INTRODUCTION TO ABERRATIONS IN OPTICAL IMAGING SYSTEMS

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1 INTRODUCTION TO ABERRATIONS IN OPTICAL IMAGING SYSTEMS JOSE SASIÄN University of Arizona ШШ CAMBRIDGE Щ0 UNIVERSITY PRESS

2 Contents Preface Acknowledgements Harold H. Hopkins Roland V. Shack Symbols 1 Introduction 1.1 Optical systems and imaging aberrations 1.2 Historical highlights References 2 Basic concepts in geometrical optics 2.1 Rays and wavefronts 2.2 Symmetry in optical imaging systems 2.3 The object and the image spaces 2.4 The aperture stop, the pupils, and the field stop 2.5 Significant planes and rays 2.6 The field and aperture vectors 2.7 Real, first-order, and paraxial rays 2.8 First-order ray invariants 2.9 Conventions for first-order ray tracing 2.10 First-order ray-trace example 2.11 Transverse ray errors 2.12 Stop shifting Exercises Further reading 3 Imaging with light rays 3.1 Collinear transformation

viii Contents 3.2 Gaussian imaging equations 28 3.3 Newtonian imaging equations 29 3.4 Derivation of the collinear transformation equations 30 3.5 Cardinal points and planes 31 3.

3 viii Contents 3.2 Gaussian imaging equations Newtonian imaging equations Derivation of the collinear transformation equations Cardinal points and planes First-order rays' congruence with the collinear transformation The camera obscura Review of linear shift-invariant systems theory Imaging with a camera obscura Optical transfer function of the camera obscura The modulation transfer function and image contrast Summary 39 Exercises 40 Further reading 40 4 Imaging with light waves Spherical, oblique, and plane waves Light diffraction by an aperture Far-field diffraction Diffraction by a circular aperture Action of an aplanatic lens system on a plane wave Fourier transforming properties of a lens system /optical relay system Imaging with an 8/optical projection system Imaging with coherent illumination Imaging with incoherent illumination Imaging with partially coherent illumination The Weyl-Lalor relationship Summary 64 Exercises 65 References 65 Further reading 66 5 The wave aberration function Theory of aberrations Learning aberration theory Heuristic approach to aberrations according to symmetry The aberration function 69

Contents ix 5.5 Determination of the wavefront deformation 73 5.6 Parity of the aberrations 73 5.7 Note on the choice of coordinates 74 5.

4 Contents ix 5.5 Determination of the wavefront deformation Parity of the aberrations Note on the choice of coordinates Summary 74 Exercises 74 References 74 The location and size of an image Change of focus and change of magnification Piston terms Change of reference sphere radius Images in the presence of defocus Chromatic aberrations Surface contributions to the chromatic aberrations Cases of zero surface contribution Chromatic coefficients for a system of thin lenses Cases of zero thin lens contribution The achromatic doublet lens 86 Exercises 87 Further reading 88 Wavefront aberrations Wavefront deformation Wave aberration fans Physical images in the presence of aberrations Wavefront variance Aberration balancing The Rayleigh-Strehl ratio 96 Exercises 98 Further reading 99 Ray aberrations Relationship between the wavefront deformation and the transverse ray error Components of the transverse ray aberrations Spot diagrams Through focus spot diagrams Images of extended objects Discussion of transverse ray aberrations Meridional and sagittal ray paths 116

X Contents 8.8 Summary 116 Exercises 117 Further reading 118 9 Ray caustics 119 9.1 Principal curvatures and caustic 119 9.2 Spherical aberration 120 9.3 Coma aberration 123 9.

5 X Contents 8.8 Summary 116 Exercises 117 Further reading Ray caustics Principal curvatures and caustic Spherical aberration Coma aberration Astigmatism aberration Curvature of the wavefront deformation Astigmatic field curves Coddington equations Physical images along the optical axis 129 Exercises 130 Further reading Aberration coefficients Spherical aberration Petzval field curvature Aberration function when the stop is at the center of curvature Aberration function when the aperture stop shifts Aberration function of a combination of two spherical surfaces Cases of zero aberration Contributions from an aspheric surface Contributions from stop shifting Aberration coefficients of a Cooke triplet lens 144 Exercises 145 Further reading Structural aberration coefficients Coefficient definition Vertex curvature of the field curves Structural aberration coefficients of a refracting surface Structural aberration coefficients of a reflecting surface Structural aberration coefficients of a thin lens Contrbutions to the structural aberration coefficients from a parallel plate Structural aberration coefficients of an optical system Application to the achromatic doublet 153

$Contents 11.9 Application to the two-mirror Mersenne telescope 157 11.10 Application to a diffractive lens 159 Exercises 160 Further reading 161 12 Pupil aberrations 162 12.1 Definitions 162 12.$

6 Contents 11.9 Application to the two-mirror Mersenne telescope Application to a diffractive lens 159 Exercises 160 Further reading Pupil aberrations Definitions Beam deformation at the entrance pupil Pupil effects Object shift equations Invariance of aberrations Chromatic pupil aberrations The Вow-Sutton conditions Second-order chromatic coefficients revisited 170 Exercises 172 Further reading Irradiance function Construction of the irradiance function Irradiance transport The element of throughput The radiance theorem Image and pupil aberrations relationships The sine condition The Herschel condition 184 Exercises 186 Further reading Sixth-order aberration coefficients Extrinsic aberrations Intrinsic aberrations Contributions from an aspheric surface Contributions from the sixth-order coefficients of asphericity Connections between pupil and image coefficients Fifth-order transverse ray aberrations Change of aberration coefficients with aperture vector location The Buchdahl-Rimmer coefficients Summary 203 Exercises 204 Further reading 204 XI

xii Contents 15 Aberrations of non-axially symmetric systems 205 15.1 Tilted component systems 205 15.2 The Shack-Thompson aberration fields 206 15.3 Plane symmetric optical systems 218 15.

7 xii Contents 15 Aberrations of non-axially symmetric systems Tilted component systems The Shack-Thompson aberration fields Plane symmetric optical systems Optical system tolerancing 222 Exercises 222 Further reading Polarization aberrations Polarization fields Amplitude transmittance and optical phase coefficients Amplitude and phase changes in the optical field Chipman's polarization aberrations Polarization fields' nodal characteristics Elliptical polarization 241 Exercises 244 Further reading Conclusion 246 Appendix: Wave coefficients 247 Index 258

INTRODUCTION TO ABERRATIONS IN OPTICAL IMAGING SYSTEMS

INTRODUCTION TO ABERRATIONS IN OPTICAL IMAGING SYSTEMS The competent and intelligent optical design of today s state-of-the-art products requires an understanding of optical aberrations. This accessible