Abstract

A method is proposed for contouring of diffused objects using digital holographic moiré interferometry in lensless Fourier transform configuration. Fringe projection moiré technique combined with digital double-exposure holography produces the contours in this method. Two digital holograms of a 10 mm aluminum alloy cube are recorded by tilting the illumination angle slightly between exposures, and a third one is recorded by translating the detector a little laterally with the final illumination angle unchanged. Upon numerical processing of the first two holograms, a plane parallel fringe system seems to be projected onto the object. This fringe system can be referred to as the modified grid. Processing of the second and the third hologram results in another grid, the reference grid. In effect, processing of the first and the third hologram combines the modified and the reference grids to produce the moiré contour fringes. The range of contour intervals obtained remains between 2.73 and 0.38 mm with seven different contours in between. The present method can measure details of a great variety of sizes on objects of large dimensional range. Deviations in the measured contour intervals from the theoretically calculated values are found to be within 12%–18%. This seems to be because of the deviation in the present experimental geometry from the ideal theoretical configuration, the hologram digitization, and the particular reconstruction algorithm used in the present experimental arrangement.

© 2012 Optical Society of America

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References

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  1. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  2. D. T. Moore and B. E. Truax, “Phase-locked moiré fringe analysis for automated contouring of diffuse surfaces,” Appl. Opt. 18, 91–96 (1979).
    [CrossRef]
  3. P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
    [CrossRef]
  4. M. Takeda and H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef]
  5. S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
    [CrossRef]
  6. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  7. C. A. Sciammarella, “Moiré in science and engineering,” in Trends in Optical Nondestructive Testing and Inspection, P. Rastogi and D. Inaudi, eds. (Elsevier, 2000), pp. 345–373.
  8. D. Post and B. Han, “Moiré interferometry,” in Springer Handbook of Experimental Solid Mechanics, W. N. Sharpe, ed. (Springer, 2008), pp. 1–26.
  9. K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, 1992), pp. 653–685.
  10. K. A. Haines and B. P. Hildebrand, “Contour generation by wave front reconstruction,” Phys. Lett. 19, 10–11 (1965).
    [CrossRef]
  11. B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
    [CrossRef]
  12. N. Abramson, “Sandwich hologram interferometry. 3: contouring,” Appl. Opt. 15, 200–205 (1976).
    [CrossRef]
  13. N. Abramson, “Holographic contouring by translation,” Appl. Opt. 15, 1018–1022 (1976).
    [CrossRef]
  14. P. Demattia and V. Fossati-Bellani, “Holographic contouring by displacing the object and the illumination beam,” Opt. Commun. 26, 17–21 (1978).
    [CrossRef]
  15. K. Asai, “Contouring method by parallel light moire holography,” Jpn. J. Appl. Phys. 17, 383–389 (1978).
    [CrossRef]
  16. O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.
  17. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef]
  18. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  19. U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,” Appl. Opt. 33, 4373–4377 (1994).
    [CrossRef]
  20. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  21. T. C. Poon, T. Yatagai, and W. Jüptner, “Digital holography—coherent optics of the 21st century: introduction,” Appl. Opt. 45, 821 (2006).
    [CrossRef]
  22. C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820 (1999).
    [CrossRef]
  23. S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
    [CrossRef]
  24. I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
    [CrossRef]
  25. D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
    [CrossRef]
  26. A. T. Saucedo, F. M. Santoyo, M. D. Torre-Ibarra, G. Pedrini, and W. Osten, “Endoscopic pulsed digital holography for 3D measurements,” Opt. Express 14, 1468–1475 (2006).
    [CrossRef]
  27. M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
    [CrossRef]
  28. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
    [CrossRef]
  29. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  30. T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
    [CrossRef]

2009

2007

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

2006

2005

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

2002

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

2001

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

2000

S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1999

1994

1991

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

1979

1978

P. Demattia and V. Fossati-Bellani, “Holographic contouring by displacing the object and the illumination beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

K. Asai, “Contouring method by parallel light moire holography,” Jpn. J. Appl. Phys. 17, 383–389 (1978).
[CrossRef]

1976

1967

1965

K. A. Haines and B. P. Hildebrand, “Contour generation by wave front reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Abramson, N.

Asai, K.

K. Asai, “Contouring method by parallel light moire holography,” Jpn. J. Appl. Phys. 17, 383–389 (1978).
[CrossRef]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Carelli, P.

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Conde, R.

O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.

Coquoz, O.

O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.

Creath, K.

K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, 1992), pp. 653–685.

De Altorio, A.

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Deiwick, M.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Delere, H.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Demattia, P.

P. Demattia and V. Fossati-Bellani, “Holographic contouring by displacing the object and the illumination beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Depeursinge, C.

O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.

Dirksen, D

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Droste, H.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Fossati-Bellani, V.

P. Demattia and V. Fossati-Bellani, “Holographic contouring by displacing the object and the illumination beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Haines, K. A.

B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
[CrossRef]

K. A. Haines and B. P. Hildebrand, “Contour generation by wave front reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Han, B.

D. Post and B. Han, “Moiré interferometry,” in Springer Handbook of Experimental Solid Mechanics, W. N. Sharpe, ed. (Springer, 2008), pp. 1–26.

Hildebrand, B. P.

B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. 57, 155–162 (1967).
[CrossRef]

K. A. Haines and B. P. Hildebrand, “Contour generation by wave front reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Hossain, M.

M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[CrossRef]

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

Juptner, W.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Jüptner, W.

Jüptner, W. P. O.

Kato, J.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Kemper, B.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Mehta, D. S.

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

Mirza, S.

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

Moore, D. T.

Ohta, S.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Osten, W.

Paoletti, D.

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Pedrini, G.

Poon, T. C.

Post, D.

D. Post and B. Han, “Moiré interferometry,” in Springer Handbook of Experimental Solid Mechanics, W. N. Sharpe, ed. (Springer, 2008), pp. 1–26.

Santoyo, F. M.

Saucedo, A. T.

Schedin, S.

Scheld, H. H.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Schirripa Spagnolo, G.

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Schnars, U.

Sciammarella, C. A.

C. A. Sciammarella, “Moiré in science and engineering,” in Trends in Optical Nondestructive Testing and Inspection, P. Rastogi and D. Inaudi, eds. (Elsevier, 2000), pp. 345–373.

Seebacher, S.

Shakher, C.

M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[CrossRef]

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

Sheoran, G.

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Takeda, M.

Taleblou, F.

O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.

Tiziani, H. J.

Torre-Ibarra, M. D.

Truax, B. E.

von Bally, G.

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Wagner, C.

Wyant, J. C.

K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, 1992), pp. 653–685.

Yamaguchi, I.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Yamamoto, H.

Yatagai, T.

Appl. Opt.

M. Takeda and H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
[CrossRef]

D. T. Moore and B. E. Truax, “Phase-locked moiré fringe analysis for automated contouring of diffuse surfaces,” Appl. Opt. 18, 91–96 (1979).
[CrossRef]

N. Abramson, “Sandwich hologram interferometry. 3: contouring,” Appl. Opt. 15, 200–205 (1976).
[CrossRef]

N. Abramson, “Holographic contouring by translation,” Appl. Opt. 15, 1018–1022 (1976).
[CrossRef]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef]

U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,” Appl. Opt. 33, 4373–4377 (1994).
[CrossRef]

T. C. Poon, T. Yatagai, and W. Jüptner, “Digital holography—coherent optics of the 21st century: introduction,” Appl. Opt. 45, 821 (2006).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820 (1999).
[CrossRef]

S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
[CrossRef]

M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

K. Asai, “Contouring method by parallel light moire holography,” Jpn. J. Appl. Phys. 17, 383–389 (1978).
[CrossRef]

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Commun.

P. Demattia and V. Fossati-Bellani, “Holographic contouring by displacing the object and the illumination beam,” Opt. Commun. 26, 17–21 (1978).
[CrossRef]

Opt. Eng.

P. Carelli, D. Paoletti, G. Schirripa Spagnolo, and A. De Altorio, “Holograhic contouring method: application to automatic measurements of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

T. M. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng. 41, 1829–1839 (2002).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

M. Hossain, G. Sheoran, D. S. Mehta, and C. Shakher, “Contouring of diffused objects by using digital holography,” Opt. Lasers Eng. 45, 684–689 (2007).
[CrossRef]

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

D Dirksen, H. Droste, B. Kemper, H. Delere, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Phys. Lett.

K. A. Haines and B. P. Hildebrand, “Contour generation by wave front reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Other

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

C. A. Sciammarella, “Moiré in science and engineering,” in Trends in Optical Nondestructive Testing and Inspection, P. Rastogi and D. Inaudi, eds. (Elsevier, 2000), pp. 345–373.

D. Post and B. Han, “Moiré interferometry,” in Springer Handbook of Experimental Solid Mechanics, W. N. Sharpe, ed. (Springer, 2008), pp. 1–26.

K. Creath and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, 1992), pp. 653–685.

O. Coquoz, C. Depeursinge, R. Conde, and F. Taleblou, “Numerical reconstruction of images from endoscopic holograms,” in Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 1992), pp. 338–339.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the setup used for digital holographic moiré contouring.

Fig. 2.
Fig. 2.

Schematic of the geometry used for recording and reconstruction of digital holograms.

Fig. 3.
Fig. 3.

Schematic of the geometry for moiré fringe formation.

Fig. 4.
Fig. 4.

Reconstructed primary image of the cube obtained after zero order removal and median filtering.

Fig. 5.
Fig. 5.

(a1)–(c1), Modified grid, reference grid, and the moiré contour fringes corresponding to 0.0025° mirror rotation and 0.10 mm detector translation; (a2)–(c2), same as (a1)–(c1) but with 0.005° mirror rotation and 0.15 mm detector translation.

Fig. 6.
Fig. 6.

(a1)–(a5), Moiré contour fringes corresponding to mirror rotation and detector translation pairs of, respectively, (0.0067°, 0.20 mm), (0.01 min., 0.25 mm), (0.0067°, 0.30 mm), (0.01 min, 0.50 mm), and (0.015°, 0.70 mm).

Tables (1)

Tables Icon

Table 1. The Experimental and Theoretical Values of the Modified and the Reference Grid Periods as well as the Moiré Contour Intervals Corresponding to the Seven Different Mirror Rotation and Detector Translation Pairs

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

O(XI,YI)=exp(ikd)iλdexp[i(k2d)(XI2+YI2)]×(XH,YH)I(XH,YH)R(XH,YH)exp[k2d(XH2+YH2)]exp[i2πλd(X1XH+Y1YH)]dXHdYH,
O(XI,YI)=exp(ikd)iλdexp[i(k2d)(XI2+YI2)]Fλd1{I(XH,YH)R(XH,YH)exp[i(k2d)(XH2+YH2)]},
R(XH,YH)=(const)exp[i(k2d)(XH2+YH2)].
O(XI,YI)=(const)exp(ikd)iλdexp[i(k2d)(XI2+YI2)]Fλd1{I(XH,YH)}.
O(m,n)=constexp(ikd)iλdexp[iπλd(m2N2ΔXH2+n2N2ΔYH2)]IDFT{I(rΔXH,sΔYH)},
ΔXI=λd/(NΔXH),ΔYI=λd/(NΔYH)
O(m,n)=constexp(ikd)iλdexp[iπλd(m2N2ΔXH2+n2N2ΔYH2)]IFFT{I(rΔXH,sΔYH)}.
I(m,n)=|O(m,n)|2=Re2|O(m,n)|+Im2|O(m,n)|,
ϕ(m,n)=arctanIm[O(m,n)]Re[O(m,n)],
ΔΦ(m,n)={Φ2(m,n)Φ1(m,n)+2πifΦ2(m,n)Φ1(m,n)<πΦ2(m,n)Φ1(m,n)2πifΦ2(m,n)Φ1(m,n)+πΦ2(m,n)Φ1(m,n)else.
lM=λ/2sinθ,
lR=(d/2t)λ,
Δh=lRlM/l,
l=lR2+lM22lRlMcosβ,

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