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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 4
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Original Articles

Approximation of Hopkins equation in Hilbert space and its application in polarized illumination modelling

, , &
Pages 517-528 | Received 06 Feb 2009, Accepted 04 Mar 2009, Published online: 16 Jun 2009
 

Abstract

In this article, we derive an analytical approximation to compute the aerial images on general geometric domains. Under the framework in Hilbert space, we develop a general approximation model for aerial image intensity, which is particularly valid for the computation of the aerial image with polarized illumination source. Our mathematical result is a generalization of classical Mercer's theorem provided that the integral kernel is Hilbert–Schmidt. By applying Synopsys's simulation tool Progen, we demonstrate the effectiveness of our proposed approximation with polarized illumination sources (65 nm and below). Since our approach setting is quite general, the proposed approximation in this article is suitable for modification in various applications.

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Acknowledgement

This research is supported in part by NSF DMS-0605181.

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