`
`- Introduction to
`Aberrationsin
`Optical Imaging
`Systems
`
`JOSE SASIAN
`
`
`
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`

`IN OPTICAL IMAGING SYSTEMS
`
`JOSE SASIAN
`University ofArizona
`
` INTRODUCTION TO ABERRATIONS
`
`
`
`CAMBRIDGE
`UNIVERSITY PRESS
`
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`CAMBRIDGE UNIVERSITY PRESS
`Cambridge, New York, Melbourne, Madrid, Cape Town,
`Singapore, S80 Pauio, Dethi, Mexico City
`Cambridge University Press
`The Edinburgh Building, Cambridge CB2 8RU, UK
`Published in the United States of America by Cambridge University Fress, New York
`
`www.cambridge.org
`Information on this title; www.cambridge.org/978 1107006331
`
`@ J. Sasidn 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 availablefromthe British Library
`
`Library of Congress Cataloging in Publication data
`Sasidn, José M.
`Introduction to aberrations in optical imaging systems / José Sasian.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 978-1-107-00633-1 (hardback)
`2. Imaging systems — Image quality.
`3. Optical engineering.
`QC6T1.S27
`2012
`621,36'7 — de23
`2012027123
`
`1, Aberration.
`
`L, Title.
`
`ISBN 978-1-107-00633-1 Hardback
`
`Cambridge University Press has no responsibility for the. persistence or
`accuracy of URLsfor external orthird-party internet websites referred to
`in this publication and does not guaraniee that any content on such
`websites is, or will remain, accurate or appropriate.
`
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`
`
`18
`
`Basic concepts in geometrical optics
`
`FH
`
`VeP
`
`
`Object
`Plane
`
`Entrance
`
`Pupil
`
`
`Figure 2.7 The aperture vector (scaled by the marginal ray height yp, at the exit
`pupil) and the field vector (scaled by the chief ray height 9 at the object plane).
`
`Image
`Plane
`
`Figure 2.8 The angle @ between the field and aperture vectors looking down the
`optical axis.
`The chief ray height in the object plane is ¥» 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 H and the aperture vector / parallel to each other
`(@ = 0). We can define sagittal rays by setting the vectors perpendicularly to each
`other (pd = 90°).
`
`4.7 Real, first-order, and paraxial rays
`Rays of light are traced through an optical system im aniterative 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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`the direction of the ray after refraction is determined by applying Snell’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 planeis reached.
`Byreal rays we mean rays oflight that are traced accurately using Snell’s law
`of refraction and that may not be closeto the optical axis. Sneil’s law is
`(2.3)
`n' sin(I’) = nsin(I),
`- where / and 7’are the angles of ray incidence and refraction, and n and n’ are the
`indices of refraction of the media surroundingthe refracting surface. The normal
`line to the surface, the incidentray, and the refracted ray are coplanar. In accurate,
`real ray tracing the actual shapeof 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,
`
`(2.4)
`ni’ = ni,
`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, are?
`
`2.7 Real, first-order, and paraxial rays
`
`19
`
`y
`
`
`Surface
`
` Optical Axis
`Figure 2.9 In object space there are threefirst-order slopes, the incident ray slope
`w, the normal line slope a, and the slope of incidence i (not an angle). The segment
`ry represents the normalline to the surface of radius r and curvature ¢ = 1 {r.
`
`nu’ =nu —
`
`nw — RA
`
`y,
`
`yoytu't,
`
`(2.5)
`
`(2.6)
`
`2 See, for example, J. Greivenkamp, Field Guide to Geometrical Optics, SPE 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 tis the distance to the next surface. The normal line slope a = ~-y /r,
`the ray slope u, and the slope of incidence i are related by @ =u —-i=—y/r.
`The first-order ray-tracing parameters are distances and ray slopes (not angles).
`Equation (2.4) is also knownasthe first-order 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 un-barred 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 pataxial ray height and
`slope is assumed to be multiplied by a small factor such as 10775 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 Smith—Helmholtz invariant,
`
`the Lagrange invariant,*
`
`ni’ =ni
`
`nyu =nyu
`
`K = nity — nuy = nAy — nAy.
`
`(2.7)
`
`(2.8)
`
`(2.9)
`
`The refraction invariant refers to the refraction in a given optical system surface.
`The Smith-Helmholtz* 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 2X for the Lagrangeinvariant is due to R. V. Shack.
`4p Culmann providesa historical note on the Smith—Helmholtz invariant in “The formation of optical images,”
`Chapter4 in M. von Rohr(ed.}, The Formation ofImages in Optical instruments, H.M.Stationery Office, 1920.
`J. L. de Lagrange was aware of the work of Smith; however, he recognized the invariance ofrelations of the
`form of Eq. (2.9).
`
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`2.9 Conventionsforfirst-order ray tracing
`
`21
`
`Consider the refraction equation for the marginal and chief rays,
`
`if
`Ru = Hu
`
`nin
`
`r o
`
`n i
`=
`hh = hu —
`r
`
`¥,
`
`(2.10)
`
`(2.11)
`
`By multiplying Eq. (2.10) by y and Eq. (2.11) by y, and eliminating the common
`term containing the radius of curvature we can write
`
`'
`
`nu'y —n'i’y =nuy — nay,
`
`(2.12)
`
`
`
`- which is invariant uponrefraction. Similarly the transfer equation for the marginal
`and chief ray is
`
`yoytu't,
`
`yuyt@e.
`
`(2.13)
`
`(2.14)
`
`» By multiplying Eq. (2.13) by n'a’ and Eq. (2.14) by n’‘u’, and eliminating the
`common term, we find
`
`nul—nlil’y=n'u'y — n'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
`
`itis calculated in an axially symmetric optical systern.
`
`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
`os ads,
`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 movementof 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
`tay.
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`
`
`Basic concepts in geometrical optics
`
`Table 2.1 First-order quantities
`
`Marginal ray
`Chief ray
`s
`i
`s!
`5
`i=u-a
`i=u—-@
`y
`z
`“u=—~y/s
`Go -y/s
`= a-y/rauci
`a=-—-y/r=u-i
`A=ni=n (* — :) y A= ni =n (- _ =)¥
`
`yr
`
`5
`
`item
`Object/pupil distance
`Image/pupil distance
`Ray slope of incidence
`Ray height at surface
`Ray slope
`Normalline slope
`Refraction invariant
`
`ro
`
`oS
`
`SORELBEETEEEEEEERATEDTEEERALHEPESTA
`
`
`
`Surface radius
`Surface curvature
`Thickness to next surface
`
`Surface optical power
`Lagrange invariant
`
`rc
`
`f
`p
`
`AK
`
`
`—
`F
`nny —nuy = nAy ~ nAy
`
`Table 2.2 Singlet constructional parameters
`
`Radius of curvature
`
`oo
`51.680 mm
`
`_
`
`Thickness to next surface Glass
`30.775 mim
`Air
`5 mm
`Bk7 (n = 1.5168)
`100mm
`Air
`
`Surface
`
`Stop
`2
`3
`Image
`
`Table 2.1 summarizes quantities in tracing first-order rays that are frequently used.
`
`4.140 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 andafirst-order ray trace is shownin Table 2.3.
`The semi-field of view is 15 degrees, the aperture stop diameter is 12.5 mm,
`and the index ofrefraction used is m = 1.5168 for Bk? glass at a wavelength of
`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, u, and ni headings, and for
`the chief ray under the y, #, and ni headings.
`
`587.5 nm.
`
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`2./7 Transverse ray errors
`
`23
`
`Table 2.3 First-order ray trace. XK = 1.67
`
`Surface
`
`oy
`
`u
`
`ni
`
`¥
`
`=|
`
`=
`
`
`Stop 0.0000=0.00006.2500 0.0000 0.2679 0.2679
`
`
`
`
`
`
`
`2.0000 =60.0000=6.0000=6.2500 =-8,.2462 «0.1767 0.2679
`
`
`3.0000
`6.2500
`-0.0625
`-0.1834
`9.1295
`0.1767
`0.0000
`Image
`0.0000
`-0.0625
`~-0.0625
`26.7949 O.1767
`0.1767
`
` Object
`
`Pupil Pupil
`
`Entrance
`
`
`
`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
`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 Ap, The real ray departs at the image plane from thefirst-order ray
`by the normalized transverse ray vector AH. Theintersection of the ray at the
`entrance pupil is given by the vector yg( + Ap) and the intersection with the
`image plane is given by the vector y, (H + AH).
`
`Plane
`
`Image
`Plane
`
`Figure 2.10 A first-order ray, shownas 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 mim).
`
`2.11 Transverse ray errors
`
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`6
`
`The location and size of an image
`
`The aberration function is constructed taking as a reference ideal imaging according
`to the collinear transformation which is congruent with Gaussian and Newtoman
`optics. Ideal 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 light 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 ofthe field
`and aperture. The aberration function to second orderis
`(6.1)
`W(H, B) = Wooo + Wroo(H - H) + Wiii(H -p) + Wonli- A).
`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 termsare a quadratic piston term as a functionofthefield of view, a quadratic
`term as a function ofthe aperture, known as change of focus, and a quadratic term
`as a function ofthe 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 Woz9 = ~yeu'/2 and the change of magnification is
`Wii = —X. However, if the reference for measuring the wavefront deformation
`is the reference sphere, centered at the ideal image point, thenthe coefficients are
`Wor = O and Wi, = 0. That is, because Gaussian or Newtonian optics describe
`
`76
`
`
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`6.1 Change offocus and change ofmagnification
`
`77
`
`
`
`Woy 4-77)
`wW,, (Ap)
`Won (B- B)
`. Figure 6.1 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-
`
`der errors in the aberration function. Thus, in aberration theory the reference
`phere is usedto define the wavefront deformation and therefore coefficients of the
`ond-order terms become zero.
`There are some cases where the second-order terms may not be zero. For exam-
`
`ie,if the observation plane does not coincide with the ideal image plane then the
`
`econd-order terms will befinite. Ifthere is a wavelength change for which the lens
`ystem has a different optical power then the second-ordet terms will not be zero,
`
`his is the case of chromatic aberrations, which will be treated below.
`
`he change-of-focus term is quadratic as a function of the aperture and inde-
`endent of the field of view. Thus, in the presenceofchangeof focus, the image of
`
`very field point over the field view changes uniformly in axial position, as shown
`
`igure 6.2, The change-of-focus term is also knownas defocus. In the presence
`{change of focus there will be fourth- and higher-order terms in the aberration
`
`
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`|P
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`78
`
`The location and size of an image
`
`
`
`ARCTRAISCCECTEa
`
`
`WATEREESECotOARNTSLATE
` SRTtAciNESSCae
`
`
`Figure 6.3 Representation of change of magnification. The image size is smaller
`(broken line) with respect to the nominal ideal image size {solid line).
`
`function, which are treated later. Thus a wavefrontthat 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 shownin 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.
`Oneoption 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 orderthere 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 1s
`
`1.
`“
`
`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 W299 represents the quadratic delay, as a function of the field of
`view, that light from an off-axis field point will experience im 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
`
`Mininum OPD
`Vartance
`
`Marginal Ray
`Focus
`
`Shapes
`Sind RYa
`WaveFans
`
`Wr
`
`He
`
`iF
`
`
`
`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-
`gle surface the aberrations are not independent of each other and one cannot
`
`hange one aberration without changing the others. However, as the number of
`surfaces 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-
`tions. 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-
`
`lant matter in optical design since in practice it is not possible to correct for
`
`
`all the orders of aberration. Usually the balanceis accomplished by minimizing
`he variance or the root mean square (RMS)of the wavefront or transverse ray
`
`Figure 7.7 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-
`front variance. This process is known as aberration balancing.
`
`
`
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`96
`
`Wavefront aberrations
`
`Forthe case of having the primary aberrations presentthe varianceof the wave-
`front becomes
`
`!
`
`;
`
`OW = BD (Wing + Woao + (Wey + Won) 1)
`+ 1 (mn + 3Mist + Want?)
`(7.9)
`4 L(Woyg)? tte (Wiss HP + oy (Weng22)?
`
`189©02 7g) 94
`
`
`For a given field point H the best focus under minimum wavefront variance takes
`place when the change of focus Wo20 and magnification W);; satisfy
`
`and
`
`Wo2 + Woo + (Wg + Wes) H’? =0
`
`1
`
`2
`3
`Wi + 3 Wisi + WauA = 0.
`
`(7.10)
`
`(7.14)
`
`Clearly the even aberrations, spherical aberration and astigmatism, can be balanced
`with a change of focus Woz9; the odd aberrations, coma and distortion, can be
`balanced with a change of magnification W);; 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 cit-
`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,’ In his investigations Lord Rayleigh had,
`
`! See Lord Rayleigh, “Investigationsin optics, with special reference to the spectroscope,” Phil. Mag. 5:8(1879),
`403-411.
`
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`7.6 The Rayleigh-Strehl ratio
`
`7
`
`in the absence of aberrations, normalized the peak irradiance to unity. However,
`the ratio is commonly referred as the Strehl ratio.
`- 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
`
`2
`
`
`psf(t, y) = (3) FT {t(x, yyehhon}
`
`fa
`
`2
`
`,
`
`fagpeay
`
`(7.12)
`
`where A, is the amplitude of an incoming plane wave,t(x, y) is the transmittance
`‘function, and f is the focal length. Using the central ordinate theorem wefindthat
`the irradiance of the point spread function at zero spatial frequency is
`
`
`
`
`
`
`Ap\*
`
`.
`
`= (54) If ix, eVOPdxdy
`
`CO
`
`2
`
`2
`
`A
`
`2
`
`= (=) I (L+ikW(x, y) ~ W(x,y)/2)dady
`
`Aperture
`
`2
`
`3
`
`A
`=~ (
`fh
`
`A= (2)
`
`dxdy +ik
`¥
`
`Aperture
`
`Aperture
`
`Wx,
`
`Jy
`
`ydxd
`
`¥
`
`2
`
`ke-= ff we, »axay
`2
`
`Aperture
`
`Hl
`
`Aperture
`
`dxdy} +k I Wix, yidedy
`
`Aperture
`
`2
`
`—K
`
`ll dxdy
`
`Aperture
`
`[ W(x, ydxdy
`
`Aperture
`
`|.
`
`(7.13)
`
`In the absence of aberrations the peak of the point spread function is
`
`A
`
`n= (%)
`
`2
`
`Hl dxdy
`
`Aperture
`
`|.
`
`(7.14)
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 15 of 17
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 15 of 17
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`

`

`98
`
`Wavefront aberrations
`
`Thenthe Rayleigh—Strehl ratio can be approximated by
`
`I
`
`fh
`
`2
`
`
`
`
`
`
`“Exhibit2023 Page 16 of 17
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`7.1. Draw the meridional and sagittal wave fansfor the field positions of H = 0,
`AH =0.7, and H = 1, for a system with one wave of spherical aberration
`Woao = 1A and one wave of coma abetration W)3; = 1A.
`7.2. Determine the wavefront deformation variance for a system with the following
`aberration function:
`WL, 8) = Woso(3 - B)* + Worl - BY + World - A).
`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).
`
`I dxdy f W(x, ydxdy|— | Wo, vidxdy
`
`~
`“1k
`
`4
`
`
`\Aperture
`Aperture
`Aperture
`;
`
`2
`
`=| — (=) o2,.
`
`2
`
`I dxdy
`
`Aperture
`
`(7.15)
`
`This simple expression relating the variance of the wavefrontoj, to the drop in the
`peak of the un-aberrated point spread function is insightful. First, for systems with
`small amounts of aberration, ~ 2/2 or less, it makes the variance of the wavefront
`an important image quality metric. Second, the term Qn/AYos, represents the
`energy that is removed from the central peak and redistributed elsewhere in the
`diffraction pattern.
`A relationship’ that is shown to be more accurate is
`
`Qn
`I
`— ex — pf,
`he a)
`
`\*
`
`2
`ow
`
`Exercises
`
`2 ta different context this relationship was derived by R. V. Shackin “Interaction of an optical system with the
`incoming wavefront in the presence of atrnospheric turbulence,” Optical Sciences, The University of Arizona,
`Technical Report 19, 1967. See also V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their
`aberration variance,” / Opt. Soc, Am. 73:6(1983), 860-861.
`
`Apple v. Corephotonics
`IPR2019-00030
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 16 of 17
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`

`

`Introduction to
`Aberrationsin
`Optical Imaging
`Systems
`
`The competent andintelligent 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 theoryof aberrations and will be valuable
`to graduate studentsin optical engineering, as well as to researchers and
`technicians in academia andindustry interested in optical imaging systems.
`Using a logical structure, uniform mathematicalnotation, and high-quality
`figures, the author helps readersto learn the theory of optical aberrations
`in a modern andefficient 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, aberrationfields, and
`polarization aberrations.It also provides a historical perspective by explaining the
`discovery of Pleattoleh and two chaptersprovide insightinto classical image
`formation; these topics of discussion are often missing in comparable books,
`
`JOSE SASIAN is Professor of Optical Sciencesat the College of Optical
`Sciences,University of Arizona. His research areas include aberration theory,
`optical design, light in gemstones,art in optics andopticsin art, optical imaging,
`and light propagationin general.
`
`Coverillustration: painting by Don Cowen, 1967/The University of Arizona
`College of Optical Sciences. Credit: Margy Green PhotoDesign.
`
`0633
`| | |
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`i1
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`2
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 17 of 17
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`ISB
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`8-1-107-0063
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`9
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`7811070
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`Apple v. Corephotonics
`IPR2019-00030
`Exhibit 2023 Page 17 of 17
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