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`
`
`HANDBOOKOF
`LENS DESIGN
`
`DANIEL MALACARA
`ZAGARIAS MALACARA
`Centro de Investigaciones en Optica, A.C.
`Leon, Mexico
`
`Marcel Dekker,Inc.
`
`New York Basel e Hong Kong
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`2/6
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`

`
`
`About the Series
`
`Library of Congress Cataloging-in-Publication Data
`
`Malacara, Daniel
`Handbook of lens design / Daniel Malacara, Zacarias Malacara.
`p.
`cm. — (Optical engineering: v. 44)
`Includes bibliographical references and index
`ISBN 0-8247-9225-4
`1. Lenses—Design and construction—Handbooks, manuals, etc.
`. Mirrors—Design and construction—Handbooks, manuals, etc.
`ww
`. Optical instruments—Design and construction—Handbooks, manuals,
`etc.
`I. Malacara, Zacarias.
`I. Title.
`II. Series:
`Optical engineering (Marcel Dekker, Inc.}:
`v. 44.
`QC385.2.D47M35 1994
`681°.423—de20
`
`94-18940
`CIP
`
`This book is printed on acid-free paper.
`
`Copyright © 1994 by MARCEL DEKKER, INC. All Rights Reserved
`
`Neither this book nor any part may be reproduced or transmitted in any form
`or by any means, electronic or mechanical,
`including photocopying, micro-
`filming, and recording, or by any information storage and retrieval system,
`without permission in writing from the publisher.
`
`MARCEL DEKKER, INC.
`270 Madison Avenue, New York, New York 10016
`
`Current printing (last digit):
`100987654321
`
`There is no doubt t!
`
`tield of optical science an
`science and engineering h
`
`propagation, manipul
`
`with matter, and its app!
`commercial, and milit
`
`contend that optical
`sc
`hi
`encompass anything that
`
`ultraviolet
`to
`the
`intra
`
`optoelectronics, photonics
`engineering.
`It remains true. 4
`
`
`
`advancedthe optical syster
`the use of traditional opt
`completed without recour:
`subject is still the corners:
`
`It is very fittin
`our series in optical
`elegant text on lens design
`
`basic principles of geomet
`elements of the design
`aberrations. A variety
`magnifiers to complex
`telescopes, microscopes. D
`
`described for manyof ths
`
`prisms
`is
`included.
`1
`optimization of optical ces
`The information pr
`course,
`for self-study. or
`engineer who has
`to ce
`conclusion, the importan
`and engineers who
`quantum-optics
`syste
`appropriately applied in th
`
`
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`
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`3/6
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`3/6
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`

`

`NS
`ews
`———_=zzz_noo)
`|
`
`/
`
`/ /
`OPTICAL
`ae
`ASSEMBLY
`
`/ /
`ae
`APERTURE
`f
`~ _ /
`
`
`
`
`
`
` _;aw SJ hs LENS K } 7 oo/ /i
`
`ray that passes throughthe off-ax:
`The intersection of the extension |
`object space with the optical 2
`Similarly, the intersection of the«
`ray in the image space with the o
`All quantities referring to the pri
`top of the symbol, for example.
`ray and w is its paraxial angle v
`
`to see that y is equal to zero ai
`
`
`axial rays (meridional rays fror
`withoutthe bar.
`The tangential and sagitta
`may now be moreformally defir
`plane that contains the princip2
`sagittal plane is a plane perper
`contains the principal ray. As wi
`tangential plane for all media ben
`a centered optical system. How
`medium, because the principal ra
`In order to trace the prin
`must know its direction in the c
`such that the principal ray passes
`
`1.6.1 Telecentric Systems
`
`Afrontal telecentric system
`at infinity. Since the stop (diaphra;
`mustbeat a finite distance to avo
`Let us consider the optical systen
`is parallel to the optical axis, si
`small defocusing by a small chan
`system does not introduce anyct
`This property makes these syste
`small defocusings do not introduc
`A rearteleceniric system hi
`(b). The stop is at the front focal |
`
`Chapter 1
`
`Geometrical Optics Principle
`
`\
`
`
`
`DIAPHRAGMS
`/
`
`Figure 1.24.- Vignetting in a lens
`
`If the light beam entering the system comesfrom a point objectoff-
`axis, as shown in Fig. 1.24, several surfaces may limit the transverse
`extension of the beam, producing an apparent aperture with a nearly
`elliptical shape. Then, the system is said to have vignetting. The vignetting
`effect appears only when the angle of incidence of the beam exceeds a
`certain limit. It is frequently desirable to avoid vignetting in a centered
`optical system, as shown in Fig. 1.25, to avoid excessive decreasing of the
`illuminance of the image at the edge of the field and, to have a better
`control of the image analysis during the design stage.
`Sometimes,
`however, vignetting is
`introduced on purpose,
`to eliminate some
`aberrationsdifficult to correct.
`As shownin Fig. 1.23, of all meridional rays going from a point
`off-axis on the object plane, to the point on the image plane, only one
`passes through the center of the stop. This ray is the principal
`ray, or
`
`DIAPHRAGMS
`
`
`
`
`
`Figure 1.25.- Stop size to avoid vignetting in a lens for a given off-axis angle
`
`34
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`

`Chapter 7
`
`Chromatic Aberrations
`
`=
`RED
`
`EXIT
`PUPIL
`
`|
`
`BLUE PRINCIP
`
`and
`
`
`
`Wemaysee that the value of this determinant is the area of the
`triangle conecting the points representing the three glasses in a diagram
`of the partial dispersion P as a function of the Abbe number V. Thus,
`if this system of equations is to have a solution, this triangle must not
`have a zero area.
`
`7.4 Magnification Chromatic Aberration
`
`The magnification chromatic aberration, also frequently called
`lateral chromatic aberration or lateral color, appears when the images
`produced by different colors have different sizes on the observing
`plane. The effect of this aberration is a blurring of the image detail for
`points off-axis. The farther away from the axis,
`the greater the
`aberration (O’Connell, 1957).
`To find an expression for the magnification chromatic aberration
`let us consider an optical system, as shown in Fig. 7.10. The paraxial
`
`Figure 7.10.- Principal rays in
`aberration
`
`sagittal image for red light
`The paraxial sagittal image
`principal ray. The heights /:
`Lagrange theorem. As point
`aberration arises because th
`red and blue paraxial
`sag
`aberration, these two images
`chromatic aberration, repre
`distance SQ from the blue ;
`ray (or viceversa, by the dis
`Now, let us consider a
`(Chromatic Difference of .
`assumein this figure that th
`for colors C and F. This is ni
`in a first approximation.
`i
`usually small distance betw«
`Thus, we may write
`
`
`
`236
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`— 5G
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`

`

`
`
`hapter 7
`
`Chromatic Aberrations
`
`:
`
`RED PHINGIEAL RAY
`
`
`
`BLUE PRINCIPAL RAY \ SsAa R
`
`EXIT
`PUPIL
`
`|
`
`.
`
`(7.59)
`
`(7.60)
`
`rea ofthe
`| diagram
`V. Thus,
`must not
`
`tycalled
`— images
`Bserving
`cetail for
`t2ier
`the
`
`berration
`} paraxial
`
`
`
`hy he
`M
`
`t
`
`\{
`
`\
`
`i
`»!
`pe
`
`Figure 7.10.- Principal rays in a system with axial and magnification chromatic
`aberration
`
`sagittal image for red light is at the point S on the red principal ray.
`The paraxial sagittal image for blue light is at the point R on the blue
`principal ray. The heights h’, and A’, may both be calculated with the
`Lagrange theorem. As pointed out before, the magnification chromatic
`aberration arises because the image magnification is different for the
`red and blue paraxial sagittal
`rays. Due to the axial chromatic
`aberration, these two imagesare at different planes. The magnification
`chromatic aberration, represented by Mchr, is defined by the lateral
`distance SQ from the blue paraxial sagittal focus to the red principal
`ray (or viceversa, by the distance PR~ SQ).
`Now, let us consider again Fig. 7.11 and define a quantity CDM
`(Chromatic Difference of Magnification), analogous to OSC. We
`assumein this figure that the exit pupil position is at the same position
`for colors C and F. This is notstrictly true but it may be considered so
`in a first approximation,
`if (/’,
`- UJ is large compared with the
`usually small distance between the pupils for the two colors C and F.
`Thus, we may write
`
`OM =
`
` i- 0
`|—
`=| h¢
`-1Cc
`k
`
`(7.61)
`
`237
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