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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 25, Iss. 12 — Dec. 1, 2008
  • pp: 3111–3119

Computation theory of partially coherent imaging by stacked pupil shift matrix

Kenji Yamazoe  »View Author Affiliations

JOSA A, Vol. 25, Issue 12, pp. 3111-3119 (2008)

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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 P , where † represents the Hermitian conjugate. This suggests that the matrix P can be regarded as a fundamental operator in partially coherent imaging.

© 2008 Optical Society of America

OCIS Codes
(110.2990) Imaging systems : Image formation theory
(110.4980) Imaging systems : Partial coherence in imaging
(110.5220) Imaging systems : Photolithography

ToC Category:
Imaging Systems

Original Manuscript: July 29, 2008
Manuscript Accepted: September 28, 2008
Published: November 26, 2008

Kenji Yamazoe, "Computation theory of partially coherent imaging by stacked pupil shift matrix," J. Opt. Soc. Am. A 25, 3111-3119 (2008)

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