Abstract

The feasibilities for optical correlation diagnostics of rough surfaces with large surface inhomogeneities by determining the transformations of the longitudinal coherence function of the scattered field are substantiated and implemented.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Bennett and L. Mattson, Introduction to Surface Roughness and Scattering, (Optical Society of America, Washington, D.C, 1999).
  2. D. Pantzer, J. Politch, and L. Ek, "Heterodyne profiling instrument for the angstrom region," Appl. Opt. 25, 4168-4172 (1986).
    [CrossRef] [PubMed]
  3. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon Press, London 1963).
  4. R. S. Sirohi ed., Speckle Metrology, (Marcel Deker, New York, 1993).
  5. O. V Angelsky., S. G. Hanson and P. P. Maksimyak, The Use of Optical-Correlation Techniques for Characterizing Scattering Object and Media - Bellingham, (SPIE Press PM71, Bellingham, 1999).
  6. O. V. Angelsky, and P. P. Maksimyak, "Optical correlation diagnostics of surface roughness" in: Handbook of Coherent Domain Optical Methods. Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed., (Kluwer Academic Publishers,Boston, 2004), Vol. 1, 43-92 (2004).
  7. O. V. Angelsky, D. N. Burkovets, P. P. Maksimyak, and S. G. Hanson "Applicability of the singular-optics concept for diagnostics of random and fractal rough surfaces," Appl. Opt. 42, 4529-4540 (2003).
    [CrossRef] [PubMed]
  8. O. V. Angelsky, S. G. Hanson, A. P. Maksimyak and P. P. Maksimyak, "Interference diagnostics of white-light vortices," Opt. Express 13, 8179-8183 (2005).
    [CrossRef] [PubMed]
  9. H. Fujii, T. Asakura and Y Shindo, "Measurement of surface roughness properties by using image speckle contrast," J. Opt. Soc. Am. 66, 1217-1222 (1976).
    [CrossRef]
  10. R. A. Spraque, "Surface roughness measurement using white light speckle," Appl. Opt. 11, 2811-2819 (1972).
    [CrossRef]
  11. J. H. Bruning, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and J. Brangaccio, "Digital wavefront measuring interfereometer for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974).
    [CrossRef] [PubMed]
  12. C. T. Farrell and M. A. Player, "Phase step measurement and variable step algorithms in phase-shifting interferometry," Meas. Sci. Technol. 3, 953-958 (1992).
    [CrossRef]
  13. O. V. Angelsky and P. P. Maksimyak, "Transformation of the longitudinal correlation function of a field propagating in a scattering medium," Opt. Spectrosc. 60, 331-336 (1986).
  14. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving of Incorrect Problems, (Nauka, Moscow, 1986, in Russian).
  15. A. V. Goncharovsky, A. M. Cherepashchuk, and A. G. Yagola, Incorrect Problems in Astrophysics, (Nauka, Moscow, 1985 in Russian).
  16. H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, "Referenceless resting of vortex optical beams," Opt. Appl. 33, 695-708 (2003).

2005 (1)

2003 (2)

1992 (1)

C. T. Farrell and M. A. Player, "Phase step measurement and variable step algorithms in phase-shifting interferometry," Meas. Sci. Technol. 3, 953-958 (1992).
[CrossRef]

1986 (2)

O. V. Angelsky and P. P. Maksimyak, "Transformation of the longitudinal correlation function of a field propagating in a scattering medium," Opt. Spectrosc. 60, 331-336 (1986).

D. Pantzer, J. Politch, and L. Ek, "Heterodyne profiling instrument for the angstrom region," Appl. Opt. 25, 4168-4172 (1986).
[CrossRef] [PubMed]

1976 (1)

1974 (1)

1972 (1)

Angelsky, O. V.

Asakura, T.

Bogatyryova, H. V.

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, "Referenceless resting of vortex optical beams," Opt. Appl. 33, 695-708 (2003).

Brangaccio, J.

Bruning, J. H.

Burkovets, D. N.

Ek, L.

Farrell, C. T.

C. T. Farrell and M. A. Player, "Phase step measurement and variable step algorithms in phase-shifting interferometry," Meas. Sci. Technol. 3, 953-958 (1992).
[CrossRef]

Felde,, Ch. V.

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, "Referenceless resting of vortex optical beams," Opt. Appl. 33, 695-708 (2003).

Fujii, H.

Gallagher, J. E.

Hanson, S. G.

Herriot, D. R.

Maksimyak, A. P.

Maksimyak, P. P.

Pantzer, D.

Player, M. A.

C. T. Farrell and M. A. Player, "Phase step measurement and variable step algorithms in phase-shifting interferometry," Meas. Sci. Technol. 3, 953-958 (1992).
[CrossRef]

Politch, J.

Polyanskii,, P. V.

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, "Referenceless resting of vortex optical beams," Opt. Appl. 33, 695-708 (2003).

Rosenfeld, D. P.

Shindo, Y

Spraque, R. A.

White, A. D.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

C. T. Farrell and M. A. Player, "Phase step measurement and variable step algorithms in phase-shifting interferometry," Meas. Sci. Technol. 3, 953-958 (1992).
[CrossRef]

Opt. Appl. (1)

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, "Referenceless resting of vortex optical beams," Opt. Appl. 33, 695-708 (2003).

Opt. Express (1)

Opt. Spectrosc. (1)

O. V. Angelsky and P. P. Maksimyak, "Transformation of the longitudinal correlation function of a field propagating in a scattering medium," Opt. Spectrosc. 60, 331-336 (1986).

Other (7)

A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving of Incorrect Problems, (Nauka, Moscow, 1986, in Russian).

A. V. Goncharovsky, A. M. Cherepashchuk, and A. G. Yagola, Incorrect Problems in Astrophysics, (Nauka, Moscow, 1985 in Russian).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, (Pergamon Press, London 1963).

R. S. Sirohi ed., Speckle Metrology, (Marcel Deker, New York, 1993).

O. V Angelsky., S. G. Hanson and P. P. Maksimyak, The Use of Optical-Correlation Techniques for Characterizing Scattering Object and Media - Bellingham, (SPIE Press PM71, Bellingham, 1999).

O. V. Angelsky, and P. P. Maksimyak, "Optical correlation diagnostics of surface roughness" in: Handbook of Coherent Domain Optical Methods. Biomedical Diagnostics, Environmental and Material Science, V. V. Tuchin, ed., (Kluwer Academic Publishers,Boston, 2004), Vol. 1, 43-92 (2004).

J. M. Bennett and L. Mattson, Introduction to Surface Roughness and Scattering, (Optical Society of America, Washington, D.C, 1999).

Supplementary Material (2)

» Media 1: AVI (4002 KB)     
» Media 2: AVI (7090 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Experimental arrangement: S - temporal source; L - solid-state laser; O1, O2, O3 and O4 - objectives; T - telescope; M1- moving mirror, M2 - mirror; D - diaphragm; BS - beamsplitter; MO1 and MO2 - micro-objectives; O - surface of interest; PC - piezo-ceramics.

Fig. 2.
Fig. 2.

Monochromatic image (460 μm × 380 μm) of a rough surface obtained in the arrangement of the Michelson interferometer.

Fig. 3.
Fig. 3.

Color intensity distributions of the resulting interference field (460 μm × 380 μm) for various optical path differences between the legs of interferometer.

Fig. 4.
Fig. 4.

Typical mutual longitudinal intensity covariance function (MLICF) of the monochromatic interference image of a rough surface and the polychromatic interference images for various optical path differences between the legs of interferometer (n -number of frame).

Fig. 5.
Fig. 5.

The longitudinal coherence function of the object field reconstructed from the MLICF shown in Fig. 4.

Fig. 6.
Fig. 6.

Evolution of the coherent monochromatic interference field (460 μm × 380 μm) for changed optical path difference between the reference and the object beams within one wavelength. (AVI movie, 4 MB)

Fig. 7.
Fig. 7.

Evolution of a white-light interference field (460 μm × 380 μm) for changed optical path difference between the reference and the object beams spanning the heights of the rough surface inhomogeneities. (AVI movie, 7 MB)

Fig. 8.
Fig. 8.

Experimentally determined longitudinal coherence function of the probing beam.

Fig. 9.
Fig. 9.

Height distribution function derived from the measured delays for the partial signals.

Fig. 10.
Fig. 10.

The reconstructed relief of a rough surface.

Equations (8)

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

Γ ( Δ z ) = 0 z max Γ 0 ( z Δ z ) f ( z ) d z ,
I m ( x , y , z ) = I 0 m + I s m ( x , y ) + 2 I 0 m I s m ( x , y ) cos { 4 π λ [ h ( x , y ) z ] } ,
I ( x , y , z ) = I 0 + I s ( x , y ) + 2 I 0 I s ( x , y ) Γ ( z z 0 ) cos { 4 π λ [ h ( x , y ) z ] } ,
B ( z ) = I m ( x , y , z 0 ) I ( x , y , z ) .
Γ = I max I min I max + I min .
B ( n ) = i = 1 N j = 1 M [ I ij m * I ij ( n ) ] ( i = 1 N j = 1 M I ij m ) ( i = 1 N j = 1 M I ij ( n ) ) ,
Γ 0 ( Δ z ) = exp [ ( Δ z 2 α ) 2 ] ,
Γ 0 ( Δ z ) = 0 z max exp [ ( Δ z 2 α ) 2 ] f ( z ) d z .

Metrics