Abstract

In this paper we extend and study the method for generating contours of diffuse objects employing a dual beam illumination coupled with electronic speckle pattern interferometry. The sensitivity and the orientation of the contour planes are analyzed. A novel method for tilting the planes of contours and experimental results incorporating phase shifting and fringe analysis are also presented. The theoretical and the experimental results show good agreement.

© 1990 Optical Society of America

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References

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  1. K. A. Haines Hildebrand, “Contour Generation by Wavefront Reconstruction,” Phys. Lett. 19, 10–11 (1965).
    [CrossRef]
  2. J. S. Zelenka, J. R. Varner, “A New Method for Generating Depth Contours Holographically,” Appl. Opt. 7, 2107–2110 (1968).
    [CrossRef] [PubMed]
  3. N. Abramson, “Sandwich Hologram Interferometry. 3: Contouring,” Appl. Opt. 15, 200–205 (1976).
    [CrossRef] [PubMed]
  4. P. DeMattia, V. Fossati-Bellani, “Holographic Contouring by Displacing the Object and the Illuminating Beam,” Opt. Commun. 26, 17–21 (1978).
    [CrossRef]
  5. J. N. Butters, R. C. Jones, C. Wykes, “Electronic Speckle Pattern Interferometry,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, city, 1975) pp. 111–157.
  6. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London1983).
  7. B. D. Bergquist, P. Montgomery, “Contouring by Electronic Speckle Pattern Interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum. Eng. 599, 189–195 (1985).
  8. A. R. Ganesan, R. S. Sirohi, “New Method of Contouring Using Digital Speckle Pattern Interferometry,” Proc. Soc. Photo-Opt. Inst. Eng. 954, 327–332 (1988).
  9. J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Physics E. 3, 214–218 (1970).
    [CrossRef]
  10. Y. Y. Hung, “Displacement and Strain Measurement,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, New York, 1975), pp. 51–71.
  11. C. Wykes, “A Theoretical Approach to the Optimization of Electronic Speckle Interferometry with Limited Laser Power,” J. Mod. Opt. 34, 539–554 (1987).
    [CrossRef]

1988 (1)

A. R. Ganesan, R. S. Sirohi, “New Method of Contouring Using Digital Speckle Pattern Interferometry,” Proc. Soc. Photo-Opt. Inst. Eng. 954, 327–332 (1988).

1987 (1)

C. Wykes, “A Theoretical Approach to the Optimization of Electronic Speckle Interferometry with Limited Laser Power,” J. Mod. Opt. 34, 539–554 (1987).
[CrossRef]

1985 (1)

B. D. Bergquist, P. Montgomery, “Contouring by Electronic Speckle Pattern Interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum. Eng. 599, 189–195 (1985).

1978 (1)

P. DeMattia, V. Fossati-Bellani, “Holographic Contouring by Displacing the Object and the Illuminating Beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

1976 (1)

1970 (1)

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Physics E. 3, 214–218 (1970).
[CrossRef]

1968 (1)

1965 (1)

K. A. Haines Hildebrand, “Contour Generation by Wavefront Reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Abramson, N.

Bergquist, B. D.

B. D. Bergquist, P. Montgomery, “Contouring by Electronic Speckle Pattern Interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum. Eng. 599, 189–195 (1985).

Butters, J. N.

J. N. Butters, R. C. Jones, C. Wykes, “Electronic Speckle Pattern Interferometry,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, city, 1975) pp. 111–157.

DeMattia, P.

P. DeMattia, V. Fossati-Bellani, “Holographic Contouring by Displacing the Object and the Illuminating Beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Fossati-Bellani, V.

P. DeMattia, V. Fossati-Bellani, “Holographic Contouring by Displacing the Object and the Illuminating Beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Ganesan, A. R.

A. R. Ganesan, R. S. Sirohi, “New Method of Contouring Using Digital Speckle Pattern Interferometry,” Proc. Soc. Photo-Opt. Inst. Eng. 954, 327–332 (1988).

Haines Hildebrand, K. A.

K. A. Haines Hildebrand, “Contour Generation by Wavefront Reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, “Displacement and Strain Measurement,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, New York, 1975), pp. 51–71.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London1983).

Jones, R. C.

J. N. Butters, R. C. Jones, C. Wykes, “Electronic Speckle Pattern Interferometry,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, city, 1975) pp. 111–157.

Leendertz, J. A.

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Physics E. 3, 214–218 (1970).
[CrossRef]

Montgomery, P.

B. D. Bergquist, P. Montgomery, “Contouring by Electronic Speckle Pattern Interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum. Eng. 599, 189–195 (1985).

Sirohi, R. S.

A. R. Ganesan, R. S. Sirohi, “New Method of Contouring Using Digital Speckle Pattern Interferometry,” Proc. Soc. Photo-Opt. Inst. Eng. 954, 327–332 (1988).

Varner, J. R.

Wykes, C.

C. Wykes, “A Theoretical Approach to the Optimization of Electronic Speckle Interferometry with Limited Laser Power,” J. Mod. Opt. 34, 539–554 (1987).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London1983).

J. N. Butters, R. C. Jones, C. Wykes, “Electronic Speckle Pattern Interferometry,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, city, 1975) pp. 111–157.

Zelenka, J. S.

Appl. Opt. (2)

J. Mod. Opt. (1)

C. Wykes, “A Theoretical Approach to the Optimization of Electronic Speckle Interferometry with Limited Laser Power,” J. Mod. Opt. 34, 539–554 (1987).
[CrossRef]

J. Physics E. (1)

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Physics E. 3, 214–218 (1970).
[CrossRef]

Opt. Commun. (1)

P. DeMattia, V. Fossati-Bellani, “Holographic Contouring by Displacing the Object and the Illuminating Beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Phys. Lett. (1)

K. A. Haines Hildebrand, “Contour Generation by Wavefront Reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

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

A. R. Ganesan, R. S. Sirohi, “New Method of Contouring Using Digital Speckle Pattern Interferometry,” Proc. Soc. Photo-Opt. Inst. Eng. 954, 327–332 (1988).

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

B. D. Bergquist, P. Montgomery, “Contouring by Electronic Speckle Pattern Interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum. Eng. 599, 189–195 (1985).

Other (3)

J. N. Butters, R. C. Jones, C. Wykes, “Electronic Speckle Pattern Interferometry,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, city, 1975) pp. 111–157.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London1983).

Y. Y. Hung, “Displacement and Strain Measurement,” in Speckle Metrology, R. K. Erf, Ed. (Springer Verlag, New York, 1975), pp. 51–71.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup of a dual beam interferometer for contouring applications.

Fig. 2
Fig. 2

Geometry of the illumination and observation directions.

Fig. 3
Fig. 3

Photographs of the contour fringes of constant depth for a pyramid. a) The contour planes are perpendicular to the Z-axis: β = 0, ϕt = 0.2 mrad, θ = 45°, and Δh = 2.23 mm. b) The object is tilted by 10° about the Y-axis: β = 0, ϕt = 0.15 mrad, θ = 45°, and Δh = 2.98 mm. c) The contour planes are inclined about the X-axis. This is realized by rotating the object along with the tilt: ϕr = 0.05 mrad, θ° = 14°, ϕt = 0.2 mrad, θ = 45°, and Δh = 2.23 mm.

Fig. 4
Fig. 4

Results obtained with the three interferogram method for the pyramid with the interferogram shown in Fig. 3(a). a) Phase maps. b) 3-D plot. c) Plot of the contour maps.

Fig. 5
Fig. 5

Results when the contour planes are inclined. The interferogram shown in Fig. 3(c) was used here. a) Phase maps. b) 3-D plot. c) Contour maps.

Fig. 6
Fig. 6

Results for a cylindrical surface whose radius of curvature is 74.5 mm: a) Photograph of the contour fringes. b) Phase maps. c) 3-D plot. d) Contour maps. The data for this interferogram are: β = 0, ϕt = 0.55 mrad, θ = 45°, and Δh = 0.81 mm.

Equations (25)

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I 1 - I 2 = 4 A 1 A 2 sin [ ϕ ( x , y ) - Δ / 2 ] sin ( Δ / 2 ) ,
Δ = 2 π λ ( k ^ 1 - k ^ 2 ) · L ,
w = ( r 2 - h 2 ) 1 / 2 ϕ t ,
Δ = 2 π λ [ ( sin θ 1 cos ϕ 1 + sin θ 2 cos ϕ 2 ) u + ( sin ϕ 1 cos θ 1 + sin ϕ 2 cos θ 2 ) v ]
u = h ϕ t cos β
v = h ϕ t sin β .
Δ = 2 π λ h ϕ t [ ( sin θ 1 cos ϕ 1 + sin ϕ 2 cos ϕ 2 ) cos β + ( sin ϕ 1 cos θ 1 + sin ϕ 2 cos θ 2 ) sin β ] .
Δ h = λ 2 ϕ t sin θ .
Δ h e = λ Δ ϕ t 2 ϕ t 2 sin θ ,
x = x cos ϕ r - y sin ϕ r
y = x sin ϕ r + y cos ϕ r .
u r = x - x = x ( 1 - cos ϕ r ) + y sin ϕ r
v r = y - y = x sin ϕ r - y ( 1 - cos ϕ r ) .
u T = u t ± u r
v T = v t ± v r ,
u T = h ϕ t cos β + { x ( 1 - cos ϕ r ) + y sin ϕ r }
v T = h ϕ t sin β + { x sin ϕ r + y ( 1 - cos ϕ r ) } .
Δ = 4 π λ [ h ϕ t + y ϕ r ] sin θ .
Δ h = λ 2 ϕ t sin θ - ( y 1 - y 2 ) ϕ r 2 ϕ t ,
θ 0 = tan - 1 [ ϕ r / ϕ t ] .
( h ϕ t + y max ϕ r ) = 2.4 λ p / ( 2 M a ) ,
I 1 = I 0 [ 1 + γ cos ( Δ - δ ) ]
I 2 = I 0 [ 1 + γ cos ( Δ ) ]
I 3 = I 0 [ 1 + γ cos ( Δ + δ ) ] ,
Δ = arctan [ I 3 - I 1 I 3 + I 1 - 2 I 2 ] tan δ / 2 ;

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