Influence of anisotropic turbulence on the long-range imaging system
by the MTF model
Linyan Cui
⇑
, Bindang Xue
School of Astronautics, Beihang University, Beijing 100191, China
highlights
Effective anisotropic factor is introduced to the derived MTF model.
Finite turbulence inner and outer scales are included in the final derived MTF model.
Increased effective anisotropic factor decreases turbulence’s influence on the imaging system.
Increased finite turbulence outer scale produces more effects on the imaging system.
article info
Article history:
Received 23 May 2015
Available online 17 August 2015
Keywords:
Non-Kolmogorov atmospheric turbulence
Anisotropy
MTF
abstract
Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both
anisotropic and non-Kolmogorov properties. In this paper, new analytic expressions for the anisotropic
non-Kolmogorov turbulence modulation transfer function (MTF) based on Rytov approximation theory
have been derived for optical plane and spherical waves propagating through weak anisotropic
non-Kolmogorov atmospheric turbulence. Compared with the previously published results where the
turbulence inner and outer scales were set separately to zero and infinite for calculation convenience,
the concept of anisotropy at different turbulence cell scales and finite turbulence inner and outer scales
are introduced to study the MTF models. Also, deviations from the classic 11/3 spectral power law
behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations
between 3 and 4. To reduce the complexity and calculation time of the analytic results, the
asymptotic-fit expressions are also derived and they fit well with the closed-form ones. Calculations
are performed to analyze the anisotropic non-Kolmogorov turbulence’s influence on the long-range
imaging system.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
Atmospheric turbulence degrades the quality of long-range
imaging system and this can be described by the MTF. In recent
years, the long-exposure MTF has been derived with the
assumption that the atmospheric turbulence is isotropic non-
Kolmogorov type. And a series of atmospheric turbulence
refractive-index fluctuations spectral models, including the classic
non-Kolmogorov spectrum [1], the generalized von Karman spec-
trum [2], the generalized exponential spectrum [3] and the gener-
alized modified atmospheric spectrum [4], have been proposed and
applied to derive the atmospheric turbulence MTF for optical
waves propagating through isotropic non-Kolmogorov turbulence
with horizontal and slant paths [3,5,6].
However, experimental and theoretical results have shown that
the atmospheric turbulence can be anisotropic [7–20]. Grechko
and et al. [9] reported a strong anisotropy in the middle atmo-
sphere from experimental observations of star scintillation.
Biferale and et al. [10] detected the information about anisotropic
turbulence in the boundary layer by using two probes with two
different geometries (horizontally and vertically). Benlenky and
et al. [11,12] experimentally observed anisotropy of the statistics
of wavefront tilt. They observed a horizontal outer scale larger than
the vertical one and the horizontal tilt variance is consistently
greater than the vertical one. Also, evidence of anisotropy in the
stratosphere has been reported in [13], where the authors used a
power spectrum with two components: anisotropic and isotropic,
and the validity of the spectrum was verified by balloon-borne
experiments. Anisotropy is usually present at high altitude, above
the atmospheric boundary layer, which extends to about 2 km in
altitude and it is more evident for large turbulence cells or eddies
http://dx.doi.org/10.1016/j.infrared.2015.08.010
1350-4495/Ó 2015 Elsevier B.V. All rights reserved.
⇑
Corresponding author.
E-mail address: cuily@buaa.edu.cn (L. Cui).
Infrared Physics & Technology 72 (2015) 229–238
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Infrared Physics & Technology
journal homepage: www.elsevier.com/locate/infrared