A source having a deterministic beam-wave amplitude distribution with a spatially random phase variation is assumed. The source distibution simulates laser reflectance from (or transmission through) a rough surface with arbitrary height deviation and a correlation yielding a Gaussian intensity covariance. The intensity covariance resulting from the assumed source propagating through atmospheric turbulence is calculated using a formalism developed previously. The resultant eight-fold intergral is evaluated in closed form retaining all phase, log-amplitude, and cross phase-log-amplitude structure functions by employing the quadratic approximation for the complex phase. Limiting case conditions of (i) a field from a partially coherent source propagating in vacuo (speckle) and (ii) a coherent beam-wave propagating through turbulence are examined. Speckle contrast calculations replicate published data using less restrictive assumptions than formerly employed, while turbulent atmosphere beam-wave calculations appear more physically reasonable than results of Ishimaru. General-case calculations show that the normalized intensity variance (contrast or fluctuation parameter) increases less rapidly with increasing turbulence as the phase variance of the source increases. A saturation phenomenon is observed at high turbulence levels as the coherence decreases, The inability to sustain high spatial frequency speckle in turbulence is reflected in the calculated intensity covariance function.
© 1979 Optical Society of AmericaPDF Article