Performance of the Optimum Apodizers in Partially Coherent Light

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Abstract
The optimum apodizers have been designed with the tacit assumption that the point-spread functions of the optical instruments that could use them are due to spatially coherent waves. In practice, there is considerable deviation from this ideal condition. In the present paper analytical expressions are given which can be used for a comprehensive study of the performance of the optimum apodizers in partially coherent illumination. The loss of coherence is assumed to be due to atmospheric turbulence. Numerical results concerning the dependence of the encircled energy, the central intensity, the expected resolution etc., for two chosen apodizers show that the performance, in partially coherent illumination, of the optimum apodizers may be contrary to their expected performance. It is therefore very important to take into account the actual state of coherence of the aperture illumination in the designing of apodizers that are to be used under non-ideal conditions.