Abstract

We present a computationally efficient method for solving the method of excess fractions used in multi-frequency interferometry for absolute phase measurement. The Chinese remainder theorem, an algorithm from number theory is used to provide a unique solution for absolute distance via a set of congruence�??s based on modulo arithmetic. We describe a modified version of this theorem to overcome its sensitivity to phase measurement noise. A comparison with the method of excess fractions has been performed to assess the performance of the algorithm and processing speed achieved. Experimental data has been obtained via a full-field fringe projection system for three projected fringe frequencies and processed using the modified Chinese remainder theorem algorithm.

© 2004 Optical Society of America

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Appl. Opt.

Astrophysical J.

C. Fabry and A. Perot, �??Measures of absolute wavelengths in the solar spectrum and in the spectrum of iron,�?? Astrophysical J. 15, 73 (1902).
[CrossRef]

Engineering

F. H. Rolt, �??The application of optics to engineering measurements,�?? Engineering 144, 162 (1937).

Interferogram Analysis

C. Creath, �??Temporal Phase Measurement,�?? in Interferogram Analysis editors D.W. Robinson G. T. Reid (Bristol, Institute of Physics Publishing 1993).

J. Phys.

M. R. Benoit, �??Applications des phenomenes d�??interference a des determinations metrologiques,�?? J. Phys. 3, 57 (1898).
[CrossRef]

Opt. Eng.

M. Reeves, A.J. Moore, D.P. Hand, J.D.C. Jones, �??Dynamic shape measurement system for laser materials processing,�?? Opt. Eng. 42, 2923 (2003).
[CrossRef]

Opt. Lasers Eng.

J. M. Huntley, �??Random phase measurement errors in digital speckle pattern interferometry,�?? Opt. Lasers Eng. 26, 131 (1997).
[CrossRef]

M. Kujawinska, J. Wojciak, �??High Accuracy Fourier Transform Fringe Pattern Analysis,�?? Opt. Lasers Eng. 14, 325 (1991).
[CrossRef]

Opt. Lett.

SPIE

I. Agurok, �??The rigorous decision of the excess fraction method in absolute distance interferometry,�?? SPIE 3134, 504 (1997).

Other

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Seventh Edition, 2002).

K. H. Rosen, Elementary number theory and its applications (Addison-Wesley publishing Co., 1988).

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