Symmetries and periodicities of partially coherent fields

The symmetries of wave fields are of practical interest in holography, phase conjugation and for automatic focusing. Periodicities of wavefields find practical applications in self-imaging, in interferometers based on the Talbot and on the Lau effect and in Fourier spectrometry. The authors show in this paper that if the operator form for the solution of the Helmholtz equation is employed, it is possible to discuss in a simple fashion both the symmetry and the periodicity of the propagating field under coherent and under partially coherent illumination