Skip to main content

Statistical modeling of the point spread function in the spherical atmosphere and a criterion for detecting image isoplanarity zones


An algorithm is proposed to simulate a point spread function by the Monte Carlo method in order to represent external channel formation in the spherical model system of the “atmosphere-earth surface.” A new way of defining isoplanarity zones of optically homogeneous extended objects is described. We demonstrate that image restoration with a specified error for these objects when they are observed on the earth’s surface from space by an ideal optical system can determine a definite point spread function set.

This is a preview of subscription content, access via your institution.


  1. E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium (Nauka Tekhnika, Minsk, 1985; Springer, Heidelberg, 1991).

    Google Scholar 

  2. A. Papulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968; Mir, Moscow, 1971).

    Google Scholar 

  3. V. E. Zuev, V. V. Belov, and V. V. Veretennikov, Linear Systems Theory in Optics of Disperse Media (Spektr Inst. Opt. Atmosf. SO RAN, Tomsk, 1997) [in Russian].

    Google Scholar 

  4. V. V. Belov, B. D. Borisov, and I. Yu. Makushkina, “Some Regularities of Formation of Side Illumination Noise in Vision System,” Opt. Atmosf. 1(2), 18–24 (1988).

    Google Scholar 

  5. V. V. Belov, G. M. Krekov, and I. Yu. Makushkina, “Isoplanarity in Vision Systems,” Opt. Atmosf. 2, 1011–1018 (1989).

    Google Scholar 

  6. V. V. Belov, “Optical Transfer Properties of External Channels and Image Isoplanarity in Vision Systems,” Opt. Atmosf. Okeana 22, 1101–1107 (2009).

    Google Scholar 

  7. V. V. Belov and M. V. Tarasenkov, “Statistical Modeling of the Intensity of Light Fluxes Reflected by the Earth’s Spherical Surface,” Opt. Atmosf. Okeana 23, 14–20 (2010) [Atmosph. Ocean Opt.23, 197 (2010)].

    Article  Google Scholar 

  8. F. X. Kneizys, E. P. Shettle, G. P. Anderson, L. W. Abreu, J. H. Chetwynd, J. E. A. Selby, S. A. Clough, and W. O. Gallery, User Guide to LOWTRAN-7, ARGL-TR-86-0177, ERP 1010, Hansom AFB, MA 01731.

  9. G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte-Carlo Method in Atmospheric Optics (Nauka, Novosibirsk, 1976) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

Original Russian Text © V.V. Belov, M.V. Tarasenkov, 2010, published in Optica Atmosfery i Okeana.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Belov, V.V., Tarasenkov, M.V. Statistical modeling of the point spread function in the spherical atmosphere and a criterion for detecting image isoplanarity zones. Atmos Ocean Opt 23, 441–447 (2010).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI:


  • Point Spread Function
  • Image Restoration
  • Spherical Geometry
  • Radiation Transfer Equation
  • Single Scattering Approximation