Abstract

We present an investigation into the phase errors that occur in fringe pattern analysis that are caused by quantization effects. When acquisition devices with a limited value of camera bit depth are used, there are a limited number of quantization levels available to record the signal. This may adversely affect the recorded signal and adds a potential source of instrumental error to the measurement system. Quantization effects also determine the accuracy that may be achieved by acquisition devices in a measurement system. We used the Fourier fringe analysis measurement technique. However, the principles can be applied equally well for other phase measuring techniques to yield a phase error distribution that is caused by the camera bit depth.

© 2003 Optical Society of America

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References

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  1. K. Creath, “Temporal Phase Measurement,” in Interferogram Analysis (IOP Publishing, Bristol, UK, 1993), pp. 94–140.
  2. J. D. Pearson, “Automated measurement of human body shape and curvature using computer vision,” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 45–57 (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  14. J. E. Greivenkamp, J. H. Bruning, Optical Shop Testing, (Wiley, New York, 1992).
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2002 (1)

1990 (1)

1987 (1)

1986 (1)

1983 (2)

1982 (1)

1981 (1)

J. C. Wyant, “Phase measurement system for adaptive optics,” AGARD Conf. Proc. 300, 65–71 (1981).

1974 (1)

1966 (1)

P. Carre, “Installation et utilisation du comparateur photoelectrique et interferential du bureu international des poids de measures,” Metrologia 2, 13–26 (1966).
[CrossRef]

?????, ?. ?.

В. Н. ВасилЬев, И. П. Гуров, “КомпЬютерная обработка сигналов приложении к интерферометрическим системам,” (СПб.:ЪХВ-Санкт-Петербург, 1998); [English translation: V. N. Vasilyev and I. P. Gurov, Computer Processing of Signals for Interferometric Systems (n.p., St. Petersburg, 1998.)]

????????, ?. ?.

В. Н. ВасилЬев, И. П. Гуров, “КомпЬютерная обработка сигналов приложении к интерферометрическим системам,” (СПб.:ЪХВ-Санкт-Петербург, 1998); [English translation: V. N. Vasilyev and I. P. Gurov, Computer Processing of Signals for Interferometric Systems (n.p., St. Petersburg, 1998.)]

Bachor, H. A.

Bone, D. J.

Born, M.

M. Born, E. Wolf, Principles of Optics, (Pergamon, New York, 1970).

Brangaccio, D. J.

Brophy, C. P.

Bruning, J. H.

Burton, D. R.

Carre, P.

P. Carre, “Installation et utilisation du comparateur photoelectrique et interferential du bureu international des poids de measures,” Metrologia 2, 13–26 (1966).
[CrossRef]

Creath, K.

K. Creath, “Temporal Phase Measurement,” in Interferogram Analysis (IOP Publishing, Bristol, UK, 1993), pp. 94–140.

Eiju, T.

Gallagher, J. E.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, Optical Shop Testing, (Wiley, New York, 1992).

Hariharan, P.

Herriot, D. R.

Ina, H.

Kobayashi, S.

Lalor, M. J.

Macy, W.

Mutoh, K.

Oreb, B. F.

Pearson, J. D.

J. D. Pearson, “Automated measurement of human body shape and curvature using computer vision,” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 45–57 (1993).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, Optical Measurement Techniques Applications (Artech House, Norwood, Mass., 1997).

Rosenfeld, D. P.

Sandeman, R. J.

Skydan, O. A.

Takeda, M.

White, A. D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, (Pergamon, New York, 1970).

Wyant, J. C.

J. C. Wyant, “Phase measurement system for adaptive optics,” AGARD Conf. Proc. 300, 65–71 (1981).

AGARD Conf. Proc. (1)

J. C. Wyant, “Phase measurement system for adaptive optics,” AGARD Conf. Proc. 300, 65–71 (1981).

Appl. Opt. (6)

J. Opt. Soc. Am. (2)

Metrologia (1)

P. Carre, “Installation et utilisation du comparateur photoelectrique et interferential du bureu international des poids de measures,” Metrologia 2, 13–26 (1966).
[CrossRef]

Other (6)

K. Creath, “Temporal Phase Measurement,” in Interferogram Analysis (IOP Publishing, Bristol, UK, 1993), pp. 94–140.

J. D. Pearson, “Automated measurement of human body shape and curvature using computer vision,” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 45–57 (1993).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, (Pergamon, New York, 1970).

P. K. Rastogi, Optical Measurement Techniques Applications (Artech House, Norwood, Mass., 1997).

В. Н. ВасилЬев, И. П. Гуров, “КомпЬютерная обработка сигналов приложении к интерферометрическим системам,” (СПб.:ЪХВ-Санкт-Петербург, 1998); [English translation: V. N. Vasilyev and I. P. Gurov, Computer Processing of Signals for Interferometric Systems (n.p., St. Petersburg, 1998.)]

J. E. Greivenkamp, J. H. Bruning, Optical Shop Testing, (Wiley, New York, 1992).

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Figures (5)

Fig. 1
Fig. 1

Graphical representation of the arcsin function from Eq. (3).

Fig. 2
Fig. 2

Minimum phase change (Δϕ) determined for systems with a variety of different camera bit depths (N).

Fig. 3
Fig. 3

Phase error for equivalent systems with different camera bit depths (N).

Fig. 4
Fig. 4

Distribution of the phase error in one period of a sinusoidal fringe pattern, caused by a respective bit depth of (a) 6 bits, (b) 8 bits, and (c) 10 bits for acquisition systems that use a rounding algorithm.

Fig. 5
Fig. 5

Distribution of the phase error in one period of a sinusoidal fringe pattern, caused by a respective bit depth of (a) 6 bits, (b) 8 bits, and (c) 10 bits for acquisition systems that use a truncating algorithm.

Tables (2)

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Table 1 Phase Error Caused by the Limited Value of Camera Bit Depth

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Table 2 Height Error Caused by the Limited Value of Camera Bit Depth for the System Described in Ref. 3

Equations (9)

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ix=a+b sin2πfx=iq+δi,
xi=12πfarcsini-ab.
φi=arcsini-ab.
Δi=2b2N-1.
-12 Δi<δi12 Δi.
mi=-Δi/2Δi/2δifδidδi=0,
σi2=-Δi/2Δi/2δi-mi2fδidδi=Δi212.
Δφ=φa-b+Δi-φa-b=arcsin22N-1-1+π2.
φerror=φa-b+Δi2-φa-b=arcsin12N-1-1+π2.

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