O Principles of Optics is one of the most highly cited and most influential
physics books ever published, and one of the classic science books of the
twentieth century. To celebrate the 60th anniversary of this remarkable
book’s first publication, the seventh expanded edition has been reprinted
with a special foreword by Sir Peter Knight. The seventh edition was the
first thorough revision and expansion of this definitive text. Amongst the
material introduced in the seventh edition is a section on CAT scans, a
chapter on scattering from inhomogeneous media, including an account of
the principles of diffraction tomography, an account of scattering from
periodic potentials, and a section on the so-called Rayleigh-Sommerfield
diffraction theory. This expansive and timeless book continues to be
invaluable to advanced undergraduates, graduate students and researchers
working in all areas of optics.
4 3 ( 2
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4 6 7 8 & 3
5 / Formerly Professor at the Universities of GoÈttingen and Edinburgh
( 4 9 / )2 / 8
7 6 6 3
Formerly Wilson Professor of Optical Physics, University of Rochester, NY
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Foreword by Sir Peter Knight
SEVENTH ANNIVERSARY EDITION
6 0 T H ANNIVERSARY O F F I R S T ( 6 9 9 2 5
20 T H ANNIVERSARY O F SEV E N T H ( 6 9 9 2 5
University Printing House, CambridgeiCB2i8BS,iUnited Kingdom
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of
education, learning and research at the highest international levels of excellence.
www.cambridge.org
Information on this title: www.cambridge.org/978110 8 477437
60th anniversary edition © Sylvia Pryce-O’Hickey, Susan Pryce,
Lois Pryce, John Pryce and Bruno Wolf
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 1959 by Pergamon Press Ltd, London
Sixth edition 1982
Reprinted Seven Times 1983-93
Reissued by Cambridge University Press 1997
Seventh (expanded) edition 1999
Reprinted with corrections 2002
15th printing 2019
60th anniversary edition 2019
Printed in the United Kingdom by TJ International Ltd, Padstow Cornwall
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Born, Max
Principles of Optics - 7th edition.
1. Optics. I. Title. II. Wolf Emil
535
QC351
80-41470.
ISBN-13 978- 1-10 8 - 47743-H7 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. Information regarding prices, travel timetables and other
factual information given in this work are correct at the time of first printing but
Cambridge Universtiy Press does not guarantee the accuracy of such
information thereafter.
Foreword
Sir Peter Knight
1 Introduction
Optics in the twenty-first century is a vibrant part of modern physics, with stunning
developments in fundamental science (imaging, correlations, and coherence, and so
much more), as well as underpinning our technological world, including providing high
bit rate optical communications, and precision laser engineering. But, 75 years ago,
optics as a major field of research had been regarded by many as a backwater. One
of the leaders of my own department at Imperial College London had described it as
“all pins and mirrors” and pushed to have it dropped from the undergraduate syllabus.
How wrong he was and how fashions have changed: the field was by then poised for
explosive development, starting with the realisation, very much pioneered by Emil Wolf,
that the study of correlations in light fields unlocked new insights. Understanding partial
coherence, the extension to higher-order correlations with the work of Hanbury Brown
and Twiss, and then of course the realisation of the laser transformed our views of the
optical world. And the magnificent monograph by Max Born and Emil Wolf was at the
fore in this revolution. With the publication of B&W, at last we had a magisterial account
of the fundamental principles and their application. What an achievement! It has become
a major sourcebook used throughout the world.
2 Physical Optics Prior to the Appearance of Born and Wolf
In the early twentieth century, authoritative books on optics, developing the basic
phenomena in a systematic fashion, were not plentiful, especially ones building up
the theoretical basis from proper electromagnetic foundations. It was, it seems, hard
to locate sound and rigorous analytic treatments of diffraction theory, let alone highlevel discussions of image formation.
Born’s own monograph Optik was published by Springer Verlag in 1933, just as he
was forced to leave Germany by the Nazis. Optik itself eventually formed the seed for
what became Born and Wolf, and was wrongly thought at the time by Born to have
had very limited sales. Springer’s scientific advisor in the 1930’s was Paul Rosbaud, an
influential figure in pre-war German science, in contact with all the important figures
in German physics and much valued by Born. He was later to be revealed as a highly
valued British Intelligence agent throughout the Nazi years as described by Kramish
(1986) and will appear again in this account of how Born and Wolf came about.
v
vi
Foreword
3 Max Born
Max Born, one of the greatest figures in twentieth-century science, is best known for his
pioneering work in the creation of quantum mechanics in the 1920s in Goettingen, for
which he was awarded the Nobel Prize much later and after an inexplicable delay where
the citation read for “fundamental research in Quantum Mechanics, especially in the
statistical interpretation of the wave function.” Born had led an extraordinarily talented
group of theoretical physicists, including Werner Heisenberg and Pascual Jordan, in
the 1920s, who had pioneered the development of quantum mechanics, developing the
matrix mechanics approach, commutation relations, and much more that underpins our
understanding of the microscopic world. Indeed, Hedwig and Max Born’s tombstone in
the Goettingen Stadtfriedhof carries the famous p,q quantum commutation relation, one
that Born himself considered to be his main single contribution to science, according to
his son Gustav (Born 2002).
But Born was truly a polymath, active in an extraordinary range of physics, including
continuum mechanics, solid state physics, and of course optics. Max Delbrück, Siegfried
Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang
Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees
under Born at Goettingen, and his assistants included Enrico Fermi, Werner Heisenberg,
Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld,
Edward Teller, Walter Heitler, and Eugene Wigner. The catastrophic rise of the Nazis
at the start of the 1930s destroyed this wonderful centre: expulsions and a mass exodus
dispersed this incredible talent around the world, and Born’s Optik appeared as a kind of
last act from this Goettingen world.
Max Born, for some years after 1933, led a peripatetic life in Cambridge and
elsewhere, before finally setting in Edinburgh as Tait Professor of Natural Philosophy,
where his group members included Kellerman, Fuchs, Schlapp, Nisbet, and others. His
Edinburgh “Natural Philosophers” – really the theoretical physics group – were housed
in High School Yard on Drummond Street, a rather dingy back street behind Thin’s
University Bookshop, with a small lecture room and a large room to house the entire
group. Born would progress round each of his group – and especially his students – every
morning, asking what progress had been made since the day before. I vividly remember
Wolf explaining to me the tensions this progression induced in the young researchers!
Born had been a prolific textbook author, on relativity, atomic physics, optics,
and crystal lattice dynamics, demonstrating his enormous breadth of interests and his
encyclopaedic knowledge. He retired from his chair in 1952 and he and his wife returned
to Germany in 1954, and he continued with active writing for many years. He finally, and
very belatedly, received his Nobel Prize in 1954 for his fundamental work in quantum
mechanics. Max Born died at age 87 in hospital in Goettingen on January 5, 1970.
Born’s very precise mathematical approach to fundamental physical phenomena must
have stemmed in part from his early academic career in Goettingen as the assistant
to David Hilbert, the doyen of mathematics at the turn of the twentieth century. Born
and Wolf beautifully displays this approach: elegant, deep, and precise. Kemmer and
Schlapp (1971), in their Royal Society Biographical Memoir of Born, captured this
precisely: “Born’s approach here, as in most of his other work, was to face his problem
in all its complexity, to devise a mathematical formulation of appropriate generality and
then to descend to the simpler, more tractable (and usually physically most interesting)
cases as clearly defined specialisations and approximations to the general formalisms.”
Foreword
vii
4 Emil Wolf
Wolf, the father of optical coherence theory, dominated optics for more than half a
century. He was born in Prague in 1922 to Jewish parents and at age 16, following the
1939 German invasion of Czechoslovakia, became a refugee, initially in Paris, and then,
after a perilous escape from Paris, arrived in England after the fall of France in 1940. He
completed high school in England and studied at the University of Bristol for his B.Sc.
in Mathematics and Physics (1945) and stayed on for his Ph.D. with E. H. Linfoot, with
a dissertation entitled “A Contribution to the Theory of Aspheric Optical Systems.”
About the time of Wolf’s Bristol thesis completion, his advisor E. H. Linfoot moved
to the Cambridge University Observatory, taking Wolf with him as his assistant for the
next two years. During this time, Wolf participated in the regular meetings then held at
Imperial College of the small UK optics community, and cemented his strong links with
Dennis Gabor, G. P. Thomson, and others.
Between January 1951 and 1954, Wolf worked at the University of Edinburgh with
Max Born, writing B&W. According to Wolf (2005), Born wrote to Appleton, the then
Principal of Edinburgh, saying that he felt the decision about appointing his assistant
should not be made by Born alone as he “would like to appoint a Wolf after a Fox” (a
previous holder of his assistantship was the atom spy Klaus Fuchs – “fox” in German)!
After Born’s retirement, Wolf led a peripatetic career for a while. After a period on the
Faculty of the University of Manchester, notably forming his close and highly successful
collaboration on partial coherence with Brian Thompson (later to be Dean in Rochester),
Wolf moved to the United States in 1959 to take a position at the University of Rochester
where he supervised many Ph.D. students who went on to highly successful careers. He
eventually became a naturalised US citizen and became the Wilson Professor of Optical
Physics at the University of Rochester. My own stay in the group of Joseph Eberly at the
University of Rochester (with an office along the corridor from Emil) in the early 1970s
was enlivened by our daily group lunches at the University Faculty Club, where new
developments in optics were vigorously dissected, and Emil showed his extraordinary
grasp of the whole swathe of optical science. In 1978 he became President of the Optical
Society of America, his spiritual home, and attended without fail the OSA Annual
Meetings, always making a point of meeting up with student members to learn about
the latest developments in optics.
5 Postwar Situation and Translation Plans for Optik
Paul Rosbaud, whom we met in an earlier section, was thanked in the preface of the
first edition of B&W for having been closely associated with the project in its early
days. Rosbaud had been involved in the earlier Born monograph Optik as a former
editor for Springer, and was by then interested in translating German texts into English.
Rosbaud after the war had moved to England, where he helped set up a publishing
company, Butterworth-Springer, with a distinguished Scientific Advisory Board that
included Alfred Egerton, Charles Galton Darwin (Born’s predecessor as Tait Professor
of Natural Philosophy in Edinburgh), Edward Salisbury, and Alexander Fleming. When
the Butterworth Company decided to pull out of the English/German liaison, Robert
Maxwell (like Wolf, a Czech wartime refugee) acquired 75 percent of the shares of
the company, while 25 percent rested with Rosbaud. The company name was changed
viii
Foreword
to Pergamon Press; the partners, with their considerable language skills, cooperated in
establishing new academic journals until 1956, when, after an inevitable disagreement,
Rosbaud left.
Maxwell from then on dominated Pergamon, with unhappy implications described
below. Maxwell himself was ejected from the board of Pergamon in October 1969.
An inquiry by the UK Government Department of Trade and Industry reported in mid1971: “We regret having to conclude that, notwithstanding Mr Maxwell’s acknowledged
abilities and energy, he is not in our opinion a person who can be relied on to exercise
proper stewardship of a publicly quoted company.” Nevertheless, Maxwell reacquired
Pergamon in 1974, although it was sold to Elsevier in 1991 after Maxwell’s strange
drowning from his yacht in the Atlantic led to the collapse of his very extensive
publishing group.
6 The Move from an Update of Optik to a New Book
As Born’s plans for a translation and updating of Optik were developing, he became
aware of a curious involvement of the US Government in the rights for the book. The
US had spent considerable sums in acquiring access to German scientific publications
before the war. Then, during the war, they had reproduced many foreign journals and
books under the aegis of the “Office of Alien Property Custodian,” which allowed
US publishers with licences to print without royalty payments to authors or original
publishers. Born, of course, had been a British citizen since before the war, yet was
caught up in all this and had made no progress in restoring his rights to Optik, despite
many appeals to the authorities. Indeed, according to Nancy Thorndike Greenspan,
Born’s biographer (Greenspan 2005), Thomas H. Creighton of the Office of Alien
Property insisted the rights were vested in the US under the Trading with the Enemy
Act, that he would need to apply to the US Government for a licence if he wanted to
use portions of Optik in the new book - and, what’s more, had to pay 2 percent royalties
on the new book as they owned the copyright! The US Government finally relented,
presumably realising that Born was far from ever being an enemy alien and had for
many years been a citizen of an allied country! They returned to Born his copyright and,
belatedly, the royalties on what he discovered were an unexpected 1,000 sales. As we
will see, this should have alerted Born to be wary in future about reliable sales figures
and royalties.
7 Update and Co-authorship
The (quite sparse in those pre-laser days) scientists working in optics in the 1940s and
1950s would gather regularly at Imperial College London for meetings of what had
been called the “Optical Society of London,” and then became the Optical Group of
the Physical Society, now the Institute of Physics. Regular attendees included Born,
Dennis Gabor, Harold Hopkins, E. H. Linfoot, and, of course, Emil Wolf. Later attendees
included Leonard Mandel, who became Wolf’s closest collaborator over many years.
The early plans envisaged Born contributing material from Optik, with new sections
contributed by proposed co-authors Dennis Gabor and Harold Hopkins. The initial plan
was to complete the book by late 1951, before Born’s retirement from the Tait chair,
although of course the writing took eight years in the end. Hopkins withdrew from the
Foreword
ix
project early in 1950, and in October 1950 Gabor, encouraged by Born, wrote to Linfoot
and Wolf asking if they could take Hopkins’ place (Wolf 2005). Eventually, Born, Gabor,
and Wolf agreed to author the new book. Wolf moved from Cambridge at the end of
January 1951 to focus on the book. But then Gabor, like Hopkins earlier, decided he
really did not have the time to devote to the writing as a full author but agreed he would
contribute a section on electron optics. So, at that point, we see the emergence of the
Born and Wolf collaboration.
The book was intended from the outset to have sections on various specialist topics
contributed by others (Wolf himself was initially drawn into the project to write one on
the diffraction theory of aberrations!). Distinguished contributors included Clemmow on
rigorous diffraction theory (and the appendix on steepest descent and stationary phase),
Wilcock on interferometers, Wayman on image- forming optics, Bhatia on ultrasonic
diffraction, Gabor on the link between geometrical optics and classical mechanics –
especially for electron optics – and so on. An appendix on the calculus of variations
is based on unpublished lectures by David Hilbert, Born’s early mentor in Goettingen,
providing a link going back a century by then to one of the greatest mathematicians in
the world.
Most of the writing was done in Edinburgh and Manchester, and finally completed
when Wolf was a guest at the Institute of Mathematical Sciences at New York University.
Born was always able to write quickly, and according to Wolf was often none too pleased
with the slow progress made overall on the Principles of Optics project. The delays in
part stemmed from the new developments in optical coherence developed principally
by Wolf. By 1957, Wolf received a letter from Born asking why the book was still
unfinished. Wolf replied that it was essentially completed, except for the chapter on
partial coherence. According to Wolf (2005), Born wrote back to ask “who apart from
you is interested in partial coherence. Leave that chapter out and send the rest of the
manuscript to the printers.” Fortunately, he resisted, and within a couple of years the
laser revolution was upon us and optical coherence became centre stage in the subject.
One of the features of the book from the outset was the careful discussion of optical
correlations, both of amplitudes and of intensities. The early Manchester experiments
carried out by Brian Thompson on the effects of partial coherence on two-beam
interference were included to illustrate the importance of first-order coherence. The
dramatic discovery of intensity correlations by Hanbury Brown and Twiss also appeared
at this time and featured in the book.
8 The First Born and Wolf
The first edition appeared in January 1959, by which time Max Born had retired from his
chair in Edinburgh to live in Bad Pyrmont in Germany. Emil Wolf was then working in
Manchester University. This first edition of Born and Wolf was very well received for its
unique comprehensiveness and depth: to quote Kemmer and Schlapp (1971), “it presents
a systematic treatment based on electromagnetic theory of all optical phenomena that can
be described in terms of a continuous distribution of matter.”
Born and Wolf appeared at an extremely opportune time: just before the realisation of
the laser, where its spatial and temporal coherence and ability to transform image science
and information technology. Suddenly, everyone needed the insights that Born and Wolf
provided. Gabor himself stated that Born and Wolf was the first systematic account
x
Foreword
of holography in an authoritative text. Serendipity played its role too: for example, as
lasers were used to explore nonlinear optics, it was necessary to understand the spatial
distribution of intensity and phase of focused laser beams, and there in B&W already
was a beautiful discussion of the very isophotes the pioneers needed to understand phase
matching.
9 The Reception of Born and Wolf
Born and Wolf was very warmly received from the outset. University teachers quarried
it for insights in their courses, researchers used it as a source of rigorous reliable
information in optical science, and the resultant excellent sales reflected the real value
the world community placed on this treasure.
10 Updates
Updates and new editions appeared on a regular basis as new developments were
carefully incorporated by Wolf. The authors had considerable difficulties for some
years with Pergamon Press over royalties, with discrepancies over sales figures and the
emergence of perhaps previously unknown editions; this led to complex legal arbitration,
described in the biography by Greenspan and in detail by Max Born’s son, Professor
Gustav Born, in an article written shortly after Maxwell’s death, entitled “Pilfering
from the Professors” in the UK magazine The Oldie, edited then by Richard Ingrams.
The British satirical magazine Private Eye, also edited by Ingrams, had previously
lampooned Maxwell as the “bouncing Czech,” a nickname originally coined by Prime
Minister Harold Wilson when Maxwell had been Labour MP for Buckingham. The
happy transition to Cambridge University Press for this edition of B&W (and the
previous two editions) put an end to what can only be described as a sorry story of
the collisions of two worlds, one of academia and what had sadly been revealed as one
of a predatory publisher. What a contrast this revealed between two Czech refugees
from Nazi tyranny with such different characters – Emil Wolf being one, and Robert
Maxwell the other, entangled over Born and Wolf! The first five revised editions were
published by Pergamon Press (1959–1975). Cambridge University Press took over the
publishing of the monograph in 1980 with a seventh expanded edition published in 1999.
I still treasure my own Pergamon and Cambridge editions complete with a handwritten
greeting from Emil.
Plans were already expressed in the preface of the first edition of B&W for a volume
II on Molecular and Atomic Optics, and volume III on Quantum Optics (one of the
earliest uses of this term, to my knowledge). Rather touchingly, the authors expressed
the hope that the CGS system of units would have returned to favour by the time these
volumes might appear. Readers of the famous 1995 monograph Optical Coherence and
Quantum Optics by Leonard Mandel and Emil Wolf, representing in itself – in a sense –
this long-awaited “volume 3,” will have noted a partial fulfillment of this hope!
11 Lasting Value, Scholarship, and Reliable Knowledge
Here one continues to find in this masterpiece of lucid authoritative writing the most
complete account of modern classical optical physics. Born and Wolf remains one of
Foreword
xi
the most influential science books of the past 75 years. Here you will find the most
precise accounts of the Kirchhoff theory of diffraction, the theory of image formation
and aberrations, of partial coherence, and the like. You will find here the principles
of diffraction tomography, of scattering by inhomogeneous media – I could go on, of
course! Its impact can be measured by the many editions and reprints it has gone through:
a book that has a treasured place on the shelves of anyone working seriously in optics.
Acknowledgements
In writing this preface to the anniversary edition, I have drawn on many years of
discussions with Emil Wolf and his colleagues, and with Max Born’s son G. V. R. Born
(Gus), as well as from the many publications of and about Born and Wolf – but especially
from a lifetime of consulting this magnificent book!
References
Born, G. V. R. (2002) The Born Family in Goettingen and Beyond (Goettingen: Institut fuer
Wissenschaftsgeschichte).
Born, M. (1933) Optik: Ein Lehrbuch der Elektromagnetische Lichttheorie (Springer, Berlin).
Greenspan, Nancy Thorndike (2005) The End of the Certain World: The Life and Science of Max
Born (New York: Basic Books).
Kemmer, N. and Schlapp, R. (1971) “Max Born 1882-1970.” Biographical Memoirs of Fellows
of the Royal Society 17: 17–52 (Royal Society, London)
Kramish, Arthur (1986) The Griffin: The Greatest Untold Espionage Story of World War II
(Houghton Mifflin, Boston).
Wolf, Emil (2005) in Tomasz P. Jannson (ed.) Tribute to Emil Wolf (SPIE Press, Bellingham)
chapter entitled “Recollections of Max Born” pp. 29–50.
Sir Peter Knight
Imperial College
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Appendices
DGB
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' * ( 1 0 @ : 1 : 'I 0 B 6 : 'I 0 G : 1 0 , A 6 D ) 1 /1 ! $
+ 4 * I 1 ** ( 9E 2 *@ ( 99E 4 DGB
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* 3 @ ( Rm m !r$
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7 jì !í$j <
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7 0} 81:143
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+*
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3 - ; < 0} 4143
0} 8193
+**
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+B,
Historical introduction
he *+ 3 0 ) 0 #
J 9 0 #
9 0 ; P( !c
+'B % $ ( !c B % $Q
&C 6 !*G+,'*,G$ { 6 ! $ % ; ; !*G,'*,@$ 8 E I 7 History and
Present State of Discoveries relating to Vision, Light and Colours !@ > / *AA@$J =
A Course of Lectures on Natural Philosophy and the Mechanical Arts > * !/ *DG$ BA'
BDGJ ( ) Geschichte der Optik vom Ursprung dieser Wissenschaft bis auf die gegenwaÈrtige Zeit @
> !% *DBD *DB$J ( 4 The Principles of Physical Optics !8 ; *+*B ( *+@, 6 7 5
= *+GB$J ( : Geschichte der Optik !/" ) *+@,$J > & Storia della Luce
!% E L @ ( *+G@$ ( ) 1 A History of the Theories of Aether and Electricity > 9 !The Classical Theories$ *+G@J > 99 !The Modern Theories 1900±1926$ *+GB 5 3 / ( { & 6 Dioptrique, MeÂteÂores ! ! $ / *,BA M6 C1$ Principia Philosophiae ! *,$
:
; J
*,@* ) 3 !3 c *GD'*,@,$ 9 *,GA 7 8 !*,*'*,,G$ Principle of Least Time{ M5 1 M 1 M51 1 & % { !*,@A'
*,+*$ & : } !*,BG'*AB$ : M 1 8 4 ; k !*,*D'*,,B$ : } % : % 0 9
5 !*,@'*A@A$ *,,, " " ! :{{$ 5 ! $ 51 *,AG 2 &K !*,'*A*$ I1 {{
: :{{ !*,@+'*,+G$ : #
0 M 1 J 3 *,@, 6 Dioptrique 3 6 3 1 - { 9 9 Oeuvres de Fermat > @ !7 *D+*$ BG
{ The Philosophical Works of & % ! 7 3 $ > 99 !3 / *ABD$ A
} & : Micrographia !*,,G$ 2
k 8 4 ; Physico-Mathesis de lumine, coloribus, et iride !% *,,G$
} : : M 1 9 5 Phil. Trans. 5 D !8 *,A@$ BAG
{{ : Traite de la lumieÁre ! *,AD / *,+$
{{2 &K MeÂm. de l'Acad. Sci. Paris 8 !*,,,'*,++$ GAGJ J. de Sav. !*,A,$ @@B
:
# ) : # P *,,+ ( % !*,@G'*,+D$Q 9 : " #
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9 *D* = !*AAB'*D@+$ { : =1
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4 { !*AAG'*D*@$ *DD # : 4 9 7 3 / !*A+'*D@A$ I #% % !*AA'*D,@$ 9 - " 0 7 *D*D - % " I 8 !*ADD'*D@A$ } :1
( =1 7 9 8 M 1 ' 8
J L. Euleri Opuscula varii argumenti !% *A,$ *,+
{ = Phil. Trans. Roy. Soc., London !*D@$ BDA Miscellaneous works of the late Thomas
Young > 9 !/ I 4 *DDG$ * *A
{ (C / 4 Nouveau Bull. d. Sci., par la Soc. Philomatique > * !*D+$ @,, MeÂm. de la Soc.
d'Arcueil > @ !*D+$
} 8 Ann. Chim. et Phys. !@$ !*D*,$ @B+J Oeuvres > * D+ *@+
:
7 8 1 9 !*D*D$ 8 1 0 60 8 O !*AD,'*DGB$ ! $ 2 8 *DG* : /C 8" !*D*+'*D+,$ 8 "
! *D*,$ " = *D*A 8 #
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# : / { !*D'*DD*$
9 8 ! *D@*$ } 6 8 " k
8 1 *DG 8 } 8" % 8 Oeuvres CompleÁtes d'Augustin Fresnel > @ !7 9 9 *D,,'*DA$ @,* A+$
{ ) & : Trans. Roy. Irish Acad. !*DBB$ * Hamilton's Mathematical Papers I /
3 ) > * ! ? 7 *+B*$ @DG
{ : / Trans. Roy. Irish Acad. !*DBB$ *G
} 8 ibid BD
k 8 MeÂm. de l'Acad. !*DB@$ B+BJ Oeuvres A,A
} / 8 Compt. Rend. Acad. Sci. Paris 48 !*DG$ GG*
: 8" / % Compt. Rend. Acad. Sci. Paris 48 !*DG$ G,@ AA*
:
# J :1 / 4 : 5 !*ADG'*DB,$ R ! $ - 0 /
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9
4
1 / 4 : 5 MeÂm. de l'Acad. ! *D@* *D@A$ BAG
{ / Exercise de MatheÂmatiques 4 !*D@D$ *,
{ 3 6 7 MeÂm. de l'Acad. : !*D@D$ ,@B
} ; ; Trans. Camb. Phil. Soc. !*DBD$J Math. Papers @G
k I 4
Phil. Mag. !B$ 8 !*DBA$ @ BD@J Proc. Roy. Irish Acad. : !*DBA$
} 8 5 Abh. Berl. Akad., Math. Kl. !*DBG$ I 4
Trans. Roy. Irish Acad ) 6 !*DD$ *G
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4 1 0 9 9
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9 : - I 8 1 !*ADA'*D@,$ {{ !*D*'*D*A$
) Phil. Mag. !G$ = !*DDD$ * % / !/ *+$
{ 5 Math. Ann. !*D,+$ B@G !*DA$ *D@
{ I ) 3 !/ & $ Phil. Mag. !$ 2 !*DA*$ G*+J 2 !*DA*$ D*
} ; < Berl. Abh. Physik., Abteilg. !*DA,$ GAJ Ges. Abh. BG@J Berl. Ber. !*DD@$ ,*J Pogg. Ann.
Physik. u. Chem. !@$ : !*DDB$ ,,BJ Ges. Abh., Nachtrag. @@
k 4 8 Experimental Researches in Electricity !/ *DB+$
} I 4 A Treatise on Electricity and Magnetism @ > !2 *DAB$
& < ) ) Pogg. Ann. Physik u. Chem. !@$ !*DG,$ *
{{: :" Sitzb. Berl. Akad. Wiss. 8 @ *DDDJ Wiedem. Ann. 42 !*DDD$ GG*J ( Electric Waves !/ 4 *D+B$ *A
{{I 8 Gilberts Ann. 9= !*D*A$ @, ) : ) !*A,,'*D@D$ *D@
!Phil. Trans. Roy. Soc. / !*D@$ B,G$ :
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0 å ˆ hí " ( % 2 7 1 ( !*DA+'*+GG$
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: & % ; < Untersuchungen uÈber das Sonnenspektrum und die Spektren der Chemischen
Elemente., Abh. kgl. Akad. Wiss. !% *D,*$ *D,B
{ 4 7 Verh. d. deutsch phys. Ges. !*+$ @@ @BA Ann. d. Physik !$ 2 !*+*$ GGB
{ 5 % Phil. Mag !,$ = !*+*B$ * A, DGA
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: 7 I ibid 49 !*+@,$ GGAJ / % TheÁse !7 *+@$J Ann. de Physique
!*$ 4 !*+@G$ @@J ( 3 K Ann. d. Physik !$ !*+@,$ B,* D+ ABJ :8 !*+@,$ BAJ :
!*+@,$ *+ ( E Collected Papers on Wave Mechanics ( 3 K !/ ; %
*+@D$J 7 4 6 Proc. Roy. Soc. 8 !*+@G$ ,@J ibid 8 !*+@,$ G,*
k ( Ann. d. Physik !$ !*+G$ *B@J 8 !*+,$ *++
:
#
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{ I % Phil. Trans. 49 !*A@D$ ,BA
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# } M" 1 # ! $ : /" Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten KoÈrpern
!/ ( I % *D+GJ /" *+,$
{ 4 Amer. Jour. Sci !B$ !*DD*$ @J 4 ( ) 4 Amer. Jour. Sci.
!B$ 42 !*DDA$ BBBJ Phil. Mag. 2 !*DDA$ +
{ ( Ann. d. Physik !$ !*+G$ D+*
} ( Berl. Sitz. !*+*G$ AAD A++ DB* D Ann. d. Physik !$ 2 !*+*,$ A,+
1.1 The electromagnetic ®eld
1.1.1 Maxwell's equations
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$ v ˆ :
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wave-front
!/"
θ2
v2, n2
θ1
v1, n1
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1.3 Scalar waves
!r " }$ !7" ' * 4 0 # # 69 !87 " 793, " # )# 155 !873"
$ # 1 > $6 3/7
#/, 0# ) # " 14 #
/ + 3
@$ ˆ #:
v$ @ $
=$ !"
= % ' 1.3.1 Plane waves
* r! ," " s! , " 0 !" ˆ !r . s "
!$"
r . s ˆ s
< 'î 'ç 'æ
s ! 2 "
r . s ˆ æ
'æ
!/"
@
@
ˆ @
@æ
@
@
ˆ @
@æ
@
@
ˆ , :
@,
@æ
2 @$ @æ$
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æ
v ˆ æ ‡ v ˆ ζ
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η
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s
r
ξ
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2 ? x
6
4 !3" - @$ ˆ #:
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ˆ !r . s
v " ‡ $ !r . s ‡ v "
!8"
$ = !æ " !æ ‡ vô
‡ ô"
ô : v
æ + $ !æ ‡ v " )
v æ 1.3.2 Spherical waves
> ˆ ! "
!9"
ˆ jj ˆ $ ‡ $ ‡ , $ B @=@ ˆ !@ =@"!@=@ " ˆ !="!@=@ " =$ ˆ
@$
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v$ @ $
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> ' !3" æ : !" !8"
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v"
‡
$ ! ‡ v "
!$"
$ ) !$"
v 1.3.3 Harmonic waves. The phase velocity
0 r#
!r# " ˆ +! ":
!/"
0 - + 0 + +! " ˆ !ù ‡ ä":
! "
/ + 7
: !. #" ù ‡ ä ' íˆ
ù
ˆ
$ð (
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ù ' $ð + +
‡ ( ( = ! ' " ! " * s 0 }/ r . s=v ! "
r.s
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‡ä :
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v
1' !6" r . s r . s ‡ ë
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$ð
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ù
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s $ð ù
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$ð ù ù
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v
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1 # ˆ $ðk ˆ
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v
ë
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g
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q ! "=ù 2 p
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2 5 !r "
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!r " ˆ
ù !r" Hù
ù !r"I ù:
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#
0 + )# # " 1 44 !9 " 77 * 4 44 !9 " $#/
1 * 4 0 " 6 !> @- 0 ? 96#" 7 / 0 L
1 ; . < + " " 3 !4 > @- + 99 "
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:
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(a)
a
t
(or z)
π  π
or
ω  k
(b)
(c)
2a
t
(or z)
2π  2π
or
δω  δk 
2 3 0 !" ! ù
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1.4.1 The general electromagnetic plane wave
, < ' E H }/
ˆ r . s v E ˆ E!r . s v "
H ˆ H!r . s v "
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s A E_ ˆ vE9
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s 3 H9 ‡ E9 ˆ # !/"
ìv
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s 3 H Eˆ
å
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å
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s 3 E: ì
+ s E . s ˆ H . s ˆ #:
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G 5 2
! " !3" E H s ) = ! " p
p
ì! ˆ å !6"
ˆ jEj ! ˆ jHj
* s ) * D = 0 L 0 A & 406 !$###" $77
y
C @ < 0 & + " ' F EEEF 1 = !0 1 997" / 3 F $3
' v : % ' v
0 !6" } !/" å $
ì $
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ð
ð
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ì $
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sˆ
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!ô‡ä"
g
! . #":
: ô r.s
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ˆù
k . r:
v
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!$"
ˆ $ !ô ‡ ä$ ":
./ , ô ' !$" ) ˆ ô ä ô ä !/"
ˆ ô ä$ ô ä$ : $
: $6
4 ä$
ä$
+' $
$
$
‡
$
ä ˆ ô !ä$
ä " ä ˆ ô !ä$
ä ": $
$
$
ä ˆ $
ä
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ä ˆ ä$
ä :
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1' !3" ' ä $
$ $ä
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$
ä
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$
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å
å
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å
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ç î ˆ ø ‡ ø
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ç ˆ
ø ‡ ø:
$ $ ! > " ' 'î 'ç î ˆ !ô ‡ ä# "
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y
ξ
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x
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‡ $ ! ô ä$
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! ô ä
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‡ $ ! ô ä$
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ä ø ‡ $ ä$ ø
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) ) , ) ! ˆ $ ˆ # / ˆ # " ) ! ˆ $ ˆ # / ˆ # " ? M { Ó " 9 1.4.3 Harmonic vector waves of arbitrary form
) 0 ) V!r " ' < , }/ !$/"
!r"I !r " ˆ !r" Hù
!r " ˆ $ !r" Hù
$ !r"I
! 7"
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/ !r"I
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!r" ˆ !r" !r"
!r" ˆ !r"
:
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!r":
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V ! 7" ù ù = ! , " ! , " p q V!r " ˆ p!r" ù ‡ q!r" ù :
4 2 !3#"
: ? M ( 9 9 % : F $ !? . <M 89$" < $
{ 1 : . D 2# ' #
# ) # 44 !93 " 6/ + & D =- }#9/ + ? " # # )# 0 44 !936" $ 7
/
4 0 = !3#" V!r " ˆ RfU!r"
ù
g
!3"
U U!r" ˆ p!r" ‡ q!r"
!3$"
R = V ' R ' ' ; 2 U U? ˆ p
q:
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q$ ‡ $ p . q
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q" ˆ p$ ‡ q$ ? ) )
E!r " ˆ RfE# !r" ù g ˆ $HE# !r" ù ‡ E?# !r" ù I
!3/"
H!r " ˆ RfH !r" ù g ˆ HH !r" ù ‡ H? !r" ù I
#
$
#
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( ˆ $ð=ù ) (9 å $
å (9 $ $ ù
h i ˆ
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68
4 0.5
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2.1.1 The vector and scalar potentials
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2.2.1 The potentials in terms of polarization and magnetization
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angle δΩ formed
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Source
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3.2.1 The differential equation of light rays
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$ ë ! " "
) }"! $ B ( " /
3 ˆ 5 0 G 8 " 1"5H 9 è3 ˆ è % è3 ˆ ð
è :
3
$ / 9 "
n12
n12
N12
n2s2
θ2
2
θ1
1
n1s1
n1s1
θ2
2
T
1
(a)
θ1
n2s2
(b)
8 " 1"5 # B "
N12
T
1
### 8 3.2.3 Ray congruences and their focal properties
!
s ˆ 3
" #
3 s ˆ :
33
F " # 3 s ˆ
s ‡ 3 s (
s" # s . s ˆ :
31
) " # $ % /" 8 ) $ ## ( "
# % 31 33 "
; v S, - ˆ " 6 v S 6" ; r
" r v 6 8 " 1"0"
& s
Q
s
P
Curve of the
normal congruence
(ray)
u constant
v constant
Surface S constant
8 " 1"0 > "
8 $ &" 7" C ( ( & & K = '" # 032 & L% '"
## 01 & L###"
1"1 + 1!
v ‡ v ‡ v S
$ " = r v ˆ r ‡ v ‡ v
‡ 3
"
7$ 3 r ‡ rv v ‡ s ˆ 3!
r rv v" & 3! r rv s " ""
Gr rv sH ˆ :
3,
v 3," # r s ˆ r= 3, 1 " # r ˆ / "
# v ( 3, ( % " ) " ( "
C "" " / }",
"
3.3 Other basic theorems of geometrical optics
C "
3.3.1 Lagrange's integral invariant
) $ " }1"3 , /(D ( s ‡
s . r ˆ :
$ % " 7" ( 7 # 0 / :# 0 " # E" *" = 6
7 " : 40 " : .
% : '" 1 = 9 ' 500" / 7" & 7 0 , = *
033" / ) $ # " 5!"
1,
### 8 T
C2
C1
K
n1
8 " 1" # ; D
$"
3
n2
s . r
3
$ / / 3 ; "
C % " % %3 % 8 " 1" % J + " + (
% + %3 + %
s . r ‡
%3
3 s3 . r ‡
+
3 s3
s . r ˆ :
1
+ N3 ˆ s 3 s3 + 1 "
3.3.2 The principle of Fermat
( 3
$ / / 3
0 / < / $ " . / }1" 32
3
( "
ˆ 3
1"1 + 12
" /
$ $ B "
. 8 D ( "
)
0 "
8 D ( 3
% % J
3 8 " 1"" ; J % 6 63 %
6 63 " 8 693 J
63 63 %9 6 "
)
; D 6 63 693 s . r 6 63 ‡ s . r 63 693
> 6 63 ˆ :
!
s . r 6 63 < 6 63 :
8 s r C′
Q2′
Q2
C
C
P2
Q1
Q2
Q1
P1
8 " 1" # 8 D "
) $ #" # 7
) $ # 2" # }1"3 3 } ) $ #"
# &" & 6 G .
/ 012H $ " # ( 8 D ( $ " I D E ) $ # }"
15
### 8 s . r 63 693 ˆ :
) }1" 3! 6 693
6 63 6 693 ˆ 6 63 :
+ ! 6 63 < 6 63
,
%
<
%
:
2
- s r % "" " $ " * 8 D "
# " & $ B 8 "
1"3" 3 % B "3 3 " # B "
9 < " 8 3 3 9 "" 3 " 8 $ 8 " 1"1 9 9 " 8 3 9 3 $ ( 53 "
M
P2
P1
8 " 1"3 8 "
B 1"1 + A
10
B
P1
P′1
P2
Caustic
8 " 1"1 & "
$ 3.3.3 The theorem of Malus and Dupin and some related theorems
J S, - ˆ S ( }1" !" - $D " * „ " 8 "
' " # % / C" F" * <
. D " # * ) # ##" * ; D "
& : " "
" / " #
55 - { B " ; < 5, M 53! 9 53!
- D " ( " ( = $ 9 "{
) ( $ &" & 6 ""
{ 7" - + < 8 2: 7 55 4 5430" ) 6 D " : : > # 0 0 2 5 3413" F - 4< " 3 &/ '" " )" C" & E" ;" / & & K = 01 " ,1"
{ " ; & & & 4- 7 9 0 312 B "
### 8 # " & $
$ 3 8 " 1""
; J 3 " # 5 6 " > ( 53 6 5 53 3 :
G 3 H ˆ G5 653 H:
5
) 5 ( 53 3 " # 653 "
)
; D 3 53 65 3
‡
3 53
s . r ‡
53 65
‡
5 s . r ˆ :
0
> 5
3
‡
53 65
ˆ :
- s 5 s . r ˆ s . r ˆ :
3
0 3 53
3 " s . r ˆ r 3 "" %
P
A2
A1
n1
n2
B2
B1
S1
S2
Q
T
8 " 1" # - < "
1"1 + " B "
/ G 3 H ˆ G5 653 H $ / /
'/0 1 ) " B ( }1" 3, $" ( . %
J B I D ) $ #"
) * /0 1 $ $ / 0 /0 % /0 1 0 /0 " #
I D " # "
* D $ 8 * 48 }5"3
"
&" * : 7 > ;
; - N &" 03"
,0% 7
7 /" ="
n } S S ! } " # S $ % &
'
( )
' * # # # 4.1.1 The point characteristic
+ , , , # , { - . / # -* ( / $ 0, 1 % & '
323 456 3, 6 3 56 37 & ! " 8 # ( % 9 : + 9 9 ; # < 5
= > $ ' >
% & ! ' ( % 35" 2 ( 5 $ ' # ( ' * : + # 9 9 ; # < 57 $ ' > - ? ) 5, 74 522 4, 9
9 @ # $ > 57 . = '
: + * # 57 7" 3
{ $ # , /) ) .2
. $ '
.
y1
P1
s1
x1
y0
s0
z1
O1
P0 x0
z0
O0
- . , , , 6 ˆ
,
:
- } 24 , , , 6 ˆ S S, , , 2
S , , $ } 2. # , , # )
, ˆ , ,
ˆ , , , , #
$ # ˆ
.
+ á â ã # / {
ˆ á
, ˆ â
ˆ ã
"
A 2
á‡
2
â‡
2
ãˆ
2 ‡ , 2 ‡ 2 ˆ 2 :
4
#
S # # )
12 ' B: !
-* # $ # # 1. ( { $ C * 4
..
8 G - , # @
@,
, ˆ
ˆ
@
@
7
,, , , $ / - 4 7 ! # D
2 2 2
@
@
@
‡
‡
ˆ 2,
3
@,
@ ,
@,
2 2 2
@
@
@
‡
‡
ˆ 2 :
5
@
@ @
# ' $ # + ,
4.1.2 The mixed characteristic
$ ! !
{
Ó !ˆ
,
Ó # E! ,
! # # $
, $ ! # ä! ˆ ä
Ó ä
Ó ä :
F 7
ä ˆ Ó ä
Ó , ä, :
2
Ó , ä,
Ó ä :
- 2
ä! ˆ
( + ˆ @ =@ ## # ! # { $ ' A ! 9 ˆ ‡ Ó , ,
# $ ! ! 9 '
."
Ra
y
. $ P1
Q1
d1
O1
- .2 $ ! # , , , , , ˆ
@!
@,
ˆ
@!
@ ,, , A , !
2 2
@!
@! 2
@!
‡
‡
ˆ 2, :
@,
@ ,
@,
.
4 ! , , , 6
"
# - .2 Ó D
Ó ˆ 4
ˆ - /
# - 6 , 4 ! , - # . - .D
! ˆ 0, - 1:
# 4 ä ‡ , ä,
3
ä ˆ
7
# 3
# 4 # # # $ # ! ' .4
8 G Q1
Q0
m 0)
, q 0,
P1
P0
( p1 , q
1 , m1 )
(p0
O1
O0
- . '
D
* , , , 6 ˆ 0, 1
! , , , 6 , ˆ 0, - 1
, ,, 6 , ˆ 0-, - 1:
ä! ˆ
Ó , ä,
ä
' . ' .+ + /
,
ä, :
5
! ˆ ! , , , 6 , + + , ˆ
@!
@,
,, ˆ
@!
@ ,
, ˆ
@!
@,
2
ˆ
@!
@ ,
ˆ
@!
:
@,
22
E! 2 22
# 4.1.3 The angle characteristic
$ ˆ ‡ Ó , ,
Ó :
, ä ˆ Ó, ä,
# Ó ä
2 ' , ˆ
@
@ ,
2
ˆ
2 @
@ 2.
2"
, . $ '
.7
' -, - . #, # - .
ˆ 0-, - 1:
24
#
- ä 3 ä, 2.
,
,,
, ä, ‡ ,
, ä,,
ä ˆ ,
,
,
,
ä
ä, :
27
$ . ' + , ,, , D
ˆ , ,, 6 , 23
+ + ,
,
@
, ˆ
@ ,
,
ˆ
@
@ ,
,,
@
, ˆ
@,,
,
,
ˆ
9
>
>
>
=
@ >
>
:>
;
@,
25
# 25 4.1.4 Approximate form of the angle characteristic of a refracting surface of
revolution
+
ˆ
2 2
‡ 2 ‡
. 2
‡ 2 2 ‡ ,
# 2 . . . . !
9 # # # # # 2 ˆ
- :
2
. ˆ =3 - . ˆ
‡ 6
3 # 2
.3
8 G . ˆ
2 ‡ 2 2 ‡ 2 2
‡ ‡ :
‡
2
3 # , # $ # #, , , , # , , , , , . , . , - ..
-, - #, # 24
ˆ 0-, 1 ‡ 0- 1
ˆ f, ‡ ,, ‡ , , g
f ‡ , ‡ g
.
# , ,, , , $ . ( }22 !# # , ,, , , ' 0 2 ‡ 2
2
@0
ˆ
ë
@
ë
@0
ˆ
@
ë
@0
ˆ
@
2 ‡ 2 2
‡ 3 ë
‡ ˆ ,
ë
‡ ˆ ,,
ë
,
ˆ ,
"
9
>
>
>
>
>
>
>
>
=
4
>
>
>
>
>
>
>
;
: >
ˆ ,
y
Q0
O0
P
)
(p 0, q 0, m 0
(p1, q1, m )
1
O
Q1
O1
z
- .. $ # $ #, # # - -, . $ $ !
,
,
,,
,
ˆ
ˆ
'
.5
9
‡ Ä >
=
,
>
‡ Ä ;
7
Ä Ä ! , = = $ 7 " ˆ
, 2
2
‡
2 ‡ ,,
0 ,
‡ 0 ,
3 , .
, 2 1 ‡
2 ‡ ,,
,
0Ä ,
‡ Ä ,,
, 2 12 ‡ :
, 1
3
$ ) # Ä Ä 6 7 3 .
# # Ä Ä E! . , ,, , 6 , ˆ
, , ‡ ‡
0 , 2 ‡ ,, , 2 1
2 , ‡ 0 ,
3 , 2 ‡ ,,
, 2 12 :
5
E! 5 $ 4 % # 4
9
>
2
2 2
>
, ˆ ,
2, ‡ ,2, ‡
,
‡
>
,
=
2,
3, ,
.,
>
>
2
2
2
2 2
>
‡ , ‡ , ‡ ;
ˆ 2 3 ˆ
, ,
2, , 2, ‡ ,2, ‡
2 , 2 ‡ ,2 ‡ :
.
E! 5 .D
, ,, 6 , ˆ , ,
‡
0 , 2 ‡ ,,
2 , ,
2,
2, ‡ ,2, 0 ,
‡ ,,
2
‡ ,2,
, 1 ,
,
‡ 0 ,
3 , 2 ‡ ,,
, 2 1 2
.
‡
, 2 1 ‡
,
3,
, 2
2, ‡ ,2, 2
2
3
2
2 ‡ ,2 2 ‡ :
2
2
‡ ,2
2 ‡ ,2 .2
",
8 G $ # , ,, , 2, ‡ ,2, ˆ 2
% 2 ‡ ,2 ˆ v2
.2 , ‡ ,, , ˆ 2 :
.
, ,, 6 , ˆ , ‡ 2 ‡ . ‡ , ˆ 9
>
>
=
, ,
2 ˆ A 2 ‡ Bv2 ‡ C 2
. ˆ D . ‡ Ev. ‡ F . ‡ G 2 v2 ‡ H 2 2 ‡ Kv2 9
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
=
,
Aˆ
‡
2 , ,
Bˆ
2 , Cˆ
,
‡
,
Dˆ
‡
‡ . , 2 2 , ,
3,
‡
Eˆ
. , 2 2 , 3 >
>
>
>
>
>
‡ >
>
F ˆ
>
>
>
2 , >
>
>
>
>
‡
>
>
>
‡
Gˆ
>
2
>
. , , , >
>
>
>
>
>
‡
>
>
Hˆ
‡
>
>
2
>
2 , , ,
>
>
>
>
>
>
‡
>
>
:
Kˆ
;
2
2 , , >
>
2 ;
..
."
) #
. $
# }" 0, , 6 # ) 2
2
2
, ˆ , ‡ ,
2
2
2
ˆ ‡ , ˆ , ‡ , # , , , , /
# , , ,, , , ) . $ '
"
4.1.5 Approximate form of the angle characteristic of a re¯ecting surface of
revolution
$ H # # #
; - .. ." !
}.. 5 6 5 (
1 + ' ' # , 5 I #
# .,
, ˆ 2
‡ ,2, 2 ,
9
>
>
=
2 ‡ ,2, 2 ‡ 3 ,
.4
>
>
2
2 2
;
‡ , ‡ :
ˆ
3 p
# ! 2 2 ‡ , 2 H , ,6 H #
! # ., .4
, ˆ ˆ ' , ,, , 1 + ' + , ˆ ˆ ' H
#
9
, ˆ , ‡ >
>
=
2
2
2
2
.7
ˆ A9 ‡ B9v ‡ C9
>
>
;
. ˆ D9 . ‡ E9v. ‡ F 9 . ‡ G9 2 v2 ‡ H9 2 2 ‡ K9v2 2
2
‡ ,2 2 (p
1, q
1, m
1)
y
Q1
Q0 (p0, q0,
O0
O1
m0)
P
x
O
- ." $ H # #, # # -, - z
$ "2
8 G 0 ‡ ,1
2 2
B9 ˆ
0 ‡ 1
2 2
C9 ˆ
2
‡
,
D9 ˆ
‡ ‡ 3
4
.
‡
‡ ‡ E9 ˆ
4
.
3
A9 ˆ
‡ 4
‡
G9 ˆ
2
4
2
‡
‡
H9 ˆ 3
2
‡
K9 ˆ ‡ :
3
2
F9 ˆ
9
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
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>
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=
>
>
>
>
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>
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>
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>
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;
.3
9 , # ( , # , # , ) 2 # $ $ 2 , 6
$ . % , # 3, / / # 3 $ # + # 3, / A / ) .2 < }.2
) "
H
4.2.1 General theorems
( J ) + 2 , $ = 3"3 / = # ' > 35" - ? 5, ' + 54{
$ 9 @ { # # 9 @ / }
+ , 4, 4 ) / - .4 J ( )
, 4, 4 # # P0
C0
A0
Q0
A1
B1
B0
P1
C1
Q1
- .4 ( : 9 = - * 3"3 2 (
. 8 9
9 ; # < 35, 27
{ ' > CCI E ** % & ! ' ( % 35" 7,6 - ? ) 5, 746 522 4,7 E $ % #
9 9 ; # < 5,7 .7 ' +
$ ! ' ( 54 3 ( '
> 9 A E & # +
> 52. 2
{ 9 9 @ $ ! ( 524 } # 0 : > + 5 + = 5"1 # E % = # 8 E % ( F ' < 9 F J ( E # < 9 57 ," E % = # F J ( < 573
".
8 G J # J C * # ( ! } / , # % , , + 4, 4 / $ - .4
0 4 1 ˆ 0, 4, 1 ‡ 4, , :
+ 3, # / , 4, 3 % 3, , , -, 4, , -, - $ #
0 1 ˆ 0, , 1 ‡ , , D
0 - 1 ˆ 0, -, 1 ‡ -, , 0- 4 1 ˆ 0-, 4, 1 ‡ 4, -, :
' 0 1 ‡ 0 - 1 ‡ 0- 4 1 ˆ 0, , 1 ‡ 0, -, 1 ‡ 0-, 4, 1 ‡ 4, , :
A# 6
< 6 ! 1 5 ˆ 5, ‡ 4, , 2
5, ˆ
3,
, ,
5 ˆ
3
# 3, 3 F 4, ˆ , $ # B ˆ , , , ˆ , , , ˆ , , , :
,
( 3 s

2 2 2
, :
‡
‡
ˆ
,
,
,
' .
"
.2 < 5 ˆ
3
0 ,
, , ,
0 , , ,
""
ˆ 4
s
2 2 2
‡
‡
,
,
,
## =, =, =, 6 # 0 =, . . . =, . . . : F .
@ , @ , @ ,
ˆ
‡
‡
, @, , @ , , @, ,
7
=, =, ' 7 . 0 , , ,
ˆ Ö , , ,
3
0 , , ,
, , ,
Ö , =, . . . 6 # Ö
, =, . . . , =, . . .
,
,
,
, , ,
ˆ Ö , , ,
:
5
Ö , , ,
,
,
,
, , ,
- 2 4 3 3,
,
Ö , ˆ , 4, ,
# # , 3, $ # 3, #
!
, 4, F# , Ö , Ø
,
ֈ
@Ø , @Ø , @Ø ,
‡
‡
:
@, , @ , , @, ,
## , =, . . . , =, ) ) 5 $ # Ø ˆ 6 Ö ˆ , :
E! ,
, ˆ 4, ! 2 5 ˆ 5, ' # #
3,
, , ˆ
3
:
2
"4
8 G $ 7 - =* 9 2
,
,
, 2
- >
, # =* , , ˆ 2
, 2
, ˆ , , ˆ :
' # # $ # # F + #{ ) ) /# # { A0
L0
B0
d
B1
d′
B1
- .7 + * L1
=* $ # =* # % + $ < I + ' 523 53
( / , 4, 4 / > , 4, 4 + 4, , ' # ! - .7
0, 1 ˆ 0, 1 04, 4 1 ˆ 04, 4 1 :
+
0, 4, 1 ˆ 5,
$ !
0 4 1 ˆ 5
04, 1 ˆ 04 , 1 ˆ 9:
5, ‡ ˆ 9 ‡ 5
‡ 5 ˆ 5, ‡ 9
5, ˆ 5 :
$ # =* # G # # { % > & 8 ( > 2 52. 436 . 5." ,
{ ( # , / , # #, # .2 < "7
% # 9 @ D 2 + '
+ ' + H 9 /# . =, 2 , , = + , ˆ ˆ =, ˆ , + +
2 (
$ # ! # ! / 4.2.2 Maxwell's `®sh-eye'
( # ˆ
,
‡ = 2
.
# , C )* # ={
}2 # !
0 }2 1
èˆ
A
p
2
2 2
. %ˆ
rˆ
,
"
9 - ? 9 + 8 G
+ = 55 356 I # <
F J { : 9 = 3 8 * 3". 336 . 8 9
9 ; # < 74
=* ) % + $ < I + ' 523 53 & # $ 5"" "25 $ ) 5 # $ & ? + # ; # 9 < > p

+
( 54. }25 # ˆ 2 2
, < < # & - & *
5.3 34,6 ( - $ = ( J ( 5". 246
G $ - # 5".B5"" "7
"3
8 G r
èˆ
% ‡ r2 r
p :
r r2 % 2 ‡ r2 2
4
# "
% ‡ r2 p ˆ
r r2 % 2 ‡ r2 2 r
%
r2 p
.% 2 r
4 è
á ˆ p
2 2
. 2
,
á E! 7 !
$ , , è, # 2
è
2
á
ˆ
2
,
2
7
) , 2
, è,
# # á !
ˆ
2
!#
2
á
:
3
ˆ è ˆ è
è ˆ ð ‡ è,
5
, 2 , #: , # #, # ˆ 2 ' ) + % 7 ˆ è ˆ á ˆ è ˆ ð ‡ á6 ˆ - .3
Circle r a
P1
O
α
P0
- .3 & =* C )*
.2 < "5
$ !
9 ˆ è 7 á
á ˆ p 2 ‡ 2
2 2
. 2
,
ˆ 2
è
‡ á2 ‡ ˆ
E! 2,
2
á2 ˆ
2
‡ 2
2,
p
2 2
. 2:
,
4.2.3 Stigmatic imaging of surfaces
# )
% / ! # #
/ ! #
! $ ! # 2 ' { - > ' ' 9 )
+ # 9 # # - - $ -4 D
+ , # , ˆ
9
ˆ
9
:
2
, - , #, - .5
- - #- # 9
ˆ
ˆ :
##,
22
' > = ' 3 5" ..36 = ' 6 ;$
5.4 ( 6 $ 5.3 25 9 G % 5"2 .4
{ C * / H
4,
8 G A
P1
φ0 Q
Q
A
P0
φ1
φ0
P1
n
n′
O
φ1
B
P0
O
S1
S0
B
S
S
S0
n′ n
- .5 &
S1
n′ n
( = #
d :
d , ˆ -#
-#
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, # #, ' , + + 2. è,
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. # /# # $ # 4.3.1 General formulae
+ / 9 9 9 9 9 ( /# 9 ˆ
0
0,
9 ˆ
02
0,
0
0,
ˆ , 2 :
2
9 ˆ
0 ˆ
‡‡ ‡
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09
09,
ˆ
092
09,
ˆ
09
09,
09 ˆ 99 ‡ 9 9 ‡ 99 ‡ 9:
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/ 09, ˆ , 0, ˆ ,
$ . $ # # 9 9 9
0, 6ˆ , 09, 6ˆ , $ , ˆ , ˆ , ˆ , 9, ˆ 9, ˆ 9, ˆ ,
A / # , , 6 /# + ) $ C * C * # }2 }.4
42
8 G ) ( , / , 9 9 9 ˆ
2 ‡
, ‡
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9 ˆ
, ‡ ,
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.
F 9 $ , ˆ ˆ , - !
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09, , 9
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ˆ
,
9 ˆ
,
,
:
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ˆ;
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3
9 ˆ ; 9
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f
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,
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, f
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% ( # $ ,
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2 ,
9 ˆ
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:
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. < /# ; 9 ˆ á;
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3
á ˆ 2 = , ⠈ = , $ $ 6 / $ !
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; 9 ˆ )9 ã9:
5
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ˆ
ˆ ˆ :
ã
)9 ; â
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9
!
,
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:
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9= 2
4.3.3 Classi®cation of projective transformations
< /# % 9 , , 2
)9= ) . , $ / # # H
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/ $ H
H
$ ) . , # # . , , , ' / )
/ # # # # +6 + $ # # # $ $ .
á â 2 â # # - 44
8 G $ . 3 . 2 + =3 ( + >
9 9 9 # I# . ,6 9 , ,
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9 # # , $ 9 ( # 9 # $ # # # & $ G A < + 5.
43
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# !
H # A B C A9 B9 C9 }." }." A9 B9 C9 A B C
, ˆ ˆ # ' H
7 #
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C
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7
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.
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F # G + , 2 # 2 # # # > , # , , ˆ
,9 ˆ
5
,
,
72
8 G ˆ
2
2 ( }. 27 , ˆ
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2
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A
22
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02
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6
8
9 ˆ 2
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2
:
8
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8
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2
9
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P P2
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,
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24
P P2 > }. 23 ä ˆ 0, 0 ä9 ˆ 09 09 F′
U′
d
d′
f′
f
δ
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f 0′
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c
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, 8
2
7
ä9 ˆ 2
2
, 22
:
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$ 9 U U9 - ..
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27
23
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2
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8 G U′
(a)
U′
(b)
U′
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(c)
(d)
U′
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Convergent
(f)
Divergent
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6 ) #6 ) #6 # U
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$ $ 23 ˆ 9 ˆ ,
9 ! # 6 2 - 24 ˆ , , 2 P ˆ P ‡ P2 ˆ
‡
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2
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! ! # , ˆ 2 ˆ
ˆ 9
2
4
ˆ =, ˆ =2 ( . # # # = # =2 # $ # # - 9
( }. 27
# , ˆ ,9 ˆ 9
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f1
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3
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! , 4.4.5 The general centred system
% G H # # /# / }. # /#
!# /# $ !# }.. }..2 }.. % #
# #
+ 2 . . . # , . . . , . . . # #
- .7 - , ,? / ? 2 2? . . . #
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;
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( / $ / # / $ + # 74
8 G Y
P0
P2
Y0 γ0 P *0
∆Z1
Y 0*
∆Z0
Y2
n0
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Y 1*
Y1
P *1
n P1 γ
n2
1
1
S1
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# @" $ + 9 ' 9 + & " 334
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z0
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$ , , ˆ , ˆ , # , $ 4.5.1 The sine condition
% , ˆ ˆ , , , ˆ , ˆ , 2 ,,
,,
, , ˆ 0, , ,6 , ,:
$ / ,
,
,
,
, ˆ ,, ˆ , ˆ , ˆ , ' &
0, , ,6 , , ˆ ,:
.
,
,,
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㠈 , , ã,
4
ã, ã #, # ) , # / E! 4 ! / # # ã, ã ã, ã # B' }.. .5
/ ( / ) , , #
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) , ã :
7
, ˆ
,
> }. , ) , = , ˆ , }.. " , = ˆ
4 - .5
,= h0
F1
- .5 $ / γ1
3,
8 G ,
ã
ˆ :
3
$ / 0
( #
/ % # }.2
9 8 ) / )
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F , , ˆ , ˆ ,
ˆ ˆ , $ 2 ,
,
, , ˆ 0, , , 6 , , 5
, , ,
ã, ã ã
ã, ˆ 0, , , 6 , , :
#
0, , , 6 , , ˆ , , :
2 ã =2 ˆ , , 2 ã, =2:
2
' , $ " # }.. "2
2
ˆ
, , ,
' ã =2 ˆ , , ã, =2:
.
% ' #, # # ' 㠈 ã, $ = , ˆ =, ˆ , = ! # / .4 ( , ( 3
&
& # $ #) H 4.6.1 Focal properties of a thin pencil
+ / #) - .2, % 3 # # # 3 ! # % 3,8 # # # # $ { + $ #
# # + / > / # ' }2 # $ + #) 6 # #) + #) # P3
P2
dS
F23
P
F12
f′
l
f
P4
F14
F34
P1
- .2, ( 9 E % 8 8 9 9
; # < 527 3"
{ $ # /# }.
32
8 G ds
l
f
K
f′
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Axis of revolution
# 6 # # #) + #) # # $ 2 . # . 2 -
.2,
$ ! 2
02 . 0. $ 9
/ 02 0. . 2 # # # # ' 2 $ $ 9
# 9 #)
# - .2 + #) # $ # % $ 9 4.6.2 Refraction of a thin pencil
.4 ( 3
% # # - .22
$ 9 # # #
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6 0, $ 09, , 6 ,9 #
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2
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F1
θ1
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θ0
F0
l0
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f 1′
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# # # ! % )
# G $ -á -â # -
.2 /
-á -â #
9 ä ä .7 9 I 37
Qβ
Lateral
chromatic
aberration
Qα
Longitudinal chromatic
aberration
P
- .2 +
# ( }.. 4 ! # ' # ä
ä
‡
ˆ ,:
0
8
2
$ ! Ĉ
3
0 8 3 # - 0 8 3 K 4"5 (
K # #
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- . S ù 0 ' 4 0 ' ù 0 ' ù 0 ' 6 D }2% %* }2% (>E
jù j ˆ jù j:
0
* ? ! % 8 *% ! 9 7 ! 4 9
ù ù # = + 3
/ B !9 ! !9 ù2 Däù ù E
%
ù DS ù 09 9'9‡ E
%ù = + ˆ R
! ù 09 9 '9
(ð2
!9
*
ù2 Däù ù E
%
ù DS ù 09 9'9‡ E
! ù 09 9 '9
ù = + ˆ R
(ð2
!9
09 9 '9 +
ù 09 9 '9 ù 09 9 '9 ù > > 8 ù > > 8 * C 0 ˆ %
ù > >
ù > >
8 ˆ ùáù
8 ˆ ùâù
%>
- ù
ù
}%'( : }2%2
&2&
$ A áù âù * ù(
Däù ù E
%ù = + ˆ R ( %ù = +ùáù
ù(
ù = + ˆ R ( %ù = +ùâù Däù ù E %ù %ù = + ˆ
ù
(ð
% ùDSù 09 9'9‡ E
!9
!:
'
%%
%(
1 %% < 'ù ˆ D%ù 3 ù E=&ð = + D 'E > % ù = + . 4 8.4.2 The total image ®eld
? > 0% 0( . % %% ( % 1 ù(
ä% ù
% = + ˆ p
%
=
+D
ùá
ù
ù
%
%
(
(ð 1
‡ ( ùá( ù ä( ù E ù ù 1 (
%2
%
ù
ä% ù
%
=
+D
ùâ
ù
= + ˆ p
ù
%
%
(ð 1 (
‡ ( ùâ( ù ä( ù E ù ù: . % ( 0% 0( 7 % # è% ù è( ù á% ù á( ù 0 + á% ù â% ù á( ù â( ù
'
%2 % %& F ' 1 %& 5
0& %
0 = + ˆ = + ˆ p
(ð
= + ˆ
%
0 = + ˆ p
(ð
‡1
1
‡1
1
%ù = + ù
ù %ù = + ù
ù ' = + ˆ ' = + ˆ >
&2'
ù ù ù(
ä% ù
ä( ù D
ù
è
ù
‡
ù
è
ù
E
%
%
(
(
(
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ù ˆ ( D% ù è% ù ä% ù ‡ ( ù è( ù ä( ù E: ù ˆ
%&
%'
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D ( ‡ ( E:
%-
j'j ˆ
&ð
&ð 0
? 1 ˆ ˆ (ð=ù> " ! 1 %& 1 % 0 = + ù %B
%ù = + ù ˆ p
(ð 0 C %&
% (
% % ‡1
(
h0 i ˆ
ˆ
0 p
%ù ù ù ù
( 0
( (ð 1
% ‡1
% (
% ù ù ù p
0 ù h0 i ˆ
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%B
ˆ
% ù ù % ù? ù? ù
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% 1
ˆ
j%ù j( j ùj( ù
>
% ù ù ˆ %ù? ? ù +
% 1
j% ù j( j ùj( ù:
h( i ˆ
>
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1
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&ð >
%*
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(%
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$ A C jÄùj j%ù j ù j%ù> j j%ù j 1
fj ùj( ‡ j ùj( gù
((
&ð >
= + %B . (( *> = + ˆ * > j%ù> = +j( :
(2
*> " j% ù> j( %( ? ( )
1 8.5.1 The rectangular aperture and the slit
7 ( (( ?
7 7î 7ç 1 00
1 }02 2- (
(
$ î‡-ç
$ î
$-ç
% ˆ *
î ç ˆ *
î
ç:
(
(
η
2b
O
2a
1 00 H ξ
0' 1 C $ î
%
D
$
î ˆ
$ $ Eˆ(
&2B
$ $
. ( $ $-( (
(
ˆ j% j ˆ
>
$ $-(
%
}02 && > ˆ * ( ( ˆ P =ë( 8( P ˆ &(
ˆ 0=0( 1 0* ˆ % 0 ˆ > 0 ˆ ð (ð 2ð . . . : 0 0 ˆ > 0% 0 ˆ ( ‡ %ð=( ? $ ˆ ð
$-( ˆ vð
v ˆ % ( 2 . . .
y
1.0
0.9
0.8
0.7
 sinx  2
y 
x 
0.6
0.5
0.4
0.3
0.2
0.1
0 1
1 0* 1 2
π
2π
3π
(
0
ˆ
:
0
x
(
&20
$ A 0% . .: 0
(
0
:
ˆ
0
ˆ
0
>
%&2>ð ˆ &&*2
(&'*ð ˆ BB('
2&B>ð ˆ %>*>
&&B*ð ˆ %&>B
0
0
(
%
>>&B%0
>>%-&0
>>>02&
>>>'>2
1 0%> 1 0 3 B L '>3 ë ˆ 'B*> 5
<
6
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> - ˆ > $ ˆ (ð=ë
> ˆ ë
(
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:
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2
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7 8 5 1 6 + - ˆ >
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1
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1 # r è @
r è ˆ î
1 ø r è ˆ ç"
@
1 ø ˆ -
1 ø ˆ -:
( ‡ - ( 1 - 1 ˆ
- ˆ - ˆ > }02 2- (ð
$r1 è ø
% ˆ *
r r è:
> >
B
0
+ ? , M C . $ ? + %*'> 222
&&>
$ A C A 0
6 (ð 0 á á
á ˆ 5 0:
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5 >
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*
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D0 5 ‡% 0E ˆ 0 ‡% 5 0
0
ˆ > 0
095 > 0909 ˆ 05 % 0:
%(
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$1
%2
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1 %> %( ˆ ð( . %%
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>
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6
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D0=0E( }0'% 0 5 % 0 ˆ > 0( 0 D5 % 0=0E ˆ >
0
+ A K 1 A (
1 * : # %*22" ! < C G &
%*&' %&*" , C ? #
2 7 7 ; < %*(( (>
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{ , = 5 , *(, , ! , %02' (02 5 5 + %0> $ ? + , 7 , ,
, %*%* C & 2-" $ 5 1 ( %*(& (&" . . . , , ! %*&2
%%-" H = 7 # %*'- %>&" = H A ? , 8 , ! , 5 %*'* 2'0"
5 = A ? , 8:, %*-' = %'-%" 5 = K ! A ? 5, 7 , ! , # ,
%*-B %%B%
0' 1 0( . 1 0 (
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0
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2(20ð ˆ %>%B&
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%
>
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>
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>
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:
:
:
:
:
:
:
y
1.0
0.9
0.8
0.7
0.6
y 

0.5
2J1(x) 2
x 
0.4
0.3
0.2
0.1
0
1 0%% 1 2
3
4
5
6
7
8
1
9
x
ˆ
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(5 % 0
:
0
%%
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0
0 5 ‡% 0
%'
5 ( 0 ˆ > ?
0
+ A K 2-%
1 A , , %&' A ? , C ? , &&(
$ A ð ˆ-ˆ> 1 0%% 0%( 1 0( 0 ˆ (ð1=ë 1ˆ
( ‡ - ( ˆ >:-%>
ë
ë
%:%%- ë
%:-%* ... :
%-
ë=( # 1> 1> 8( 1> (ð
11 1 ø
P > >
(
1> (ð (5 % $1
ˆ (
1 1 ø
ë > >
$1
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5 % 0
0:
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0
>
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C %% ˆ > 5 % 0 %' %B
ˆ >
1 0%( 1 5 L - '>3 ë ˆ 'B*> 5
<
. # 7 5 = K 0' 1 &&2
1
0.8
1st
dark ring
2nd
dark ring
3rd
dark ring
0.6
0.4
0.2
x
0
2
4
6
8
10
1 0%2 % 5 (> 0 5 (% 0 12
1 5 (% 0
5 % 0
ˆ 5 > 05 % 0
5 % 0
0
0
% (
D5 0 ‡ 5 (% 0E:
ˆ
( 0 >
%B 1> ˆ %
5 (> $1> 5 > > ˆ % 5 % > ˆ >
5 (% $1> %0
H 1 0%2 1 5 % $1> ˆ > 5 (> $1> 1 5 (> $1> >%-( >>*>
>>-( *> 8.5.3 Other forms of aperture
1 ?
{ # H , , ' %00% (%& 5 !. ( 5 9 ! 2 8 $ % 7 7 ; < %0**)%*(> '%2
{ 1 F }0-(
<
1 K + + . #( , , & 6, #$, 9 , = %0*& 5 <
1 G $ 3 , , #, !, %*&' %BB)(%>
&&&
$ A 1 # A% A( A( 7î ì A% 1 1 A% $ î‡-ç
î ç:
%*
%% - ˆ *
A%
+ 1 A( %( - ˆ *
$ î‡-ç
A(
(> î ç
î9 ˆ
î ç:
%( - ˆ ì*
%
î
ì
î9 ç9 ç9 ˆ ç
$ì î9‡-ç9
A%
(>
(%
î9 ç9 ˆ ì%% ì -:
((
1 0 ì@% %@ì" 1 ì( ; 1 1 0%& ? 5 = / # 7% 7( . . . 7/
î% ç% 1 î( ç( . . . î / ç / Aperture
Diffraction
pattern
1 0%& 7 1 0' 1 % - ˆ *
A
ˆ*
$Dî ‡î9 ‡ç ‡ç9-E
$D î ‡-ç E
î9 ç9
$ î9‡-ç9
A
&&'
î9 ç9
(2
A > - (2
$ î ‡-ç (
>
- ˆ -
ˆ > -
$D î î ‡-ç ç E
:
(&
}B( 6
. > - }B( %B (& 1 / ˆ ( (& ˆ > f( ‡
$D î% î( ‡-ç% ç( E
‡
$D î( î% ‡-ç( ç% E
g
ˆ & > ( %(ä
ä ˆ $D î(
î% ‡ -ç(
ç% E:
# ? ? F ‡% % A ˆ . F / @
- / > -:
('
! = / 1 : # 2 , 2 , %*%& %%&& +
86 K 5 < / 1 , %*2%
&2'
&&-
$ A 1 0%' 1 '- L <
# @ ë ˆ 'B*> 5
. # 7 5 = K 5 6 6
4 6ˆ - 1 7 6ˆ (ð
/ / % / / ( 1 0%' # )
8.6.1 Diffraction gratings
>? 5 ? @
# 4 îç > > 1 0% ç6 4 î ç6 0- 1 &&B
ζ
(l0,m0)
O
A
B
1 0%- ! ξ
> î ç ˆ # D$> î ‡ > çE
ù = 4 î ç 4 î ç ˆ
î ç
:
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%
î ç > > 4 4 > ()" jj ˆ % ()
F 4 @ 4 j => j # 2 1 0%- 4 6
A }02 2*
A }02 (2 #
6 / 6 #
î ç6
ç î 1 0%B
5 è> 7æ è 7æ 4 &&0
$ A ζ
d
θ0
O
ξ
θ
1 0%B 5 - ˆ > > ˆ è> ˆ è ˆ > ˆ è è> }0' (2 ? î ˆ ?
ç ˆ >
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%:
(
% ˆ % > / %
$
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2
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0
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j% > j $ # 2 + % > > > >
> 5 > 0- 1 &&*
1 0%0 +
# 2 #& ˆ è> & 2 # 1 2 è # 2 ˆ è # 2 è . 2
#& ˆ è
è> ˆ B
(ð =ë ˆ $ 1 ' @ > "
/ 0 / ( ( 0 0 ð . / $ =( / ( è> ˆ
è
ë
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0
B
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B
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$ A 1
(a)
O
λ
d
p
2λ
d
1
(b)
O
p
λ
s
2λ
s
λ
s
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s
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s
1
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O
λ
d
1 0%* 2λ
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p
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9
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7 %> 1 0%*
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%%
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H &
3
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#
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1 0(> < &'(
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0 Ä9 ˆ
6 jj
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5
6 6 6 + 7 8 1 6 >(? H %B0'{ 6 1 { %0%* 1 / = 6
6 # 1 " , H }
6 1 , H . 5,
7 , ! , # , %*&* &%2
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H : %000 '% %%B
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F ? = 1 H ë% ˆ >:& ì
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‡ % ‡ %ë ˆ ë ‡ äë
äë %
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2B*" ? %& d
λ1
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1 2
1.8
p
0
3rd order
6
3
4
5
3.6
5.4
2nd order
5th order
9
7.2
4th order
6th order
p
1 0(2 ? A ? = < C 2%('2& %*(-" , 7 , * :,
%*22 -**
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G
L
T
F
1 0(& 5 G
L
P
S
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αα
β
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S
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G
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P1
P0
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F H 9 1 ! + F 8.6.2 Resolving power of image-forming systems
1 }02 2- : 1 ? }B-2
? 6 1)< 6 4 4 = 5 4 4 ? C H / }B-2 5 4 1 Äë
ë=Äë 1 6
ä0 äè %=ä0 %=äè #
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6 6 0=ð( ˆ >:0%% >B2'
0- 1 r å < r < (5 % $1
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5
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5 A ? 8 , , , # < + ! %*'% %>*
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$ A I/I0
1.0
0.9
0.8
0.7
0.6
0.5
(a)
0.4
(c)
(b)
0.3
0.2
0.1
0.0
0
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1 5 %( %2
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ε(u)
ε(u)
0.20
1.0
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0
2
4
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10
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20
30
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50
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etri
shado cal
w
7π
5π
3π
11π
9π
61π
59π
57π
55π
53π
51π
49π
47π
45π
43π
41π
39π
37π
35π
33π
31π
29π
27π
25π
23π
21π
19π
17π
15π
13π
5π
1π
π 0π
1 2
3π
83π
81π
79π
77π
75π
73π
71π
69π
67π
65π
63π
Focal
plane
Optic
42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 7 6 5 4 3 2 1 0 1 2 3 axis
Distance in wavelengths
Image
point
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