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Computational Lithography by Xu Ma, Gonzalo R. Arce

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Appendix G

Formula Derivation in Chapter 10

The derivation of Eq. (10.18) is as follows:

(G.1) equation

For the OPC optimization in the first type of optical lithography system, all the entries of img have real values. In addition, according to Eq. 10.7, img, where img. Thus,

(G.2) equation

The derivation of Eq. (10.19) is as follows:

(G.3) equation

Therefore,

(G.4) equation

The derivation of Eq. (10.20) is as follows:

(G.5) equation

Therefore,

(G.6) equation

The derivation of Eq. (10.21) is as follows:

equation

(G.7)

Therefore,

(G.8)

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