Aberrated point-spread function for Gauss-shaped wavefront errors

The shape of the intensity point-spread function of an incoherent imaging system in the case of a Gauss-shaped wavefront error is found to depend significantly on the error position inside the exit pupil. The imaging performance is specified via the encircled energy within the Airy disc as an integral measure and via the Strehl ratio evaluated according to Marechal as a local measure. Both measures are compared to each other. The results are generalized to a finite number of sparsely distributed GauB-shaped wavefront errors in the limit ofan optically smooth surface. The influence of a single Gauss-shaped wavefront error on the optical transfer function is shown as an example. As an additional result the derivations allow to discuss qualitatively the shape of the aberrated point-spread function for weak aberrations of any shape.