Full text of article: Russian language.

Abstract:
Longitudinal coherence of optical field of an extended spatially noncoherent light source is considered depending on parameters of frequency and angular spectra of this field. The expressions for function and length of longitudinal coherence of an optical field are received depending on width frequency and width of angular spectra of the field. The competing influence of angular and frequency spectra of the field on its longitudinal coherence is discussed. The experimental researches with use scanning Michelson interferometer of longitudinal shift confirming the theoretical results are executed.

Key words:
optical coherence, length of coherence, coherence function, interference of waves, Michelson interferometer.

References:

1. Born, M. Principles of Optics / M. Born, E. Wolf; translate from english – Moscow: Nauka, 1973. – 720 p. – (in Russian). (M. Born and E. Wolf. Principles of Optics, 4st. ed. / Pergamon Press. Oxford, 1970)
2. Mandel, L. Optical Coherence and Quantum Optics / L. Mandel, E. Wolf; translate from english – Moscow: Nauka, Fizmatlit, 2000. – 896 p. – (in Russian). (L. Mandel and E. Wolf. Optical Coherence and Quantum Optics, 1st. ed. / Cambridge University Press. Cambridge, 1995)
3. Soroko, L.M. Holography and Coherent Optics / L.M. Soroko – Moscow: Nauka, 1971. – 616 p. – (in Russian). (L.M. Soroko. Holography and Coherent Optics / Plenum Press. New York, 1980)
4. Rytov, S.M. Principles of Statistical Radiophysics, Vol. 2 / S.M. Rytov, Yu.A. Kravtsov, V.I. Tatarskii – Moscow: Nauka, 1978. – 464 p. – (in Russian). (S.M. Rytov, Yu.A. Kravtsov, and V.I. Tatarskii. Principles of Statistical Radiophysics, vol. I-IV / Springer-Verlag. Berlin, 1987)
5. Akhmanov, S.A. Introduction to statistical radiophysics and optics / S.A. Akhmanov, Yu.E. D’yakov, A.S. Chirkin – Moscow: Nauka, 1981. – 640 p. – (in Russian).
6. Goodman, J.W. Statistical optics / J.W. Goodman; translate from english – Moscow: Mir, 1988. – 528 p. – (in Russian). (J.W. Goodman. Statistical optics / John Wiley & Sons. New York, 1985)
7. Zarubin, A.M. Three-dimensional generalization of Van Cittert-Zernike theorem to wave and particle scattering // Opt. Commun. – 1993. – Vol. 100 – P. 491-507.
8. Ryabukho, V.P. Interference of laser speckle fields / V.P. Ryabukho, I.S. Klimenko, L.I. Golubentseva // Proc. SPIE. – 1994. – Vol. 2340. – P. 513-522.
9. Rosen, J. Longitudinal partial coherence of optical radiation / J. Rosen, A. Yariv // Opt. Commun. – 1995. – Vol. 117. – P. 8-12.
10. Lokshin, G.R. Spatial periodicity in coherent and incoherent speckle patterns. / G.R Lokshin, A.V Uchenov, M.A Entin // J. Commun. Technol. El. – 2000. – Vol. 45, N 4. – P.384-393.
11. Ryabukho, V. Influence of longitudinal spatial coherence on signal of a scanning interferometer / V. Ryabukho, D. Lyakin, M. Lobachev // Opt. Lett. – 2004. – Vol. 29, N 7. – P.667-669.
12. Ryabukho, V.P. The effects of longitudinal spatial coherence of light in interference experiments / V.P. Ryabukho, D.V. Lyakin // Opt. and Spectr. – 2005. Vol. 98, N 2. – P. 273–283.
13. Ryabukho, V. Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra / V. Ryabukho, D. Lyakin, M. Lobachev // Opt. Lett. – 2005. – Vol. 30, N 3. – P.224-226.
14. Ryabukho, V.P. The Wiener - Khintchine theorem in the theory of spatial coherence in the courses of statistical optics and radiophysics / V.P. Ryabukho, D.V. Lyakin // Phys. in Higher Educ. – 2005. – Vol. 11, N 3. – P. 107-108. (in Russian)
15. Ryabukho, V.P. Longitudinal purely spatial coherence of a light field / V.P. Ryabukho, D.V. Lyakin, V.V. Lychagov // Opt. and Spectr. – 2006. – Vol. 100, N 5. – P. 724–733.
16. Abdulhalim, I. Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope // J. of Modern Optics. – 2001. – Vol. 48, N 2. – P.279-302.
17. Abdulhalim, I. Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy // J. Opt. A: Pure Appl. Opt. – 2006. Vol. 8. – P.952–958.
18. Rosen, J. Longitudinal spatial coherence applied for surface profilometry // J. Rosen, M. Takeda // Appl. Opt. 2000. Vol.39. No.23. P.4107-4111.
19. Wang, W. Sinthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications / W. Wang, H. Kozaki, J. Rosen, M. Takeda // Applied Optics, 2002. V.41. No.10. P.1962-1971.
20. Gokhler, M. Spatial coherence radar applied for tilted surface profilometry / M. Gokhler, D. Zhihui, J. Rosen, M. Takeda // Opt. Eng. 2003. V.42. N.3. P.830-836.
21. Gokhler, M. Synthesis of multiple peak spatial degree of coherence for imaging through absorbing media / M. Gokhler, J. Rosen // Applied Optics. 2004. V.44 . N.15 P.2921-2927.
22. Gokhler, M. General configuration for using the longitudinal spatial coherence effect / M. Gokhler, J. Rosen // Opt. Commun. 2005. V.252. - P.22-28.
23. Handbook of optical coherence tomography / B.E. Bouma. and G.J. Tearney, eds. // NY: Marcel Dekker Inc. 2002. 740 p.
24. Fercher, A.F. Optical coherence tomography - principles and applications / A.F. Fercher, W. Drexler, C.K. Hitzenberger, T. Lasser // Report Prog. Phys., 2003. N.66 P. 239-303.
25. Gurov, I.P. Optical coherent tomography: principles, problems and perspectives. // Problems of coherent and nonlinear optics. Editors I.P. Gurov and S.A. Kozlov, St. Petersburg: IPMO. 2004. P. 6-30.
26. Liu, H. Spatial longitudinal coherence length of a thermal source and its influence on lens less ghost imaging / H. Liu, S. Han // Opt. Lett. – 2008. – Vol. 33, N 8. – P.824-826.
27. Ferri, F. Longitudinal coherence in thermal ghost imaging / F. Ferri, D. Magatti, V.G. Sala, A. Gatti // Appl. Phys. Lett. – 2008. – Vol. 92, N 261109. – P.261109-1 - 261109-3.
28. Wolf, E. Invariance of the spectrum of light on propagation // Phys. Rev. Letters. – 1986. – Vol.56. – P. 1370-1372.
29. Wolf, E. Non-cosmological redshifts of spectral lines // Nature. – 1987. – Vol. 326. – P. 363-366.
30. D'yakov, Yu.E. Diffractive changes in the frequency spectrum of propagating radiation (the Wolf effect) // Quant. Electron. – 1993. – Vol. 23, N 11. – P. 931-938.
31. Tatarskii, V.I. An intuitive introduction to the Wolf effect // Pure Appl. Opt. – 1998. – Vol. 7, N 5. – P. 953-957.
32. Ryabukho, V.P. What type of coherence of the optical field is observed in the michelson interferometer / V.P. Ryabukho, D.V. Lyakin, V.V. Lychagov // Opt. and Spectr. – 2007. - Vol. 102, N 6. – P. 918–926.
33. Ryabukho, V.P. Laser interferometer with fine-focused beams to monitor the spatial position of an object / V.P. Ryabukho, V.L. Khomutov, D.V. Lyakin, K.V. Konstantinov // Tech. Phys. Lett. – 1998. – Vol. 24, N 2. – P. 132-134.
34. Vishnyakov, G.N. Tomographic microscopy of three-dimensional phase objects in spatially incoherent light / G.N. Vishnyakov, G.G. Levin, V.L. Minaev // Opt. and Spectr. – 2003. – Vol. 95, N 1. – P. 134–138.
35. Tychinskii, V.P. Coherent phase microscopy of intracellular processes. Physics – Uspekhi. 2001. V.171. N.6. P.649-662.
36. Tychinskii, V.P. Dynamic phase microscopy: is “dialog” with a cell possible? Physics – Uspekhi. 2007. V.177. N.5. P.535-552.

---

© 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