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

It is the purpose of this tutorial paper to place bispectrum estimation in a digital signal processing framework in order to aid engineers in grasping the utility of the available bispectrum estimation techniques, to discuss application problems that can directly benefit from the use of the bispectrum, and to motivate research in this area Three general reasons are behind the use of bispectrum in signal processing and are addressed in the paper: to extract information due to deviations from normality, to estimate the phase of parametric signals, and to detect and characterize the properties of nonlinear mechanisms that generate time series

Bispectrum estimation: A digital signal processing framework

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

The diffraction tomography theorem is adapted to one-dimensional length measurement. The resulting spectral interferometry technique is described and the first length measurements using this technique on a model eye and on a human eye in vivo are presented.

Measurement of intraocular distances by backscattering spectral interferometry

Interferometre a modulation de phase sinusoidale dans lequel une onde de reference est facilement modulee en phase avec un miroir vibrant

Sinusoidal phase modulating interferometry for surface profile measurement

We propose a sinusoidal phase modulating laser diode interferometer
that is insensitive to vibrations of the optical components and
fluctuations in the optical wavelength of the laser diode. These external
disturbances cause fluctuations in the phase of the interference signal.
After we analyze the sinusoidal phase modulation in a laser diode interferometer,
we describe the method of the feedback control of the injection
current of the laser diode to eliminate the phase fluctuations of the interference
signal. We construct two sinusoidal phase modulating interferometers
for movement measurements and surface profile measurements,
respectively. The experimental results make it clear that the interferometers
work well in mechanically noisy circumstances.

Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance

A theoretical analysis of the measurement accuracy in sinusoidal phase modulating (SPM) interferometry is presented. The measurement accuracy is dependent on multiplicative and additive noise. The characteristics of SPM interferometry in the presence of this noise are made clear. Theoretical results show clearly that SPM interferometry has a high measurement accuracy of the order of 1 nm.

Analysis of measurement accuracy in sinusoidal phase modulating interferometry

We describe a sinusoidal phase modulating interferometer in which a CCD image sensor detects four values by integrating the time-varying intensity in an interference pattern for intervals of one-quarter period of the phase modulation. The optimum amplitude and phase of the sinusoidal phase modulation are determined. The measurement error caused by the additive noise and the deviation from the optimum phase modulation is analyzed. The experimental results for surface profiles of magnetic sliders show that the sinusoidal phase modulating interferometer proposed here yields a measurement accuracy of the order of 1 nm.

Sinusoidal phase modulating interferometer using the integrating-bucket method

Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer-Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.

Osami Sasaki

Papers

Sinusoidal phase modulating interferometry for surface profile measurement

Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance

Analysis of measurement accuracy in sinusoidal phase modulating interferometry

Sinusoidal phase modulating interferometer using the integrating-bucket method

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms.