In this day of digitalization, you can work within the technology of optics without having to fully understand the science behind it. However, for those who wish to master the science, rather than merely be its servant, it's essential to learn the nuances, such as those involved with studying fringe patterns produced by optical testing interferometers. When Interferogram Analysis for Optical Testing originally came to print, it filled the need for an authoritative reference on this aspect of fringe analysis. That it was also exceptionally current and highly accessible made its arrival even more relevant. Of course, any book on something as cutting edge as interferogram analysis, no matter how insightful, isn't going to stay relevant forever. The second edition of Interferogram Analysis for Optical Testing is designed to meet the needs of all those involved or wanting to become involved in this area of advanced optical engineering. For those new to the science, it provides the necessary fundamentals, including basic computational methods for studying fringe patterns.
For those with deeper experience, it fills in the gaps and adds the information necessary to complete and update one's education. Written by the most experienced researchers in optical testing, this text discusses classical and innovative fringe analysis, principles of Fourier theory, digital image filtering, phase detection algorithms, and aspheric wavelength testing. It also explains how to assess wavefront deformation by calculating slope and local average curvature.
(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
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2nd Revised edition
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