Estimating the optimal sampling rate using wavelet transform: an application to optical turbulence.

Sampling rate and frequency content determination for optical quantities related to light propagation through turbulence are paramount experimental topics. Some papers about estimating properties of the optical turbulence seem to use ad hoc assumptions to set the sampling frequency used; this chosen sampling rate is assumed good enough to perform a proper measurement. On the other hand, other authors estimate the optimal sampling rate via fast Fourier transform of data series associated to the experiment. When possible, with the help of analytical models, cut-off frequencies, or frequency content, can be determined; yet, these approaches require prior knowledge of the optical turbulence. The aim of this paper is to propose an alternative, practical, experimental method to estimate a proper sampling rate. By means of the discrete wavelet transform, this approach can prevent any loss of information and, at the same time, avoid oversampling. Moreover, it is independent of the statistical model imposed on the turbulence.

[1]  Lonnie H. Hudgins,et al.  Wavelet transforms and atmopsheric turbulence. , 1993, Physical review letters.

[2]  Colin Bradley,et al.  Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization. , 2006, Applied optics.

[3]  V. Lukin,et al.  Optical wave phase fluctuations. , 1981, Applied optics.

[4]  Edgar L. Andreas,et al.  Scintillometer Wind Measurements over Complex Terrain , 2000 .

[5]  Anna Consortini,et al.  Estimate method for outer scale of atmospheric turbulence , 2002 .

[6]  L R Bissonnette.  Atmospheric scintillation of optical and infrared waves: a laboratory simulation. , 1977, Applied optics.

[7]  Guy Potvin,et al.  Wind effects on scintillation decorrelation times , 2005 .

[8]  L. Andrews,et al.  Characterizing the propagation path in moderate to strong optical turbulence. , 2006, Applied optics.

[9]  H. Yura.  Physical model for strong optical-amplitude fluctuations in a turbulent medium , 1974 .

[10]  Steven F. Clifford,et al.  Temporal-Frequency Spectra for a Spherical Wave Propagating through Atmospheric Turbulence , 1971 .

[11]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[12]  N Ben-Yosef,et al.  Sample size influence on optical scintillation analysis. Analytical treatment of the higher-order irradiance moments. , 1988, Applied optics.

[13]  G. Tyler.  Bandwidth considerations for tracking through turbulence , 1994 .

[14]  Alejandra Figliola,et al.  Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function , 1998 .

[15]  Ronald L. Fante,et al.  Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence , 1974 .

[16]  David A Kozlowski,et al.  Low Earth orbit satellite-to-ground optical scintillation: comparison of experimental observations and theoretical predictions. , 2011, Optics letters.

[17]  Ivan Prochazka,et al.  Optical signal path delay fluctuations caused by atmospheric turbulence. , 2005, Optics letters.

[18]  J. Cisternas,et al.  Influence of turbulence strength on temporal correlation of scintillation. , 2011, Optics letters.

[19]  Darryl P. Greenwood,et al.  Bandwidth specification for adaptive optics systems , 1977 .