through pupil located by observing the corneal reflexobserving the corneal reflex Usually .4mm nasal to center of pupilUsually .4mm nasal to center of pupil 1.0mm of displacement = 22 prism diopters/12.5 1.0mm of displacement = 22 prism diopters/12.5

degrees of rotationdegrees of rotation OD= OS normallyOD= OS normally

► Angle kappa Angle kappa is the difference between the is the difference between the pupillary axis and the LOS.pupillary axis and the LOS. Usually 5 degrees (range 3-7) temporal (+)Usually 5 degrees (range 3-7) temporal (+) If negative then kappa is nasal to pupillary axisIf negative then kappa is nasal to pupillary axis


►Useful to determine strabismusUseful to determine strabismus► Important in refractive surgery.Important in refractive surgery.

Do you center on the pupillary axis or the Do you center on the pupillary axis or the line of sight?line of sight?

What would give you a better outcome?What would give you a better outcome?►Lasik- LOSLasik- LOS►CK- center on pupilCK- center on pupil►Custom with iris registration- center on pupilCustom with iris registration- center on pupil

Stiles- Crawford EffectStiles- Crawford Effect

► It refers to the directional sensitivity of the cone It refers to the directional sensitivity of the cone photoreceptors; specifically to the phenomenon that photoreceptors; specifically to the phenomenon that light passing near the edge of the light passing near the edge of the pupil is less efficient is less efficient at evoking sensation than light passing through the at evoking sensation than light passing through the center of the pupil.center of the pupil.

►A photoreceptor acts like a retinal optic fibre, it A photoreceptor acts like a retinal optic fibre, it captures light that hits it at a narrow angle from its captures light that hits it at a narrow angle from its normal. The acceptance angle of a cone is narrow, normal. The acceptance angle of a cone is narrow, approximately 5°, rods have larger acceptance angles.approximately 5°, rods have larger acceptance angles.

►The "Stiles-Crawford" effect reduces the detrimental The "Stiles-Crawford" effect reduces the detrimental effects of light scatter on the retina at effects of light scatter on the retina at photopic levels levels

Stiles Crawford EffectStiles Crawford EffectEffect of PositionEffect of Position

AccommodationAccommodation

► Anterior curvature of lens changes as Anterior curvature of lens changes as the CM contracts, allowing zonular the CM contracts, allowing zonular relaxationrelaxation Far point-Far point- object position that allows image object position that allows image

to fall on the retina w/o accommodationto fall on the retina w/o accommodation Near point-Near point- closest point at which object is closest point at which object is

seen clearly using maximum seen clearly using maximum accommodationaccommodation

RangeRange is the difference between the two is the difference between the two Amplitude Amplitude is the range in dioptersis the range in diopters

AccommodationAccommodation

► Amplitude = near point (D)- far point (D)Amplitude = near point (D)- far point (D)► Accommodation needed = where you Accommodation needed = where you

want to see (D) – far point (D)want to see (D) – far point (D)

ProblemProblem

AC/A ratioAC/A ratio

►Neural linkage of accommodative triadNeural linkage of accommodative triad►How many prism diopters of How many prism diopters of

convergence occurs for each diopter of convergence occurs for each diopter of accommodation accommodation Normal is 3:1 to 5:1Normal is 3:1 to 5:1

AC/A ratioAC/A ratio

Sometimes there is too much Sometimes there is too much convergence for any given amount of convergence for any given amount of accommodation (accommodation (esoeso) )

Sometimes there is not enough (Sometimes there is not enough (exoexo))►Either can cause problems with Either can cause problems with

accommodative amplitudesaccommodative amplitudes►If you converge too much, you will If you converge too much, you will

accommodate lessaccommodate less►If you converge not enough, you will If you converge not enough, you will

accommodate moreaccommodate more

Thick Lenses/Multiple Lens Systems. What we’ll do today ► Thick lens theory Concepts Cardinal points explained ► Schematic eyes Exact Reduced.

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