Synthetic aperture ladar resolution through turbulence

The theory is developed for the resolution of a coherent optical synthetic aperture imaging system viewing an object through turbulence. The turbulence induces wave distortions that in turn induce errors in the phase history data collected over the synthetic aperture. The image effects of the phase history errors are space-variant and include broadening of the point spread function as well as geometric distortions. The effect of wave distortions on the intensity image impulse response is related to the usual wave structure function (sum of the log-amplitude and phase structure functions) at the synthetic aperture center frequency. The turbulence-induced limit on resolution is determined for synthetic apertures or any size, without restriction on the size of the real sampling aperture. The results have commonalties to the well-known limit on the resolution of incoherent real aperture imaging systems. A relationship is derived for the resolution of an optical synthetic aperture image forming system relative to the resolution of a passive optical real aperture image forming system viewing through the same inhomogeneous medium.