The pupil function of an optical system is taken to have correlated random amplitudes and phases arising from an external cause, such as optical propagation through turbulence. For the general case, where the restriction of isotropy need not apply, the unnormalized random optical transfer function is derived and its first two moments evaluated. Normalization issues are also treated. It is shown that when the cross correlation of random amplitude and random phase is not an even function, a phase shift term is induced. The impact of this shift is discussed in terms of the image of an edge. While isotropy eliminates dependence on the cross correlation of amplitude and phase for the first moment of the transfer function, it does not similarly affect all second-moment behavior.
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