Analytic results for the partially coherent edge response of a perfect imaging system
Joseph J.M. Braat (TU Delft - ImPhys/Optics)
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Abstract
The edge response of a perfect optical system with partially coherent object illumination is characterized, among other things, by its central intensity in the image plane, that is, the intensity in the image plane at the position of an infinitely sharp knife-edge transition as predicted by the geometrical optics approximation. Other important parameters are the central steepness and the typical oscillations of the edge response in the image plane. I produce a new analytic expression for the value of the central intensity in a one-dimensional optical system as a function of the degree of coherence in the illuminated object. This new result is then successfully implemented by me in the more common two-dimensional imaging systems. To obtain the full intensity profile of the edge response, I switch to Fourier imaging analysis by periodic continuation of the knife-edge object. A comparison is made between the exact value of the central intensity obtained in the spatial domain and the corresponding (approximated) values resulting from the Fourier domain analysis. The edge response of an optical imaging system plays an important role in optical precision metrology. In my analysis, I evaluate the systematic errors (aliasing) that are associated with intensity calculations in the Fourier domain as a function of the frequency sampling density.
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