Abstract

Electronic circuitry that is helpful for measuring optical phase from three-phase input signals is described. Six flash analog-to-digital converters in conjunction with a read-only memory resolve a digital byte (or more) per turn of phase. That digital phase may then be digitally low pass filtered with an adder and multiplier accumulator to expand the dynamic range by counting turns and shrinking the subdivisions.

© 1989 Optical Society of America

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References

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  1. L. Mertz, “Complex Homodyne Reception from Discrete Photons,” Appl. Opt. 27, 3429 (1988).
    [CrossRef] [PubMed]
  2. L. Mertz, “Phase Estimation with Few Photons,” Appl. Opt. 23, 1638 (1984).
    [CrossRef] [PubMed]
  3. L. Mertz, “Real-Time Fringe-Pattern Analysis,” Appl. Opt. 22, 1535, 3313 (1983).
    [CrossRef]
  4. L. Mertz, “Complex Interferometry,” Appl. Opt. 22, 1530 (1983).
    [CrossRef] [PubMed]
  5. C. R. Tilford, “Analytical Procedure for Determining Lengths from Fractional Fringes,” Appl. Opt. 16, 1857 (1977).
    [CrossRef] [PubMed]
  6. M. Shao et al., “The Mark III Stellar Interferometer,” Astron. Astrophys. 193, 357 (1988).
  7. K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
    [CrossRef]
  8. K. G. Wesolowicz, R. E. Sampson, “Laser Radar Range Imaging Sensor for Commercial Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 783, 152 (1987).
  9. A. Sommerfeld, Optics (Academic, New York, 1954), p. 70.
  10. P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 415.
  11. Y. Ichioka, M. Inuiya, “Direct Phase Detecting System,” Appl. Opt. 11, 1507 (1972).
    [CrossRef] [PubMed]

1988 (2)

M. Shao et al., “The Mark III Stellar Interferometer,” Astron. Astrophys. 193, 357 (1988).

L. Mertz, “Complex Homodyne Reception from Discrete Photons,” Appl. Opt. 27, 3429 (1988).
[CrossRef] [PubMed]

1987 (1)

K. G. Wesolowicz, R. E. Sampson, “Laser Radar Range Imaging Sensor for Commercial Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 783, 152 (1987).

1985 (1)

K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

1984 (1)

1983 (2)

L. Mertz, “Complex Interferometry,” Appl. Opt. 22, 1530 (1983).
[CrossRef] [PubMed]

L. Mertz, “Real-Time Fringe-Pattern Analysis,” Appl. Opt. 22, 1535, 3313 (1983).
[CrossRef]

1977 (1)

1972 (1)

Cheng, Y.

K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

Creath, K.

K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

Hill, W.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 415.

Horowitz, P.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 415.

Ichioka, Y.

Inuiya, M.

Mertz, L.

Sampson, R. E.

K. G. Wesolowicz, R. E. Sampson, “Laser Radar Range Imaging Sensor for Commercial Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 783, 152 (1987).

Shao, M.

M. Shao et al., “The Mark III Stellar Interferometer,” Astron. Astrophys. 193, 357 (1988).

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1954), p. 70.

Tilford, C. R.

Wesolowicz, K. G.

K. G. Wesolowicz, R. E. Sampson, “Laser Radar Range Imaging Sensor for Commercial Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 783, 152 (1987).

Wyant, J. C.

K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

Appl. Opt. (5)

Appl. Opt. 22 (1)

L. Mertz, “Real-Time Fringe-Pattern Analysis,” Appl. Opt. 22, 1535, 3313 (1983).
[CrossRef]

Astron. Astrophys. (1)

M. Shao et al., “The Mark III Stellar Interferometer,” Astron. Astrophys. 193, 357 (1988).

Opt. Acta (1)

K. Creath, Y. Cheng, J. C. Wyant, “Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry,” Opt. Acta 32, 1455 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

K. G. Wesolowicz, R. E. Sampson, “Laser Radar Range Imaging Sensor for Commercial Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 783, 152 (1987).

Other (2)

A. Sommerfeld, Optics (Academic, New York, 1954), p. 70.

P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 415.

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Figures (9)

Fig. 1
Fig. 1

Test interferometer for providing three-phase signals.

Fig. 2
Fig. 2

Elliptical x-y trace of signals A vs B. Dot at lower left is with beam blocked.

Fig. 3
Fig. 3

Circuitry to resolve six sectors of phase.

Fig. 4
Fig. 4

Performance of six-sector circuitry: (a) xy trace of sinϕ vs cosϕ while scanning fringes; (b) upper = ϕ, lower = B signal.

Fig. 5
Fig. 5

Circuitry for a byte of phase resolution.

Fig. 6
Fig. 6

Three-phase signals above PROM map to same scale but not the same permutation as the six sectors.

Fig. 7
Fig. 7

Performance of circuitry of Fig. 5; upper trace is phase output, lower trace is B signal.

Fig. 8
Fig. 8

Circuitry of the polar innovations filter.

Fig. 9
Fig. 9

Performance of the filter following a slight hammer tap to the apparatus table: sample clock 1 MHz; N = 256; 0.5 ms/div; full scale for each trace λ/32; upper trace phase input ϕ lower trace filtered phase output Φ.

Equations (3)

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UPHI  =  PHI  +  ANINT ( UPHI−PHI ) ,
Φ t = Φ t 1 ( Φ t 1 ϕ t ) + ANINT ( Φ t 1 ϕ t ) = Φ t 1 ( Φ t 1 ϕ t ) R,
Φ t + 1 = Φ t N 1 ( Φ t ϕ t ) R,

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