Test images of a sector star versus radial and axial merit functions

The radial and axial point spread function (PSF) and the 3D modulation transfer function (MTF) were calculated to demonstrate the influence of phase only filters in classical optical imaging systems. The 3D line spread function (LSF) makes it possible to discuss the influence of the degree of coherence in the optical imaging system with the phase only filter as well. First, the phase only filter under discussion was divided in five equally area annuli. The phase variations are either linearly increasing or decreasing with the annulus number or alternating between 0 and π. Second we have used a filter that consists on one phase annulus with a phase shift of π in different positions over the pupil. Numerical and experimental results are shown in this paper. A spatial light modulator (SLM) was used to obtain experimentally the influence of the different phase only filters on the image of a sector star. The merit functions for filters with a phase shift of π in one annulus are also studied. These filters produce a wide variety of responses in dependence of the position of the phase shifting annulus. By studying the merit functions, a clear prediction of the imaging behaviour of an optical system is possible as well. The conclusion of our work has been that it is necessary to study the influence of the filter on the different merit functions in order to design an optimum filter for a given application.

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