(30) * << * >> * Russian * English * Content * All Issues

Most probable estimates of parameters of optical signals with allowance for shot and background noise
V.S. Sobolev1, Y.A. Poleshchuk

1Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk

 PDF, 157 kB


Full text of article: Russian language.

Based on the example of a Gaussian pulse, a likelihood equation is derived for optimal evaluation of the parameters of optical signals with allowance for shot and background noise. The Fisher information matrix and the Cramer-Rao boundaries were developed as characteristics of the quality of the estimates obtained. An algorithm for the numerical solution of the likelihood equation is proposed. By means of a model experiment, the possibility of its implementation is shown, and the quality parameters of the resulting estimates are determined.

Optical Signal, Shot Noise, Background Noise, Gaussian pulse, Fisher information matrix, Cramer-Rao boundaries..

Sobolev VS, Poleshchuk YA. Most Probable Estimates of Parameters of Optical Signals with Allowance for Shot and Background Noise. Computer Optics 2006; 30: 98-106.


  1. Shestov NS. Selection of optical signals on the background of random noise [In Russian]. Moscow: “Sovetskoe Radio”; 1967.
  2. Kuriksha AA. Quantum optics and optical location [In Russian]. Moscow: “Svyaz” Publisher; 1973.
  3. Sheremetyev AG. Statistical theory of laser communication [In Russian]. Moscow: “Svyaz” Publisher; 1971.
  4. Sheremetyev AG. Coherent fiber optic communication [In Russian]. Moscow: “Radio i Svyaz” Publisher; 1991.
  5. Malashin MS, Kalinskiy RP, Borisov YuB. Basics of designing laser radar systems [In Russian]. Moscow: “Vysshaya Shkola” Publisher; 1983.
  6. Trishenkov MA. Photo-receiving properties and CCD. Detection of weak optical signals [In Russian]. Moscow: “Radio i Svyaz” Publisher; 1992.
  7. Besson O, Galtier F. Estimating particles velocity from laser measurements: maximum likelihood and Cramer-Rao bounds. IEEE Trans Signal Process 1996; 44(12): 3056-3068. DOI: 10.1109/78.553479.
  8. Sobolev VS, Prokopenko MN. Maximum-likelihood estimates of the frequency and other parameters of signals of laser Doppler measuring systems operating in the one-particle-scattering mode. Quantum Electron 2000; 30(12): 1109-1114. DOI: 10.1070/QE2000v030n12ABEH001873.
  9. Sobolev VS, Feshenko AA. Accurate Cramer-Rao bounds for a laser Doppler anemometer. IEEE Trans Instrum Meas 2006; 55(2): 659-666. DOI: 10.1109/TIM.2006.870334.
  10. Levin BR. Theoretical foundations of statistical radio engineering [In Russian]. Moscow: “Sovetskoe Radio” Publisher; 1968.
  11. Sage AP, Melse JL. Estimation theory with applications to communication and control. New York: McGraw-Hill; 1971. ISBN: 978-0-07-054429-1.
  12. Minkoff J. Signal processing fundamentals and applications for communications and sensing systems. Boston, London: Artech House; 2002. ISBN: 978-1-58053-360-7.
  13. Glauber RJ. Optical coherence and photon statistics. In Book: De Witt C, Blandin A, Cohen-Tannoudji C, eds. Quantum optics and electronics. New York: Gordon and Breach; 1965: 63.
  14. Bykov VP. Laser electrodynamics. Moscow: “Fizmatlit” Publisher; 2006.
  15. Loudon R. The quantum theory of light. 3rd ed. Oxford: Oxford University Press; 2001. ISBN: 978-0-19-850176-3.
  16. Goodman JW. Statistical optics. New York, Chichester, Brisbane, Toronto, Singapore: John Wiley and Sons; 1985. ISBN: 978-0-471-01502-4.
  17. Drugov AA, Kuznetcov EM. Semiconductors 1976; 10(8): 1429.
  18. Drugov AA, Kuznetcov EM. Semiconductors 1977; 11(8): 1616.
  19. Vetohin SS, Gulakov NR, Pertsev AN, Reznikov VI. Single-electron photodetectors [In Russian]. Moscow: "Atomizdat" Publisher, 1979.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20