Abstract

We propose a digital holographic interference analysis method based on a 2-frame phase-shifting technique for measuring an optical mirror surface. The technique using 2-frame phase-shifting digital interferometry is more efficient than multi-frame phase-shifting techniques because the 2-frame method has the advantage of a reduced number of interferograms, and then takes less time to acquire the wanted topography information from interferograms. In this measurement system, 2-frame phase-shifting digital interferograms are acquired by moving the reference flat mirror surface, which is attached to a piezoelectric transducer, with phase step of 0 or <TEX>$\pi$</TEX>/2 in the reference beam path. The measurements are recorded on a CCD detector. The optical interferometry is designed on the basis of polarization characteristics of a polarizing beam splitter. Therefore the noise from outside turbulence can be decreased. The proposed 2-frame algorithm uses the relative phase difference of the neighbor pixels. The experiment has been carried out on an optical mirror which flatness is less than <TEX>$\lambda$</TEX>/4. The measurement of the optical mirror surface topography using 2-frame phase-shifting interferometry shows that the peak-to-peak value is calculated to be about <TEX>$0.1779{\mu}m$</TEX>, the root-mean-square value is about <TEX>$0.034{\mu}m$</TEX>. Thus, the proposed method is expected to be used in nondestructive testing of optical components.

© 2009 Optical Society of Korea

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References

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  1. D. Malacara, Optical Shop Testing (John Wiley & Sons. Inc., New York, USA, 1978)
  2. Y. I. Ostrovsky, M. M. Butusov, and G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, USA, 1980)
  3. J. C. Wyant, "Interferometric optical metrology : basic principles and new systems," Laser Focus 18, 65-71 (1982)
  4. U. Schnars and W. Jueptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994)
    [Crossref]
  5. B. Skarman, J. Becker, and K. Wozniak, "Simultaneous 3-D PIV and temperature measurements using a new CCD-based holographic interferometer," Flow Meas. Instrum. 7, 1-6 (1996)
    [Crossref]
  6. J. H. Bruning, "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974)
    [Crossref]
  7. I. Yamaguchi, O. Inomoto, and J. Kato, "Surface shape measurement by phase shifting digital holography," in Proc. 4th International Workshop on Automatic Processing of Fringe Patterns (Alkademie, Berlin, Germany, 2001), pp. 365-372
  8. P. Hariharan, "Digital phase-shifting interferometry : a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-0505 (1987)
    [Crossref]
  9. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 610-612 (1998)
  10. J. Schwider, "Phase shifting interferometry : reference phase error reduction," Appl. Opt. 28, 3889-3892 (1989)
    [Crossref]
  11. S. K. Gil, H. J. Byun, H. J. Lee, S. H. Jeon, and J. R. Jeong, "Optical encryption of binary data information with 2-step phase-shifting digital holography," Proc. SPIE 6488, 648835 (2007)
    [Crossref]
  12. M.-O. Jeong, N. Kim, and J.-H. Park, "Elemental image synthesis for integral imaging using phase-shifting digital holography," J. Opt. Soc. Korea 12, 275-280 (2008)
    [Crossref]
  13. D. Kim and Y. J. Cho, "3-D surface profile measurement using an acousto-optic tunable filter based on spectral phase shifting technique," J. Opt. Soc. Korea 12, 281-287 (2008)
    [Crossref]
  14. J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Appl. Opt. 19, 1510-1518 (1980)
    [Crossref]
  15. D. Malacara, "Wavefront fitting with discrete orthogonal polynomials in a unit radius circle," Opt. Eng. 29, 672-675 (1990)
    [Crossref]
  16. F. Dubois. O. Monnom, C. Yourassowsky, and J. C. Legros, "Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies," Appl. Opt. 41, 2621-2626 (2002)
    [Crossref]

2008 (2)

M.-O. Jeong, N. Kim, and J.-H. Park, "Elemental image synthesis for integral imaging using phase-shifting digital holography," J. Opt. Soc. Korea 12, 275-280 (2008)
[Crossref]

D. Kim and Y. J. Cho, "3-D surface profile measurement using an acousto-optic tunable filter based on spectral phase shifting technique," J. Opt. Soc. Korea 12, 281-287 (2008)
[Crossref]

2007 (1)

S. K. Gil, H. J. Byun, H. J. Lee, S. H. Jeon, and J. R. Jeong, "Optical encryption of binary data information with 2-step phase-shifting digital holography," Proc. SPIE 6488, 648835 (2007)
[Crossref]

2002 (1)

F. Dubois. O. Monnom, C. Yourassowsky, and J. C. Legros, "Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies," Appl. Opt. 41, 2621-2626 (2002)
[Crossref]

2001 (1)

I. Yamaguchi, O. Inomoto, and J. Kato, "Surface shape measurement by phase shifting digital holography," in Proc. 4th International Workshop on Automatic Processing of Fringe Patterns (Alkademie, Berlin, Germany, 2001), pp. 365-372

1998 (1)

I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 610-612 (1998)

1996 (1)

B. Skarman, J. Becker, and K. Wozniak, "Simultaneous 3-D PIV and temperature measurements using a new CCD-based holographic interferometer," Flow Meas. Instrum. 7, 1-6 (1996)
[Crossref]

1994 (1)

1990 (1)

D. Malacara, "Wavefront fitting with discrete orthogonal polynomials in a unit radius circle," Opt. Eng. 29, 672-675 (1990)
[Crossref]

1989 (1)

J. Schwider, "Phase shifting interferometry : reference phase error reduction," Appl. Opt. 28, 3889-3892 (1989)
[Crossref]

1987 (1)

P. Hariharan, "Digital phase-shifting interferometry : a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-0505 (1987)
[Crossref]

1982 (1)

J. C. Wyant, "Interferometric optical metrology : basic principles and new systems," Laser Focus 18, 65-71 (1982)

1980 (2)

Y. I. Ostrovsky, M. M. Butusov, and G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, USA, 1980)

J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Appl. Opt. 19, 1510-1518 (1980)
[Crossref]

1978 (1)

D. Malacara, Optical Shop Testing (John Wiley & Sons. Inc., New York, USA, 1978)

1974 (1)

J. H. Bruning, "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974)
[Crossref]

Appl. Opt. (1)

Applied Optics (5)

J. H. Bruning, "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974)
[Crossref]

P. Hariharan, "Digital phase-shifting interferometry : a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-0505 (1987)
[Crossref]

J. Schwider, "Phase shifting interferometry : reference phase error reduction," Appl. Opt. 28, 3889-3892 (1989)
[Crossref]

J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Appl. Opt. 19, 1510-1518 (1980)
[Crossref]

F. Dubois. O. Monnom, C. Yourassowsky, and J. C. Legros, "Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies," Appl. Opt. 41, 2621-2626 (2002)
[Crossref]

Flow Measurement and Instrumentation (1)

B. Skarman, J. Becker, and K. Wozniak, "Simultaneous 3-D PIV and temperature measurements using a new CCD-based holographic interferometer," Flow Meas. Instrum. 7, 1-6 (1996)
[Crossref]

in Proc. 4th International Workshop on Automatic Processing of Fringe Patterns (1)

I. Yamaguchi, O. Inomoto, and J. Kato, "Surface shape measurement by phase shifting digital holography," in Proc. 4th International Workshop on Automatic Processing of Fringe Patterns (Alkademie, Berlin, Germany, 2001), pp. 365-372

Journal of the Optical Society of Korea (2)

M.-O. Jeong, N. Kim, and J.-H. Park, "Elemental image synthesis for integral imaging using phase-shifting digital holography," J. Opt. Soc. Korea 12, 275-280 (2008)
[Crossref]

D. Kim and Y. J. Cho, "3-D surface profile measurement using an acousto-optic tunable filter based on spectral phase shifting technique," J. Opt. Soc. Korea 12, 281-287 (2008)
[Crossref]

Laser Focus (1)

J. C. Wyant, "Interferometric optical metrology : basic principles and new systems," Laser Focus 18, 65-71 (1982)

Opt. Eng. (1)

D. Malacara, "Wavefront fitting with discrete orthogonal polynomials in a unit radius circle," Opt. Eng. 29, 672-675 (1990)
[Crossref]

Opt. Lett. (1)

I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 610-612 (1998)

Proc. SPIE (1)

S. K. Gil, H. J. Byun, H. J. Lee, S. H. Jeon, and J. R. Jeong, "Optical encryption of binary data information with 2-step phase-shifting digital holography," Proc. SPIE 6488, 648835 (2007)
[Crossref]

Other (2)

D. Malacara, Optical Shop Testing (John Wiley & Sons. Inc., New York, USA, 1978)

Y. I. Ostrovsky, M. M. Butusov, and G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, USA, 1980)

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