Abstract

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

© 2008 Optical Society of America

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