Abstract

An automatic fringe detection algorithm applied to moire deflectometry is presented. This algorithm is based on a set of points linked together and with a behavior similar to a rubber band, in which these points are attracted to fit the moire fringes. The collective behavior of these points gives rise to a final state which is their regularly spaced alignment along the fringe pattern. The algorithm is dynamic in the sense that it tracks the fringe even when it suffers continuous deformations. Once the rubber band is adapted, the rubber band’s points coordinates are obtained and their distance to the starting straight line is found, as required by moire deflectometry.

© 1990 Optical Society of America

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References

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  1. O. Kafri, I. Glatt, “Moire Deflectometry: A Ray Deflection Approach to Optical Testing,” Opt. Eng. 24, 944–960 (1985).
    [CrossRef]
  2. D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978).
  3. O. Kafri, A. Livnat, “Tunable Moire Grating for Optical Mapping,” Opt. Lett. 4, 314–316 (1979).
    [CrossRef] [PubMed]
  4. O. Kafri, A. Livnat, “Reflective Surface Analysis Using Moire Deflectometry,” Appl. Opt. 20, 3098–3100 (1981).
    [CrossRef] [PubMed]
  5. I. Glatt, O. Kafri, “Determination of the Focal Length of Nonparaxial Lenses by Moire Deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
    [CrossRef] [PubMed]
  6. I. Glatt, A. Livnat, O. Kafri, D. Heller, “Autocollimator Based on Moire Deflectometry,” Appl. Opt. 23, 2673–2674 (1984).
    [CrossRef] [PubMed]
  7. Z. Karny, O. Kafri, “Refractive-Index Measurements by Moire Deflectometry,” Appl. Opt. 21, 3326–3328 (1982).
    [CrossRef] [PubMed]
  8. O. Kafri, K. M. Kreske, E. Keren, “Refractive Index Measurement of Optical Windows by an Interferometric-Deflectometric Method,” Appl. Opt. 27, 4602–4603 (1988).
    [CrossRef] [PubMed]
  9. I. Glatt, A. Livnat, O. Kafri, “Direct Determination of Modulation Transfer Function by Moire Deflectometry,” J. Opt. Soc. Am. A 2, 107–110 (1985).
    [CrossRef]
  10. Z. Karny, S. Lavi, O. Kafri, “Direct Determination of the Number of Transverse Modes of a Light Beam,” Opt. Lett. 8, 409–411 (1983).
    [CrossRef] [PubMed]
  11. D. F. Heller, O. Kafri, J. Krasinski, “Direct Birefringence Measurements Using Moire Ray Deflection Techniques,” Appl. Opt. 24, 3037–3040 (1985).
    [CrossRef] [PubMed]
  12. J. Krasinski, D. F. Heller, O. Kafri, “Phase Object Microscopy Using Moire Deflectometry,” Appl. Opt. 24, 3032–3036 (1985).
    [CrossRef] [PubMed]
  13. O. Kafri, “Noncoherent Method for Mapping Phase Objects,” Opt. Lett. 5, 555–557 (1980).
    [CrossRef] [PubMed]
  14. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
    [CrossRef] [PubMed]
  15. E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698–705 (1983).
    [CrossRef] [PubMed]
  16. G. S. Rau, E. Bar-Ziv, “Deflection Mapping of Flames Using the Moire Effect,” Appl. Opt. 23, 2686–2692 (1984).
    [CrossRef] [PubMed]
  17. E. Bar-Ziv, “Effect of Diffraction on the Moire Image for Temperature Mapping in Flames,” Appl. Opt. 23, 4040–4044 (1984).
    [CrossRef] [PubMed]
  18. J. Stricker, “Analysis of 3-D Phase Objects by Moire Deflectometry,” Appl. Opt. 23, 3657–3659 (1984).
    [CrossRef] [PubMed]
  19. J. Stricker, “Diffraction Effects and Special Advantages in Electric Heteodyne Moire Deflectometry,” Appl. Opt. 25, 895–902 (1986).
    [CrossRef] [PubMed]
  20. J. Stricker, “Electronic Heterodyne Readout of Fringes in Moire Deflectometry,” Opt. Lett. 10, 247–249 (1985).
    [CrossRef] [PubMed]
  21. J. Stricker, “Performance of Moire Deflectometry With Deferred Electronic Heterodyne Readout,” J. Opt. Soc. Am. A 4, 1798–1806 (1987).
    [CrossRef]
  22. Amar Choudry, “Automated Fringe Reduction Techniques,” Proc. Soc. Photo-Opt Instrum Eng. 816, 49–55 (1987).
  23. K. Creath, “Phase Measurement Interferometric Techniques,” Prog. Opt. 26, 351–391 (1988).
  24. M. Kass, A. Witkin, D. Terzopolos, “Snakes: Active Contour Models,” in Proceedings, First International Conference on Computer Vision (IEEE, New York1987), pp. 259–268.

1988 (2)

1987 (3)

1986 (1)

1985 (5)

1984 (4)

1983 (2)

1982 (1)

1981 (2)

1980 (1)

1979 (1)

Bar-Ziv, E.

Choudry, Amar

Amar Choudry, “Automated Fringe Reduction Techniques,” Proc. Soc. Photo-Opt Instrum Eng. 816, 49–55 (1987).

Creath, K.

K. Creath, “Phase Measurement Interferometric Techniques,” Prog. Opt. 26, 351–391 (1988).

Glatt, I.

Heller, D.

Heller, D. F.

Kafri, O.

O. Kafri, K. M. Kreske, E. Keren, “Refractive Index Measurement of Optical Windows by an Interferometric-Deflectometric Method,” Appl. Opt. 27, 4602–4603 (1988).
[CrossRef] [PubMed]

I. Glatt, O. Kafri, “Determination of the Focal Length of Nonparaxial Lenses by Moire Deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
[CrossRef] [PubMed]

I. Glatt, A. Livnat, O. Kafri, “Direct Determination of Modulation Transfer Function by Moire Deflectometry,” J. Opt. Soc. Am. A 2, 107–110 (1985).
[CrossRef]

O. Kafri, I. Glatt, “Moire Deflectometry: A Ray Deflection Approach to Optical Testing,” Opt. Eng. 24, 944–960 (1985).
[CrossRef]

J. Krasinski, D. F. Heller, O. Kafri, “Phase Object Microscopy Using Moire Deflectometry,” Appl. Opt. 24, 3032–3036 (1985).
[CrossRef] [PubMed]

D. F. Heller, O. Kafri, J. Krasinski, “Direct Birefringence Measurements Using Moire Ray Deflection Techniques,” Appl. Opt. 24, 3037–3040 (1985).
[CrossRef] [PubMed]

I. Glatt, A. Livnat, O. Kafri, D. Heller, “Autocollimator Based on Moire Deflectometry,” Appl. Opt. 23, 2673–2674 (1984).
[CrossRef] [PubMed]

Z. Karny, S. Lavi, O. Kafri, “Direct Determination of the Number of Transverse Modes of a Light Beam,” Opt. Lett. 8, 409–411 (1983).
[CrossRef] [PubMed]

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698–705 (1983).
[CrossRef] [PubMed]

Z. Karny, O. Kafri, “Refractive-Index Measurements by Moire Deflectometry,” Appl. Opt. 21, 3326–3328 (1982).
[CrossRef] [PubMed]

O. Kafri, A. Livnat, “Reflective Surface Analysis Using Moire Deflectometry,” Appl. Opt. 20, 3098–3100 (1981).
[CrossRef] [PubMed]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef] [PubMed]

O. Kafri, “Noncoherent Method for Mapping Phase Objects,” Opt. Lett. 5, 555–557 (1980).
[CrossRef] [PubMed]

O. Kafri, A. Livnat, “Tunable Moire Grating for Optical Mapping,” Opt. Lett. 4, 314–316 (1979).
[CrossRef] [PubMed]

Karny, Z.

Kass, M.

M. Kass, A. Witkin, D. Terzopolos, “Snakes: Active Contour Models,” in Proceedings, First International Conference on Computer Vision (IEEE, New York1987), pp. 259–268.

Keren, E.

Krasinski, J.

Kreske, K. M.

Lavi, S.

Livnat, A.

Rau, G. S.

Sgulim, S.

Stricker, J.

Terzopolos, D.

M. Kass, A. Witkin, D. Terzopolos, “Snakes: Active Contour Models,” in Proceedings, First International Conference on Computer Vision (IEEE, New York1987), pp. 259–268.

Witkin, A.

M. Kass, A. Witkin, D. Terzopolos, “Snakes: Active Contour Models,” in Proceedings, First International Conference on Computer Vision (IEEE, New York1987), pp. 259–268.

Appl. Opt. (13)

O. Kafri, A. Livnat, “Reflective Surface Analysis Using Moire Deflectometry,” Appl. Opt. 20, 3098–3100 (1981).
[CrossRef] [PubMed]

E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263–4266 (1981).
[CrossRef] [PubMed]

Z. Karny, O. Kafri, “Refractive-Index Measurements by Moire Deflectometry,” Appl. Opt. 21, 3326–3328 (1982).
[CrossRef] [PubMed]

E. Bar-Ziv, S. Sgulim, O. Kafri, E. Keren, “Temperature Mapping in Flames by Moire Deflectometry,” Appl. Opt. 22, 698–705 (1983).
[CrossRef] [PubMed]

I. Glatt, A. Livnat, O. Kafri, D. Heller, “Autocollimator Based on Moire Deflectometry,” Appl. Opt. 23, 2673–2674 (1984).
[CrossRef] [PubMed]

G. S. Rau, E. Bar-Ziv, “Deflection Mapping of Flames Using the Moire Effect,” Appl. Opt. 23, 2686–2692 (1984).
[CrossRef] [PubMed]

J. Stricker, “Analysis of 3-D Phase Objects by Moire Deflectometry,” Appl. Opt. 23, 3657–3659 (1984).
[CrossRef] [PubMed]

E. Bar-Ziv, “Effect of Diffraction on the Moire Image for Temperature Mapping in Flames,” Appl. Opt. 23, 4040–4044 (1984).
[CrossRef] [PubMed]

J. Krasinski, D. F. Heller, O. Kafri, “Phase Object Microscopy Using Moire Deflectometry,” Appl. Opt. 24, 3032–3036 (1985).
[CrossRef] [PubMed]

D. F. Heller, O. Kafri, J. Krasinski, “Direct Birefringence Measurements Using Moire Ray Deflection Techniques,” Appl. Opt. 24, 3037–3040 (1985).
[CrossRef] [PubMed]

J. Stricker, “Diffraction Effects and Special Advantages in Electric Heteodyne Moire Deflectometry,” Appl. Opt. 25, 895–902 (1986).
[CrossRef] [PubMed]

O. Kafri, K. M. Kreske, E. Keren, “Refractive Index Measurement of Optical Windows by an Interferometric-Deflectometric Method,” Appl. Opt. 27, 4602–4603 (1988).
[CrossRef] [PubMed]

I. Glatt, O. Kafri, “Determination of the Focal Length of Nonparaxial Lenses by Moire Deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

O. Kafri, I. Glatt, “Moire Deflectometry: A Ray Deflection Approach to Optical Testing,” Opt. Eng. 24, 944–960 (1985).
[CrossRef]

Opt. Lett. (4)

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

Amar Choudry, “Automated Fringe Reduction Techniques,” Proc. Soc. Photo-Opt Instrum Eng. 816, 49–55 (1987).

Prog. Opt. (1)

K. Creath, “Phase Measurement Interferometric Techniques,” Prog. Opt. 26, 351–391 (1988).

Other (2)

M. Kass, A. Witkin, D. Terzopolos, “Snakes: Active Contour Models,” in Proceedings, First International Conference on Computer Vision (IEEE, New York1987), pp. 259–268.

D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup and the coordinate system: G1 and G2 are the Ronchi rulings, ϕ is a deviation ray angle, and Δ is a first Talbot distance.

Fig. 2
Fig. 2

Distorted lines of the moire pattern; distance hy is the deviation of the fringe in respect to the unperturbed moire fringe in the ith point mass on the rubber band.

Fig. 3
Fig. 3

Moire deflectograms of a candle’s flame: (a) initial deflectogram; (b) rubber band on the same deflectogram before being adapted to the moire pattern; (c) deflectgram with the adapted rubber band.

Fig. 4
Fig. 4

Plot of the hy terms for the adapted rubber band points.

Equations (6)

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ϕ x ( x , y ) = θ h y Δ = 1 n s Z i Z f n ( x , y , z ) x d z ,
X t + 1 ( i ) = X t ( i ) + f p x ( i ) Y t + 1 ( i ) = Y t ( i ) + f p y ( i ) , t = 0 , 1 , 2 , 1 < i < 30
X t ( i ) = [ X t ( i - 1 ) + X t ( i ) + X t ( i + 1 ) ] / 3 Y t ( i ) = [ Y t ( i - 1 ) + Y t ( i ) + Y t ( i + 1 ) ] / 3.
X t ( 1 ) = C 1 ; X t ( 30 ) = C 2 Y t ( 1 ) = C 3 ; Y t ( 30 ) = C 4 .
f p x t ( i ) = P X - 1 , Y ( i ) - P X - 1 , Y ( i ) f p y t ( i ) = P X , Y + 1 ( i ) - P X , Y - 1 ( i ) .
f p x ( i ) = ( 1 / N ) t = 1 N f p x t ( i ) f p y ( i ) = ( 1 / N ) t = 1 N f p y t ( i ) .

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