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Spie Press Book

Optics of Diffractive and Gradient-Index Elements and Systems
Author(s): Grigoriy I. Greisukh; Sergei T. Bobrov; Sergei A. Stepanov
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Book Description

The use of diffractive and gradient-index (GRIN) lenses as components of imaging optical systems has been investigated for several decades. The elements have proved competitive in their unique focusing and aberration properties and in terms of their additional degrees of freedom for optical design. This book systematically examines the physical principles of diffractive and GRIN elements.

Book Details

Date Published: 1 April 1997
Pages: 414
ISBN: 9780819424518
Volume: PM42

Table of Contents
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Preface. ix
Notation of Principal Variables. xix
1 Introduction to Theory of Diffractive Elements. 1
1.1 Diffraction by infinitely thin structures. 3
1.2 Focusing properties of diffractive lenses. 10
1.3 Aberrations of infinitely thin optical elements. 22
1.3.1 Aspheric refracting surface 26
1.3.2 Diffractive lens on an aspheric surface 30
References. 34
2 Introduction to Theory of Gradient-Index Elements 36
2.1 Ray paths in inhomogeneous media. 36
2.2 Focusing properties of inhomogeneous media. 41
2.3 Paraxial optics of gradient-index singlets. 48
References. 53
3 Ray Tracing and Estimation of Image Quality 55
3.1 Ray tracing through hybrid optical systems 56
3.1.1 Tracing in homogeneous and inhomogeneous media. 56
3.1.2 Intersection with a predetermined surface 65
3.1.3 Deflection by an infinitely thin optical element. 70
3.1.4 Tracing through a diffractive corrector 76
3.2 Criteria of image evaluation in optical system design. 81
3.2.1 Main functions and numerical criteria of point image evaluation 81
3.2.2 Image quality criteria based on a spot diagram. 91
3.2.3 Analysis of correlation statistics of numerical criteria 97
References. 104
4 Aberration Calculations of Homogeneous Optical Systems. 106
4.1 Transformation of aberrations of propagating aberrated spherical waves 107
4.2 Calculation of wave-front aberrations. 123
4.3 First-order chromatic aberrations. 136
References. 144
5 Aberration Calculations of Inhomogeneous Optical Systems. 146
5.1 First-order chromatic aberrations. 146
5.2 Third-order monochromatic aberrations. 155
5.3 Higher-order aberrations. Pseudorays 164
5.3.1 Definitions and basic principles. 164
5.3.2 A pseudoray in a medium confined by two spherical
surfaces 167
5.3.3 Pseudoray deflection by an infinitely thin optical element..182
References. 187
6 Correction Capabilities of Optical Elements of Different Types. 189
6.1 Diffractive lens 189
6.1.1 Monochromatic aberrations 189
6.1.2 Effect of substrate 195
6.1.3 Chromatic variation of spherical aberration 202
6.2 Homogeneous refractive lens. 206
6.2.1 Refracting surface. 206
6.2.2 Thick lens. 211
6.2.3 Thin lens 220
6.3 Gradient-index lens. 223
6.3.1 Wood lens 223
6.3.2 Lens with spherical surfaces. 225
References. 230
7 High-Resolution Objectives Using Diffractive Lenses 232
7.1 Diffractive doublet. 232
7.1.1 Third-order aberration-free design. 233
7.1.2 Effect of substrates. 240
7.1.3 Design with unit magnification. 247
7.2 Front-to-back proportional and symmetric triplets. 250
7.3 Shortened triplet. 260
7.4 Triplet containing two aspherics 270
7.5 Fourier-transform objective. 279
References. 287
8 Homogeneous Hybrid Optical Systems. 288
8.1 Aberration properties of simple objectives 289
8.1.1 Refractive-diffractive doublet. 289
8.1.2 Front-to-back symmetric triplets. 295
8.1.3 Correction of chromatic aberrations 300
8.2 Compensated refracting surface 305
8.2.1 Principles and analysis of aberrations. 305
8.2.2 Imaging objectives using compensated surfaces 310
8.3 Objectives for optical disk systems. 317
References. 328
9 Hybrid Objectives Using Gradient-Index Lenses 330
9.1 Doublet including Smith lens 331
9.2 Design including a diffractive aspheric. 335
9.3 Gradient-diffractive doublet 344
9.4 Front-to-back symmetric triplet. 351
References. 359
10 Design of Diffractive Lenses from the Point of View of Their Fabrication 361
10.1 Diffraction efficiency of surface-relief elements 362
10.1.1 Sawtooth relief (kinoform). 362
10.1.2 Stairstep relief. 367
10.2 Design of a planar structure 372
10.3 Effects of manufacturing inaccuracies. 376
References. 386
Index. 389

Preface

The search for new passive optical elements has focused lately on diffractive optics and gradient-index (GRIN) elements. The term diffractive optics covers a wide range of optical elements that perform any kind of wavefront transformation using diffraction. GRIN elements are made of transparent materials with a continuously varying refractive index.

Possibilities for using diffractive and GRIN lenses as components of imaging optical systems have been investigated for several decades. The elements have proved competitive in their unique focusing and aberration properties and in terms of their additional degrees of freedom for optical design. Initial investigations have shown that high optical characteristics can be achieved for simple systems consisting of a few elements combined in a variety of ways.

This book systematically examines the physical principles of diffractive and GRIN elements. It presents universal methods of paraxial and aberration calculations, as well as those for evaluating image quality (both individual elements and optical systems). The text presents advantages and disadvantages of the various elements and considers methods for the the most effective use of these elements.


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