Imaging of coherently illuminated objects through turbulence: plane-wave illumination

The average spectrum and energy spectrum of the short-exposure image intensity are evaluated for the case of an object illuminated by a monochromatic plane wave and viewed through atmospheric turbulence, assuming a complex Gaussian model for the turbulence. In general, the average image energy spectrum contains diffraction-limited information about the complex amplitude reflectivity of the object, but, unlike in the case of incoherent imaging, it is generally not possible to extract this information in a straightforward manner. This is illustrated by a computer simulation example of imaging a double-point object in incoherent and coherent illumination. When the object is optically rough and it is physically possible to average over an object ensemble (e.g., the object rotates slightly), then the image energy spectrum is more simply related to the object energy spectrum. The possibilities for diffraction-limited object reconstruction are discussed, and it is pointed out that the image bispectrum does not provide diffraction-limited imaging, in contrast to the case of incoherent imaging. 1