Abstract

Electronic speckle contouring is concerned with shape measurement by using fringe-projection techniques in electronic speckle pattern interferometry (ESPI). Conventional in-plane and out-of-plane displacement-sensitive ESPI instrumentation may be used for contouring without any alterations to the optical hardware. The contour maps of three-dimensional diffuse objects are obtained by small shifts of optical fibers carrying the object-illumination and reference beams. It is theoretically demonstrated and experimentally verified that the fringe patterns produced are identical to projected fringe contours and may be analyzed in the usual way. Phase measurement and digital image processing are used for data reduction.

© 1992 Optical Society of America

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References

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  1. B. D. Berquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry (ESPI),” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).
    [CrossRef]
  2. D. Kerr, R. Rodríquez-Vera, F. Mendoza-Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, Fu-Pen Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).
  3. P. C. Montgomery, “Forward looking innovations in electronic speckle pattern interferometry,” Ph.D. dissertation (Loughborough University of Technology, Loughborough, England, 1987).
  4. S. Winther, G. A. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84 (Budapest), G. Lupkoviks, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).
    [CrossRef]
  5. A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry (DSPI),” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 327–332 (1988).
    [CrossRef]
  6. C. Joenathan, B. Pfister, H. J. Tiziani, “Contouring by electronic speckle pattern interferometry employing dual beam illumination,” Appl. Opt. 29, 1905–1911 (1990).
    [CrossRef] [PubMed]
  7. G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
    [CrossRef]
  8. K. J. Gasvik, “Moiré technique by means of digital image processing,” Appl. Opt. 22, 3543–3548 (1983).
    [CrossRef] [PubMed]
  9. J. D. Hovanesian, Y. Y. Hung, “Moiré contour-sum contour-difference, and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).
    [CrossRef] [PubMed]
  10. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  11. D. Robinson, D. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
    [CrossRef]
  12. D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
    [CrossRef]

1990 (2)

1986 (1)

D. Robinson, D. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

1985 (1)

1984 (1)

G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
[CrossRef]

1983 (1)

1971 (1)

Berquist, B. D.

B. D. Berquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry (ESPI),” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).
[CrossRef]

Creath, K.

Ganesan, A. R.

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry (DSPI),” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 327–332 (1988).
[CrossRef]

Gasvik, K. J.

Hovanesian, J. D.

Hung, Y. Y.

Joenathan, C.

Kerr, D.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
[CrossRef]

D. Kerr, R. Rodríquez-Vera, F. Mendoza-Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, Fu-Pen Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Mendoza Santoyo, F.

Mendoza-Santoyo, F.

D. Kerr, R. Rodríquez-Vera, F. Mendoza-Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, Fu-Pen Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Messer, H. I.

G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
[CrossRef]

Montgomery, P.

B. D. Berquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry (ESPI),” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).
[CrossRef]

Montgomery, P. C.

P. C. Montgomery, “Forward looking innovations in electronic speckle pattern interferometry,” Ph.D. dissertation (Loughborough University of Technology, Loughborough, England, 1987).

Pfister, B.

Reid, G. T.

G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
[CrossRef]

Rixon, R. C.

G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
[CrossRef]

Robinson, D.

D. Robinson, D. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Rodríquez-Vera, R.

D. Kerr, R. Rodríquez-Vera, F. Mendoza-Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, Fu-Pen Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

Sirohi, R. S.

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry (DSPI),” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 327–332 (1988).
[CrossRef]

Slettemoen, G. A.

S. Winther, G. A. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84 (Budapest), G. Lupkoviks, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).
[CrossRef]

Tiziani, H. J.

Tyrer, J. R.

Williams, D.

D. Robinson, D. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Winther, S.

S. Winther, G. A. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84 (Budapest), G. Lupkoviks, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

D. Robinson, D. Williams, “Digital phase stepping speckle interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Opt. Lasers Tech. (1)

G. T. Reid, R. C. Rixon, H. I. Messer, “Absolute and comparative measurements of three dimensional shape by phase measuring moiré topography,” Opt. Lasers Tech. 16, 315–319 (1984).
[CrossRef]

Other (5)

B. D. Berquist, P. Montgomery, “Contouring by electronic speckle pattern interferometry (ESPI),” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.599, 189–195 (1985).
[CrossRef]

D. Kerr, R. Rodríquez-Vera, F. Mendoza-Santoyo, “Surface contouring using electronic speckle pattern interferometry,” in Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, Fu-Pen Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 668–679 (1991).

P. C. Montgomery, “Forward looking innovations in electronic speckle pattern interferometry,” Ph.D. dissertation (Loughborough University of Technology, Loughborough, England, 1987).

S. Winther, G. A. Slettemoen, “An ESPI contouring technique in strain analysis,” in Symposium Optika ’84 (Budapest), G. Lupkoviks, A. Podmaniczky, eds., Proc. Soc. Photo-Opt. Instrum. Eng.473, 44–47 (1984).
[CrossRef]

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry (DSPI),” in Optical Testing and Metrology II, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 327–332 (1988).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Measurable vector data, (b) possible vector combinations. α is the angle between d and n ^ vectors, and R is their resultant vector.

Fig. 2
Fig. 2

(a) Basic dual-beam ESC optical geometry, (b) simplified geometry for dual-beam ESC.

Fig. 3
Fig. 3

Layout of in-plane-sensitive ESPI apparatus for dual-beam illumination in ESC.

Fig. 4
Fig. 4

Grid fringes on a plane surface by single-source displacement.

Fig. 5
Fig. 5

(a), (b) Grid fringes on a spherical surface with one source displaced; (c), (d) depth fringes on the same surface with both sources displaced.

Fig. 6
Fig. 6

Fringe frequency against source displacement.

Fig. 7
Fig. 7

Layout of out-of-plane-sensitive ESPI apparatus for dual-source in ESC.

Fig. 8
Fig. 8

Out-of-plane-sensitive ESC contour data from a spherical surface: (a), depth fringes; (b), unwrapped phase map; (c), wire-mesh isometric.

Equations (32)

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U 1 = A 1 exp { i [ ϕ s 1 ( x , z ) + k 1 · r 1 ] } ,
U 2 = A 2 exp { i [ ϕ s 2 ( x , z ) + k 2 · r 2 ] } ,
I ( x ) = U 1 + U 2 2 = U 1 2 + U 2 2 + U 1 U 2 * + U 1 * U 2 = I 1 + I 2 + 2 I 1 I 2 cos φ ,
φ = [ ( ϕ s 1 - ϕ s 2 ) + ( k 1 · r 1 ) - ( k 2 · r 2 ) ] .
I ( x ) = I 1 + I 2 + 2 I 1 I 2 cos φ ,
φ = [ ( ϕ s 1 - ϕ s 2 ) + ( k 1 · r 1 ) - ( k 2 · r 2 ) ] .
I - I = 2 I 1 I 2 ( cos φ - cos φ ) = 4 I 1 I 2 sin ( ϕ s - Δ / 2 ) sin ( Δ / 2 ) ,
ϕ s = ϕ s 2 - ϕ s 1 ,
Δ = ( k 1 · r 1 - k 2 · r 2 ) + ( k 1 · r 1 - k 2 · r 2 ) ,
Δ = ( k 1 · r 1 - k 2 · r 2 ) - ( k 1 · r 1 - k 2 · r 2 ) .
k 1 = k r 1 r 1 ,             k 2 = k r 2 r 2 .
Δ = k [ ( r 1 - r 2 ) - ( r 1 - r 2 ) ] .
r 1 = [ ( x 1 - x ) 2 + ( z 1 - z ) 2 ] 1 / 2 , l 1 + r 2 2 l 1 - x 1 x l 1 - z 1 z l 1 ,
Δ = k [ ( l 1 - l 1 ) + r 2 2 ( 1 l 1 - 1 l 1 ) - ( l 2 - l 2 ) - r 2 2 ( 1 l 2 - 1 l 2 ) + x ( x 2 l 2 - x 1 l 1 + x 1 l 1 - x 2 l 2 ) - z ( z 1 l 1 - z 2 l 2 - z 1 l 1 + z 2 l 2 ) .
sin α = x 1 l 1 , sin β = x 2 l 2 , cos α = z 1 l 1 , cos β = z 2 l 2 , sin ( α + Δ α ) = x 1 l 1 , sin ( β + Δ β ) = x 2 l 2 , cos ( α + Δ α ) = z 1 l 1 , cos ( β + Δ β ) = z 2 l 2 .
Δ = k [ x ( Δ S 1 l 1 cos α - Δ S 2 l 2 cos β ) - z ( Δ S 1 l 1 sin α - Δ S 2 l 2 sin β ) ] .
x ( Δ S 1 λ l 1 cos α - Δ S 2 λ l 2 cos β ) - z ( Δ S 1 λ l 1 sin α - Δ S 2 λ l 2 sin β ) = n ,
Δ z = ( Δ S 1 λ l 1 sin α - Δ S 2 λ l 2 sin β ) - 1 .
x ( Δ S 2 λ l cos β ) - z ( Δ S 2 λ l sin β ) = n .
Δ z = ( Δ S 2 λ l sin β ) - 1 .
p = λ l Δ S 2 sin β
ν = Δ S 2 sin β λ l .
x ( Δ S x λ l cos β ) + y ( Δ S y λ l cos β ) = n ,
tan θ = Δ S y Δ S x ,
Δ S 1 x = 100 μ m ,             Δ S 1 y = 0.
Δ S 1 x = 0 ,             Δ S 1 y = 120 μ m .
Δ S 1 x = 50 μ m ,             Δ S 1 y = 100 μ m .
Δ S 1 x = - 50 μ m ,             Δ S 1 y = 100 μ m ,
Δ S 1 x = 60 μ m , Δ S 1 y = 0 , Δ S 2 x = 0 , Δ S 2 y = 0.
Δ S 1 x = 0 , Δ S 1 y = 0 , Δ S 2 x = 60 μ m , Δ S 2 y = 0 ,
Δ S 1 x = 60 μ m , Δ S 1 y = 0 , Δ S 2 x = 60 μ m , Δ S 2 y = 0.
Δ S 1 x = 100 μ m , Δ S 1 y = 0 , Δ S 2 x = 100 μ m , Δ S 2 y = 0 ,

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