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E-raamat: Foundations of Optical System Analysis and Design

(University of Calcutta, Kolkata)
  • Formaat: 774 pages
  • Ilmumisaeg: 06-Feb-2022
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498744959
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Foundations of Optical System Analysis and DesignSuurem pilt
  • Formaat: 774 pages
  • Ilmumisaeg: 06-Feb-2022
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498744959
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Since the incorporation of scientific approach in tackling problems of optical instrumentation, analysis and design of optical systems constitute a core area of optical engineering. A large number of software with varying level of scope and applicability is currently available to facilitate the task. However, possession of an optical design software, per se, is no guarantee for arriving at correct or optimal solutions. The validity and/or optimality of the solutions depend to a large extent on proper formulation of the problem, which calls for correct application of principles and theories of optical engineering. On a different note, development of proper experimental setups for investigations in the burgeoning field of optics and photonics calls for a good understanding of these principles and theories.

With this backdrop in view, this book presents a holistic treatment of topics like paraxial analysis, aberration theory, Hamiltonian optics, ray-optical and wave-optical theories of image formation, Fourier optics, structural design, lens design optimization, global optimization etc. Proper stress is given on exposition of the foundations.

The proposed book is designed to provide adequate material for self-learning the subject. For practitioners in related fields, this book is a handy reference.

Foundations of Optical System Analysis and Synthesis provides











A holistic approach to lens system analysis and design with stress on foundations





Basic knowledge of ray and wave optics for tackling problems of instrumental optics





Proper explanation of approximations made at different stages





Sufficient illustrations for facilitation of understanding





Techniques for reducing the role of heuristics and empiricism in optical/lens design





A sourcebook on chronological development of related topics across the globe

This book is composed as a reference book for graduate students, researchers, faculty, scientists and technologists in R & D centres and industry, in pursuance of their understanding of related topics and concepts during problem solving in the broad areas of optical, electro-optical and photonic system analysis and design.
Preface xix
Acknowledgments xxv
Author Brief Biography xxvii
1 Introduction
1(18)
1.1 An Early History of Optical Systems and Optics
1(7)
1.1.1 Early History of Mirrors
1(1)
1.1.2 Early History of Lenses
1(1)
1.1.3 Early History of Glass Making
2(1)
1.1.4 Ancient History of Optics in Europe, India and China
2(1)
1.1.5 Optics Activities in the Middle East in 10th Century CE
3(1)
1.1.6 Practical Optical Systems of the Early Days
3(1)
1.1.7 Reading stones and Discovery of Eyeglasses
4(1)
1.1.8 Revival of Investigations on Optics in Europe by Roger Bacon in the 13th century CE
4(1)
1.1.9 Optics during Renaissance in Europe
4(1)
1.1.10 Invention of Telescope and Microscope
5(1)
1.1.11 Investigations on Optics and Optical Systems by Johannes Kepler
6(1)
1.1.12 Discovery of the Laws of Refraction
6(1)
1.1.13 Discovery of the phenomena of Diffraction, Interference and Double Refraction
7(1)
1.1.14 Newton's Contributions in Optics and Rømer's Discovery of Finite Speed of Light
7(1)
1.1.15 Contributions by Christian Huygens in Instrumental Optics and in Development of the Wave Theory of Light
8(1)
1.2 Metamorphosis of Optical Systems in the Late Twentieth Century
8(1)
1.3 Current Definition of Optics
9(1)
1.4 Types of Optical Systems
10(2)
1.5 Classification of Optical Systems
12(1)
1.6 Performance Assessment of Optical Systems
12(1)
1.7 Optical Design: System Design and Lens Design
13(1)
1.8 Theories of Light
13(1)
References
14(5)
2 From Maxwell's Equations to Thin Lens Optics
19(42)
2.1 Maxwell's Equations
19(1)
2.2 The Wave Equation
20(3)
2.3 Characteristics of the Harmonic Plane Wave Solution of the Scalar Wave Equation
23(4)
2.3.1 Inhomogeneous Waves
26(1)
2.4 Wave Equation for Propagation of Light in Inhomogeneous Media
27(3)
2.4.1 Boundary Conditions
28(2)
2.5 Vector Waves and Polarization
30(4)
2.5.1 Polarization of Light Waves
31(3)
2.6 Propagation of Light in Absorbing/Semi-Absorbing Media
34(4)
2.7 Transition to Scalar Theory
38(1)
2.8 `Ray Optics' Under Small Wavelength Approximation
39(3)
2.8.1 The Eikonal Equation
39(1)
2.8.2 Equation for Light Rays
40(2)
2.9 Basic Principles of Ray Optics
42(12)
2.9.1 The Laws of Refraction
43(1)
2.9.1.1 A Plane Curve in the Neighbourhood of a Point on It
44(1)
2.9.1.2 A Continuous Surface in the Neighbourhood of a Point on It
44(1)
2.9.1.3 Snell's Laws of Refraction
45(3)
2.9.2 Refraction in a Medium of Negative Refractive Index
48(1)
2.9.3 The Case of Reflection
49(1)
2.9.3.1 Total Internal Reflection
49(1)
2.9.4 Fermat's Principle
49(2)
2.9.5 The Path Differential Theorem
51(1)
2.9.6 Malus-Dupin Theorem
52(2)
2.10 Division of Energy of a Light Wave Incident on a Surface of Discontinuity
54(2)
2.10.1 Phase Changes in Reflected and Transmitted Waves
55(1)
2.10.2 Brewster's Law
56(1)
2.11 From General Ray Optics to Parabasal Optics, Paraxial Optics and Thin Lens Optics
56(2)
References
58(3)
3 Paraxial Optics
61(54)
3.1 Raison d'etre for Paraxial Analysis
61(1)
3.2 Imaging by a Single Spherical Interface
62(1)
3.3 Sign Convention
63(1)
3.4 Paraxial Approximation
64(11)
3.4.1 On-Axis Imaging
64(2)
3.4.1.1 Power and Focal Length of a Single Surface
66(1)
3.4.2 Extra-Axial Imaging
67(3)
3.4.3 Paraxial Ray Diagram
70(1)
3.4.4 Paraxial Imaging by a Smooth Surface of Revolution about the Axis
71(4)
3.5 Paraxial Imaging by Axially Symmetric System of Surfaces
75(4)
3.5.1 Notation
75(1)
3.5.2 Paraxial Ray Tracing
75(3)
3.5.3 The Paraxial Invariant
78(1)
3.6 Paraxial Imaging by a Single Mirror
79(2)
3.7 The General Object-Image Relation for an Axisymmetric System
81(4)
3.7.1 A Geometrical Construction for Finding the Paraxial Image
84(1)
3.7.2 Paraxial Imaging and Projective Transformation (Collineation)
85(1)
3.8 Cardinal Points in Gaussian Optics
85(14)
3.8.1 Determining Location of Cardinal Points from System Data
86(2)
3.8.2 Illustrative Cases
88(1)
3.8.2.1 A Single Refracting Surface
88(1)
3.8.2.2 A System of Two Separated Components
89(2)
3.8.2.3 A Thick Lens with Different Refractive Indices for the Object and the Image Spaces
91(5)
3.8.2.4 A Thin Lens with Different Refractive Indices for the Object and the Image Spaces
96(1)
3.8.2.5 Two Separated Thin Lenses in Air
97(2)
3.9 The Object and Image Positions for Systems of Finite Power
99(2)
3.10 Newton's Form of the Conjugate Equation
101(1)
3.11 Afocal Systems
102(2)
3.12 Vergence and Power
104(1)
3.13 Geometrical Nature of Image Formation by an Ideal Gaussian System
105(3)
3.13.1 Imaging of a Two-Dimensional Object on a Transverse Plane
105(1)
3.13.2 Imaging of Any Line in the Object Space
106(2)
3.13.3 Suitable Values for Paraxial Angle and Height Variables in an Ideal Gaussian System
108(1)
3.14 Gaussian Image of a Line Inclined with the Axis
108(2)
3.15 Gaussian Image of a Tilted Plane: The Scheimpflug Principle
110(2)
3.15.1 Shape of the Image
111(1)
3.16 Gaussian Image of a Cube
112(1)
References
112(3)
4 Paraxial Analysis of the Role of Stops
115(42)
4.1 Aperture Stop and the Pupils
115(5)
4.1.1 Conjugate Location and Aperture Stop
117(3)
4.2 Extra-Axial Imagery and Vignetting
120(3)
4.2.1 Vignetting Stop
122(1)
4.3 Field Stop and the Windows
123(6)
4.3.1 Field of View
123(1)
4.3.2 Field Stop, Entrance, and Exit Windows
124(1)
4.3.2.1 Looking at an Image Formed by a Plane Mirror
124(1)
4.3.2.2 Looking at Image Formed by a Convex Spherical Mirror
124(1)
4.3.2.3 Imaging by a Single Lens with a Stop on It
125(1)
4.3.2.4 Imaging by a Single Lens with an Aperture Stop on it and a Remote Diaphragm in the Front
125(1)
4.3.2.5 Appropriate Positioning of Aperture Stop and Field Stop
126(1)
4.3.2.6 Aperture Stop and Field Stop in Imaging Lenses with No Dedicated Physical Stop
127(1)
4.3.2.7 Imaging by a Multicomponent Lens System
128(1)
4.3.2.8 Paraxial Marginal Ray and Paraxial Pupil Ray
129(1)
4.4 Glare Stop, Baffles, and the Like
129(1)
4.5 Pupil Matching in Compound Systems
130(1)
4.6 Optical Imaging System of the Human Eye
131(6)
4.6.1 Paraxial Cardinal Points of the Human Eye
132(1)
4.6.1.1 Correction of Defective Vision by Spectacles
133(1)
4.6.1.2 Position of Spectacle Lens with Respect to Eye Lens
133(1)
4.6.2 Pupils and Centre of Rotation of the Human Eye
133(1)
4.6.2.1 Position of Exit Pupil in Visual Instruments
133(3)
4.6.3 Visual Magnification of an Eyepiece or Magnifier
136(1)
4.7 Optical (Paraxial) Invariant: Paraxial Variables and Real Finite Rays
137(7)
4.7.1 Different Forms of Paraxial Invariant
138(1)
4.7.1.1 Paraxial Invariant in Star Space
138(1)
4.7.1.2 A Generalized Formula for Paraxial Invariant H
139(1)
4.7.1.3 An Expression for Power K in Terms of H and Angle Variables of the PMR and the PPR
139(1)
4.7.2 Paraxial Ray Variables and Real Finite Rays
140(1)
4.7.2.1 Paraxial Ray Variables in an Ideal Gaussian System
140(1)
4.7.2.2 Paraxial Ray Variables in a Real Optical System
141(1)
4.7.2.3 Choice of Appropriate Values for Paraxial Angles u and u
142(2)
4.8 Angular Magnification in Afocal Systems
144(1)
4.9 F-number and Numerical Aperture
145(3)
4.10 Depth of Focus and Depth of Field
148(5)
4.10.1 Expressions for Depth of Focus, Depth of Field, and Hyperfocal Distance for a Single Thin Lens with Stop on It
148(3)
4.10.2 General Expressions for Depth of Focus, Depth of Field, and Hyperfocal Distance for an Axisymmetric Imaging System
151(2)
4.11 Telecentric Stops
153(1)
4.12 Stops in Illumination Systems
154(2)
4.12.1 Slide Projector
154(1)
4.12.2 The Kohler Illumination System in Microscopes
155(1)
References
156(1)
5 Towards Facilitating Paraxial Treatment
157(22)
5.1 Matrix Treatment of Paraxial Optics
157(8)
5.1.1 The Refraction Matrix and the Translation/Transfer Matrix
158(1)
5.1.2 The System Matrix
159(2)
5.1.3 The Conjugate Matrix
161(1)
5.1.4 Detailed Form of the Conjugate Matrix in the Case of Finite Conjugate Imaging
162(1)
5.1.4.1 Location of the Cardinal Points of the System: Equivalent Focal Length and Power
163(2)
5.2 Gaussian Brackets in Paraxial Optics
165(4)
5.2.1 Gaussian Brackets: Definition
166(1)
5.2.2 Few Pertinent Theorems of Gaussian Brackets
166(1)
5.2.3 Elements of System Matrix in Terms of Gaussian Brackets
167(2)
5.3 Delano Diagram in Paraxial Design of Optical Systems
169(7)
5.3.1 A Paraxial Skew Ray and the y, y Diagram
170(1)
5.3.2 Illustrative y, y Diagrams
171(1)
5.3.3 Axial Distances
172(2)
5.3.4 Conjugate Lines
174(1)
5.3.5 Cardinal Points
175(1)
References
176(3)
6 The Photometry and Radiometry of Optical Systems
179(16)
6.1 Radiometry and Photometry: Interrelationship
179(3)
6.2 Fundamental Radiometric and Photometric Quantities
182(4)
6.2.1 Radiant or Luminous Flux (Power)
182(1)
6.2.2 Radiant or Luminous Intensity of a Source
183(1)
6.2.3 Radiant (Luminous) Emittance or Exitance of a Source
183(1)
6.2.4 Radiance (Luminance) of a Source
184(1)
6.2.4.1 Lambertian Source
184(1)
6.2.5 Irradiance (Illuminance/Illumination) of a Receiving Surface
185(1)
6.3 Conservation of Radiance/Luminance (Brightness) in Optical Imaging Systems
186(1)
6.4 Flux Radiated Into a Cone by a Small Circular Lambertian Source
187(1)
6.5 Flux Collected by Entrance Pupil of a Lens System
188(1)
6.6 Irradiance of an Image
189(1)
6.7 Off-Axial Irradiance/Illuminance
190(2)
6.8 Irradiance/Illuminance From a Large Circular Lambertian Source
192(1)
6.8.1 Radiance (Luminance) of a Distant Source
193(1)
References
193(2)
7 Optical Imaging by Real Rays
195(66)
7.1 Rudiments of Hamiltonian Optics
195(8)
7.1.1 Hamilton's Point Characteristic Function
197(1)
7.1.1.1 Hamilton-Bruns' Point Eikonal
198(2)
7.1.2 Point Angle Eikonal
200(1)
7.1.3 Angle Point Eikonal
200(1)
7.1.4 Angle Eikonal
201(1)
7.1.5 Eikonals and their Uses
202(1)
7.1.6 Lagrangian Optics
202(1)
7.2 Perfect Imaging with Real Rays
203(24)
7.2.1 Stigmatic Imaging of a Point
203(1)
7.2.2 Cartesian Oval
204(1)
7.2.2.1 Finite Conjugate Points
204(2)
7.2.2.1.1 Real Image of an Axial Object Point at Infinity
206(3)
7.2.2.1.2 Virtual Image of an Axial Object Point at Infinity
209(1)
7.2.2.2 Cartesian Mirror for Stigmatic Imaging of Finite Conjugate Points
209(2)
7.2.2.2.1 Parabolic Mirror for Object/Image at Infinity
211(1)
7.2.2.2.2 Perfect Imaging of 3-D Object Space by Plane Mirror
212(1)
7.2.3 Perfect Imaging of Three-Dimensional Domain
212(1)
7.2.3.1 Sufficiency Requirements for Ideal Imaging by Maxwellian `Perfect' Instrument
213(2)
7.2.3.2 Impossibility of Perfect Imaging by Real Rays in Nontrivial Cases
215(1)
7.2.3.3 Maxwell's `Fish-Eye' Lens and Luneburg Lens
216(2)
7.2.3.3.1 A Polemic on `Perfect Imaging' by Maxwell's Fish-Eye Lens
218(1)
7.2.4 Perfect Imaging of Surfaces
219(1)
7.2.4.1 Aplanatic Surfaces and Points
219(3)
7.2.5 Stigmatic Imaging of Two Neighbouring Points: Optical Cosine Rule
222(1)
7.2.5.1 Abbe's Sine Condition
223(2)
7.2.5.2 Herschel's Condition
225(1)
7.2.5.3 Incompatibility of Herschel's Condition with Abbe's Sine Condition
226(1)
7.3 Real Ray Invariants
227(11)
7.3.1 Skew Ray Invariant
227(1)
7.3.1.1 A Derivation of the Skew Ray Invariance Relationship
228(1)
7.3.1.2 Cartesian Form of Skew Ray Invariant
229(1)
7.3.1.3 Other Forms of Skew Ray Invariant
230(1)
7.3.1.4 Applications of the Skew Invariant
231(1)
7.3.1.4.1 The Optical Sine Theorem
231(1)
7.3.1.4.2 Relation between a Point and a Diapoint via a Skew Ray from the Point
232(1)
7.3.1.4.3 Sagittal Magnification Law
233(1)
7.3.1.4.4 Feasibility of Perfect Imaging of a Pair of Object Planes Simultaneously
233(2)
7.3.2 Generalized Optical Invariant
235(1)
7.3.2.1 Derivation of Generalized Optical Invariant
236(2)
7.4 Imaging by Rays in the Vicinity of an Arbitrary Ray
238(14)
7.4.1 Elements of Surface Normals and Curvature
239(1)
7.4.1.1 The Equations of the Normals to a Surface
239(1)
7.4.1.2 The Curvature of a Plane Curve: Newton's Method
240(1)
7.4.1.3 The Curvatures of a Surface: Euler's Theorem
241(2)
7.4.1.4 The Normals to an Astigmatic Surface
243(3)
7.4.2 Astigmatism of a Wavefront in General
246(1)
7.4.2.1 Rays in the Neighbourhood of a Finite Principal Ray in Axisymmetric Systems
247(1)
7.4.2.2 Derivation of S and T Ray Tracing Formulae
247(4)
7.4.2.3 The Sagittal Invariant
251(1)
7.5 Aberrations of Optical Systems
252(1)
References
253(8)
8 Monochromatic Aberrations
261(52)
8.1 A Journey to the Wonderland of Optical Aberrations: A Brief Early History
261(1)
8.2 Monochromatic Aberrations
262(26)
8.2.1 Measures of Aberration
262(3)
8.2.1.1 Undercorrected and Overcorrected Systems
265(1)
8.2.2 Ray Aberration and Wave Aberration: Interrelationship
265(3)
8.2.3 Choice of Reference Sphere and Wave Aberration
268(1)
8.2.3.1 Effects of Shift of the Centre of the Reference Sphere on Wave Aberration
268(2)
8.2.3.1.1 Longitudinal Shift of Focus
270(3)
8.2.3.1.2 Transverse Shift of Focus
273(2)
8.2.3.2 Effect of Change in Radius of the Reference Sphere on Wave Aberration
275(1)
8.2.3.2.1 Wave Aberration and Hamilton-Bruns' Eikonal
276(1)
8.2.3.2.2 Wave Aberration on the Exit Pupil
276(1)
8.2.4 Caustics and Aberrations
277(1)
8.2.5 Power Series Expansion of the Wave Aberration Function
278(4)
8.2.5.1 Aberrations of Various Orders
282(4)
8.2.5.2 Convergence of the Power Series of Aberrations
286(1)
8.2.5.3 Types of Aberrations
286(2)
8.3 Transverse Ray Aberrations Corresponding to Selected Wave Aberration Polynomial Terms
288(11)
8.3.1 Primary Spherical Aberration
288(1)
8.3.1.1 Caustic Surface
289(2)
8.3.2 Primary Coma
291(2)
8.3.3 Primary Astigmatism
293(3)
8.3.4 Primary Curvature
296(2)
8.3.5 Primary Distortion
298(1)
8.3.6 Mixed and Higher Order Aberration Terms
298(1)
8.4 Longitudinal Aberrations
299(4)
8.5 Aplanatism and Isoplanatism
303(5)
8.5.1 Coma-Type Component of Wave Aberration and Linear Coma
304(1)
8.5.2 Total Linear Coma from Properties of Axial Pencil
304(3)
8.5.3 Offence against Sine Condition (OSC)
307(1)
8.5.4 Staeble -- Lihotzky Condition
307(1)
8.6 Analytical Approach for Correction of Total Aberrations
308(1)
References
308(5)
9 Chromatic Aberrations
313(30)
9.1 Introduction
313(1)
9.2 Dispersion of Optical Materials
313(8)
9.2.1 Interpolation of Refractive Indices
315(2)
9.2.2 Abbe Number
317(1)
9.2.3 Generic Types of Optical Glasses and Glass Codes
318(3)
9.3 Paraxial Chromatism
321(17)
9.3.1 A Single Thin Lens: Axial Colour and Lateral Colour
321(3)
9.3.2 A Thin Doublet and Achromatic Doublets
324(2)
9.3.2.1 Synthesis of a Thin Lens of a Given Power Kd and an Arbitrary V#
326(1)
9.3.3 Secondary Spectrum and Relative Partial Dispersion
327(3)
9.3.4 Apochromats and Superachromats
330(1)
9.3.5 `Complete' or `Total' Achromatization
331(1)
9.3.5.1 Harting's Criterion
332(1)
9.3.6 A Separated Thin Lens Achromat (Dialyte)
333(2)
9.3.7 A One-Glass Achromat
335(1)
9.3.8 Secondary Spectrum Correction with Normal Glasses
336(1)
9.3.9 A Thick Lens or a Compound Lens System
337(1)
9.4 Chromatism Beyond the Paraxial Domain
338(1)
References
338(5)
10 Finite or Total Aberrations from System Data by Ray Tracing
343(26)
10.1 Evaluation of Total or Finite Wavefront Aberration (Monochromatic)
344(17)
10.1.1 Wave Aberration by a Single Refracting Interface in Terms of Optical Path Difference (OPD)
344(1)
10.1.2 Rays' Own Focus and Invariant Foci of Skew Rays
345(2)
10.1.3 Pupil Exploration by Ray Tracing
347(3)
10.1.4 A Theorem of Equally Inclined Chords between Two Skew Lines
350(1)
10.1.5 Computation of Wave Aberration in an Axi-Symmetric System
350(10)
10.1.6 Computation of Transverse Ray Aberrations in an Axi-Symmetric System
360(1)
10.2 Measures for Nonparaxial Chromatism
361(5)
10.2.1 Spherochromatism
362(1)
10.2.2 Conrady Chromatic Aberration Formula
363(2)
10.2.3 Image Space Associated Rays in Conrady Chromatic Aberration Formula
365(1)
10.2.4 Evaluation of Exact Chromatic Aberration using Object Space Associated Rays
365(1)
References
366(3)
11 Hopkins' Canonical Coordinates and Variables in Aberration Theory
369(28)
11.1 Introduction
369(1)
11.2 Canonical Coordinates: Axial Pencils
370(1)
11.3 Canonical Coordinates: Extra-Axial Pencils
371(3)
11.4 Reduced Pupil Variables
374(1)
11.5 Reduced Image Height and Fractional Distortion
375(1)
11.6 Pupil Scale Ratios
375(5)
11.6.1 Entrance Pupil Scale Ratios ρs and ρτ
378(1)
11.6.2 Exit Pupil Scale Ratios ρ's and ρ'τ
379(1)
11.7 Ws and Wτ from S and T Ray Traces
380(5)
11.8 Local Sagittal and Tangential Invariants for Extra-Axial Images
385(6)
11.9 Reduced Coordinates on the Object/Image Plane and Local Magnifications
391(1)
11.10 Canonical Relations: Generalized Sine Condition
392(3)
References
395(2)
12 Primary Aberrations from System Data
397(20)
12.1 Introduction
397(1)
12.2 Validity of the Use of Paraxial Ray Parameters for Evaluating Surface Contribution to Primary Wavefront Aberration
398(2)
12.3 Primary Aberrations and Seidel Aberrations
400(1)
12.4 Seidel Aberrations in Terms of Paraxial Ray Trace Data
401(10)
12.4.1 Paraxial (Abbe's) Refraction Invariant
401(1)
12.4.2 Seidel Aberrations for Refraction by a Spherical Interface
402(2)
12.4.3 Seidel Aberrations in an Axi-Symmetric System Consisting of Multiple Refracting Interfaces
404(1)
12.4.4 Seidel Aberrations of a Plane Parallel Plate
404(2)
12.4.5 Seidel Aberrations of a Spherical Mirror
406(2)
12.4.6 Seidel Aberrations of a Refracting Aspheric Interface
408(1)
12.4.6.1 Mathematical Representation of an Aspheric Surface
408(2)
12.4.6.2 Seidel Aberrations of the Smooth Aspheric Refracting Interface
410(1)
12.5 Axial Colour and Lateral Colour as Primary Aberrations
411(4)
References
415(2)
13 Higher Order Aberrations in Practice
417(12)
13.1 Evaluation of Aberrations of Higher Orders
417(1)
13.2 A Special Treatment for Tackling Higher Order Aberrations in Systems With Moderate Aperture and Large Field
418(2)
13.3 Evaluation of Wave Aberration Polynomial Coefficients From Finite Ray Trace Data
420(5)
References
425(4)
14 Thin Lens Aberrations
429(28)
14.1 Primary Aberrations of Thin Lenses
429(2)
14.2 Primary Aberrations of a Thin Lens (with Stop on It) in Object and Image Spaces of Unequal Refractive Index
431(7)
14.3 Primary Aberrations of a Thin Lens (with Stop on It) With Equal Media in Object and Image Spaces
438(1)
14.4 Primary Aberrations of a Thin Lens (with Stop on It) in Air
439(6)
14.5 Structural Aberration Coefficients
445(1)
14.6 Use of Thin Lens Aberration Theory in Structural Design of Lens Systems
446(1)
14.7 Transition from Thin Lens to Thick Lens and Vice Versa
447(5)
14.8 Thin Lens Modelling of Diffractive Lenses
452(1)
References
452(5)
15 Stop Shift, Pupil Aberrations, and Conjugate Shift
457(26)
15.1 Axial Shift of the Aperture Stop
457(6)
15.1.1 The Eccentricity Parameter
457(2)
15.1.2 Seidel Difference Formula
459(2)
15.1.3 Stop-Shift Effects on Seidel Aberrations in Refraction by a Single Surface
461(1)
15.1.4 Stop-Shift Effects on Seidel Aberrations in an Axi-Symmetric System
462(1)
15.1.5 Stop-Shift Effects on Seidel Aberrations in a Single Thin Lens
463(1)
15.1.6 Corollaries
463(1)
15.2 Pupil Aberrations
463(12)
15.2.1 Relation between Pupil Aberrations and Image Aberrations
466(5)
15.2.2 Effect of Stop Shift on Seidel Spherical Aberration of the Pupil
471(3)
15.2.3 Effect of Stop Shift on Seidel Longitudinal Chromatic Aberration of the Pupil
474(1)
15.2.4 A Few Well-Known Effects of Pupil Aberrations on Imaging of Objects
474(1)
15.3 Conjugate Shift
475(6)
15.3.1 The Coefficients of Seidel Pupil Aberrations After Object Shift in Terms of the Coefficients of Seidel Pupil Aberrations Before Object Shift
477(1)
15.3.2 The Coefficients of Seidel Pupil Aberrations Before Object Shift in Terms of Coefficients of Seidel Image Aberrations Before Object Shift
478(1)
15.3.3 The Coefficients of Seidel Image Aberrations After Object Shift in Terms of Coefficients of Seidel Pupil Aberrations After Object Shift
478(1)
15.3.4 Effects of Conjugate Shift on the Coefficients of Seidel Image Aberrations
479(2)
15.3.5 The Bow--Sutton Conditions
481(1)
References
481(2)
16 Role of Diffraction in Image Formation
483(38)
16.1 Raison d'etre for `Diffraction Theory of Image Formation'
483(2)
16.2 Diffraction Theory of the Point Spread Function
485(10)
16.2.1 The Huygens--Fresnel Principle
485(3)
16.2.2 Diffraction Image of a Point Object by an Aberration Free Axi-Symmetric Lens System
488(5)
16.2.3 Physical Significance of the Omitted Phase Term
493(2)
16.2.4 Anamorphic Stretching of PSF in Extra-Axial Case
495(1)
16.3 Airy Pattern
495(6)
16.3.1 Factor of Encircled Energy
499(2)
16.4 Resolution and Resolving Power
501(15)
16.4.1 Two-Point Resolution
503(1)
16.4.2 Rayleigh Criterion of Resolution
503(2)
16.4.3 Sparrow Criterion of Resolution
505(2)
16.4.4 Dawes Criterion of Resolution
507(1)
16.4.5 Resolution in the Case of Two Points of Unequal Intensity
508(1)
16.4.6 Resolution in the Case of Two Mutually Coherent Points
508(2)
16.4.7 Breaking the Diffraction Limit of Resolution
510(1)
16.4.7.1 Use of Phase-Shifting Mask
510(2)
16.4.7.2 Superresolution over a Restricted Field of View
512(2)
16.4.7.3 Confocal Scanning Microscopy
514(1)
16.4.7.4 Near Field Superresolving Aperture Scanning
515(1)
References
516(5)
17 Diffraction Images by Aberrated Optical Systems
521(42)
17.1 Point Spread Function (PSF) for Aberrated Systems
521(9)
17.1.1 PSF of Airy Pupil in Different Planes of Focus
522(2)
17.1.2 Distribution of Intensity at the Centre of the PSF as a Function of Axial Position of the Focal Plane
524(1)
17.1.3 Determination of Intensity Distribution in and around Diffraction Images by Aberrated Systems
524(2)
17.1.4 Spot Diagrams
526(4)
17.2 Aberration Tolerances
530(8)
17.2.1 Rayleigh Quarter-Wavelength Rule
531(1)
17.2.2 Strehl Criterion
532(1)
17.2.3 Strehl Ratio in Terms of Variance of Wave Aberration
533(2)
17.2.3.1 Use of Local Variance of Wave Aberration
535(1)
17.2.3.2 Tolerance on Variance of Wave Aberration in Highly Corrected Systems
536(1)
17.2.3.3 Tolerance on Axial Shift of Focus in Aberration-Free Systems
537(1)
17.2.3.4 Tolerance on Primary Spherical Aberration
538(1)
17.3 Aberration Balancing
538(10)
17.3.1 Tolerance on Secondary Spherical Aberration with Optimum Values for Primary Spherical Aberration and Defect of Focus
540(2)
17.3.2 Tolerance on Primary Coma with Optimum Value for Transverse Shift of Focus
542(1)
17.3.3 Tolerance on Primary Astigmatism with Optimum Value for Defect of Focus
543(2)
17.3.4 Aberration Balancing and Tolerances on a FEE-Based Criterion
545(3)
17.4 Fast Evaluation of the Variance of Wave Aberration from Ray Trace Data
548(2)
17.5 Zernike Circle Polynomials
550(6)
17.6 Role of Fresnel Number in Imaging/Focusing
556(1)
17.7 Imaging/Focusing in Optical Systems with Large Numerical Aperture
556(1)
References
557(6)
18 System Theoretic Viewpoint in Optical Image Formation
563(74)
18.1 Quality Assessment of Imaging of Extended Objects: A Brief Historical Background
563(2)
18.2 System Theoretic Concepts in Optical Image Formation
565(4)
18.2.1 Linearity and Principle of Superposition
566(1)
18.2.2 Space Invariance and Isoplanatism
566(2)
18.2.3 Image of an Object by a Linear Space Invariant Imaging System
568(1)
18.3 Fourier Analysis
569(9)
18.3.1 Alternative Routes to Determine Image of an Object
570(1)
18.3.2 Physical Interpretation of the Kernel of Fourier Transform
570(2)
18.3.3 Reduced Period and Reduced Spatial Frequency
572(2)
18.3.4 Line Spread Function
574(1)
18.3.5 Image of a One-Dimensional Object
575(1)
18.3.6 Optical Transfer Function (OTF), Modulation Transfer Function (MTF), and Phase Transfer Function (PTF)
575(3)
18.3.7 Effects of Coherence in Illumination on Extended Object Imagery
578(1)
18.4 Abbe Theory of Coherent Image Formation
578(2)
18.5 Transfer Function, Point Spread Function, and the Pupil Function
580(24)
18.5.1 Amplitude Transfer Function (ATF) in Imaging Systems Using Coherent Illumination
581(2)
18.5.1.1 ATF in Coherent Diffraction Limited Imaging Systems
583(1)
18.5.1.2 Effects of Residual Aberrations on ATF in Coherent Systems
584(1)
18.5.2 Optical Transfer Function (OTF) in Imaging Systems Using Incoherent Illumination
585(7)
18.5.2.1 OTF in Incoherent Diffraction Limited Imaging Systems
592(3)
18.5.2.2 Effects of Residual Aberrations on OTF in Incoherent Systems
595(2)
18.5.2.3 Effects of Defocusing on OTF in Diffraction Limited Systems
597(2)
18.5.2.4 OTF in Incoherent Imaging Systems with Residual Aberrations
599(2)
18.5.2.5 Effects of Nonuniform Real Amplitude in Pupil Function on OTF
601(1)
18.5.2.6 Apodization and Inverse Apodization
602(2)
18.6 Aberration Tolerances based on OTF
604(4)
18.6.1 The Wave Aberration Difference Function
604(2)
18.6.2 Aberration Tolerances based on the Variance of Wave Aberration Difference Function
606(2)
18.7 Fast Evaluation of Variance of the Wave Aberration Difference Function from Finite Ray Trace Data
608(1)
18.8 Through-Focus MTF
609(1)
18.9 Interrelationship between PSF, LSF, ESF, BSF, and OTF
610(6)
18.9.1 Relation between PSF, LSF, and OTF for Circularly Symmetric Pupil Function
611(1)
18.9.2 Relation between ESF, LSF, and OTF
612(4)
18.9.3 BSF and OTF
616(1)
18.10 Effects of Anamorphic Imagery in the Off-Axis Region on OTF Analysis
616(5)
18.11 Transfer Function in Cascaded Optical Systems
621(1)
18.12 Image Evaluation Parameters in Case of Polychromatic Illumination
621(5)
18.12.1 Polychromatic PSF
622(1)
18.12.2 Polychromatic OTF
622(4)
18.13 Information Theoretic Concepts in Image Evaluation
626(2)
References
628(9)
19 Basics of Lens Design
637(30)
19.1 Statement of the Problem of Lens Design
637(1)
19.2 Lens Design Methodology
638(3)
19.3 Different Approaches for Lens Design
641(1)
19.4 Tackling Aberrations in Lens Design
642(3)
19.4.1 Structural Symmetry of the Components on the Two Sides of the Aperture Stop
642(1)
19.4.2 Axial Shift of the Aperture Stop
643(1)
19.4.3 Controlled Vignetting
643(1)
19.4.4 Use of Thin Lens Approximations
643(1)
19.4.5 D-number and Aperture Utilization Ratio
644(1)
19.5 Classification of Lens Systems
645(5)
19.5.1 Afocal Lenses
645(1)
19.5.2 Telephoto Lenses and Wide-Angle Lenses
645(1)
19.5.3 Telecentric Lenses
646(1)
19.5.4 Scanning Lenses
647(1)
19.5.5 Lenses with Working Wavelength beyond the Visible Range
647(3)
19.5.6 Unconventional Lenses and Lenses using Unconventional Optical Elements
650(1)
19.6 A Broad Classification of Lenses based on Aperture, Field of View, Axial Location of Aperture Stop, Image Quality, and Generic Type of Lens Elements
650(1)
19.7 Well-Known Lens Structures in Infinity Conjugate Systems
651(5)
19.8 Manufacturing Tolerances
656(2)
References
658(9)
20 Lens Design Optimization
667(44)
20.1 Optimization of Lens Design: From Dream to Reality
667(5)
20.2 Mathematical Preliminaries for Numerical Optimization
672(12)
20.2.1 Newton--Raphson Technique for Solving a Nonlinear Algebraic Equation
672(1)
20.2.2 Stationary Points of a Univariate Function
673(1)
20.2.3 Multivariate Minimization
673(1)
20.2.3.1 Basic Notations
673(2)
20.2.3.2 The Method of Steepest Descent
675(1)
20.2.3.3 Newton's Method
676(1)
20.2.4 Nonlinear Least-Squares
677(3)
20.2.4.1 The Gauss--Newton Method
680(1)
20.2.4.2 The Levenberg--Marquardt Method
681(1)
20.2.5 Handling of Constraints
682(2)
20.3 Damped Least-Squares (DLS) Method in Lens Design Optimization
684(14)
20.3.1 Degrees of Freedom
684(1)
20.3.2 Formation of the Objective Function
685(2)
20.3.3 Least-Squares Optimization with Total Hessian Matrix
687(1)
20.3.4 General Form of the Damping Factor λr
688(1)
20.3.5 The Scaling Damping Factor λr
688(1)
20.3.6 Truncated Defect Function
689(2)
20.3.7 Second-Derivative Damping Factor λr
691(2)
20.3.8 Normal Equations
693(1)
20.3.9 Global Damping Factor λ
694(3)
20.3.10 Control of Gaussian Parameters
697(1)
20.3.11 Control of Boundary Conditions
697(1)
20.3.11.1 Edge and Centre Thickness Control
697(1)
20.3.11.2 Control of Boundary Conditions Imposed by Available Glass Types
698(1)
20.4 Evaluation of Aberration Derivatives
698(3)
References
701(10)
21 Towards Global Synthesis of Optical Systems
711(22)
21.1 Local Optimization and Global Optimization: The Curse of Dimensionality
711(1)
21.2 Deterministic Methods for Global/Quasi-Global Optimization
711(4)
21.2.1 Adaptive/Dynamic Defect Function
712(1)
21.2.2 Partitioning of the Design Space
712(1)
21.2.3 The Escape Function and the `Blow-Up/Settle-Down' Method
713(1)
21.2.4 Using Saddle Points of Defect Function in Design Space
713(1)
21.2.5 Using Parallel Plates in Starting Design
714(1)
21.3 Stochastic Global Optimization Methods
715(4)
21.3.1 Simulated Annealing
715(1)
21.3.2 Evolutionary Computation
716(1)
21.3.3 Neural Networks, Deep Learning, and Fuzzy Logic
717(1)
21.3.4 Particle Swarm Optimization
718(1)
21.4 Global Optimization by Nature-Inspired and Bio-Inspired Algorithms
719(2)
21.5 A Prophylactic Approach for Global Synthesis
721(3)
21.6 Multi-Objective Optimization and Pareto-Optimality
724(1)
21.7 Optical Design and Practice of Medicine
725(1)
References
726(7)
Epilogue 733(2)
Index 735
Prof. Lakshminarayan Hazra obtained his M. Tech. and Ph.D. degrees from the University of Calcutta, and after several years in M/s National Instruments Limited, Calcutta and the Central Scientific Instruments Organisation (C.S.I.O.), Chandigarh, he joined the faculty of the Department of Applied Physics of the University of Calcutta in 1979.

Early in his career, he devised new techniques for imaging in telescopes working in turbulent medium, and in collaboration with Prof. H. H. Hopkins of University of Reading, U.K., he designed a remote access zoom objective for monitoring open-heart surgery in 1983. Prof. Hazra developed new methods for structural design of optical systems, as well as developed the optical design software Ray Analysis Package (RAP). He pioneered the use of Walsh functions in image analysis and synthesis, and, in association with researchers at Laval University in Canada, investigated the exact surface relief profile of diffractive lenses in the non-paraxial region.

He took the lead in establishing the Department of Applied Optics and Photonics at the University of Calcutta in 2005. He is currently associated as an Emeritus Professor with this department. He is a Distinguished Fellow of the Optical Society of India (OSI) where he was General Secretary for more than 15 years, and currently he is the Editor-in-chief of the OSI Journal of Optics published in collaboration with M/s Springer. He is a fellow of both the Optical Society of America and the SPIE. Prof. Hazra is the representative for the Indian Territory in the International Commission for Optics. He was conferred the Eminent Teacher Award by the University of Calcutta in 2019.

Prof. Hazra has published more than 100 papers in archival journals, and a few research monographs. He has delivered more than 250 invited talks on his research in different parts of India and in many countries of the world, namely U.S.A., U.K., Canada, Japan, Austria, Poland, France, Germany, Netherlands, Italy, Slovenia, Malaysia, China, Finland, Russia etc. He provides consultancy services to industry on optical instrumentation, and regularly works for promotion of applied and modern optics. He was a Nuffield Foundation Fellow (1982-83) in U.K., a visiting Professor (1991 97) at the Centre dOptique, Photonique et Lasers, Laval University in Quebec, Canada, an Erasmus Mundus Visiting Professor in the OpSciTech program of the European Commission in 2008, and a Visiting (Invitation) Professor of the Japan Society for Promotion of Science in 2012.

His areas of research interest are Optical System Design, Zoom Lens Design, Diffractive Optics, Optical and Ophthalmic Instrumentation, Aberration Theory, Theories of Image Formation, Super Resolution, Global Optimization, Laser Beam Shaping, Optical Tweezers, Fractal Optics, Metamaterials, Pareto-optimality and Solar Concentrator Optics. He has undertaken major research projects (funded by government agencies and private industries) on many of these topics. He has supervised the theses of more than twenty doctoral students, and more than a hundred Bachelor and Master level students in India and abroad.
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