## Fast fine-pixel aerial image calculation in partially coherent imaging by matrix representation of modified Hopkins equation

Applied Optics, Vol. 49, Issue 20, pp. 3909-3915 (2010)

http://dx.doi.org/10.1364/AO.49.003909

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### Abstract

A fast computation algorithm for fine-pixel aerial images is presented that modifies the transmission cross coefficient approach of Hopkins as a product of two matrices. The spatial frequency of the image is calculated by the sum of diagonal and off-diagonal elements of the matrix. Let *N*, *M* be the number of the point sources, the sampling number for fast Fourier transform, and the sampling number in the spatial frequency domain ranging twice the pupil size, respectively. The calculation time of this method is proportional to *A* and *B* are constants and generally *M* or *M* is small enough, which is the fine-pixel condition, this method runs faster than the source integration method. If the coherence factor is 0.9 and

© 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: October 19, 2009

Revised Manuscript: May 25, 2010

Manuscript Accepted: June 14, 2010

Published: July 6, 2010

**Citation**

Kenji Yamazoe, "Fast fine-pixel aerial image calculation in partially coherent imaging by matrix representation of modified Hopkins equation," Appl. Opt. **49**, 3909-3915 (2010)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-20-3909

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