Abstract

A phase-shifting procedure that is applicable to four-wave holographic inteferometry is described. The technique can be used to obtain whole-field phase maps with all methods that use holographic moiré fringes.

© 1992 Optical Society of America

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References

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  1. P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
    [CrossRef]
  2. P. Hariharan, “Quasi-heterodyne holographic interferometry,” Opt. Eng. 24, 632–638 (1985).
  3. P. Hariharan, B. F. Oreb, “Stroboscopic holographic interferometry: application of digital techniques,” Opt. Commun. 59, 83–86 (1986).
    [CrossRef]
  4. P. Hariharan, B. F. Oreb, “Two index holographic contouring: application of digital techniques,” Opt. Commun. 51, 142–144 (1984).
    [CrossRef]
  5. K. Creath, “Phase-measurement interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 5, pp. 349–393.
    [CrossRef]
  6. K. Creath, “Holographic contour and deformation measurement using a 1.4 million element detector array,” Appl. Opt. 28, 2170–2175(1989).
    [CrossRef] [PubMed]
  7. P. K. Rastogi, L. Pflug, “A holographic technique featuring broad range sensitivity to contour diffuse objects,” J. Mod. Opt. 38, 1673–1683 (1991).
    [CrossRef]
  8. P. K. Rastogi, M. Barillot, G. Kaufmann, “Comparative phase shifting holographic interferometry,” Appl. Opt. 30, 722–728 (1991).
    [CrossRef] [PubMed]
  9. P. K. Rastogi, E. Denarie, “Visualization of in-plane displacement fields using phase shifting holographic moiré: application to crack detection and propagation,” Appl. Opt. (to be published).
  10. P. K. Rastogi, “Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection,” J. Mod. Opt. 38, 1251–1263 (1991).
    [CrossRef]
  11. P. K. Rastogi, “Comparative holographic moiré interferometry,” Appl. Opt. 23, 924–927 (1984).
    [CrossRef] [PubMed]
  12. P. K. Rastogi, “Comparative holographic interferometry: a nondestructive inspection system for detection of flaws,” Exp. Mech. 25, 325–337 (1985).
    [CrossRef]
  13. C. A. Sciammarella, J. A. Gilbert, “A holographic moiré technique to obtain separate patterns for components of displacements,” Exp. Mech. 16, 215–220 (1976).
    [CrossRef]
  14. C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
    [CrossRef]
  15. P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
    [CrossRef]
  16. P. K. Rastogi, “A real-time holographic moiré technique for the measurement of slope change,” Opt. Acta 31, 159–167 (1984).
    [CrossRef]

1991 (3)

P. K. Rastogi, L. Pflug, “A holographic technique featuring broad range sensitivity to contour diffuse objects,” J. Mod. Opt. 38, 1673–1683 (1991).
[CrossRef]

P. K. Rastogi, “Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection,” J. Mod. Opt. 38, 1251–1263 (1991).
[CrossRef]

P. K. Rastogi, M. Barillot, G. Kaufmann, “Comparative phase shifting holographic interferometry,” Appl. Opt. 30, 722–728 (1991).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

P. Hariharan, B. F. Oreb, “Stroboscopic holographic interferometry: application of digital techniques,” Opt. Commun. 59, 83–86 (1986).
[CrossRef]

1985 (2)

P. Hariharan, “Quasi-heterodyne holographic interferometry,” Opt. Eng. 24, 632–638 (1985).

P. K. Rastogi, “Comparative holographic interferometry: a nondestructive inspection system for detection of flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

1984 (3)

P. Hariharan, B. F. Oreb, “Two index holographic contouring: application of digital techniques,” Opt. Commun. 51, 142–144 (1984).
[CrossRef]

P. K. Rastogi, “A real-time holographic moiré technique for the measurement of slope change,” Opt. Acta 31, 159–167 (1984).
[CrossRef]

P. K. Rastogi, “Comparative holographic moiré interferometry,” Appl. Opt. 23, 924–927 (1984).
[CrossRef] [PubMed]

1982 (2)

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

1981 (1)

P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
[CrossRef]

1976 (1)

C. A. Sciammarella, J. A. Gilbert, “A holographic moiré technique to obtain separate patterns for components of displacements,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Barillot, M.

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Creath, K.

K. Creath, “Holographic contour and deformation measurement using a 1.4 million element detector array,” Appl. Opt. 28, 2170–2175(1989).
[CrossRef] [PubMed]

K. Creath, “Phase-measurement interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 5, pp. 349–393.
[CrossRef]

Denarie, E.

P. K. Rastogi, E. Denarie, “Visualization of in-plane displacement fields using phase shifting holographic moiré: application to crack detection and propagation,” Appl. Opt. (to be published).

Gilbert, J. A.

C. A. Sciammarella, J. A. Gilbert, “A holographic moiré technique to obtain separate patterns for components of displacements,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Hariharan, P.

P. Hariharan, B. F. Oreb, “Stroboscopic holographic interferometry: application of digital techniques,” Opt. Commun. 59, 83–86 (1986).
[CrossRef]

P. Hariharan, “Quasi-heterodyne holographic interferometry,” Opt. Eng. 24, 632–638 (1985).

P. Hariharan, B. F. Oreb, “Two index holographic contouring: application of digital techniques,” Opt. Commun. 51, 142–144 (1984).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Jacquot, P.

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

Kaufmann, G.

Monneret, J.

P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
[CrossRef]

Narayanan, R.

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

Oreb, B. F.

P. Hariharan, B. F. Oreb, “Stroboscopic holographic interferometry: application of digital techniques,” Opt. Commun. 59, 83–86 (1986).
[CrossRef]

P. Hariharan, B. F. Oreb, “Two index holographic contouring: application of digital techniques,” Opt. Commun. 51, 142–144 (1984).
[CrossRef]

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Pflug, L.

P. K. Rastogi, L. Pflug, “A holographic technique featuring broad range sensitivity to contour diffuse objects,” J. Mod. Opt. 38, 1673–1683 (1991).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, M. Barillot, G. Kaufmann, “Comparative phase shifting holographic interferometry,” Appl. Opt. 30, 722–728 (1991).
[CrossRef] [PubMed]

P. K. Rastogi, L. Pflug, “A holographic technique featuring broad range sensitivity to contour diffuse objects,” J. Mod. Opt. 38, 1673–1683 (1991).
[CrossRef]

P. K. Rastogi, “Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection,” J. Mod. Opt. 38, 1251–1263 (1991).
[CrossRef]

P. K. Rastogi, “Comparative holographic interferometry: a nondestructive inspection system for detection of flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

P. K. Rastogi, “A real-time holographic moiré technique for the measurement of slope change,” Opt. Acta 31, 159–167 (1984).
[CrossRef]

P. K. Rastogi, “Comparative holographic moiré interferometry,” Appl. Opt. 23, 924–927 (1984).
[CrossRef] [PubMed]

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
[CrossRef]

P. K. Rastogi, E. Denarie, “Visualization of in-plane displacement fields using phase shifting holographic moiré: application to crack detection and propagation,” Appl. Opt. (to be published).

Sciammarella, C. A.

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

C. A. Sciammarella, J. A. Gilbert, “A holographic moiré technique to obtain separate patterns for components of displacements,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Spajer, M.

P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
[CrossRef]

Appl. Opt. (3)

Exp. Mech. (3)

P. K. Rastogi, “Comparative holographic interferometry: a nondestructive inspection system for detection of flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

C. A. Sciammarella, J. A. Gilbert, “A holographic moiré technique to obtain separate patterns for components of displacements,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

C. A. Sciammarella, P. K. Rastogi, P. Jacquot, R. Narayanan, “Holographic moiré in real time,” Exp. Mech. 22, 52–63 (1982).
[CrossRef]

J. Mod. Opt. (2)

P. K. Rastogi, L. Pflug, “A holographic technique featuring broad range sensitivity to contour diffuse objects,” J. Mod. Opt. 38, 1673–1683 (1991).
[CrossRef]

P. K. Rastogi, “Visualization and measurement of slope and curvature fields using holographic interferometry: an application to flaw detection,” J. Mod. Opt. 38, 1251–1263 (1991).
[CrossRef]

Opt. Acta (1)

P. K. Rastogi, “A real-time holographic moiré technique for the measurement of slope change,” Opt. Acta 31, 159–167 (1984).
[CrossRef]

Opt. Commun. (3)

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

P. Hariharan, B. F. Oreb, “Stroboscopic holographic interferometry: application of digital techniques,” Opt. Commun. 59, 83–86 (1986).
[CrossRef]

P. Hariharan, B. F. Oreb, “Two index holographic contouring: application of digital techniques,” Opt. Commun. 51, 142–144 (1984).
[CrossRef]

Opt. Eng. (1)

P. Hariharan, “Quasi-heterodyne holographic interferometry,” Opt. Eng. 24, 632–638 (1985).

Opt. Lasers Eng. (1)

P. K. Rastogi, M. Spajer, J. Monneret, “In-plane deformation measurement using holographic moiré,” Opt. Lasers Eng. 2, 79–103 (1981).
[CrossRef]

Other (2)

K. Creath, “Phase-measurement interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 5, pp. 349–393.
[CrossRef]

P. K. Rastogi, E. Denarie, “Visualization of in-plane displacement fields using phase shifting holographic moiré: application to crack detection and propagation,” Appl. Opt. (to be published).

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Figures (1)

Fig. 1
Fig. 1

Schematic of the experimental arrangement for obtaining phase maps that correspond to the in-plane displacement component sx.

Equations (6)

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I ( x , y ) = 2 I 0 ( x , y ) { 1 + ( V / 2 ) [ cos φ 1 ( x , y ) + cos φ 2 ( x , y ) ] } ,
I 1 = 2 I 0 ( x , y ) ( 1 + ( V / 2 { cos ) [ φ 1 ( x , y ) - ( 2 π ) / 3 ] + cos [ φ 2 ( x , y ) - ( 4 π ) / 3 ] } ) ,
I 2 = 2 I 0 ( x , y ) { 1 + ( V / 2 ) [ cos φ 1 ( x , y ) + cos φ 2 ( x , y ) ] } ,
I 3 = 2 I 0 ( x , y ) ( 1 + ( V / 2 ) { cos [ φ 1 ( x , y ) + ( 2 π ) / 3 ] + cos [ φ 2 ( x , y ) + ( 4 π ) / 3 ] } )
φ 1 ( x , y ) - φ 2 ( x , y ) = 2 tan - 1 3 ( I 1 - I 3 ) 2 I 2 - I 1 - I 3 .
s x ( x , y ) = ϕ ( x , y ) λ 4 π sin θ ,

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