Optical Shop Testing 3e

Daniel Malacara, PhD, is a Professor at the Centro de Investigaciones en Optica, Leon, Gto, Mexico. A designer and constructor of optical instruments, including telescopes, he is well known for his books, including Optical Shop Testing, which has been translated into several languages. Dr. Malacara is a Fellow of the Optical Society of America and of SPIE, the International Society of Optical Engineering.

Preface. Contributors. Chapter 1. Newton, Fizeau, and Haidinger Interferometers (M Mantravadi and D Malacara). 1.1 Introduction. 1.2 Newton Interferometer. 1.2.1 Source and Observer's Pupil Size Considerations. 1.2.2 Some Suitable Light Sources. 1.2.3 Materials for the Optical Flats. 1.2.4 Simple Procedure for Estimating Peak Error. 1.2.5 Measurement of Spherical Surfaces . 1.2.6 Measurement of Aspheric Surfaces. 1.2.7 Measurement of Flatness of Opaque Surfaces. 1.3 Fizeau Interferometer. 1.3.1 The Basic Fizeau Interferometer. 1.3.2 Coherence Requirements for the Light Source. 1.3.3 Quality of Collimation Lens Required. 1.3.4 Liquid Reference Flats. 1.3.5 Fizeau Interferometer with Laser Source. 1.3.6 Multiple-Beam Fizeau Setup. 1.3.7 Testing Nearly Parallel Plates. 1.3.8 Testing the Inhomogeneity of Large Glass or Fused Quartz Samples. 1.3.9 Testing the Parallelism and Flatness of the Faces of Rods, Bars and Plates. 1.3.10 Testing Cube Corner and Right-Angle Prisms. 1.3.11 Fizeau Interferometer for Curved Surfaces. 1.3.12 Testing Concave and Convex Surfaces. 1.4 Haidinger Interferometer. 1.4.1 Applications of Haidinger Fringes. 1.4.2 Use of Laser Source for Haidinger Interferometer. 1.4.3 Other Applications of Haidinger Fringes. 1.5 Absolute Testing of Flats. Chapter 2. Twyman-Green Interferometer (D Malacara). 2.1 Introduction. 2.2 Beam-Splitter. 2.2.1 Optical Path Difference Introduced by the Beam Splitter Plate. 2.2.2 Required Accuracy in the Beam Splitter Plate. 2.2.3 Cube Beam Splitter. 2.3 Coherence Requirements. 2.3.1 Spatial Coherence. 2.3.2 Temporal Coherence. 2.4 Uses of a Twyman-Green Interferometer. 2.4.1 Testing of Prisms and Diffraction Rulings. 2.4.2 Testing of Lenses. 2.4.3 Testing of Microscope Objectives. 2.5 Compensation of Intrinsic Aberrations in the Interferometer. 2.6 Unequal-Path Interferometer. 2.6.1 Some Special Designs. 2.6.2 Improving the Fringe Stability. 2.7 Open Path Interferometers. 2.7.1 Mach-Zehnder Interferometers. 2.7.2 Triangular Interferometers. 2.7.3 Oblique Incidence Interferometers . 2.8 Variations from the Twyman-Green Configuration. 2.8.1 Interferometers with Diffractive Beam Splitters. 2.8.2 Phase Conjugating Interferometer. 2.9 Typical Interferograms and their Analysis. 2.9.1 Analysis of Interferograms of Arbitrary Wavefronts. Chapter 3. Common-Path Interferometers (D Malacara and S Mallick). 3.1 Introduction. 3.2 Burch's Interferometer Employing Two Matched Scatter Plates. 3.2.1 Fresnel Zone Plate Interferometer. 3.2.2 Burch and Fresnel Zone Plate Interferometer for Aspheric Surfaces. 3.2.3 Burch and fresnel Zone Plate Interferometers for Phase Shifting. 3.3 Birefringent Beam Splitters. 3.3.1 Savart Polariscope. 3.3.2 Wollaston Prism. 3.3.3 Double-Focus Systems. 3.4 Lateral Shearing Interferometers. 3.4.1 Use of a Savart Polariscope. 3.4.2 Use of a Wollaston Prism. 3.5 Double-Focus Interferometer. 3.6 Saunders's Prism Interferometer. 3.7 Point Diffraction Interferometer. 3.8 Zernike Tests with Common-Path Interferometers. 3.9 Measurement of the Optical Transfer Function. Chapter 4. Lateral Shear Interferometers (M Strojnik G Paez and M Mantravadi). 4.1 Introduction. 4.2 Coherence Properties of the Light Source. 4.3 Brief Theory of Lateral Shearing Interferometry. 4.3.1 Interferograms of Spherical and Flat Wavefronts. 4.3.2 Interferogams of Primary Aberrations upon Lateral Shear. 4.4 Evaluation of an Unknown Wavefront. 4.5 Lateral Shearing Interferometers in Collimated Light (White Light Compensated). 4.5.1 Arrangements Based on the Jamin Interferometer. 4.5.2 Arrangements Based on the Michelson Interferometer. 4.5.3 Arrangements Based on a Cyclic Interferometer. 4.5.4 Arrangements Based on the Mach-Zehnder Interferometer. 4.6 Lateral Shearing Interferometers in Convergent Light (White-light Compensated). 4.6.1 Arrangements Based on the Michelson Interferometer. 4.6.2 Arrangements Based on the Mach-Zehnder Interferometer. 4.7 Lateral Shearing Interferometers Using Lasers. 4.7.1 Other Applications of the Parallel Plate Interferometer. 4.8 Other Types of Lateral Shearing Interferometers. 4.8.1 Lateral Shearing Interferometers Based on Diffraction. 4.8.2 Lateral Shearing Interferometers Based on Polarization. 4.9 Vectorial Shearing Interferometer. 4.9.1 Shearing Interferometry. 4.9.2 Directional Shearing Interferometer. 4.9.3 Interferograms of Primary Aberrations upon Vectorial Shear. 4.9.4 Experimental Results. 4.9.5 Similarities and Differences with Other Interferometers. Chapter 5. Radial, Rotational, and Reversal Shear Interferometer (D Malacara). 5.1 Introduction. 5.2 Radial Shear Interferometers. 5.2.1 Wavefront Evaluation from Radial Shear Interferograms. 5.2.2 Single-Pass Radial Shear Interferometers. 5.2.3 Double-Pass Radial Shear Interferometers. 5.2.4 Laser Radial Shear Interferometers. 5.2.5 Thick-Lens Radial Shear Interferometers. 5.3 Rotational Shear Interferometers. 5.3.1 Source Size Uncompensated Rotational Shear Interferometers. 5.3.2 Source Size Compensated Rotational Shear Interferometer. 5.4 Reversal Shear Interferometers. 5.4.1 Some Reversal Shear Interferometers. Chapter 6. Multiple-Beam Interferometers (C Roychudhuri). 6.1 Multiple-Beam Fizeau Interferometer. 6.2 Fringes of Equal Chromatic Order. 6.3 Reduction of Fringe Interval in Multiple-Beam Interferometry. 6.4 Plane Parallel Fabry-Perot Interferometer. 6.5 Tolansky Fringes with Fabry-Perot Interferometer. 6.6 Multiple-Beam Interferometer for Curved Surfaces. Chapter 7. Multiple-Pass Interferometers (P Hariharan). 7.1 Multipass Interferometry. 7.2 Multiple Pass Configurations to Reduce Vibrations. Chapter 8. Foucault, Wire, and Phase Modulation Tests (J Ojeda-Casta eda). 8.1 Introduction. 8.2 Foucault or Knife-Edge Test. 8.2.1 Description. 8.2.2 Geometrical Theory. 8.2.3 Physical Theory. 8.3 Wire Test. 8.3.1 Geometrical Theory. 8.3.2 Physical Theory. 8.4 Platzeck-Gaviola Test. 8.4.1 Geometrical Theory. 8.5 Phase Modulation Tests. 8.5.1 Zernike Test and its Relation to the Smart Interferometer. 8.5.2 Lyot Test. 8.5.3 Wolther Test. 8.6 Ritchey-Common Test. 8.7 Conclusions. Chapter 9. Ronchi Test (A Cornejo-Rodriguez). 9.1 Introduction. 9.2 Geometrical Theory. 9.2.1 Ronchi Patterns for Prymary Aberrations. 9.2.2 Ronchi Patterns for Aspherical Surfaces. 9.3 Wavefront Shape Deformation. 9.3.1 General Case. 9.3.2 Surfaces with Rotational Symmetry. 9.4 Physical Theory. 9.4.1 Mathematical Treatment. 9.4.2 Fringe Contrast and Sharpness. 9.4.3 Physical vs Geometrical Theory. 9.5 Practical Aspects of the Ronchi Test. 9.6 Some Related Tests. 9.6.1 Concentric Circular Grid. 9.6.2 Phase Shifting Ronchi Test. 9.6.3 Side Band Ronchi Test. 9.6.4 Lower Test. 9.6.5 Ronchi-Hartmann and Null Hartmann Tests. Chapter 10. Hartmann, Hartmann-Shack and Other Screen Tests (D Malacara-Doblado). 10.1 Introduction. 10.2 Some Practical Aspects. 10.3 Hartmann Test Using a Rectangular Screen. 10.4 Wavefront Retrieval. 10.4.1 Focus and Tilt Removal. 10.4.2 Trapezoidal Integration. 10.4.3 Southwell Algorithm. 10.4.4 Polynomial Fitting. 10.4.5 Other Methods. 10.5 Hartmann Test Using a Screen with Four Holes. 10.5.1 Four Holes in Cross. 10.5.2 Four Holes in X. 10.6 Hartmann Test of Ophthalmic Lenses. 10.7 Hartmann Test Using Non-Rectangular Screens. 10.7.1 Radial Screen. 10.7.2 Helical Screen. 10.8 Hartmann-Shack Test. 10.9 Crossed Cylinder Test. 10.10 Testing with an Array of Light Sources or Printed Screens. 10.10.1 Testing Convergent Lenses. 10.10.2 Testing Concave and Convex Surfaces. 10.11 Michelson-Gardner Test. 10.12 Other Developments and Summary. Chapter 11. Star Tests (D Malacara). 11.1 Introduction. 11.2 Star Test with Small Aberrations. 11.2.1 The Aberration Free Airy Pattern. 11.2.2 The Defocused Airy Pattern. 11.2.3 Polychromatic Light. 11.2.4 Systems with Central Obstructions. 11.2.5 Effects of Small Aberrations. 11.2.6 Gaussian Beams. 11.2.7 Very Small Convergence Angles (Low Fresnel Numbers). 11.3 Practical Aspects with Small Aberrations. 11.3.1 Effects of Visual Star Testing. 11.3.2 The Light Source for Star Testing. 11.3.3 The Arrangement of the Optical System for Star Testing. 11.3.4 Microscope Objectives. 11.4 The Star Test with Large Aberrations. 11.4.1 Spherical Aberration. 11.4.2 Longitudinal Chromatic Aberration. 11.4.3 Axial Symmetry. 11.4.4 Astigmatism and Coma. 11.4.5 Distortion. 11.4.6 Non-Null Tests. 11.5 Wavefront Retrieval with Slope and Curvature Measurements. 11.5.1 The Laplacian and Local Average Curvatures. 11.5.2 Wavefront Determination with Iterative Fourier Transforms. 11.5.3 Irradiance Transport Equation. 11.6 Wavefront Determination with two Images Using the Irradiance Transport Equation. 11.7 Wavefront Determination with a Single Defocused Image Using Fourier Transform Iterations. 11.8 Wavefront Determination with Two or Three Defocused Images Using Fresnel Transform Iterations. Chapter 12. Testing of Aspheric Wavefronts and Surfaces. (D Malacara). 12.1 Introduction. 12.2 Imaging of the Interference Pattern in Non-Null Tests. 12.3 Some Null Testing Configurations. 12.3.1 Flat and Concave Spherical Surfaces. 12.3.2 Telescope Refracting Objectives. 12.3.3 Concave Paraboloidal Surfaces. 12.3.4 Concave Ellipsoidal or Spheroidal Surfaces. 12.4 Testing of Convex Hyperboloidal Surfaces. 12.4.1 Hindle Type Tests. 12.4.2 Testing by Refraction. 12.5 Testing of Cylindrical Surfaces. 12.6 Early Compensators. 12.6.1 Couder and Ross Compensators. 12.6.2 Dall Compensator. 12.7 Refractive Compensators. 12.7.1 Refractive Offner Compensator. 12.7.2 General Comments about Refracting Compensators. 12.7.3 Shafer Compensator. 12.8 Reflecting Compensators. 12.8.1 Reflecting Offner Compensators. 12.8.2 Reflecting Adaptive Compensator. 12.9 Other Compensators for Concave Conicoids. 12.10 Interferometers Using Real Holographic Compensators. 12.10.1 Holographic Wavefront Storage. 12.10.2 Holographic Test Plate. 12.11 Interferometers Using Synthetic Holographic Compensators. 12.11.1 Computer-Generated Holograms (CGHs). 12.11.2 Using a CGH in an Interfeometer. 12.11.3 Off-Axis CGH Aspheric Compensator. 12.11.4 On-Axis CGH Aspheric Compensator. 12.11.5 Combination of CGH with Null Optics. 12.12 Interferometers Using Synthetic Holographic Compensators. 12.12.1 Fabrication of Computer-Generated Holograms (CGHs). 12.12.2 Using a CGH in an Interfeometer. 12.12.3 Off-Axis CGH Aspheric Compensator. 12.12.4 In-Line CGH Aspheric Compensator. 12.12.5 Combination of CGH with Null Optics. 12.13 Aspheric Testing with Two-Wavelength Holography. 12.14 Wavefront Stitching. 12.14.1 Annular Zones. 12.14.2 Circular Zones. 12.14.3 Dynamic Tilt Switching. Chapter 13. Zernike Polynomial and Wavefront Fitting (V Mahajan). 13.1 Introduction. 13.2 Aberrations of a Rotationally Symmetric System With a Circular Pupil. 13.2.1 Power Series Expansion. 13.2.2 Primary or Seidel Aberration Function. 13.2.3 Secondary or Schwarzschild Aberration Function. 13.2.4 Zernike Circle Polynomial Expansion. 13.2.5 Zernike Circle Polynomials as Balanced Aberrations for Minimum Wave Aberration Variance. 13.2.6 Relationships Between Coefficients of Power-Series and Zernike-Polynomial Expansions. 13.2.7 Conversion of Seidel Aberrations into Zernike Aberrations. 13.2.8 Conversion of Zernike Aberrations into Seidel Aberrations. 13.3 Aberrations of a System With a Circular Pupil, but Without an Axis of Rotational Symmetry. 13.3.1 Zernike Circle Polynomial Expansion 3.2 Relationships Among the Indices n, m, and j. 13.3.3 Isometric, Contour, and PSF Plots for a Zernike Circle Polynomial Aberration. 13.3.4 Primary Zernike Aberrations. 13.4 Aberrations of a Rotationally Symmetric System With an Annular Pupil. 13.4.1 Balanced Aberrations. 13.4.2 Zernike Annular Polynomials. 13.4.3 Isometric, Contour, and PSF Plots for a Zernike Annular Polynomial Aberration. 13.5 Determination of Zernike Coefficients From Discrete Wavefront Error Data. 13.5.1 Introduction. 13.5.2 Orthonormal Coefficients and Aberration Variance. 13.5.3 Orthonormal Polynomials. 13.5.4 Zernike Coefficients. 13.5.5 Numerical Example. 13.6 Summary Acknowledgment. Chapter 14. Phase Shifting Interferometry (J H Bruning and H Schreiber). 14.1 Introduction. 14.2 Fundamental Concepts. 14.3 Advantages of PSI. 14.4 Methods of Phase Shifting. 14.5 Detecting the Wavefront Phase. 14.6 Data Collection. 14.6.1 Temporal methods. 14.6.2 Spatial Methods. 14.7 PSI Algorithms. 14.7.1 Three Step Algorithms. 14.7.2 Least-Squares Algorithms. 14.7.3 Carre Algorithm. 14.7.4 Family of Averaging Algorithms. 14.7.5 Hariharan Algorithm. 14.7.6 2 + 1 Algorithm. 14.7.7 Methods to Generate Algorithms. 14.7.8 Methods to Evaluate Algorithms. 14.7.9 Summary of Algorithms. 14.8 Phase Shift Calibration. 14.9 Error Sources. 14.9.1 Phase Shift Errors. 14.9.2 Detector Nonlinearities. 14.9.3 Source Stability. 14.9.4 Quantization Errors. 14.9.5 Vibration Errors. 14.9.6 Air Turbulence. 14.9.7 Extraneous Fringes and Other Coherent Effects. 14.9.8 Interferometer Optical Errors. 14.10 Detectors and Spatial Sampling. 14.10.1 Solid State Sensors. 14.10.2 Spatial Sampling. 14.11 Quality Functions. 14.11.1 Modulation. 14.11.2 Residues. 14.11.3 Filtering. 14.12 Phase Unwrapping. 14.12.1 Unwrapping in one dimension. 14.12.2 2-D Phase Unwrapping. 14.12.3 Path-Following Algorithms. 14.12.4 Path Independent Methods. 14.13 Aspheres and Extended Range PSI Techniques. 14.13.1 Aliasing. 14.13.2 Sub-Nyquist Interferometry. 14.13.3 Two Wavelength PSI . 14.13.4 Sub-Aperture Stitching. 14.14 Other Analysis Methods. 14.14.1 Zero Crossing Analysis. 14.14.2 Synchronous Detection. 14.14.3 Heterodyne Interferometry. 14.14.4 Phase Lock Interferometry. 14.14.5 Spatial Synchronous and Fourier Methods. 14.15 Computer Processing and Output. 14.16 Implementation and Applications. 14.16.1 Commercial Instrumentation. 14.16.2 Interferometer Configurations . 14.16.3 Absolute Calibration. 14.16.4 Sources. 14.16.5 Alignment Fiducials. 14.17 Future Trends for PSI. Chapter 15. Surface Profilers Multiple Wavelength, and White Light Intereferometry. (J Schmit, K Creath and J C Wyant). 15.1 Introduction to Surface Profilers. 15.1.1 Contact Profilometers. 15.1.2 Optical Profilometers. 15.1.3 Interferometric Profilers. 15.1.4 Terms and Issues in Determining System Performance. 15.2 Contact Profilometers. 15.2.1 Stylus Profilers. 15.2.2 Scanning Probe Microscopes. 15.2.3 Comparison of AFM and Stylus Profiler. 15.3 Optical Profilers. 15.3.1 Optical Focus Sensors. 15.3.2 Confocal Microscopy . 15.4 Interferometric Optical Profilers. 15.4.1 Common Features. 15.5 Two-Wavelength and Multiple-Wavelength Techniques. 15.5.1 Two-Wavelengths Phase Measurement. 15.5.2 Multiple-Wavelength Phase Measurement. 15.5.3 Reducing Measurement Time . 15.6 White Light Interference Optical Profilers . 15.6.1 White Light Interference. 15.6.2 Image Buildup. 15.6.3 Signal Processing of White Light Interferograms. 15.6.4 Light Sources. 15.6.5 Dispersion in White Light Fringes. 15.6.6 Other Names for Interferometric Optical Profilers. 15.7 Wavelength Scanning Interferometer. 15.7.1 Wavelength Tunable Light Sources. 15.7.2 Image Build-up. 15.7.3 Signal Analysis. 15.7.4 Film and Plate Thickness Measurement. 15.8 Spectrally Resolved White Light Interferometry (SRWLI). 15.8.1 Image Buildup. 15.8.2 Signal Analysis. 15.8.3 Other Names for Spectral Interferometry. 15.9 Polarization Interferometers. 15.9.1 Differential Interference Contrast Microscope (Nomarski). 15.9.2 Geometric Phase Shifting. 15.10 Optical Ranging Methods. 15.11 Summary. Chapter 16. Optical Metrology of Diffuse Surfaces. (K Creath, J Schmit and J C Wyant). 16.1 Moir' and Fringe Projection Techniques. 16.1.1 Introduction. 16.1.2 What is Moire? 16.1.3 Moir' and Interferograms. 16.1.4 Historical Review. 16.1.5 Fringe Projection. 16.1.6 Shadow Moire. 16.1.7 Projection Moire. 16.1.8 Two-Angle Holography. 16.1.9 Common Features. 16.1.10 Comparison to Conventional Interferometry. 16.1.11 Coded and Structured Light Projection. 16.1.12 Applications. 16.1.13 Summary. 16.2 Holographic and Speckle Tests. 16.2.1 Introduction. 16.2.2 Holographic Interferometry for Nondestructive Testing. 16.2.3 Speckle Interferometry and Digital Holography. Chapter 17. Angle, Prisms, Curvature, and Focal Length Measurements (Z Malacara). 17.1 Introduction. 17.2 Angle Measurements. 17.2.1 Divided Circles and Goniometers. 17.2.2 Autocollimator. 17.2.3 Interferometric Measurements of Angles. 17.3 Testing of Prisms. 17.4 Radius of Curvature Measurements. 17.4.1 Mechanical Measurement of Radius of Curvature. 17.4.2 Optical Measurement of Radius of Curvature. 17.5 Focal Length Measurements. 17.5.1 Nodal Slide Bench. 17.5.2 Focimeters. 17.5.3 Other Focal Length Measurements. Chapter 18. Mathematical Representation of an Optical Surface and Its Characteristics. 18.1 Definition of an Optical Surface. 18.1.1 Parameters for Conic Surfaces. 18.1.2 Some Useful Expansions of z. 18.1.3 Aberration of the Normals to the Surface. 18.2 Caustic Produced by an Aspheric Surface. 18.3 Primary Aberrations of Spherical Surfaces. 18.3.1 Spherical Aberration of and Aspherical Surface. 18.3.2 Coma of a Concave Mirror. 18.3.3 Astigmatism of a Concave Mirror. 18.4 Astigmatic Surfaces. 18.4.1 Toroidal Surface. 18.4.2 Astigmatic Ellipsoidal and Oblate Spheroidal Surfaces. 18.4.3 Sphero-Cylindrical Surface. 18.4.4 Testing Astigmatic Surfaces. 18.4.5 Comparison Between Astigmatic Surfaces. 18.5 Off-Axis Conicoids. 18.5.1 Off-Axis Paraboloids. Appendix Optical Testing Programs. Index.