Advertisement

Atmospheric and Oceanic Optics

, Volume 27, Issue 1, pp 75–87 | Cite as

Measurement technique of turbulence characteristics from jitter of astronomical images onboard an aircraft: Part 1. Main ergodic theorems

  • V. V. Nosov
  • V. P. Lukin
Optical Instrumentation

Abstract

Aspects of constructing statistical characteristics of random functions for discrete-continuous averaging that corresponds to the end-time response of a measuring device are investigated. This averaging is usually implemented in practice, and any discrete sequence of empirical values of a random function is partially averaged over some argument range. The rate of convergence of the variance of deviation of the time-average from the ensemble average (generalizations of the Taylor ergodic theorem) is estimated. These estimates provide the probability of convergence. It is shown that the rate of convergence depends on the integral scales of random function correlation. The scales are determined by the type of averaging; they differ for continuous, discrete, and discrete-continuous averaging. Relationships between the scales are found. An equation that connects the correlation functions of nonaveraged and partially averaged random processes is found. It is ascertained that the correlation function of a nonaveraged process can be satisfactorily retrieved from partially averaged data, even at very long ranges of the partial averaging.

Keywords

Correlation Function Random Process Random Function Ensemble Average Oceanic Optic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. I. Taylor, “Diffusion by continuous movements,” Proc. London Math. Soc. 20(2), 196–211 (1921).zbMATHGoogle Scholar
  2. 2.
    A. N. Kolmogorov, Basic Concepts of the Probability Theory (Nauka, Moscow, 1974) [in Russian].Google Scholar
  3. 3.
    Yu. V. Prokhorov and Yu. A. Rozanov, Probability Theory (Basic Concepts, Limiting Theorems, and Random Processes) (Nauka, Moscow, 1973), 2nd ed. [in Russian].Google Scholar
  4. 4.
    A. S. Monin and A. M. Yaglom, Statistical Hydromechanics (Nauka, Moscow, 1967), Vol. 2 [in Russian].Google Scholar
  5. 5.
    V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, 1967) [in Russian].Google Scholar
  6. 6.
    V. P. Lukin, E. V. Nosov, and B. V. Fortes, “The efficient outer scale of atmospheric turbulence,” Atmos. Ocean. Opt. 10(2), 100–106 (1997).Google Scholar
  7. 7.
    B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).CrossRefGoogle Scholar
  8. 8.
    V. P. Lukin, “Optical measurements of the outer scale of the atmospheric turbulence,” Atmos. Ocean. Opt. 5(4), 229–242 (1992).Google Scholar
  9. 9.
    V. P. Lukin, “Investigation of some pecularities in the structure of large-scale atmospheric turbulence,” Atmos. Ocean. Opt. 5(12), 834–840 (1992).Google Scholar
  10. 10.
    V. V. Nosov, O. N. Emaleev, V. P. Lukin, and E. V. Nosov, “Semiempirical hypotheses of turbulence theory in the anisotropic boundary layer,” Atmos. Ocean. Opt. 18(10), 756–772 (2005).Google Scholar
  11. 11.
    V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1976) [in Russian].Google Scholar
  12. 12.
    V. V. Nosov, V. P. Lukin, E. V. Nosov, N. N. Botygina, O. N. Emaleev, and A. V. Torgaev, “Influence of photo-detector response time on operation of monostatic and bistatic airborne meters of turbulence: Part I, Part II,” Proc. SPIE 6522, 65220Q, 65220R (2006).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • V. V. Nosov
    • 1
  • V. P. Lukin
    • 1
  1. 1.V.E. Zuev Institute of Atmospheric OpticsTomskRussia

Personalised recommendations