Imaging of Extended Polychromatic Sources and Generalized Transfer Functions

Abstract

The problem of imaging with partially coherent polychromatic illumination is solved in terms of the most general formulation of coherence theory due to Wolf. It is shown that for this problem the frequency domain analysis is still valid and depends for its applicability only on the linearity and stationarity of the system being studied. The appropriate transfer function is seen to be the product of the frequency dependent aperture distribution considered as a function of spatial frequency µ1 multiplying its complex conjugate evaluated at another frequency µ2. In earlier papers by the present author several theorems relating to the existence and propagation of partially coherent fields were obtained. In the present paper these theorems are used to deduce the limiting forms of the generalized transfer functions referred to above. In particular the form of the transfer function for coherent and incoherent radiation is obtained with no approximation on the spectral width of the radiation. Further it is shown that introducing the quasi-monochromatic approximation reduces the generalized transfer functions to the familiar forms found in the literature.