Interferogram Analysis for Optical Testing

Abstract

(condensed). Review and Comparison of the Main Interferometric Systems: Two-Wave Interferometers and Configurations Used in Optical Testing. Twyman-Green Interferometer. Fizeau Interferometers. Typical Interferograms in Twyman-Green and Fizeau Interferometers. Lateral Shear Interferometers. Ronchi Test. Hartmann Test. Fringe Projection. Talbot Interferometry and Moire Deflectometry. Common Light Sources Used in Interferometry. Aspherical Compensators and Aspheric Wavefronts. Imaging of the Pupil on the Observation Plane. Multiple-Wavelength Interferometry. Fourier Theory Review: Introduction. Fourier Series. Fourier Transforms. The Convolution of Two Functions. The Cross-Correlation of Two Functions. Sampling Theorem. Sampling of a Periodical Function. Sampling of a Periodical Function with Interval Averaging. Fast Fourier Transform. Digital Image Processing: Introduction. Histogram and Gray-Scale Transformations. Space and Frequency Domain of Interferograms. Digital Processing of Images. Some Useful Spatial Filters. Square Window Filter. Hamming and Hanning Window Filters. Cosinusoidal and Sinusoidal Window Filters. Extrapolation of Fringes Outside of the Pupil. Light Detectors Used To Digitize Images. Fringe Contouring and Polynomial Fitting: Fringe Detection Using Manual Digitizers. Fringe Tracking and Fringe Skeletonizing. Global Polynomial Interpolation. Local Interpolation by Segments. Wavefront Representation by an Array of Gaussians.References. Periodic Signal Phase Detection and Algorithms Analysis: Least Squares Phase Detection of a Sinusoidal Signal. Quadrature Phase Detection of a Sinusoidal Signal. Discrete Low-Pass Filtering Functions. Fourier Description of Synchronous Phase Detection. Synchronous Detection Using a Few Sampling Points. Signal Amplitude Measurement. Characteristic Polynomial of a Sampling Algorithm. General Error Analysis of Synchronous Phase-Detection Algorithms. Some Sources of Phase Error. Shifting Algorithms with Respect to the Phase Origin. Optimization of Phase-Detection Algorithms. Influence of Window Function of Sampling Algorithms. Conclusions. Appendix: Derivative of the Amplitude of the Fourier Transform of the Reference Sampling Functions. References. Phase-Detection Algorithms: General Properties of Synchronous Phase-Detection Algorithms. Three-Step Algorithms To Measure the Phase. Four-Step Algorithms To Measure the Phase. Five-Step Algorithm. Algorithms with Symmetrical N +1 Phase Steps. Combined Algorithms in Quadrature. Detuning-Insensitive Algorithms for Distorted Signals. Algorithms Corrected for Nonlinear Phase-Shifting Error. Continuous Sampling in a Finite Interval. Asynchronous Phase-Detection Algorithms. Algorithm Summary. References. Phase-Shifting Interferometry: Phase-Shifting Basic Principles. An Introduction to Phase Shifting. Phase-Shifting Schemes and Phase Measurement. Heterodyne Interferometry. Phase-lock Detection. Sinusoidal Phase Oscillation Detection. Practical Sources of Phase Error. Selection of the Reference Sphere in Phase-Shifting Interferometry. Paraxial Focus. Best Focus. Marginal Focus. Optimum Tilt and Defocusing in Phase-Shifting Interferometry. References. Spatial Linear and Circular Carrier Analysis: Spatial Linear Carrier Analysis. Space-Domain Phase Demodulation with a Linear Carrier. Basic Space-Domain Phase Demodulation Theory. Circular Spatial Carrier Analysis. Phase Demodulation with a Circular Carrier. Fourier Transform Phase Demodulation with a Linear Carrier. Fourier Transform Phase Demodulation with a Circular Carrier. References. Interferogram Analysis with Moire Methods: Moire Techniques. Moire Formed by Two Interferograms with a Linear Carrier. Moire Formed by Two Interferograms with a Circular Carrier. Summary of Moire Effects. Holographic Interpretation of Moire Patterns. Conclusion. References. Interferogram Analysis without a Carrier: Introduction. Mathematical Model of the Fringes. The Phase Tracker. The N-Dimensional Quadrature Transform. Conclusion. References. Phase Unwrapping: The Phase Unwrapping Problem. Unwrapping Consistent Phase Maps Unwrapping Noisy Phase Maps. Unwrapping Subsampled Phase Maps. Conclusions. References. Wavefront Curvature Sensing: Wavefront Determination by Slope Sensing. Wavefront Curvature Sensing. Wavefront Determination with Defocused Images. Conclusions. References. Index. Short TOC