Abstract

The use of a second-order digital phase-locked loop (DPLL) to demodulate fringe patterns is presented. The second-order DPLL has better tracking ability and more noise immunity than the first-order loop. Consequently, the second-order DPLL is capable of demodulating a wider range of fringe patterns than the first-order DPLL. A basic analysis of the first- and the second-order loops is given, and a performance comparison between the first- and the second-order DPLL’s in analyzing fringe patterns is presented. The implementation of the second-order loop in real time on a commercial parallel image processing system is described. Fringe patterns are grabbed and processed, and the resultant phase maps are displayed concurrently.

© 2000 Optical Society of America

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References

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  1. K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. Institute of Physics, Bristol, UK, 1993), Chap. 4, pp. 94–140.
  2. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  3. M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J Mod. Opt. 40, 2087–2094 (1993).
    [CrossRef]
  4. M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
    [CrossRef]
  5. J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt Eng. 36, 2025–2030 (1996).
    [CrossRef]
  6. P. Brennan, Phase Locked Loops: Principles and Practice (Macmillan, London, 1996), pp. 188–193.
  7. A. Blanchard, Phase-Locked Loops: Application to Coherent Receiver Design (Wiley, New York, 1976), pp. 154–161.
  8. F. M. Gardner, Phaselock Techniques (Wiley, New York, 1979), pp. 47–53.
  9. F. M. Gardner, “Frequency granularity in digital phaselock loops,” IEEE Trans. Commun. 44, 749–758 (1996).
    [CrossRef]
  10. Darlington User Guide SHARC3000 (Spectrum Signal Processing, Burnaby, B.C., 1996).
  11. J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
    [CrossRef]

1996 (2)

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt Eng. 36, 2025–2030 (1996).
[CrossRef]

F. M. Gardner, “Frequency granularity in digital phaselock loops,” IEEE Trans. Commun. 44, 749–758 (1996).
[CrossRef]

1995 (1)

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

1993 (1)

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

1982 (1)

1974 (1)

J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
[CrossRef]

Blanchard, A.

A. Blanchard, Phase-Locked Loops: Application to Coherent Receiver Design (Wiley, New York, 1976), pp. 154–161.

Brennan, P.

P. Brennan, Phase Locked Loops: Principles and Practice (Macmillan, London, 1996), pp. 188–193.

Creath, K.

K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. Institute of Physics, Bristol, UK, 1993), Chap. 4, pp. 94–140.

Gardner, F. M.

F. M. Gardner, “Frequency granularity in digital phaselock loops,” IEEE Trans. Commun. 44, 749–758 (1996).
[CrossRef]

F. M. Gardner, Phaselock Techniques (Wiley, New York, 1979), pp. 47–53.

Garodnick, J.

J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
[CrossRef]

Greco, J.

J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
[CrossRef]

Ina, H.

Kobayashi, S.

Kozlowski, J.

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt Eng. 36, 2025–2030 (1996).
[CrossRef]

Malacara, D.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

Rodriguez-Vera, R.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Schilling, D.

J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
[CrossRef]

Serra, G.

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt Eng. 36, 2025–2030 (1996).
[CrossRef]

Servin, M.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Takeda, M.

IEEE Trans Commun (1)

J. Garodnick, J. Greco, D. Schilling, “Response of an all digital phase-locked loop,” IEEE Trans Commun 22, 751–763 (1974).
[CrossRef]

IEEE Trans. Commun. (1)

F. M. Gardner, “Frequency granularity in digital phaselock loops,” IEEE Trans. Commun. 44, 749–758 (1996).
[CrossRef]

J Mod. Opt. (1)

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt Eng. (1)

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt Eng. 36, 2025–2030 (1996).
[CrossRef]

Opt. Lasers Eng. (1)

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringepattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
[CrossRef]

Other (5)

K. Creath, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. Institute of Physics, Bristol, UK, 1993), Chap. 4, pp. 94–140.

P. Brennan, Phase Locked Loops: Principles and Practice (Macmillan, London, 1996), pp. 188–193.

A. Blanchard, Phase-Locked Loops: Application to Coherent Receiver Design (Wiley, New York, 1976), pp. 154–161.

F. M. Gardner, Phaselock Techniques (Wiley, New York, 1979), pp. 47–53.

Darlington User Guide SHARC3000 (Spectrum Signal Processing, Burnaby, B.C., 1996).

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Figures (12)

Fig. 1
Fig. 1

Block diagram of a DPLL.

Fig. 2
Fig. 2

Block diagram of a second-order DPLL.

Fig. 3
Fig. 3

Forward-and-backward scanning technique of a fringe pattern’s image. Note that the same line is scanned twice.

Fig. 4
Fig. 4

Forward or backward scanning technique of a fringe pattern’s image. Note that the same line is scanned just once.

Fig. 5
Fig. 5

(a) Fringe pattern, (b) and (c) demodulated phase maps of the fringe pattern with the second-order DPLL, (d) with the first-order DPLL (arbitrary scale).

Fig. 6
Fig. 6

(a) Fringe pattern, (b) and (c) its demodulated phase maps generated with the second-order DPLL, and (d) phase map produced by the first-order DPLL (arbitrary scale).

Fig. 7
Fig. 7

Effect of taking the digital filter accumulator’s content as an initial condition on the proposed algorithm. The forward-and-backward scanning algorithm is used here.

Fig. 8
Fig. 8

Effect of taking the digital filter accumulator’s content as an initial value on the second-order DPLL algorithm. The forward or backward scanning scheme is used here.

Fig. 9
Fig. 9

Effect of transient response on the second-order DPLL.

Fig. 10
Fig. 10

Effect of transient response on the first- and the second-order DPLL’s.

Fig. 11
Fig. 11

Effect of noise on the proposed algorithm.

Fig. 12
Fig. 12

Block diagram of Darlington video card.

Equations (22)

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gx=ax+bxcosω0x+ϕx,
dgxdx=cx=2 sinω0x+ϕx.
mx-1=cosω0x+ϕˆx-1,
ϕex=2 sinω0x+ϕxcosω0x+ϕˆx-1=sinϕx-ϕˆx-1+sin2ω0x+ϕx+ϕˆx-1.
ϕˆx=ϕˆx-1+G1ϕex+sx,
sx=sx-1+G2ϕex,
gx, y=ax, y+bx, ycosω0x+ϕx, y.
cx, y=gx+1, y-gx, y.
ϕˆx+1, y=ϕˆx, y+G1cx, ycosω0x+ϕˆx, y+sx+1, y,
sx+1, y=sx, y+G2cx, ycosω0x+ϕˆx, y.
ϕˆfx+1, y=ϕˆfx, y+G1cx, ycosω0x+ϕˆfx, y+sfx+1, y
sfx+1, y=sfx, y+G2cx, ycosω0x+ϕˆfx, y
ϕˆf1, 1=0,
sf1, 1=0,
ϕˆbx, y=ϕˆbx+1, y+G1cx, ycosω0x+ϕˆbx+1, y+sbx, y,
sbx, y=sbx+1, y+G2cx, ycosω0x+ϕˆbx+1, y,
ϕˆbL, 1=ϕˆfL, 1,
sbL, 1=-sfL, 1,
ϕˆfx+1, y+1=ϕˆfx, y+1+G1cx, y+1cosω0x+ϕˆfx, y+1+sfx+1, y+1,
sfx+1, y+1=sfx, y+1+G2cx, y+1cosω0x+ϕˆfx, y+1,
ϕˆf1, y+1=ϕˆb1, y,
sf1, y+1=-sb1, y.

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