Abstract

The use of different pupils for storing each speckled image in speckle photography is employed to determine multiple in-plane rotations. The method consists of recording a four-exposure specklegram where the rotations are done between exposures. This specklegram is then optically processed in a whole field approach rendering isothetic fringes, which give detailed information about the multiple rotations. It is experimentally demonstrated that the proposed arrangement permits the depiction of six isothetics in order to measure either six different angles or three nonparallel components for two local general in-plane displacements.

© 2007 Optical Society of America

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References

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  1. J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, 1975).
  2. R. K. Erf, Speckle Metrology (Academic, 1978).
  3. R. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).
  4. C. J. Tay, S. L. Toh, H. M. Shang, and J. Zhang, "Whole-field determination of surface roughness by speckle correlation," Appl. Opt. 34, 2324-2335 (1995).
    [CrossRef] [PubMed]
  5. F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).
  6. J. M. Burch and M. J. Tokarski, "Production of multiple beam fringes from photographic scatters," Opt. Acta 15, 101-111 (1968).
  7. E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
    [CrossRef]
  8. F. P. Chiang and A. Asundi, "Perspective effect in the white-light speckle method," Appl. Opt. 21, 1708-1710 (1982).
    [CrossRef] [PubMed]
  9. F. D. Chiang and R. P. Khetan, "Strain analysis by one-beam laser speckle interferometry. I. Single aperture method," Appl. Opt. 15, 2205-2215 (1976).
    [CrossRef] [PubMed]
  10. F. P. Chiang and C. J. Lin, "Stress analysis of in-plane vibration of 2D structures by a laser speckle method," Appl. Opt. 19, 2705-2707 (1980).
    [CrossRef] [PubMed]
  11. D. Duffy, "Moiré gauging of in-plane displacement using double aperture imagining," Appl. Opt. 11, 1778-1781 (1972).
    [CrossRef] [PubMed]
  12. F. D. Chiang and R. P. Khetan, "Strain analysis by one-beam laser speckle interferometry 2: Multiaperture method," Appl. Opt. 18, 2175-2186 (1979).
    [CrossRef] [PubMed]
  13. L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
    [CrossRef]
  14. M. Tebaldi, L. Angel, M. Trivi, and N. Bolognini, "Phase-object detection by use of double-exposure fringe modulated speckle patterns," J. Opt. Soc. Am. A 20, 116-129 (2003).
    [CrossRef]
  15. L. Angel, M. Tebaldi, N. Bolognini, and M. Trivi, "Speckle photography with different pupils in a multiple exposure scheme," J. Opt. Soc. Am. A 17, 107-119 (2000).
    [CrossRef]
  16. L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
    [CrossRef]
  17. L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
    [CrossRef]

2003 (1)

2001 (2)

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

2000 (1)

1999 (1)

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

1995 (1)

1982 (2)

F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).

F. P. Chiang and A. Asundi, "Perspective effect in the white-light speckle method," Appl. Opt. 21, 1708-1710 (1982).
[CrossRef] [PubMed]

1980 (1)

1979 (1)

1976 (1)

1972 (1)

1970 (1)

E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
[CrossRef]

1968 (1)

J. M. Burch and M. J. Tokarski, "Production of multiple beam fringes from photographic scatters," Opt. Acta 15, 101-111 (1968).

Adachi, J.

F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).

Anastasi, R.

F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).

Angel, L.

M. Tebaldi, L. Angel, M. Trivi, and N. Bolognini, "Phase-object detection by use of double-exposure fringe modulated speckle patterns," J. Opt. Soc. Am. A 20, 116-129 (2003).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel, M. Tebaldi, N. Bolognini, and M. Trivi, "Speckle photography with different pupils in a multiple exposure scheme," J. Opt. Soc. Am. A 17, 107-119 (2000).
[CrossRef]

Archbold, E.

E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
[CrossRef]

Asundi, A.

Beaty, J.

F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).

Bolognini, N.

M. Tebaldi, L. Angel, M. Trivi, and N. Bolognini, "Phase-object detection by use of double-exposure fringe modulated speckle patterns," J. Opt. Soc. Am. A 20, 116-129 (2003).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel, M. Tebaldi, N. Bolognini, and M. Trivi, "Speckle photography with different pupils in a multiple exposure scheme," J. Opt. Soc. Am. A 17, 107-119 (2000).
[CrossRef]

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

Burch, J. M.

E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
[CrossRef]

J. M. Burch and M. J. Tokarski, "Production of multiple beam fringes from photographic scatters," Opt. Acta 15, 101-111 (1968).

Chiang, F. D.

Chiang, F. P.

Dainty, J. C.

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, 1975).

Duffy, D.

Ennos, A. E.

E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
[CrossRef]

Erf, R. K.

R. K. Erf, Speckle Metrology (Academic, 1978).

Khetan, R. P.

Lin, C. J.

Shang, H. M.

Sirohi, R.

R. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).

Tay, C. J.

Tebaldi, M.

M. Tebaldi, L. Angel, M. Trivi, and N. Bolognini, "Phase-object detection by use of double-exposure fringe modulated speckle patterns," J. Opt. Soc. Am. A 20, 116-129 (2003).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel, M. Tebaldi, N. Bolognini, and M. Trivi, "Speckle photography with different pupils in a multiple exposure scheme," J. Opt. Soc. Am. A 17, 107-119 (2000).
[CrossRef]

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

Toh, S. L.

Tokarski, M. J.

J. M. Burch and M. J. Tokarski, "Production of multiple beam fringes from photographic scatters," Opt. Acta 15, 101-111 (1968).

Toro, L. Angel

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

Trivi, M.

M. Tebaldi, L. Angel, M. Trivi, and N. Bolognini, "Phase-object detection by use of double-exposure fringe modulated speckle patterns," J. Opt. Soc. Am. A 20, 116-129 (2003).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel, M. Tebaldi, N. Bolognini, and M. Trivi, "Speckle photography with different pupils in a multiple exposure scheme," J. Opt. Soc. Am. A 17, 107-119 (2000).
[CrossRef]

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

Zhang, J.

Appl. Opt. (6)

J. Mod. Opt. (1)

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Fringe visibility analysis with different scale apertures in speckle photography," J. Mod. Opt. 43, 1749-1765 (2001).
[CrossRef]

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

Opt. Acta (2)

J. M. Burch and M. J. Tokarski, "Production of multiple beam fringes from photographic scatters," Opt. Acta 15, 101-111 (1968).

E. Archbold, J. M. Burch, and A. E. Ennos, "Recording of in-plane surface displacement by double-exposure speckle photography," Opt. Acta 17, 883-898 (1970).
[CrossRef]

Opt. Commun. (2)

L. Angel, M. Tebaldi, M. Trivi, and N. Bolognini, "Properties of speckle patterns generated through multiaperture pupils," Opt. Commun. 192, 37-47 (2001).
[CrossRef]

L. Angel Toro, M. Tebaldi, M. Trivi, and N. Bolognini, "Optical operations based on speckle modulation by using a photorefractive crystal," Opt. Commun. 168, 55-64 (1999).
[CrossRef]

Opt. Eng. (1)

F. P. Chiang, J. Adachi, R. Anastasi, and J. Beaty, "Subjective laser speckle method and its application to solid mechanics problems," Opt. Eng. 21, 379-390 (1982).

Other (3)

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, 1975).

R. K. Erf, Speckle Metrology (Academic, 1978).

R. Sirohi, ed., Speckle Metrology (Marcel Dekker, 1993).

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangements for (a) recording step (R, random diffuser; L, lens; P, pupil mask; S, specklegram) and (b) analysis step (S, specklegram; L 1 and L 2 , lenses; M, filtering mask; I, isothetics plane).

Fig. 2
Fig. 2

(a) Multiple-aperture pupils indicated by (1), (2), (3), and (4). (b) Diffraction patterns corresponding to each pupil. (c) Diffraction patterns corresponding to a four-exposure specklegram. In each spot the numbers indicate which images (pupils) contribute to this spot.

Fig. 3
Fig. 3

Four-exposure diffraction pattern scheme. The isothetic fringes obtained by filtering out each spot are displayed. In each spot, the angle θ in which the diffuser was rotated is indicated.

Fig. 4
Fig. 4

Intensity profiles along a direction perpendicular to each isothetic fringe pattern. The corresponding diffracted spot, the isothetic fringe period, and the measured rotation θ* angle are indicated in each case.

Equations (8)

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P ( u , v ) = n = 1 N a n ( u , v ) ,
G ( U , V ) = k = 1 Q G k ( U , V ) .
G k ( U , V ) = { S k ( S k ) * } ( U , V ) ,
S k ( χ , ς ) = P k ( χ Z C f 1 , ς Z C f 1 ) × T k ( χ M f 1 , ς M f 1 ) ,
T k ( χ M f 1 , ς M f 1 ) = A k ( x , y ) × exp ( i 2 π λ M f 1 ( χ x + ς y ) ) d x d y .
{ P k ( χ Z C f 1 , ς Z C f 1 ) P k ( χ Z C f 1 , ς Z C f 1 ) } ( U , V ) 0.
| T | = { T 1 for   inner   spots T 2 for   outer   spots .
θ * = { λ f 2 T 1 1 Λ when   filtering   at   an   inner   spot λ f 2 T 2 1 Λ when   filtering   at   an   outer   spot .

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