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

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

Even when corrected with the best spectacles or contact lenses, normal human eyes still suffer from monochromatic aberrations that blur vision when the pupil is large. We have successfully corrected these aberrations using adaptive optics, providing normal eyes with supernormal optical quality. Contrast sensitivity to fine spatial patterns was increased when observers viewed stimuli through adaptive optics. The eye's aberrations also limit the resolution of images of the retina, a limit that has existed since the invention of the ophthalmoscope. We have constructed a fundus camera equipped with adaptive optics that provides unprecedented resolution, allowing the imaging of microscopic structures the size of single cells in the living human retina.

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Supernormal vision and high-resolution retinal imaging through adaptive optics

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

VIII. IX. X. XI. XII. Sign Conventions Aberration-Free Image Spherical Wavefront, Defocus, and Lateral Shift Angular, Transverse, and Longitudinal Aberration Seidel Aberrations A. Spherical Aberration B. Coma C. Astigmatism D. Field Curvature E. Distortion Zernike Polynomials Relationship between Zernike Polynomials and Third-Order Aberrations Peak-to-Valley and RMS Wavefront Aberration Strehl Ratio Chromatic Aberrations Aberrations Introduced by Plane Parallel Plates Aberrations of Simple Thin Lenses 2 4 9 12 15 18 22 24 26 28 28

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Basic Wavefront Aberration Theory for Optical Metrology

This paper describes a technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interferometry (TWLI) to extend the phase measurement range of conventional single-wavelength PSI. To verify theoretical predictions, experiments have been performed using a solid-state linear detector array to measure 1-D surface heights. Problems associated with TWLPSI and the experimental setup are discussed. To test the capability of the TWLPSI, a very fine fringe pattern was used to illuminate a 1024 element detector array. Without temporal averaging, the repeatability of measuring a surface having a sag of ~100 μm is better than 25-A (0.0025%) rms.

Two-wavelength phase-shifting interferometry (A)

Two-wavelength phase shifting interferometry.

This paper describes a method to enhance the capability of two-wavelength phase-shifting interferometry. By introducing the phase data of a third wavelength, one can measure the phase of a very steep wave front. Experiments have been performed using a linear detector array to measure surface height of an off-axis parabola. For the wave front being measured the optical path difference between adjacent detector pixels was as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 25-A rms (λ = 6328 A).

Multiple-wavelength phase-shifting interferometry

An analysis is performed to determine the accuracy with which an ac heterodyne lateral shear interferometer can measure wavefront aberrations if a white light extended source is used with the interferometer, and shot noise is the predominate noise source. The analysis shows that for uniform circular or square sources larger than a derived minimum size, the wavefront measurement accuracy depends only upon the radiance of the source and not upon the angular subtense of the source. For a 1-msec integration time, a 25-cm(2) collecting area, and a source radiance of 10 W/m(2)-sr the rms wavefront error is approximately 1/30 wave, assuming the signal is shot noise limited. It is shown that for both uniform circular and square sources an optimum shear distance is approximately (1/2) the aperture diameter required to resolve the light source. Comments are made on the optimum shear for nonuniform radiance distributions.

James C. Wyant

Papers

Basic Wavefront Aberration Theory for Optical Metrology

Two-wavelength phase-shifting interferometry (A)

Two-wavelength phase shifting interferometry.

Multiple-wavelength phase-shifting interferometry

Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems.