Abstract

A fringe analysis technique is proposed to automatically mea- sure 3-D object shape. A grating pattern is projected onto an object, and the grating pattern deforms in accordance with the 3-D object. This de- formed grating image is analyzed by means of the subfringe integration algorithm (SIA), in which the phase is retrieved using N bucket integra- tion. Only one frame of the image is sufficient to obtain the phase distri- bution and the object shape at every pixel on measured object. Theoret- ical analysis, experimental results, and simulation calculations are presented. © 1997 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(97)03009-2) Optical measurements of 3-D object shapes has found wide application in various fields because of its potential advan- tages: high accuracy and noncontact and fully automated measurement. Most of the current research is aimed at de- veloping the phase measurement technique, and several methods of phase shifting to measure the 3-D object shape have been developed. The phase shifting moiretopography technique 1 can achieve much higher accuracy, but it re- quires a complicated phase shifting arrangement. In con- trast to moiretopography, space-phase demodulation ana- lyzes the deformed grating itself instead of the moirefringe pattern, and requires only one image pattern to obtain the phases of the deformed grating. Some impressive research has been done. Fourier transform profilometry 2 ~FTP! is free from the shortcomings associated with the moireto- pography, but the FTP method is computationally intensive in transformation and inverse transformation. Since the choice of the filtering window is related to the practical problem, it is not easy to automatically process the fringe signals. Spatial phase detection 3 ~SPD! and finite-duration impulse response low-pass digital filter 4 ~FIR DF! are two excellent methods in which the phase is demodulated by sinusoidally fitting and numerical integration similar to that used in communication techniques. But the phase demodu- lation of the SPD method is at the middle point of every carrier interval, not at every pixel. Only an average phase value is obtained in every sampling space period, which limits the resolution. The phase calculation of the FIR DR method, similar to FTP, is very complex. It seems that one- step phase-shift grating projection 5 ~OPGP! is simpler than other phase demodulation algorithms, but it requires the fringe period to occupy the special carrier interval ~e.g., either 4-pixel width or 8-pixel width!. The aim of this paper is to present an alternative space- phase extraction method, the subfringe integration algo- rithm ~SIA!, for measuring the 3-D objects shape. The SIA technique is similar to the form of projection optics geom- etry, but the phase demodulation algorithm is quite differ- ent. The SIA technique extends the phase extraction algo- rithm proposed by Wyant, 6 which integrated the intensity over a finite time interval. In our work, an SIA that inte- grates the intensity over a finite space interval is discussed. The phase is demodulated using an N integrating bucket algorithm similar to correlation detection, which is used in communication techniques. Since SIA evaluates the fringe pattern in the space domain instead of the temporal domain, it is easier to program than other phase extraction methods. Because it demodulates the space phase at every pixel on points, it has high measurement accuracy and spatial reso- lution. Another advantage of the SIA technique is that the processing speed of this technique is faster than that of FTP, which is very useful in on-line inspection.

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