A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Publisher Summary This chapter describes the phase-measurement interferometry techniques. For all techniques, a temporal phase modulation is introduced to perform the measurement. By measuring the interferogram intensity as the phase is shifted, the phase of the wavefront can be determined with the aid of electronics or a computer. Phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acousto-optic or electro-optic modulator, or using a Zeeman laser. Phase-measurement techniques using analytical means to determine phase all have some common denominators. There are different equations for calculating the phase of a wavefront from interference fringe intensity measurements. The precision of a phase-measuring interferometer system can be determined by taking two measurements, subtracting them, and looking at the root-meansquare of the difference wavefront. The chapter discusses the simulation results. The elimination of the errors that reduce the measurement accuracy depends on the type of measurement being performed. Phase-measurement interferometry (PMI) can be applied to any two-beam interferometer, including holographic interferometers. Applications can be divided into: surface figure, surface roughness, and metrology.

V Phase-Measurement Interferometry Techniques

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

Temporal phase-unwrapping algorithm for automated interferogram analysis.

Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations

Introductory digital image processing optical techniques intensity based analysis methods temporal phase measurement methods spatial phase measurement methods phase unwrapping methods analysis methods in speckle photography and PIV applications.

Interferogram Analysis: Digital Fringe Pattern Measurement Techniques

The application of a general-purpose image-processing computer system to automatic fringe analysis is presented. Three areas of application have been examined where the use of a system based on a random access frame store has enabled a processing algorithm to be developed to suit a specific problem. Furthermore, it has enabled automatic analysis to be performed with complex and noisy data. The applications considered are strain measurement by speckle interferometry, position location in three axes, and fault detection in holographic nondestructive testing. A brief description of each problem is presented, followed by a description of the processing algorithm, results, and timings.

Automatic fringe analysis with a computer image-processing system

Digital phase stepping speckle interferometry

Investigation of the Fourier-transform method of fringe pattern analysis

A modified holographic interferometer is described which enables automatic fringe pattern analysis to be achieved when recording transient events. The introduction of a phase grating enables the method of phase-stepping fringe analysis to be applied to a wide range of measurement problems. The theory is developed, and an analysis of the sources of error is presented with the aid of computer simulations. Initial experimental results confirm the utility of the method and its potential application in pulsed laser holography. The method can in principle be applied to electronic speckle pattern interferometry.

David W. Robinson

Papers

Interferogram Analysis: Digital Fringe Pattern Measurement Techniques

Automatic fringe analysis with a computer image-processing system

Digital phase stepping speckle interferometry

Investigation of the Fourier-transform method of fringe pattern analysis

Multichannel phase-stepped holographic interferometry