’ Introduction to
`
`Aberrations in
`
`Optical Imaging
`Systems
`
`JOSE SASIAN
`
`
`
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`

`IN OPTICAL IMAGING SYSTEMS
`
`JOSE SASIAN
`University ofArizonu
`
` INTRODUCTION TO ABERRATIONS
`
`
`
`CAMBRIDGE
`UNIVERSITY PRESS
`
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`--..:A
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`CAMBRIDGE UNIVERSITY PRESS
`
`Cambridge, New York, Melbourne, Madrid, Cape Town,
`Singapore, sec Pauio, Dethi, Mexico City
`Cambridge University Press
`The Edinburgh Building, Cambn'dge CB2 SRU, UK
`
`Published in the United States of America by Cambridge University Press, New York
`
`www.cambridgeorg
`Information on this title: www.carnbridgecrng? 81 107006331
`
`©J. Sasian 2013
`
`This publication is in copyright. Subject to statutory exception
`and to the provisions of relevant collective licensing agreements,
`no reproduction of any part may take place without the written
`permission of Cambridge University Press.
`
`First published 2013
`
`A catalog recordfor this publication is availabiefi'om the British Library
`
`Library of Congress Cataloging in Publication data
`Sasian, Jose M.
`Introduction to aberrations in optical imaging systems I lose Sasian.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 9784—107-00633—1 (hardback)
`
`1. Aberration.
`
`2. imaging systems ~ Image quality.
`QC671.327
`2012
`621 .367 — dc23
`20i202712l
`
`3. Optical engineering.
`
`I. Title.
`
`iSBN 978-1401006334 Hardback
`
`Cambridge University Press has no responsibility for the persistence or
`accuracy of URLs for external or third-party internet websites referred to
`in this publication and does not guarantee that any content on such
`websites is, or will remain, accurate or appropriate.
`W
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`
`
`18
`
`Basic concepts in geometrical optics
`
`
`Pupil
`
`Entrance
`
`Image
`Plane
`
`Figure 2.7 The aperture vector {scaled by the marginal ray height 32% at the exit
`pupil) and the field vector (scaled by the chief ray height 370 at the object plane).
`
` E EE
`
`K.
`-
`
`
`
`Figure 2.8 The angle (it between the field and aperture vectors looking down the
`optical axis.
`
`The chief ray height in the object plane is yo and the marginal ray height at the
`exit pupil is y}? The magnitude of the aperture vector is p, and the magnitude of
`the field vector is H.
`Using the field and aperture vectors we can define fans of rays in a meridional
`plane by setting the field vector PI and the aperture vector f5 parallel to each other
`(gb = 0). We can define sagittal rays by setting the vectors perpendicularly to each
`other (ti) n: 90°).
`
`2.7 Real, first-order, and paraxial rays
`
`Rays of light are traced through an optical system in an iterative manner. The
`initial. data are the spatial coordinates of a point and the direction of the ray. The
`ray is traced by finding its intersection coordinates with the next surface. Then
`
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`EEEE
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`:
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`l E
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`E.
`E.
`5.”
`
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`
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`
`
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`

`2.7Real, first-order, andparaxial rays
`
`19
`
`
`
`
`y
`
`Surface
`
` Optical Axis
`
`Figure 2.9 In object space there are three first-order slopes, the incident ray slope
`n, the normal line siope 0.1, and the slope of incidence i (not an angle). The segment
`W represents the normal line to the surface of radius r and curvature c : 1 / r.
`
`the direction of the ray after refraction is determined by applying Sneil’s law.
`For spherical surfaces or conic surfaces the ray intersection is determined using
`closed-form equations. For other surfaces an iterative algorithm is used until the
`intersection point is found to a high degree of accuracy. This ray-tracing process is
`repeated until the image plane is reached.
`By real rays we mean rays of light that are traced accurately using Snell’s law
`of refraction and that may not be close to the optical axis. Snell’s law is
`
`n” sinU’) = n sin(I),
`
`(2.3)
`
`- Where I and I’ are the angles of ray incidence and refraction, and n and n’ are the
`indices of refraction of the media surrounding the refracting sulface. The normal
`line to the surface, the incident ray, and the refracted ray are coplanar. In accurate,
`real ray tracing the actual shape of the refracting surface is used.
`By first-order rays we mean rays of light that are a first approximation to the
`'_-path of a real ray. First—order rays are traced using a linear approximation to Snell’s
`- law,
`
`
`
`n’i’ = m'.
`
`(2.4)
`
`The optical surfaces are considered planar as shown in Figure 2.9, but with
`_
`_'optical power properties. The first-order ray—tracing equations, for refraction and
`transfer respectively, are2
`
`n’u’ = nu. —
`
`n’w—n
`r
`
`y,
`
`y” = y + u’t,
`
`(2.5)
`
`(2.6)
`
`2 See, for example, J. Greivenkarnp, Field Guide to Geometrical Optics, SPIE Press, 2004.
`
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`

`20
`
`Basic concepts in geometrical optics
`
`where u and u” are the slopes of the incident and refracted rays, r is the vertex
`radius of curvature of the refracting surface, y is the first-order ray-height at the
`surface, and t is the distance to the next surface. The normal line slope at = wy/r,
`the ray slope u, and the slope of incidence i are related by or = u — i = — y / r.
`The first—order ray-tracing parameters are distances and ray slopes (not angles).
`Equation (2.4) is also known. as the firstworder refraction invariant. The first—order
`trace of the marginal and chief rays provides sufficient data for calculating several
`optical entities of a system, as we shall see. First-order quantities associated with
`a marginal ray are written unabarrecl and quantities associated with a chief ray are
`written with a bar above the symbol.
`,
`By paraxial rays we mean rays extremely close to the optical axis that are also
`traced with the first~order ray equations. However, each paraxial ray height and
`slope is assumed to be multiplied by a small factor such as 10~25 to insure that the
`ray is very close to the optical axis. In actual calculations there is cancelation of
`these factors and the factors are not explicitly written down.
`
`2.8 First-order ray invariants
`
`There are some first-order ray quantities that are invariant in an optical system
`under ray refraction, ray transfer, or ray refraction and transfer. These are:
`
`the refraction invariant,
`
`the SmithmHelmholtz invariant,
`
`n’i’ = mi
`
`n’y’rt’ = 113?”
`
`the Lagrange invariant?
`
`2K = rally —— may 2 nEy — my.
`
`(2.7)
`
`(2.8)
`
`(2.9)
`
`The refraction invariant refers to the refraction in a given optical system surface.
`The Smith—"Helmholtz4 invariant applies to ray quantities in an object or image
`plane. The Lagrange invariant applies to ray quantities at any plane throughout an
`optical system.
`
`3 The use of the symbol JR for the Lagrange invariant is due to R. V. Shack.
`4 P. Culrnann provides a historical note on the Smith—Helmholtz invariant in “The formation of optical images,”
`Chapter 4 in M. von Rohr (ed). The Formation ofi'mager in Optical instruments, HM. Stationery Office, 1920.
`J. L. de Lagrange was aware of the work of Smith; however, he recognized the invariance of relations of the
`form of Eq. (2.9).
`
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`\ s E
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`:-r
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`E3a
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`i"it
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`

`
`
`2.9 Conventions forfirst—order ray tracing
`
`21
`
`Consider the refraction equation for the marginal and chief rays,
`
`!
`I
`HM —HM"""
`
`n’—n
`F
`
`ya
`
` l—I -
`
`n’——n__
`I’LM $11M. —
`%
`1"
`
`(2.10)
`
`(an)
`
`By multiplying Eq. (2.10) by 37 and Eq. (2.11) by y, and eliminating the common
`
`'
`
`term containing the radius of curvature we can write
`
`
`
`11%;”? — n’E’y = nu? — nEy,
`
`(2.12)
`
`- which is invariant upon refraction. Similarly the transfer equation for the marginal
`
`and chief ray is
`
`
`
`v=y+ut
`
`vmy+na
`
`(an)
`
`(2M)
`
`- By multiplying Eq. (2.13) by 31’? and Eq. (2.14) by It’u’, and eliminating the
`common term, we find
`
`n’u’ji’ — n’if’y’ = n’n’y— ~ n’ii’y,
`
`(2.15)
`
`which is invariant upon transfer. Therefore we have an invariant upon refraction
`
`and transfer, that is, a quantity that does not depend on the transverse plane where
`
`
`
`it is calculated in an axially symmetric optical system.
`
`2.9 Conventions for first~order ray tracing
`
`There are several sign. conventions that need to be observed so that formulas provide
`
`
`
`
`
`correct results. These conventions relate to distances, angles, and ray slopes, and
`follow standard Cartesian coordinate conventions:
`
`
`
`
`
`_"1 Ray heights are positive if above the optical axis and negative if below the optical
`
`_
`
`- axis.
`'2 Distances are positive if measured to the right of the reference surface, negative
`if measured to the left.
`
`'3 Ray slopes are positive if a counter-clockwise movement of the axis needs to be
`
`'
`
`
`
`.done to reach the ray. Slopes are negative if a clockwise movement of the axis
`' needs to be done.
`
`Primed quantities refer to image space; un-primed quantities refer to object space.
`
`Barred quantities refer to the chief ray; un—barred quantities refer to the marginal
`ray.
`
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`

`
`
`22
`
`Basic concepts in geometrical optics
`
`Table 2.} First—order quantities
`
`WI
`
`Marginal ray
`
`Chief ray
`
`tem
`
`WA:WWW$WWMVKI¢A¥WMWIX§M
`
`
`
`
`
`
`Objectfpupil distance
`Image/pupil distance
`Ray slope of incidence
`Ray height at surface
`Ray slope
`Norrnallineslope
`Refraction invariant
`
`Surface radius
`Surface curvature
`Thickness to next surface
`
`Surface optical power
`
`Lagrange invariant
`
`S
`l
`5’
`X
`i : a e or
`i 2 BE —~ at
`)2
`y
`in :- —y/s
`i : ei/E
`am—y/r:u_i
`EzeWrz'flei
`A = m' = n (~1- — l) y E : of 2 n (l —— i) 7
`r:3
`
`r
`
`5
`
`r
`
`s
`
`I
`I”
`<13
`)K: nfiy — rm”)? :‘ nAy w my
`
`_
`
`Table 2.2 Singlet constructional parameters
`
`Surface
`
`Radius of curvature
`
`Thickness to next surface Glass
`
`Stop
`2
`3
`Image
`
`oo
`”51.680 min
`
`.
`
`30.775 min
`5 nun
`100mm
`
`Air
`Bk7 (n = 1.5168)
`Air
`
`Table 2.1 summarizes quantities in tracing first-order rays that are frequently used.
`
`2.10 First-order ray-trace example
`First—order ray tracing is used to obtain information about an optical system. In
`particular the ideal size and location of the image, and aberration coefficients are
`calculated from first-order data. For the singlet lens ofFigure 2.5 the constructional
`parameters are given in Table 2.2 and a first—order ray trace is shown in Table 2.3.
`The semi-field of. view is 15 degrees, the aperture stop diameter is 12.5 mm,
`and the index of refraction used is a = 1.5168 for 131(7 glass at a wavelength of
`587.5 nm.
`Table 2.3 shows the ray height intersection in millimeters, the ray slope after
`refraction with each surface, and the refraction invariant for the marginal and chief
`rays. Quantities for the marginal ray are under the y, n, and m’ headings, and for
`the chief ray under the 37, "it", and mi headings.
`
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`

`2.)] Transverse ray errors
`
`23
`
`Table 2.3 First-order my trace. )K m 1.67
`
`Surface
`
`y
`
`Lt!
`
`m'
`
`37
`
`El
`
`3n...|
`
`Stop
`2.0000
`3.0000
`
`6.2500
`6.2500
`6.2500
`
`0.0000
`0.0000
`410625
`
`0.0000
`0.0000
`«0.1834
`
`0.0000
`8.2462
`9.1295
`
`0.2679
`0.1767
`0.1767
`
`0.2679
`0.2679
`0.0000
`
`Image
`
`0.0000 —0.0625 —0.0625
`
`26.7949
`
`0.1767
`
`0.1767
`
`
`
`Image
`Plane
`
`Figure 2.10 A first‘order ray, shown as a broken line, travels with no error. A real
`ray, shown as a solid line, usually travels on a path that deviates from the first~order
`ray.
`
`The marginal ray-height (6.25 mm) at surface three divided by the ray slope
`(0.0625) after refraction gives the distance to the image plane (100 mm). The
`radius of the image size is given by the chief ray height at the image plane
`' (26.7949 mm).
`
`
`
`2.11 Transverse ray errors
`
`As will be shown, first—order rays propagate in an ideal manner. A first-order ray
`
`defined by the tip of the field and aperture vectors passes perfectly through the
`I images of these vectors at the entrance pupil and at the image plane as shown in
`- Figure 2.10.
`A real ray usually does not follow the path of the first-order ray and at the
`
`entrance pupil it departs from the first—order ray by the normalized transverse ray
`error vector A5. The real ray departs at the image plane from the firstworder ray
`by the normalized transverse ray vector All}. The intersection of the ray at the
`entrance pupil is given by the vector 32,365 + Ap) and the intersection with the
`image planeIS given by the vector 1(Hy + AH).
`
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`

`
`
`6
`
`The location and size of an image
`
`The aberration function is constructed taking as a reference ideai imaging according
`to the collinear transformation which is congruent with Gaussian and Newtonian
`optics. Idea}. imaging then provides the location and size of an image. This chapter
`discusses the second-order terms in the aberration function and chromatic aberra-
`tions. Second—order terms represent differences or changes with respect to Gaussian
`and Newtonian imaging and are a change of image location (focus), a change of
`image size (magnification), and a piston term. When these effects depend on the
`wavelength of fight they are called chromatic aberrations.
`
`6.1 Change of focus and change of magnification
`
`The aberration function includes terms of second order as a function of the field
`and aperture. The aberration function to second order is
`
`W(f}116) x W000 + “7200617" 53+ W111(§ ' ,3) + Wozoffi ' ,3)-
`
`(6-1)
`
`The zero—order term is a piston term which uniformly advances or delays the
`wavefront and has no effect on the image quality of a point object. The second-
`order terms are a quadratic piston term as a function of the field of view, a quadratic
`term as a function of the aperture, known as change of focus, and a quadratic term
`as a function of the field and the aperture, known as change of magnification. These
`terms are shown graphically in Figure 6.1.
`The coefficients in the aberration function depend on the reference chosen
`to measure the wavefront deformation and on how the wavefront deformation
`is defined. For example, if the reference is the exit pupil plane then the coeffi-
`cient for change of focus is W020 2 -~ yga’ / 2 and the change of magnification is
`Wm = ——}K. However, if the reference for measuring the wavefront deformation
`is the reference sphere, centered at the ideal image point, then the coefficients are
`W020 = 0 and W; 11 m 0. That is, because Gaussian or Newtonian optics describe
`
`76
`
`
`
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`

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`
`
`
`6.] Change offocas and change ofmagnification
`
`77
`
`
`
`
`
`
`
`Wmmn)
`min. a)
`malls-i5)
`' Figure 6.] Second-order terms in the aberration function represent changes in the
`ideal properties of an optical system.
`
`
`
`
`
`" Figure 6.2 Representation of change of focus. The optical system focuses not at
`- the nominal ideal image plane (solid line) but at a different location (broken line).
`Alternatively, the observation plane Where the reference sphere is centered does
`- not coincide with the ideal image plane.
`
`
`longitudinal position and transverse size of an image, there are no second
`rater errors in the aberration function. Thus, in aberration theory the reference
`here is used to define the wavefront deformation and therefore coefficients of the
`
`
`
`
`
`
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`

`l m
`
`78
`
`The location and size ofcm image
`
`
`
`an/raw.mmm/amgmmw
`
`{/&WMWWWWW
`_""1MWKW"mMWWfl/A‘W
`
`
`
`
`
`_._Mmrrfli___
`
`
`
`
`
`Figure 6.3 Representation of change of magnification. The image size is smaller
`(broken line) with respect to the nominai ideal image size (solid line).
`
`function, which are treated later. Thus a wavefront that is spherical remains spher—
`ical regardless of a change of reference; this should be reflected in the description
`by having second—, fourth, and higher—order terms.
`The change—of—magnification term is linear as a function of the aperture and
`linear as a function of the field of view. This term is a rigid tilt of the wavefront
`
`and represents a change in the size of the image, as shown in Figure 6.3.
`
`6.2 Piston terms
`
`As a function of the aperture, piston terms represent a uniform wavefront delay
`or advance and do not degrade image quality in the images of point objects.
`Occasionally, however, it is of interest to account for piston terms. Then piston
`terms depend on the reference used to measure the wavefront delay or advance.
`One option is to measure the piston terms with respect to the entrance and exit pupil
`on axis points. In this case the second-order piston term is zero because the pupils
`are conjugated. To second order there is no delay or optical path difference (OPD)
`between the pupils. Another option is to measure the piston term with respect to
`the object point and the exit pupil. In this case we have that the quadratic piston
`term is
`
`E M
`
`l
`
`.
`
`Equation (6.2) represents the sag, to second order of approximation, of a sphere
`centered at the entrance pupil point and passing through the on—axis object point,
`The piston term W200 represents the quadratic delay, as a function of the field of
`view, that light from an off—axis field point wiil experience in arriving at the exit
`pupil, on-axis point. This delay is with respect to the wavefront emerging from the
`on-axis field point.
`
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`

`7.5 Aberration balancing
`
`95
`
`Paraxial Focus
`
`Minimum OPD
`Variance
`
`Marginal Ray
`Focus
`
`Shapes
`szzp vlv,7%,)
`
`H’
`
`H"
`
`W
`
`WaveFans
`
`Figure 7.? Representation of spherical aberration and focus balancing. OPD stands
`
`for optical path difference.
`
`
`e are using two different terms in the aberration function to minimize the wave—
`_ ont variance. This process is known as aberration balancing.
`
`
`
`7.5 Aberration balancing
`
`
`in practice they
`Although we have introduced optical aberrations individually,
`
`appear in combination according to the wave aberration function. For a sin-
`e surface the aberrations are not independent of each other and one cannot
`
`hange one aberration without changing the others. HOWever, as the number of
`
`stirfaces increases, the dependence decreases and the aberrations become essen—
`ally independent of each other. The result is that in analyzing a lens system
`
`one can find any combination, in type and magnitude, of fourth~order aberra-
`
`_t10ns. In the actual design of a lens system the designer allows some residual
`
`amount of fourth-order aberrations to balance the higher-order aberrations that
`are usually present. An example in case is shown in Figure 7.7 where spheri-
`
`cal aberration is balanced with defocus. That is, the observation plane is axi—
`ally moved from the Gaussian image location. Aberration balancing is an impor—
`
`
`
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`

`
`
`For a given field point I} the best focus under minimum wavefront variance takes
`place when the change of focus W020 and magnification W11 1 satisfy
`
`and
`
`W020 + W040 + (W220 ‘i' Ewan) H2 2 0
`
`1
`
`2
`3
`W111+§W131H+W311H =0.
`
`(7-10)
`
`(7.11)
`
`Clearly the even aberrations, spherical aberration and astigmatism, can be balanced
`with a change of focus W020; the odd aberrations, coma and distortion, can be
`balanced with a change of magnification Wm for a given field point.
`
`7.6 The Rayleigh—Strehl ratio
`
`Imaging with light waves is obtained as a convolution of the geometrical image
`with the point spread function of the imaging system. For a system with a Cir“
`cular aperture the irradiance of the point spread function is the Airy pattern.
`In the presence of. aberrations the central peak of the Airy pattern decreases in
`value.
`
`A first estimate of the decrease of image quality in a system that has small
`amounts of aberration is the ratio of the peak of the point spread function in the
`presence of aberrations to the peak in the absence of aberrations. The concept of
`using the decrease in the peak of the point spread function as a metric for image
`quality was introduced by Lord Rayleigh.1 In his investigations Lord Rayleigh had,
`
`} See Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 5:8(1879),
`40341 1.
`
`
`
`96
`
`Wavefiont aberrations
`
`For the case of having the primary aberrations present the variance of the wave-
`front becomes
`
`1
`
`1
`
`1
`
`,
`
`2
`
`2
`
`2
`
`01.21! = E (W020 + W040 + (W220 + Ell/222) H2)
`+ 1 (W111 + §W131H + Wana)
`1
`2
`1
`2
`l
`...__ W
`W
`w W H
`H
`+180( 040) + 72 (Wm ) + 24(
`222
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`2 2
`)
`
`.
`
`.
`(7 9)
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`Apple V. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page ..f 17
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`Apple v. Corephotonics
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`7.6 The RayleigheStrehl ratio
`
`97
`
`in the absence of aberrations, normalized the peak irradiance to unity. However,
`
`the ratio is commonly referred as the Strehl ratio.
`I Let us assume an imaging system that may have small amounts of wavefront
`
`W{x, y) aberration. The point spread function for incoherent illumination is
`
`
`
`
`pSfOC. y) e (30
`
`A
`
`2
`
`
`
`FT{t (x, yummxvfi}
`
`_
`
`,
`
`(7.12)
`
`where A p is the amplitude of an incoming piane wave, r(x, y) is the transmittance
`'jfunction, and f is the focal length. Using the central ordinate theorem we find that
`3 the irradiance of the point spread function at zero spatial frequency is
`
`
`
`.
`2
`A
`12(3553) ff t<x.y>e”‘Wdedy
`
`DO
`
`2
`
`'
`
`2
`
`;(fi)
`
`2
`
`A
`
`2 (T?)
`
`ff (1+ikW(x,y)wk2W2(xsy)/2)dx‘iy
`
`Aperture
`
`f] dxdy—f—ikf W(x,y)dxdy
`
`Aperture
`
`Aperture
`
`k2
`— 3 [f wax, needy
`
`Aperture
`
`2
`
`2
`
`2
`
`2
`
`EE?
`
`(£3)2
`fl
`
`ff dxdy
`
`Aperture
`
`+k2
`
`f WU: y)dxd
`’
`
`Aperture
`
`3’
`
`452
`
`ff dxdy
`
`Aperture
`
`f W2(x,y)dxdy
`
`Aperture
`
`.
`
`(7.13)
`
`In the absence of aberrations the peak of the point spread function is
`
`A
`
`10 m (if?)
`
`2
`
`[f dxdy
`
`Aperture
`
`2
`
`.
`
`(7.14)
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`Apple V. Corephotonics
`IPR2019-00030
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`Exhibit 2023 Pa_e 15 of 17
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`Apple v. Corephotonics
`IPR2019-00030
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`
`
`98
`
`Wavefront aberrations
`
`Then the Rayleigh—Strehl ratio can be approximated by
`
`2
`
`ff dxdy
`
`I 1
`
`0
`
`N
`=1—k
`
`2
`
`f W2(x,y)dxdy m
`
`f W(x,y)dxdy
`
`
`Aperture
`Aperture
`Aperture
`2
`
`2
`
`2
`
`=1—(Tfi) 0,3,.
`
`f] dxdy
`
`Aperture
`
`(7.15)
`
`This simple expression relating the variance of the wavefront 0%, to the drop in the
`peak of the un-aberrated point spread function is insightful. First, for systems with
`small amounts of aberration, Nit / 2 or less, it makes the variance of the wavefront
`an important image quality metric. Second, the term (2n/A)20L2V represents the
`energy that is removed from the central peak and redistributed elsewhere in the
`diffraction pattern.
`A relationship2 that is shown to be more accurate is
`
`I N
`_ 2 ex
`[0
`
`p
`
`271!
`_ _
`A
`
`2
`
`2
`OW
`
`Exercises
`
`7.1. Draw the meridional and sagittal wave fans for the field positions of H = 0,
`H = 0.7, and H = 1, for a system with one wave of spherical aberration
`
`W049 = “L and one wave of coma aberration W13; 2: UL.
`
`7.2. Determine the wavefront deformation variance for a system with the following
`aberration function:
`MEI. [6) = W060(5 - o3 + W04005 - a2 + Wear? - 5).
`What change of focus minimizes the variance?
`7.3. Verify that the variance of the wavefront deformation in the presence of the
`primary aberrations is given by Eq. (7.9).
`
`2 In a different context this relationship was derived by R. V. Shack in “Interaction of an optical system with the
`incoming wavefront in the presence of atmospheric turbulence,” Optical Sciences, The University of An‘zona,
`Technical Report 19, 1967. See also V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their
`abenration variance,” J. Opt. Soc. Am. 73:6(1983), 8607861.
`
`
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`Apple V. Corephotonics
`IPR2019-00030
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`Exhibit 2023 Pae 16 of 17
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 16 of 17
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`

`Introduction to
`
`Aberrations in
`
`Optical Imaging
`
`Systems
`
`The competent and intelligent optical design of today‘s state—of—the-art products
`
`requires an understanding of optical aberrations. This accessible book provides
`
`an excellent introduction to the wave theory of aberrations and will be valuable
`
`to graduate students in optical engineering, as well as to researchers and
`
`technicians in academia and industry interested in optical imaging systems.
`
`Using a logical structure, uniform mathematical notation, and high-quality
`
`figures, the author helps readers to learn the theory of optical aberrations
`
`in a modern and efficient manner. In addition to essential topics such as the
`
`aberration function, wave aberrations, ray caustics, and aberration coefficients,
`
`this text covers pupil aberrations, the irradiance function, aberration fields, and
`
`polarization aberrations. It also provides a historical perspective by explaining the
`discovery of aberrations, and two chapters provide insight into classical image
`formation; these topics of discussion are often missing in comparable books.
`
`105 E SAS lAN is Professor of Optical Sciences at the College of Optical
`
`Sciences, University of Arizona. His research areas include aberration theory,
`
`optical design, light in gemstones, art in optics and optics in art, optical imaging,
`
`and light propagation in general.
`
`Cover illustration: painting by Don Cowen, 1967/The University of Arizona
`
`College of Optical Sciences. Credit: Margy Green PhotoDesign.
`
`9 7811 070
`
`
`Apple V. Corephotonics
`IPR2019-00030
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`Exhibit 2023 Page 17 of 17
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`IS_BN 978—1—10?—00633—1
`
`06331 >
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 17 of 17
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`