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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References

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Appl. Opt. (6)

Astrophysical J. (1)

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 (1)

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

Interferogram Analysis (1)

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

J. Phys. (1)

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

Opt. Eng. (1)

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. (2)

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. (1)

SPIE (1)

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

Other (2)

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

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

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Figures (5)

Fig. 1.
Fig. 1.

Comparison between Excess Fractions, CRT and Modified CRT algorithms with phase measurement noise of 2π/200 radians.

Fig. 2.
Fig. 2.

Comparison between Excess Fractions, CRT and Modified CRT algorithms with phase measurement noise of 2π/500 radians.

Fig. 3.
Fig. 3.

Experimental arrangement.

Fig. 4. (a)
Fig. 4. (a)

Wrapped phase map from an engine port model.

Fig. 4. (b)
Fig. 4. (b)

Unwrapped phase map from an engine port model.

Equations (3)

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x φ 1 ( mod λ 1 ) , x φ 2 ( mod λ 2 ) , , x φ r ( mod λ r ) ,
x = Λ 1 Λ 1 φ 1 + Λ 2 Λ 2 φ 2 + + Λ r Λ r φ r ,
Δ x = i = 1 r Λ i Λ i Δ φ i

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