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`IMMERVISION Ex. 2016
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`IIAIIIIBIIIIK IIF
`[ENS DESIGN
`
`IIAIIIEl MALAGABA
`
`ZAGABIAS MAlAflAflA
`Centro de Investigaciones en Opt/ca, A.C.
`Leén, Mexico
`
`New York- Basel - Hong Kong
`
`Marcel Dekker, Inc.
`
`2/6
`
`2/6
`
`

`

`
`
`About the Series
`
`Library of Congress Cataloging-in-Pulilication Data
`
`Malacara Daniel
`Handbook of lens design “ Daniel Mttlaczu’a. Zacarias .Vlalaezira.
`p.
`cm. v- (Optical engineering: v. 44)
`Includes bibliographical references and index
`ISBN 0—8247-9225-4
`l. Lenses—Design and construetioiiiHandhooks. manuals. etc.
`2. Mirrors—Design and constructionalInndhooks. manuals. etc.
`3. Optical instrunients~Design and constructioniHandbooks. manuals.
`etc.
`I. Malacara. Zacarias.
`11. Title.
`III. Series:
`Optical engineering (Marcel Dekker, Inc ‘2. v 44,
`QC385.2.D47M35 £994
`68l‘.423—dc20
`
`94718940
`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):
`10 9
`8 7 6 5 4 3 2
`1
`
`There is no dog“: ::
`
`tieid of optical scietic: 4::
`>eience and engineer;
`'
`
`propagation. manipuL
`faith matter. and it: e :-
`
`commercial, and mim
`contend that optical st
`
`encompass anything ti
`..
`
`ultraviolet
`to
`the
`...._'_-
`
`optoelectronics. photo::.-:
`engineering.
`It remains true. ‘
`
`
`
`.deanced the optical s). >1»:
`the use of traditional wiz:
`completed without rec. :«
`subject is still the cor"
`'
`
`It is very fittin
`our series in optical
`elegant text on lens ties
`..
`
`haste principles of gem .
`'.
`elements of the (lest;
`aberrations. A \‘arie:}
`magnifiers to compex
`telescopes. microscopes. 7
`
`described for many or 2::
`
`prisms
`is
`included.
`optimization of optic-J. us
`The informatio: ::
`course,
`for selfrstud}.
`.
`:
`engineer who has
`to e;
`conclusion, the impor‘
`
`and engineers who
`quantum—optics
`syste
`appropriately applied {:1 :E'
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`
`
`3/6
`
`3/6
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`

`

`Chapter 1
`
`Geometrical Optics Principle
`
`LENS
`ASSEMBLY
`
`DIAPHRAGM5
`
`FREE
`,
`/ /
`OFT553151
`/ /1
`
`
`\ APERTURE
`/
`7
`7
`
`LENS 1 15,! ‘
`
`LENS 2 ix
`LENS 3 b/ 7
`
`. ../_ /// ,
`
`Figure 1.24.- Vignetting in a lens
`
`If the light beam entering the system comes from a point object off-
`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
`aberrations difficult to correct.
`
`As shown in Fig. 123, 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
`
`ray that passes through the off—ax
`The intersection of the extension .
`
`object space with the optical a
`Similarly, the intersection of the i
`ray in the image space with the o
`All quantities referring to the pn
`top of the symbol, for example.
`ray and i7 is its paraxial angle v
`
`to see that )7 is equal to zero at
`
`
`axial rays (meridional rays "or
`without the bar.
`
`The tangential and sagitta
`may now be more formally defir
`plane that contains the princrpe
`sagittal plane is a plane perper
`contains the principal ray. As w;
`tangential plane for all media ban
`a centered optical system. Hou
`medium, because the principal raj
`In order to trace the pnr
`must know its direction in the t
`
`such that the principal ray passes
`
`1.6.1 Telecentric Systems
`
`Afiontal Ielecentric systerr
`at infinity. Since the stop (diaphra;
`must be at a finite distance to ave
`
`Let us consider the optical systen
`is parallel to the optical axis, si
`small defocusing by a small Chan
`system does not introduce any cl
`This property makes these systei
`small defocusings do not introdu.
`A rear telecentric system h:
`(b), The stop is at the front focal 1
`
`FREE
`
`OPT/CAL
`
`DIAPHHAGMS
`
`LENS
`ASSEMBLY
`
`
`
`
`
`
`
`
`
`mi...
`///
`
`
`Figure 1.25.- Step size to avoid vignetting in a lens for a given off-axis angle
`
`34
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`

`and
`
`Chapter 7
`
`Chromatic Aberrations
`
`EXIT
`I’UI’IL
`
`_-
`H“
`
`
`
`We may see 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
`
`236
`
`l
`
`HLUL‘ PR1}:(I?
`
`
`
`Figure 7.10.- Principal rays in
`aberration
`
`sagittal image for red light
`The paraxial sagittal image
`principal ray. The heights 12
`Lagrange theorem. As point<
`aberration arises because th
`
`sag
`red and blue paraxial
`aberration, these two images
`chromatic aberration, repre
`distance SQ from the blue I
`ray (or viceversa, by the dis
`Now, let us consider a
`
`(Chromatic Difi‘erence 0f .
`assume in this figure that th:
`for colors Cand F. This is m
`
`i
`in a first approximation.
`usually small distance betwc
`Thus, we may write
`
`
`
`
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`

`

`
`
`hapter 7
`
`Chromatic Aberrations
`
`,
`
`EXIT
`PUPIL
`
`l
`
`K
`
`(7.59)
`
`(7.60)
`
`'ea of the
`
`; diagram
`V. Thus,
`must not
`
`1:: called
`e images
`bierving
`Cetail for
`:ater the
`
`terration
`: garaxial
`
`RED PRINCIPA? RM
`BLUE PRINCIPAL RAY
`‘\"\b
`‘\ //:,// E
`/Q/
`
`,
`hf
`
`g
`
`l,
`.
`l
`r
`7
`,
`
`S /
`Q
`.
`h C
`M
`
`1
`
`lr
`r
`r
`r
`r
`r
`
`
`
`i
`I
`12.
`1
`>‘
`I
`l
`1i:
`4‘7 7* rififi
`
`3
`
`1
`
`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’F and h ’C 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 images are 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 Difierence of Magnification), analogous to OSC. We
`assume in this figure that the exit pupil position is at the same position
`for colors C and F. This is not strictly true but it may be considered so
`in a first approximation,
`if (1 ’F - T’k)
`is large compared with the
`usually small distance between the pupils for the two colors C and F.
`Thus, we may write
`
` 1f 7 7
`QM= r
`jhé
`/' —1
`C
`k
`
`(7.61)
`
`237
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