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

Phase shifting algorithms for fringe projection profilometry: A review

A new method of phase determination in hologram interferometry is described. The Fresnel holograms, which represent the undeformed and the deformed states of the object, are generated on a CCD target and stored electronically. No lens or other imaging device is used. The reconstruction is done from the digitally stored holograms with mathematical methods. It is shown that the intensity as well as the phase can be calculated from the digitally sampled holograms. A comparison of the phases of the undeformed and the deformed states permits direct determination of the interference phase.

Direct phase determination in hologram interferometry with use of digitally recorded holograms

If the best phase measurements are to be achieved, phase-stepping methods need algorithms that are 112 insensitive to the harmonic content of the sampled waveform and 122 insensitive to phase-shift miscalibration. A method is proposed that permits the derivation of algorithms that satisfy both requirements, up to any arbitrary order. It is based on a one-to-one correspondence between an algorithm and a polynomial. Simple rules are given to permit the generation of the polynomial that corresponds to the algorithm having the prescribed properties. These rules deal with the location and multiplicity of the roots of the polynomial. As a consequence, it can be calculated from the expansion of the products of monomials involving the roots. Novel algorithms are proposed, e.g., a six-sample one to eliminate the effects of the second harmonic and a 10-sample one to eliminate the effects of harmonics up to the fourth order. Finally, the general form of a self-calibrating algorithm that is insensitive to harmonics up to an arbitrary order is given.

Design of algorithms for phase measurements by the use of phase stepping

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.

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

A TV system has been developed for detecting and displaying a two-dimensional hologram image that permits concomitant (real-time) hologram interferometry The optics employed are the same as for electronic speckle pattern interferometry (ESPI), wherein a uniform reference field interferes at zero offset angle with a speckled image of an object Rather than detecting spatial modulation to indicate interference, as in ESPI, this system modulates the phase of the reference beam by 120° between picture frames to vary speckle irradiance Each incoming frame is compared with the two previous frames, and only pixels that vary in brightness are passed as white pixels in the video output The use of binary-valued pixels allows inexpensive data processing at standard video rates

Electro-Optic Holography System For Vibration Analysis And Nondestructive Testing

L'interferometrie heterodyne est generalement obtenue en introduisant un deplacement Doppler entre les 2 faisceaux d'un interferometre de facon a ce que sa figure de franges soit convertie en une figure d'eclairement fluctuant. La phase des fluctuations est proportionnelle a l'ordre des franges et peut etre mesuree

William R. Brohinsky

Papers

Electrooptic holography and its application to hologram interferometry.

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

Electro-Optic Holography System For Vibration Analysis And Nondestructive Testing

Measurement of phase change in heterodyne Interferometry: a novel scheme