## Two matrix approaches for aerial image formation obtained by extending and modifying the transmission cross coefficients

JOSA A, Vol. 27, Issue 6, pp. 1311-1321 (2010)

http://dx.doi.org/10.1364/JOSAA.27.001311

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### Abstract

This paper physically compares two different matrix representations of partially coherent imaging with the introduction of matrices **E** and **Z**, containing the source, object, and pupil. The matrix **E** is obtained by extending the Hopkins transmission cross coefficient (TCC) approach such that the pupil function is shifted while the matrix **Z** is obtained by shifting the object spectrum. The aerial image *I* can be written as a convex quadratic form **T** is the TCC matrix and *N* is the number of the point sources for a given unpolarized illumination. Therefore, the matrix **Z** requires fewer than *N* eigenfunctions for a complete aerial image formation, while the matrix **E** or **T** always requires *N* eigenfunctions. More importantly, **Z** is physically more meaningful than with the matrix **E**. The matrix **Z** is decomposed as **B** is a singular matrix, suggesting that the matrix **B** as well as **Z** is a principal operator characterizing the degree of coherence of the partially coherent imaging.

© 2010 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

**History**

Original Manuscript: November 6, 2009

Revised Manuscript: March 12, 2010

Manuscript Accepted: April 6, 2010

Published: May 12, 2010

**Citation**

Kenji Yamazoe, "Two matrix approaches for aerial image formation obtained by extending and modifying the transmission cross coefficients," J. Opt. Soc. Am. A **27**, 1311-1321 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-6-1311

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