Computation theory of partially coherent imaging by stacked pupil shift matrix

A theory of partially coherent imaging is presented. In this theory, a singular matrix P is introduced in a spatial frequency domain. The matrix P can be obtained by stacking pupil functions that are shifted according to the illumination condition. Applying singular-value decomposition to the matrix P 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 P is that the relationship between the matrix P and the TCC matrix T is T=P(dagger)P, where dagger represents the Hermitian conjugate. This suggests that the matrix P can be regarded as a fundamental operator in partially coherent imaging.