The irradiance of a partially coherent light propagated under the influence of multiple random effects is shown to be the convolution of the irradiance propagated in a vacuum with the system’s point spread function representing the random effects. This is true regardless of whether the propagation is far-field or not. We also show that the far-field irradiance of any laser system, regardless of complexity, can be expressed in terms of three basic parameters; laser power, field area, and a pupil factor. A general analytical formula for the far-field irradiance distribution for partially coherent laser sources of any complexity is derived. The formula includes multiple random effects including strong turbulence, random beam jitter, partial coherence, in addition to laser system pupil effects. An efficient matrix based numerical solution is also developed to verify the accuracy of the formula. Applications to the propagation of clipped Gaussian or flat-top beams with an obscuration, both as a single beam or an array of beams, are shown to give accurate results over the whole range of weak to strong turbulence as compared to numerical modeling.
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