Full text of article: Russian language.

Abstract:
Optical schemes for displacement speckle-interferometers in which the maximal values of amplitude of photo-electric signal are achieved by the matching of interfering wave fields are considered. The analysis of requirements for determination of a relative position of interferometer optical elements, reference and testing surfaces for calculation of speckle-interferometers optical schemes is carried out in view of parameters of Gaussian laser beam. Expressions for estimation of expected values of average, most probable value and dispersion of photo-electric signal in speckle-interferometers with matching interfering fields are obtained at the smooth and speckle-modulated reference waves.

Key words:
speckle fields, speckle interferometer of displacements, Gaussian beam, wave fronts matching, statistical parameters of interferometer signal.

References:

1. Laser speckle and related phenomena. Topics in Applied Physics / Ed. J.C.Dainty. V.9. – Berlin: Springer-Verlag, 1975. – 286 p.
2. Françon, M. La granularité laser (spekle) et ses application en optique / М. Françon – Masson, Paris, 1978.
3. Speckle Metrology (selected papers) / Ed. R.Sirohi. SPIE Milestone Series. 1991. – V. MS35. – 668 p.
4. Goodman, J.W. Speckle Phenomena in Optics: Theory and Applications / J.W. Goodman – Roberts & Company, Publishers, Englewood, CO, 2006. – 387 p.
5. Gurov, I.P., Dzhabiev, A.N. Interferometric systems for distance testing of objects / I.P. Gurov, A.N. Dzhabiev – St. Petersburg: StPSUITMO, 2000. – 190 p. – (in Russian).
6. Ryabukho, V.P., Klimenko, I.S., Golubentseva, L.I. Interference of laser speckle fields // V.P. Ryabukho, I.S. Klimenko, L.I.Golubentseva // Proc. SPIE. 1994. – Vol. 2340. – P. 513-522.
7. Aranchuk, V.M., Zatsepin, N.N. Dependence between signal amplitude of Doppler speckle interferometer and ratio of speckle size and receiver aperture size / V.M. Aranchuk, N.N. Zatsepin // Zhurnal Tekhnicheskoi Fiziki. 1988. – Vol. 58. – No. 10. – P. 2060-2062. – (in Russian).
8. Aranchuk, V.M. Signal/noise ratio of Doppler speckle-interferometer for diffuse objects vibration measurement / V.M. Aranchuk // Optics within Life Sciences. – Amsterdam: Elsevier, 1994. – Vol. 3. Optical methods in biomedical and environmental sciences. – P. 361-364.
9. Veselov, L.M., Popov I.A. Measurement of frequency and amplitude of object vibrations by method of the dynamic speckle-interferometry / L.M. Veselov, I.A. Popov // Zhurnal Tekhnicheskoi Fiziki. – 1990. – Vol. 60. – No. 10. – P. 182-184. – (in Russian).
10. Ryabukho, V.P., Ul'yanov, S.S. Amplitude-and-phase modulation of vibration speckle-interferometer signal / V.P. Ryabukho, S.S. Ul'yanov // Pis’ma v Zhurnal Tekhnicheskoi Fiziki. – 1991. – Vol. 17. – No. 13. – P. 11-16. – (in Russian).
11. Ul'yanov, S.S., Ryabukho, V.P., Tuchin, V.V. Speckle interferometry for biotissue vibration measurement / S.S. Ul'yanov, V.P. Ryabukho, V.V. Tuchin // Optical Engineering. – 1994. – Vol. 33. – No. 3. – P. 908-914.
12. Presnyakov, Yu.P., Schepinov, V.P. Using of speckle effect for the rough surface oscillations analysis / Yu.P. Presnyakov, V.P. Schepinov // Zhurnal Tekhnicheskoi Fiziki. – 1997. – Vol. 67. – No. 8. – P. 71-75. – (in Russian).
13. Zhuravlev, O.A. Development of the automated method of research of vibrating characteristics of power installations / O.A. Zhuravlev, S.Yu. Komarov, K.N. Popov, A.B. Prokof’ev // Computer Optics. – 2001. – Nо. 21. – P. 143-149 (in Russian).
14. Osipov, M.N., Popov M.A. Measurement of small dynamic displacement by Michelson interferometer with spherical wave fronts / М.N. Osipov, M.A. Popov // Computer optics. – 2007. – Т. 31. – No. 4. – P. 55-57 (in Russian).
15. Gorbatenko, B.B. Laser speckle-interferometer for the measurement of the temperature changes of the interelectrode distances of vacuum microwave devices / B.B. Gorbatenko, I.S. Klimenko, V.P. Ryabukho, О.V. Serova, L.А. Surmenko // Electronnaya tekhika. Ser. Electronika SVCh. – 1987. – No. 7(401). – P. 53-55. – (in Russian).
16. Vikram, Ch. Real-time longitudinal displacement analysis of rough surfaces by observing fringes with in objective laser speckles / Ch. Vikram // Optik. –1983. – Vol. 63. – No. 2. – P.171-175.
17. Vladimirov, A.P. Using speckle optics for studying the localization and determination of non-reversible deformations / A.P. Vladimirov, A.A. Gorohov, E.N. Galkin, A.L. Lisin. // Proc. SPIE. – 2000. – Vol. 4002. – P. 128-134.
18. Vladimirov, A.P., Mikushin V.I. Interferometric determination of vector components of relative displacements: theory and experiment / A.P. Vladimirov, V.I. Mikushin // Proc. SPIE. – 1999. – Vol. 3726. – P. 38-43.
19. Norgia, M., Donati, S., D’Alessandro, D. Interferometric measurements of displacement on a diffusing target by a speckle tracking technique / M. Norgia, S. Donati, D. D’Alessandro // IEEE Journal of quantum electronics. – 2001. – Vol. 37. – No. 6. – P. 800-806.
20. Zotov, N.M. Using of laser Doppler anemometry for the displacements research / N.M. Zotov, А.S. Ponomarev, А.М. Chmutin, V.А. Chuyko // Izvestiya vuzov. Priborostroenie. – 1987. – Vol. 30. – No 7. – P. 69-72. – (in Russian).
21. Ryabukho V.P., Ul'yanov S.S. Spectral characteristics of dynamic speckle-fields interference signal for surfaces motion measurements / V.P. Ryabukho, S.S. Ul'yanov // Measurement. – 1992. – Vol. 10. – No. 1. – P. 39-42.
22. Dubnischev, Yu.N., Rinkevichus, B.S. Methods of laser Doppler anemometry / Yu.N. Dubnischev, B.S. Rinkevichus – М.: Nauka, 1982. – 303 p. – (in Russian).
23. Rinkevichus, B.S. Laser diagnostics of flows / B.S. Rinkevichus – М.: МEI, 1990. –288 p. – (in Russian).
24. Ul'yanov, S.S. Speckle-interferometrical method in application to the blood and lymph flow monitoring in microvessels / S.S. Ul'yanov, V.V. Tuchin, A.A. Bednov, et al. – Laser Med. Sci. – 1996. – No. 11. – P. 97-107.
25. Dubnischev, Yu.N. Laser Doppler measurements technologies / Yu.N. Dubnischev – Novosibirsk: publ. NSTU, 2003. – 414 p. – (in Russian).
26. Abramov, A.J. Research of processes of mutual diffusion in thin transparent media by  methods of laser interferometry / A.J. Abramov, O.V. Dikov, V.P. Rjabuho, A.B. Shipovskaja // Computer optics. – 2008. – Vol. 32. – No. 3. – P. 253-264 (in Russian).
27. Ryabukho V.P. Interference of partially developed speckle fields / V.P. Ryabukho // Optics and spectroscopy. – 1995. – Vol. 78. – No. 6. – P. 878-884.
28. Ryabukho V.P. Interference of speckle fields in the diffraction zone of focused spatially modulated laser beam by a random phase screen / V.P. Ryabukho // Optics and spectroscopy. – 2003. – Vol. 94. – No. 3. – P.453-460.
29. Lyakin, D.V. Laser scanning interference system for determination of bedded microstructures thickness / D.V. Lyakin, М.I. Lobachev, А.F. Rezchikov, V.P. Ryabukho, I.F. Minenkova // Mekatronika, avtomatizatsia, upravlenie. – 2003. – No. 4. – P. 10-14. – (in Russian).
30. Lyakin, D.V. Laser interferometer with the sharply focused beam in system of three connected interferometers / D.V. Lyakin, V.V. Lychagov, V.P. Ryabukho, М.I. Lobachev // Computer Optics. – 2006. – No. 30. – P.53-61. – (in Russian).
31. Marcuse, D. Light transmission optics / D. Marcuse – New York, 1972.
32. Goncharenko, А.М. Gaussian beams / А.М. Goncharenko – Minsk: Nauka i tekhnika, 1977. – 144 p. – (in Russian).
33. Goodman, J.W. Statistical properties of laser speckle patterns / J.W. Goodman // Laser speckle and related phenomena. Topics in Applied Physics /Ed. J.C. Dainty – Berlin: Springer-Verlag, 1975. – Р. 9-77.
34. Koronkevich, V.P., Khanov, V.А. Modern laser interferometers / V.P. Koronkevich, V.А. Khanov – Novosibirsk: Nauka, 1985. – 181 p. – (in Russian).
35. Keem, T. Simple real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system / T. Keem, S. Gonda, I. Misumi, Q. Huang, T. Kurosawa // Applied Optics. – 2005. – Vol. 44. – No. 17. – P. 3492-3498.
36. Sun, Q., Wabinski, W., Bruns, T. Investigation of primary vibration calibration at high frequencies using the homodyne quadrature sine-approximation method: problems and solutions / Q. Sun, W. Wabinski, T. Bruns // Meas. Sci. Technol. – 2006. – No. 17. – P. 2197-2205.
37. Gorbatenko, B.B. Interference method of measurement of relative displacements of diffusing reflecting surfaces and equipment for its realization / B.B. Gorbatenko, I.S. Klimenko, V.P. Ryabukho, L.А. Surmenko // Author's certificate № 1374042 (SSSR). – 1988. – Bul. № 6.
38. Veselov, L.М., Popov, I.А. Informational characteristics of time-dependent in time speckle pattern / L.М. Veselov, I.А. Popov // Optika i spektroskopiya. – 1993. – Vol. 74. – No. 6. – P. 1155-1158. – (in Russian).
39. Goodman, J.W. Statistical optics / J.W. Goodman – John Wiley & Sons, New York, 1985
40. Rytov, S.М., Kravtsov, Yu.А., Тatarskii, B.I. Principles of Statistical Radiophysics. Vol. 2. / Ed. S.М. Rytov – М.: Nauka, 1978. – 464 p. – (in Russian). (S.М. Rytov, Yu.А. Kravtsov, B.I. Тatarskii. Principles of Statistical Radiophysics. Vol. I-IV / Springer-Verlag, Berlin. 1987).
41. Tikhonov, V.I. Statistical Radiophysics / V.I. Tikhonov – М.: Radio i cvyaz, 1982. – 624 p. – (in Russian).
42. Gonorovskii, I.S. Radio engineering circuits and signals / I.S. Gonorovskii – М.: Sov. Radio, 1977. – 608 p. – (in Russian).
43. Angelsky, O.V., Maksimyak, P.P. Optical correlation diagnostics of surface roughness / O.V. Angelsky, P.P. Maksimyak // Handbook of Coherent Domain Optical Methods. Biomedical Diagnostics, Environmental and Material Science / Ed. by V.V. Tuchin – Kluwer Academic Publishers, Boston, 2004. – V.1. – P. 43-92.
44. Gradshteyn, I.S., Ryzhyk, I.М. Tables of integrals, sums, series and products / I.S. Gradshteyn, I.M. Ryzhyk – М.: Nauka, 1971. – 1100 p. – (in Russian).
45. Brodshteyn I.N., Semendyaev К.А. Mathematics handbook / I.N. Brodshteyn, К.А. Semendyaev – М.: Nauka, 1986. – 975 p. – (in Russian).

---

© 2009, ИСОИ РАН
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: ko@smr.ru ; тел: +7 (846) 332-56-22, факс: +7 (846 2) 332-56-20