Abstract
A theory of partially coherent imaging is presented. In this theory, a singular matrix is introduced in a spatial frequency domain. The matrix can be obtained by stacking pupil functions that are shifted according to the illumination condition. Applying singular-value decomposition to the matrix generates eigenvalues and eigenfunctions. Using eigenvalues and eigenfunctions, the aerial image can be computed without the transmission cross coefficient (TCC). A notable feature of the matrix is that the relationship between the matrix and the TCC matrix T is , where † represents the Hermitian conjugate. This suggests that the matrix can be regarded as a fundamental operator in partially coherent imaging.
© 2008 Optical Society of America
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