| Using the extended Huygens Fresnel principle, the effect of the atmospheric turbulence on the statistical properties of a polychromatic speckle field, generated by a diffuse target, is studied in detail. The results, substantiated by experimental data, indicate that the atmospheric perturbation increases the variance of the received intensity substantially and is sensitive to the wavelength, beam size and beam geometry. The results for the covariance of the received intensity, normalized to the variance, indicate that, at low turbulence levels, reduction in vacuum speckle contrast ratio (VSCR) also reduces the normalized covariance but, with further increase in the turbulence level, reduction in the vacuum speckle contrast ratio increases the normalized covariance. Also it is found that for small detector spacings, the normalized covariance remains approximately constant even with substantial increase in the turbulence level. By resolving the time delayed covariance of the received intensity (TDC), into coherent and incoherent terms, it is shown that for large time delays, the time delayed covariance is determined by the incoherent fluctuations and for poor vacuum speckle contrast ratio, the time delayed covariance is not very sensitive to the wind velocity. Finally it is shown that due to the atmospheric perturbation the the probability density function of the received intensity changes from an M-distribution of a sum of exponential distributions in vacuum to a K-distribution or a weighted sum of K-distributions in the presence of the turbulent atmosphere. |
