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

Interferogram Analysis For Optical Testing, Second Edition

A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.

Shearing interferometer for phase shifting interferometry with polarization phase shifter.

Quantitative data can be extracted from holographic interference fringes using Phase-Measurement Interferometry (PMI) techniques. These techniques are used to determine the phase of the secondary interference fringe pattern and can be divided broadly into spatial and temporal techniques. Temporal techniques introduce a known phase shift between the object and reference beams in an interferometer and take a series of data over time as the phase shift is varied. Spatial techniques rely on encoding the phase shift information spatially in a single interferogram by using a large number of fringes as a carrier for the phase information which are generated by tilting the reference wavefront relative to the test wave front. Temporal techniques which process data in electronics are known as heterodyne techniques and were discussed in the last chapter. The processing of spatial phase-measurement data will be discussed in the next chapter. Temporal techniques which process the data analytically on a point-by-point basis will be the concentration of this chapter.

Phase-Shifting Holographic Interferometry

Direct measurement of fringe amplitude and phase using a heterodyne interferometer operating in broadband light

Twyman-Green. This Letter describes a method by which the frequency shift equals 4N times the rotation rate, where N is the number of rotating components available. The advantage of this method over previously described methods is that a higher heterodyne frequency is possible than with the previously described techniques. Let the light entering an interferometer, shown in Fig. 1, be separated into two orthogonal linear polarizations using, for example, a polarization beam splitter P. Each component travels a separate path through the interferometer cavity seeing a different optical phase retardation. Upon recombination the light passes through the frequency shifter and onto a detector plane, where the temporally varying optical signal has a phase equal to the net phase difference between the two paths inside the interferometer. The frequency shifter, which we shall describe using Jones calculus 3 and the complex wave representation of light, consists of a stationary quarterwave plate (QS) followed by a series of rotating halfwave plates (Hr) separated by stationary halfwave plates (HS), followed by a stationary linear polarizer (LS). The following analysis demonstrates a frequency shift of eight times the rotation rate of the halfwave plates. We begin by treating the horizontal (X) component, which we represent by

Richard N. Shagam

Papers

Optical frequency shifter for heterodyne interferometers using multiple rotating polarization retarders.

Null Ronchi gratings from spot diagrams.