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

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

Fringe projection techniques: Whither we are?

http://eia.udg.es/~qsalvi/papers/2010-PR.pdf

A state of the art in structured light patterns for surface profilometry

The high resolution surface profile of a 3-D diffuse object is obtained by measurement of the phase distribution across the image of a projected sinusoidal grating deformed by the surface. A shearing polarization interferometer is used for projection. Deformed grating images are detected by an array camera and processed by a microcomputer. Surface height resolutions of better than 10 μm have been attained, limited essentially by electronic quantization noise. In contrast to direct deformed grating analysis, this method, based on phase-shifting interferometric techniques, is capable of accurate measurement even with coarse projected gratings and low density image sensing arrays. Areas of application include industrial quality control, biostereometrics, robotics, and solid modeling for computer graphics.

Automated phase-measuring profilometry of 3-D diffuse objects

When a sinusoidal grating is projected on either a reference plane or a diffuse object to be measured, every point along a line normal to the grating lines, on the reference plane as well as the object, can be characterized by a unique phase value. By measuring this phase accurately using phase modulation methods and by determining points on the reference plane and the object having identical phases, it is shown that the object height can be computed. A working system requires a projector, a translatable sinusoidal grating, and a detector array interfaced to a microcomputer. Results of measurements on diffuse test objects are described and errors are analyzed.

Automated phase-measuring profilometry: a phase mapping approach.

Optical three-dimensional sensing by phase measuring profilometry

Phase measurements of deformed grating images are used in performing improved optical profilometry. In one embodiment, phase differences between images of an object and a reference plane are used to obtain a measure of the object height.

Method and apparatus for surface profilometry

A method is presented that permits a vast increase in the capability of projection moire topography. It involves simultaneous translation of the reference and object gratings to generate high-definition contour fringes without any of the artifacts associated with ordinary moire. Experimental results are presented for single- and double-projection arrangements for a general 3-D object and an inclined-plane test surface. Clear contouring fringes for angles of inclination up to 80° are shown, and fringe densities higher than the grating frequency are obtained. Coupled with the flexibility of projection moire, this technique is shown to be particularly suited for computer-assisted moire fringe pattern analysis. Means of practical implementation in on-line processing system are proposed.

Maurice Halioua

Papers

Automated phase-measuring profilometry of 3-D diffuse objects

Automated phase-measuring profilometry: a phase mapping approach.

Optical three-dimensional sensing by phase measuring profilometry

Method and apparatus for surface profilometry

Projection moire with moving gratings for automated 3-D topography