ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ryabukho V. P., Ljakin D. V., Lychagov V. V. Longitudinal coherence of optical field. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 5, pp. 30-42. DOI: 10.18500/0869-6632-2009-17-5-30-42

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 509)
Article type: 

Longitudinal coherence of optical field

Ryabukho Vladimir Petrovich, Saratov State University
Ljakin Dmitrij Vladimirovich, Federal State Budgetary Institute of Science Institute of Problems of Precise Mechanics and Control of the Russian Academy of Sciences
Lychagov Vladislav Valerevich, Saratov State University

Spatial coherence of an optical field in a direction of its propagation depending on parameters of frequency and angular spectra of the field is considered. The expressions for function and length of longitudinal coherence are derived depending on width of frequency and angular spectra. The competing influence of angular and frequency spectra of a field on its longitudinal coherence is discussed. The experimental study with use the Michelson interferometer of longitudinal shift confirming theoretical results are executed.

  1. Born M, Wolf E. Principles of optics. United Kingdom: Pergamon Press; 1973. 720 p.
  2. Mandel L, Wolf E. Optical coherence and quantum optics. Cambridge: Cambridge University Press; 1995. 896 p.
  3. Soroko LM. Basics of Holography and Coherent Optics. Moscow: Nauka; 1971. 616 p. (In Russian).
  4. Rytov SM, Kravtsov YuA, Tatar VI. Introduction to statistical radiophysics. V.2. Random fields. Moscow: Nauka; 1978. 464 p. (In Russian).
  5. Akhmanov SA, Dyakov YuE, Chirkin AS. Introduction to statistical radiophysics and optics. Moscow: Nauka; 1981. 640 p. (In Russian).
  6. Goodman JW. Statistical Optics. New-York: Wiley; 1988. 528 p.
  7. Zarubin AM. Three-dimensional generalization of Van Cittert–Zernike theorem to wave and particle scattering. Opt. Commun. 1993;100(5-6):491–507. DOI: 10.1016/0030-4018(93)90251-Y.
  8. Ryabukho VP, Klimenko IS, Golubentseva LI. Interference of laser speckle fields. Proc. SPIE. 1994;2340:513–522. DOI: 10.1117/12.195955.
  9. Rosen J, Yariv A. Longitudinal partial coherence of optical radiation. Opt. Commun. 1995;117(1-2):8–12. DOI: 10.1016/0030-4018(95)00086-N.
  10. Lokshin GR, Uchenov AV, Entin MA. Spatial periodicity in coherent, non-coherent and speckle fields. Journal of Communications Technology and Electronics. 2000;45(4):416–426.
  11. Abdulhalim I. Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope. J. Mod. Opt. 2001;48(2):279–302. DOI: 10.1080/09500340150203620.
  12. Ryabukho V. Lyakin D., Lobachev M. Influence of longitudinal spatial coherence on signal of a scanning interferometer. Opt. Lett. 2004;29(7):667–669. DOI: 10.1364/OL.29.000667.
  13. Ryabukho VP, Lyakin DV. The effects of longitudinal spatial coherence of light in interference experiments. Optics and Spectroscopy. 2005;98(2):273–283. DOI: 10.1134/1.1870071.
  14. Ryabukho V, Lyakin D, Lobachev M. Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra. Opt. Lett. 2005;30(3):224–226. DOI: 10.1364/ol.30.000224.
  15. Ryabukho VP, Lyakin DV, Lychagov VV. Longitudinal purely spatial coherence of a light field. Optics and Spectroscopy. 2006;100(5):724–733. DOI: 10.1134/S0030400X06050146.
  16. Abdulhalim I. Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy. J. Opt. A: Pure Appl. Opt. 2006;8(11):952–958. DOI: 10.1088/1464-4258/8/11/004.
  17. Ryabukho VP, Lyakin DV. The wiener - khintchine theorem in the theory of spatial coherence in the courses of statistical optics and radiophysics. Fizicheskoe obrazovanie v vuzah. 2005;11(3):107–118.
  18. Wolf E. Invariance of the spectrum of light on propagation. Phys. Rev. Lett. 1986;56(13):1370–1372. DOI: 10.1103/PhysRevLett.56.1370.
  19. D'yakov YuE. Diffractive changes in the frequency spectrum of propagating radiation (the Wolf effect). Quantum Electron. 1993;23(11):931–938.
  20. Ryabukho VP, Lyakin DV, Lychagov VV. What type of coherence of the optical field is observed in the Michelson interferometer. Optics and Spectroscopy. 2007;102(6):918–926. DOI: 10.1134/S0030400X07060197.
  21. Ryabukho VP, Khomutov VL, Lyakin DV, Konstantinov KV. Laser inter-ferometer with sharp-focused beams to control the spatial position of the object. Technical Physics Letters. 1998;24(4):19–24.
  22. Tychinskii VP. Coherent phase microscopy of intracellular processes. Phys. Usp. 2001;44(6):617–629. DOI: 10.3367/UFNr.0171.200106e.0649.
  23. Tychinskii VP. Dynamic phase microscopy: is а 'dialogue' with the cell possible?” Phys. Usp. 2007;50(5):513–528. DOI: 10.3367/UFNr.0177.200705c.0535.
  24. Vishnyakov GN, Levin GG, Minaev VL. Tomographic Microscopy of Three-Dimensional Phase Objects in Spatially Incoherent Light. Optics and Spectroscopy. 2003;95(1):134–138. DOI: 10.1134/1.1595228.
  25. Liu H, Han S. Spatial longitudinal coherence length of a thermal source and its influence on lensless ghost imaging. Opt Lett. 2008;33(8):824-826. DOI: 10.1364/ol.33.000824.
  26. Ferri F, Magatti D, Sala VG, Gatti A. Longitudinal coherence in thermal ghost imaging. Appl. Phys. Lett. 2008;92(26):261109-3. DOI: 10.1063/1.2945642.
Short text (in English):
(downloads: 84)