General formulation for light propagation and imaging through atmospheric turbulence and naturally derived turbulence measurement procedures

Abstract

Atmospheric turbulence is described in terms of a general formulation that does not assume any particular form for the turbulence structure function. The formulation allows for the possibility of Kolmogorov turbulence without bestowing any special favor to this type of turbulence. Expressions are obtained for the two-point correlation function of the complex amplitudes (i.e., Atmospheric MTF) and for the more general function, the two-point two-wavelength correlation function of the complex amplitudes. A cardinal set of measurement procedures naturally derives from these two functions that enables both the integrated strength and the average structure function of the turbulence in a propagation path to be characterized. Kolmogorov and non-Kolmogorov types of turbulence structure are measured impartially by these procedures. The measurement procedures are based on certain key properties of point-object images, properties that carry the essential information about the integrated effects of all mechanisms in the propagation path that affect the wavefronts. These mechanisms can include, but are not limited to, atmospheric turbulence, boundary layer turbulence, telescope aberrations, and the (corrective) effects of adaptive optics. The measurement procedures enable full end-to-end characterization of the entire propagation path between object and image. They take account of amplitude scintillation as well as phase variation in the wavefronts. Once the entire path has been characterized, certain wavelengths can be identified that lead to optimum image resolution. For HEL systems, optimum wavelengths lead to maximum irradiance at the target and maximum target lethality range. Large performance improvements are attained by use of optimum rather than non-optimum wavelengths.