Table of Contents

Preface

List of Acronyms

1 Properties of Optical Systems

1.1 Optical Properties of a Single Spherical Surface

      1.1.1 Sign conventions

      1.1.2 Planar refractive surfaces

      1.1.3 Spherical refractive surfaces

      1.1.4 Reflective surfaces

      1.1.5 Gaussian imaging equation

      1.1.6 Newtonian imaging equation

      1.1.7 The thin lens

1.2 Aperture and Field Stops

      1.2.1 Aperture stop definition

      1.2.2 Marginal and chief rays

      1.2.3 Vignetting

      1.2.4 Field stop definition

1.3 First-Order Properties of an Optical System

      1.3.1 Gaussian imaging with multiple surfaces

      1.3.2 Paraxial raytracing

      1.3.3 Spherical Cardinal points

      1.3.4 Entrance and exit pupils

      1.3.5 Extension of Gaussian imaging to thick systems

      1.3.6 Longitudinal magnification

      1.3.7 Lagrange invariant and the AΩ product

      1.3.8 Numerical aperture, f-number, and working f-number

      1.3.9 Depth of focus

      1.3.10 Field of view

      1.3.11 Front and back focal distances

Bibliography

2 Diffraction and Aberrations

2.1 Limitations of Optical Systems

      2.1.1 Black box optical system based on Cardinal points and pupils

      2.1.2 Wavefront picture of optical imaging

      2.1.3 Detector Diffraction-limited systems and connection to Fresnel diffraction

      2.1.4 Point spread function (PSF)

      2.1.5 Sign and coordinate system conventions

      2.1.6 Optical path length (OPL), optical path difference (OPD), and wavefront error

      2.1.7 Transverse ray error and spot diagrams

2.2 Aberrations of Rotationally Symmetric Optical Systems

      2.2.1 Piston and tilt

      2.2.2 Primary aberrations

2.3 Aberrations of General Optical Systems

      2.3.1 Examples of non–rotationally symmetric systems

      2.3.2 Generalization of primary aberrations to the on-axis case

      2.3.3 Orthogonal functions

      2.3.4 Zernike polynomials

      2.3.5 Examples of different orders of Zernike polynomials

      2.3.6 Fitting Zernike polynomials to wavefront error

      2.3.7 Pupil size conversion

      2.3.8 Different variations found in the literature

References

Bibliography

3 Optical Quality Metrics

3.1 Introduction

3.2 Through-Focus PSF and Star Test

      3.2.1 Diffraction-limited case (defocus)

      3.2.2 Seidel spherical aberration

      3.2.3 Zernike spherical aberration

      3.2.4 Seidel astigmatism

      3.2.5 Zernike astigmatism

      3.2.6 Seidel coma

      3.2.7 Zernike coma

3.3 Measures of Distortion

      3.3.1 Conventional case

      3.3.2 Scheimpflug imaging

3.4 Resolution Targets

      3.4.1 Rayleigh criterion

      3.4.2 1951 USAF target

3.5 PSF and Wavefront-based Metrics

      3.5.1 Strehl ratio

      3.5.2 Peak-to-valley error, variance, and RMS wavefront error

      3.5.3 Relationship to Zernike coefficients

      3.5.4 Relationship to Strehl ratio

      3.5.5 Encircled and ensquared energy

      3.5.6 Example of optical quality metrics

      3.5.7 Diffraction-limited case (defocus)

3.6 Optical Transfer Function

      3.6.1 Modulation transfer function

      3.6.2 Phase transfer function

      3.6.3 Fourier transform relationship to PSF

      3.6.4 Autocorrelation of pupil function

      3.6.5 Line spread function

Bibliography

4 Optical Surfaces and Their Fabrication

4.1 Introduction

4.2 Optical Surfaces

      4.2.1 Flats

      4.2.2 Spheres

      4.2.3 Conoids

      4.2.4 Even and odd aspheres

      4.2.5 Forbes Q polynomials

      4.2.6 Astigmatic and freeform surfaces

4.3 Isolated Defect 1/f Noise: Dislocations

      4.3.1 Glass and plastics

      4.3.2 Dispersion formulas

      4.3.3 Infrared and ultraviolet materials

4.4 Fabrication Techniques

      4.4.1 Grinding and polishing spherical and flat surfaces

      4.4.2 Grinding and polishing aspheric surfaces

      4.4.3 Diamond turning and oscillating tool head

      4.4.4 Magnetorheological finishing

      4.4.5 Ion beam figuring

      4.4.6 Molding optical elements

References

Bibliography

5 Non-interferometric Testing

5.1 Autocollimator Tests

5.2 Surface Radius of Curvature

      5.2.1 Lens gauge

      5.2.2 Spherometer

      5.2.3 Autostigmatic measurements

5.3 Measurement of First-Order Properties of Optical Systems

      5.3.1 Measurement based on the Gaussian imaging equation

      5.3.2 Neutralization test

      5.3.3 Autocollimation technique

      5.3.4 Focimeter

      5.3.5 Focal collimator

      5.3.6 Recipricol magnification

      5.3.7 Nodal-slide lens bench

5.4 Measurement of Wavefront Error and Transverse Ray Error

      5.4.1 Foucault knife-edge test

      5.4.2 Wire and Ronchi test

      5.4.3 Hartmann screen test

      5.4.4 Shack–Hartmann sensor

      5.4.5 Fitting Shack–Hartmann data to Zernike polynomials

      5.4.6 Moiré deflectometry

References

Bibliography

6 Basic Interferometry and Optical Testing

6.1 Review of Two-Beam Interference

      6.1.1 Plane waves

      6.1.2 General wavefront shapes

      6.1.3 Visibility

      6.1.4 Coherence

6.2 Fizeau Interferometer

      6.2.1 Classical Fizeau interferometer

      6.2.2 Newton's rings

6.3 Twymann–Green Interferometer

6.4 Mach–Zender Interferometer

6.5 Lateral Shearing Interferometer

6.6 Lateral Shearing Interferometer

6.7 Lateral Shearing Interferometer

      6.7.1 Phase-shifting techniques

      6.7.2 Reconstruction algorithms

      6.7.3 Phase unwrapping

6.8 Testing Aspheric Surfaces

References

Bibliography

Preface

This book is a continued development of the notes for a course called Optical Specification, Fabrication and Testing that I teach at the University of Arizona College of Optical Sciences. The course is required for undergraduate optical engineering students in their final semester of study. At this point in their academic career, the students have a solid background in optics and are focusing on the next phase of their lives, typically securing a job in industry. In reviewing the coursework that the students have taken over their undergraduate career, I find that the topics tend to be compartmentalized. We teach geometrical optics in one course, interference and diffraction in another course, and aberrations in still another. The goal for the course and for this book is to connect the dots between these chunks of knowledge and to illustrate the development of an optical system from the initial layout, to design and aberration analysis, to fabrication, and finally to testing and verification of the individual components and the system performance. This book also seeks to cover more specialized topics such as fitting Zernike polynomials, representing aspheric surfaces with the Forbes Q polynomials, and testing with the Shack–Hartmann wavefront sensor. These topics are covered in more detail than is found in other textbooks, and the techniques are developed to the point where readers can pursue their own analysis or modify to their particular situations. Finally, there is also a limit on the detail that can be provided on any of the topics found in the book. Bibliographic references have been provided at the end of each chapter to facilitate more in-depth study.

I would like to thank John Greivenkamp, José Sasián, Bill Duncan, Ping Zhou, and Greg Forbes for their valuable suggestions in improving the manuscript. I wish to also thank the peer reviewers. Their thorough reading of the material and constructive comments have greatly enhanced the content. Thanks also go to Tim Lamkins and editor Dara Burrows for their help in turning a batch of messy notes into a quality book. I appreciate all of the members of the SPIE staff who have helped in the production of the book. Finally, with much love, I owe many thanks to my wife, Diana, and to my children, Max and Marie, for their unwavering love and support.

Jim Schwiegerling
October 2014