Abstract

A novel technique called a two-dimensional digital phase-locked loop (DPLL) for fringe pattern demodulation is presented. This algorithm is more suitable for demodulation of fringe patterns with varying phase in two directions than the existing DPLL techniques that assume that the phase of the fringe patterns varies only in one direction. The two-dimensional DPLL technique assumes that the phase of a fringe pattern is continuous in both directions and takes advantage of the phase continuity; consequently, the algorithm has better noise performance than the existing DPLL schemes. The two-dimensional DPLL algorithm is also suitable for demodulation of fringe patterns with low sampling rates, and it outperforms the Fourier fringe analysis technique in this aspect.

© 2002 Optical Society of America

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  1. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  2. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W. R. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.
  3. Y. Ichioka, M. Inuiya, “Direct phase detection system,” Appl. Opt. 11, 1507–1514 (1972).
    [CrossRef] [PubMed]
  4. M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
    [CrossRef]
  5. M. Gdeisat, D. Burton, M. Lalor, “Real-time fringe pattern demodulation with a second-order digital phase-locked loop,” Appl. Opt. 39, 5326–5336 (2000).
    [CrossRef]
  6. J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
    [CrossRef]
  7. M. Hagiwara, M. Nakagawa, “DSP-type first order digital phase locked loop using linear phase detector,” Electron. Commun. Jpn. (Part I: Communications). 69, 99–107 (1986).
    [CrossRef]
  8. M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
    [CrossRef]
  9. M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
    [CrossRef]
  10. M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355–365 (1995).
    [CrossRef]
  11. L. Rabiner, R. Schafer, “On the behaviour of minimax FIR digital Hilbert transformers,” Bell Syst. Tech. J. 53, 363–390 (1974).
    [CrossRef]
  12. F. Stremler, Introduction to Communication Systems (Addison-Wesley, Reading, Mass., 1989).
  13. C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1, 103–110 (1992).
    [CrossRef]
  14. R. Schafer, A. Oppenheim, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

2001

M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
[CrossRef]

2000

M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
[CrossRef]

M. Gdeisat, D. Burton, M. Lalor, “Real-time fringe pattern demodulation with a second-order digital phase-locked loop,” Appl. Opt. 39, 5326–5336 (2000).
[CrossRef]

1997

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

1995

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

1993

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

1992

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1, 103–110 (1992).
[CrossRef]

1986

M. Hagiwara, M. Nakagawa, “DSP-type first order digital phase locked loop using linear phase detector,” Electron. Commun. Jpn. (Part I: Communications). 69, 99–107 (1986).
[CrossRef]

1982

1974

L. Rabiner, R. Schafer, “On the behaviour of minimax FIR digital Hilbert transformers,” Bell Syst. Tech. J. 53, 363–390 (1974).
[CrossRef]

1972

Burton, D.

M. Gdeisat, D. Burton, M. Lalor, “Real-time fringe pattern demodulation with a second-order digital phase-locked loop,” Appl. Opt. 39, 5326–5336 (2000).
[CrossRef]

M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
[CrossRef]

Creath, K.

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W. R. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

Cuevas, F.

M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
[CrossRef]

Gdeisat, M.

M. Gdeisat, D. Burton, M. Lalor, “Real-time fringe pattern demodulation with a second-order digital phase-locked loop,” Appl. Opt. 39, 5326–5336 (2000).
[CrossRef]

M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
[CrossRef]

Gorecki, C.

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1, 103–110 (1992).
[CrossRef]

Hagiwara, M.

M. Hagiwara, M. Nakagawa, “DSP-type first order digital phase locked loop using linear phase detector,” Electron. Commun. Jpn. (Part I: Communications). 69, 99–107 (1986).
[CrossRef]

Ichioka, Y.

Ina, H.

Inuiya, M.

Kobayashi, S.

Kozlowski, J.

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

Lalor, M.

M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
[CrossRef]

M. Gdeisat, D. Burton, M. Lalor, “Real-time fringe pattern demodulation with a second-order digital phase-locked loop,” Appl. Opt. 39, 5326–5336 (2000).
[CrossRef]

Malacara, D.

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

Nakagawa, M.

M. Hagiwara, M. Nakagawa, “DSP-type first order digital phase locked loop using linear phase detector,” Electron. Commun. Jpn. (Part I: Communications). 69, 99–107 (1986).
[CrossRef]

Oppenheim, A.

R. Schafer, A. Oppenheim, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Quiroga, J.

M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
[CrossRef]

Rabiner, L.

L. Rabiner, R. Schafer, “On the behaviour of minimax FIR digital Hilbert transformers,” Bell Syst. Tech. J. 53, 363–390 (1974).
[CrossRef]

Rodriguez-Vera, R.

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern 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]

Schafer, R.

L. Rabiner, R. Schafer, “On the behaviour of minimax FIR digital Hilbert transformers,” Bell Syst. Tech. J. 53, 363–390 (1974).
[CrossRef]

R. Schafer, A. Oppenheim, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Serra, G.

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

Servin, M.

M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
[CrossRef]

M. Servin, R. Rodriguez-Vera, D. Malacara, “Noisy fringe pattern 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]

Stremler, F.

F. Stremler, Introduction to Communication Systems (Addison-Wesley, Reading, Mass., 1989).

Takeda, M.

Appl. Opt.

Bell Syst. Tech. J.

L. Rabiner, R. Schafer, “On the behaviour of minimax FIR digital Hilbert transformers,” Bell Syst. Tech. J. 53, 363–390 (1974).
[CrossRef]

Electron. Commun. Jpn. (Part I: Communications).

M. Hagiwara, M. Nakagawa, “DSP-type first order digital phase locked loop using linear phase detector,” Electron. Commun. Jpn. (Part I: Communications). 69, 99–107 (1986).
[CrossRef]

J. Mod. Opt.

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.

Meas. Sci. Technol.

M. Gdeisat, D. Burton, M. Lalor, “Real-time hybrid fringe pattern analysis using a linear digital phase locked loop for demodulation and unwrapping,” Meas. Sci. Technol. 11, 1480–1492 (2000).
[CrossRef]

Opt. Commun.

M. Servin, J. Quiroga, F. Cuevas, “Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop,” Opt. Commun. 200, 87–97 (2001).
[CrossRef]

Opt. Eng.

J. Kozlowski, G. Serra, “New modified phase locked loop method for fringe pattern demodulation,” Opt. Eng. 36, 2025–2030 (1997).
[CrossRef]

Opt. Lasers Eng.

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

Pure Appl. Opt.

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1, 103–110 (1992).
[CrossRef]

Other

R. Schafer, A. Oppenheim, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, W. R. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

F. Stremler, Introduction to Communication Systems (Addison-Wesley, Reading, Mass., 1989).

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Figures (11)

Fig. 1
Fig. 1

Block diagram of a DPLL.

Fig. 2
Fig. 2

Block diagram of a conventional DPLL.

Fig. 3
Fig. 3

Block diagram of a linear DPLL.

Fig. 4
Fig. 4

Example of the two-dimensional DPLL algorithm in operation.

Fig. 5
Fig. 5

Dual scanning algorithm.

Fig. 6
Fig. 6

(a) Fringe pattern demodulated with the two-dimensional second-order conventional DPLL employing (b) 1 × 1, (c), 7 × 7, and (d) 15 × 15 window sizes.

Fig. 7
Fig. 7

(a) Fringe pattern demodulated with the two-dimensional second-order conventional DPLL algorithm employing (b) 1 × 1, (c) 3 × 3, and (d) 9 × 9 window sizes.

Fig. 8
Fig. 8

(a) Wrapped phase map for the fringe pattern shown in Fig. 6(a). The demodulated phase maps were generated with the two-dimensional linear DPLL with (b) 1 × 1 and (c) 3 × 3 window sizes. (d) The demodulated phase map produced with the iterative linear DPLL algorithm after 50 iterations.

Fig. 9
Fig. 9

(a) Fringe pattern demodulated with the two-dimensional linear DPLL algorithm that employs (b) 1 × 1, (c) 3 × 3, and (d) 7 × 7 window sizes.

Fig. 10
Fig. 10

(a) Fringe pattern shown in Fig. 9(a) demodulated with the two-dimensional conventional DPLL algorithm by use of a 9 × 9 window. (b) The demodulated phase map for the fringe pattern produced with the Fourier fringe analysis technique.

Fig. 11
Fig. 11

(a) Fringe pattern and its demodulated phase maps produced with a two-dimensional linear DPLL by use of (b) and (e) 1 × 1, (c) 3 × 3, and (f) 5 × 5 window sizes. (d) The fringe pattern in (a) smoothed by use of a 5 × 5 moving average window.

Equations (4)

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θx=tan-1qxcx,
gx, y=ax, y+bx, ycos2πf0x+ϕx, y,
cx, y=gx+1, y-gx, y.
ϕex, y=19i=-11j=-11 P2πf0x+i+ϕx+i, y+j-2πf0x+i+ϕˆx-1+i, y+j,

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