Aberrations in
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`Optical Imaging
`Systems
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`JOSE SASIAN
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`CAMBRIDGE
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`APPLE V COREPHOTONICS
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`Published in the United States of America by Cambridge University Press, New York
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`www.cambtidgeorg
`Information on this title: www.cambridge.org/9781 10700633]
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`© J. Sasian 2013
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`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
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`A catalog recordfor this pribiicaliun is available from 1/16 Britt's/r Library
`
`Library of Congress Cataloging in Publication data
`Sasian, José M.
`Introduction to aberrations in optical imaging systems / José Sasian.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 978-1401006334 (hardback)
`2. Imaging systems — Image quality.
`31 Optical engineering.
`QC671.527
`2012
`621.36’7—dc23
`2012027121
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`l, Aberration.
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`1. Title.
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`ISBN 978-1-10700633—1 Hardback
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`Cambridge University Press has no responsibility for the persistence or
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`APPLE V COREPHOTONICS
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`5.6 Parity of the aberrations
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`73
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`. mine of the angle (1) between these vectors. Table 5.1 summarizes the first four
`4 rs of aberrations using both vector and algebraic expressions. The fourth-order
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`-
`s are often called the primary aberrations. The ten sixth—order terms can be
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`ided into two groups. The first group (first six terms) can be considered as an
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`‘ x rovement upon the primary aberrations by their increased field dependence, and
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`~ second group (last four terms) represents new wavefront deformation forms.
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`re 5.1 shows the shape (aperture dependence only) of the zero, second, fourth,
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`. the new wavefront shapes of the sixth—order aberrations.
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`In Table 5.1 the piston terms represent a uniform phase change across the
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`. rture that does not degrade the image quality. Physically piston terms represent
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`time delay or advance in the time of arrival of the wavefront as it propagates
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`.
`the object to the exit pupil. The second-order term magnification represents a
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`-
`«. ge of magnification and the focus term represents a change in the axial location
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`the image. The coefficients for magnification and focus are set to zero given
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`—,. Gaussian and Newtonian optics accurately predict the size and location of an
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`' m ge. However, a focus term is usually added to minimize aberrations or to select
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`observation plane other than the ideal image plane. In addition, the change of
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`< gnification and focus with respect to the wavelength are known as the transverse
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`. longitudinal chromatic aberrations respectively.
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`5.5 Determination of the wavefront deformation
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`hen rays of light do not pass through an ideal image point, the wavefront must
`deformed. The wavefront deformation is measured with the aid of a reference
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`I re. The reference sphere for a given field point passes through the on-axis exit
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`n'l point and its center coincides with the ideal image. As shown in Figure 5.3
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`wavefront deformation multiplied by the index of refraction is the optical path
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`‘
`'-
`'een the wavefront and the reference sphere measured along the ray.
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`By convention the wavefront deformation is negative if the wavefront lags the
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`-erence sphere and positive if it leads the reference sphere. The units of the
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`—
`'efront deformation are linear dimensions of millimeters, micrometers, etc.
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`'ever, often the wavefront deformation is divided by the wavelength of light A,
`i
`.
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`. then the deformation is expressed in waves. The reference sphere is centered at
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`- '
`t3)", [:1 in the image plane. Note that the tip of the aperture vector defines where
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`* ray intersects the exit pupil plane. In this manner the aperture vector designates
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`~ same pupil point for all field points. This definition eventually makes easier the
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`. ulation of sixth—order coefficients that are coordinate—system dependent.
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`5.6 Parity of the aberrations
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`I : aberrations can be classified as even or odd aberrations. For example, spherical
`daemtion, astigmatism, field curvature, and the chromatic change of focus are even
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`74
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`The wave aberration function
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`aberrations. Coma, distortion, and the chromatic change of magnification are odd
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`aberrations. The parity is found by observation of the algebraic power parity of
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`the field and aperture vectors in the aberration coefficients. The odd aberrations
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`have the important property that they cancel, or tend to cancel, in a system that
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`has symmetry about the stop. That is, each half of the system contributes the same
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`amount of aberration but with opposite algebraic sign. In contrast, in a symmetrical
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`system the even aberrations from each half of the system add, rather than cancel.
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`5.7 Note on the choice of coordinates
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`The aberration theory developed in this book uses polar coordinates with the field
`vector If serving as a reference to define the polar angle ¢ and the aperture vector
`[5. Given the system’s axial symmetry, inherently only three variables are necessary,
`II; I,
`|,5|, and cos(¢), and eventually this leads to many simplifications. The other
`obvious choice is the use of Cartesian coordinates, which for historical reasons.
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`previous works on wave aberration theory, and simplicity, are little used in the
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`present treatment.
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`5.8 Summary
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`In this chapter we have introduced the aberration function as a polynomial depend—
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`ing on the field and aperture of the system. The terms in the aberration function
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`represent aberrations as a wavefront deformation with respect to a reference sphere.
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`The aberration coefficients provide the maximum amplitude of the deformation as
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`an optical path. The aberration function provides a wealth of insight into the nature
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`of an optical system and its aberrations. Symmetry considerations are important in
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`developing the aberration function.
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`Exercises
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`5.1. Using symmetry considerations, explain why the sine of the angle between
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`the field and aperture vector does not appear in the aberration function.
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`5.2. Determine the aberration function up to fourth order of a system that has two
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`orthogonal planes of symmetry. The intersection of these planes defines the
`optical axis. Use the unit vector ? to specify the direction of one of the planes
`of symmetry, and the field 131 and aperture ,5 vectors.
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`References
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`[l] W. R. Hamilton, “Theory of systems of rays,” Trans. R. Irish Acad. 15(1828), 69—174.
`[2] W. R. Hamilton, “Supplement to an essay on the theory of systems of rays,” Trans. R.
`Irish Acad. 16(1830), 1—61.
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`APPLE V COREPHOTONICS
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`APPLE V COREPHOTONICS
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