What we believe to be a new illumination scheme that achieves space invariance and permits analytical determination of the image intensity distribution is proposed for partially coherent imaging systems. No additional lenses are needed for phase correction in front of the object and no restriction on illumination coherence is required. Conditions on the axial placement of the condenser with respect to the source and the object are specifically derived in terms of the condenser focal length and the distance from the object to the objective lens. By attaining space invariance, this new illumination scheme permits the use of transfer functions without approximation on illumination coherence. In addition, this illumination method establishes an exact Fourier transform relationship between the illumination and source mutual intensities, and thus significantly simplifies the analysis. Comparison with Köhler illumination is also presented. This apparatus is especially favorable for x-ray microscopy where lenses in this spectral region typically have a low efficiency.
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