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

Synthetic aperture radar interferometry is an imaging technique for measuring the topography of a surface, its changes over time, and other changes in the detailed characteristic of the surface. By exploiting the phase of the coherent radar signal, interferometry has transformed radar remote sensing from a largely interpretive science to a quantitative tool, with applications in cartography, geodesy, land cover characterization, and natural hazards. This paper reviews the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering.

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Synthetic aperture radar interferometry

We first provide an overview of 3-D shape measurement us- ing various optical methods. Then we focus on structured light tech- niques where various optical configurations, image acquisition tech- niques, data postprocessing and analysis methods and advantages and limitations are presented. Several industrial application examples are presented. Important areas requiring further R&D are discussed. Finally, a comprehensive bibliography on 3-D shape measurement is included, although it is not intended to be exhaustive. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00101-X)

Overview of three-dimensional shape measurement using optical methods

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

This article describes the principles and major applications of digital recording and numerical reconstruction of holograms (digital holography). Digital holography became feasible since charged coupled devices (CCDs) with suitable numbers and sizes of pixels and computers with sufficient speed became available. The Fresnel or Fourier holograms are recorded directly by the CCD and stored digitally. No film material involving wet-chemical or other processing is necessary. The reconstruction of the wavefield, which is done optically by illumination of a hologram, is performed by numerical methods. The numerical reconstruction process is based on the Fresnel–Kirchhoff integral, which describes the diffraction of the reconstructing wave at the micro-structure of the hologram. In the numerical reconstruction process not only the intensity, but also the phase distribution of the stored wavefield can be computed from the digital hologram. This offers new possibilities for a variety of applications. Digital holography is applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media. Further applications are imaging and microscopy, where it is advantageous to refocus the area under investigation by numerical methods.

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Digital recording and numerical reconstruction of holograms

This paper discusses the possibilities of recording electrooptic holograms using a TV camera and digital frame storage for applications to hologram interferometry. The technique of reference beam phase stepping is proposed to allow determination of object beam amplitude and phase for every pixel element. The use of binary levels for both picture display and camera readout is discussed along with estimates of computation times.

Electrooptic holography and its application to hologram interferometry.

This paper describes the use of an Electro-Optic Holography system for measuring vibration patterns on diffusely reflecting objects. The system provides a high-quality display of fringes for identifying modal frequencies and setting vibration levels after which image brightness data can be transferred to a host computer. A bias vibration is introduced into the illumination beam to shift the 0 fringes so that fringe shift algorithms can be used to determine vibration amplitude. Using this approach, high spatial density displacement fields for vibrating objects were obtained directly form the time-average interferograms recorded by the Electro-Optic Holography system. These results show good correlation with the reconstructions from the holograms and with the vibration characteristics predicted by the Finite Element Methods.

Measurement Of Vibration Patterns Using Electro-Optic Holography

A method of holographic vibration analysis is presented that permits the extraction of vibration amplitudes by means of measurements from a photodiode-array camera from time-average hologram reconstructions, concomitant (real-time) hologram interferometry, or a speckle interferometer with an electronic holography readout system. A sinusoidal phase modulation is introduced into one of the beams of the hologram interferometer to offset the argument of the Bessel-function fringes. Irradiance values from time-average interferograms with zero, plus, and minus offsets can be processed numerically by a method analogous to that used for cosine fringes from a phase-step interferometer. This permits the evaluation of vibration amplitudes with the same facilities used for static displacements. The mathematical theory of this process is presented.

Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects

TV holograms for spatial phase stepping are formed with a small angular offset between the object and the reference beams to give a spatial frequency bias to the pattern recorded by the TV camera. It is common to set the bias so that there is a 90° or 120°phase shift between adjacent pixels and to use the irradiance of three or more adjacent pixels to evaluate the phase of the interference. We report the Fourier-transform evaluation of such recordings to obtain their phase data. We also demonstrate the direct calculation of the phase difference between successive recordings without intermediate calculation of the random phase of each hologram. This technique is proposed as an approach to pulsed TV holography.

Fourier-transform evaluation of phase data in spatially phase-biased TV holograms

Since its discovery in 1969, speckle interferometry has be-come a very active area of research, so much so that there now exists quite a collection of techniques that are applicable to a wide variety of problems. Because of the surprising versatility offered by such a wide range of techniques, the potential user of such technology may become con-fused as to what can and cannot be done, and, further, what process is suitable for what task. This review is provided, therefore, to set the various techniques into context, point out their similarities, and delineate their differences.

Karl A. Stetson

Papers

Electrooptic holography and its application to hologram interferometry.

Measurement Of Vibration Patterns Using Electro-Optic Holography

Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects

Fourier-transform evaluation of phase data in spatially phase-biased TV holograms

A Review of Speckle Photography and Interferometry