An extended, Rayleigh-Sommerfeld integral method is used to derive expressions for the mutual coherence function and radiation intensity derived from a planar, partially coherent source propagating through the atmosphere. The derived results reduce to previous results for (i) coherent radiation propagation in the atmosphere and (ii) the relations relating the far-field intensity angular distribution and the source coherence for a partially coherent source <i>in vacuo</i>. A mathematical description of the predicted results in terms of the vacuum distribution and scattering functions (related to the Fourier-transformed two-source mutual coherence function) is permitted by this development. Analytical results are calculated for a homogeneous atmosphere and a source coherence that simulates a laser-illuminated rough surface. The effective far-field range is determined by the source size, wavelength, and source coherence length. The phase of the calculated mutual coherence function is determined by the field-point separation for off-axial propagation directions. Numerical results for the amplitude and phase coherence lengths are calculated and illustrated as a function of the source size, source coherence length, propagation angle, range, and refractive-index structure constant.
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