B. Analytical Fourier Transformations

In this appendix we derive analytical expressions for the Fourier coefficients of the elementary geometrical patterns that result from the decomposition of the photomask as described in Section 4.4.1. Following (4.105), we have to evaluate integrals like

 

$$\mathcal{P}_{nm} = \frac{1}{ab}\iint\limits_{(x,y)\in\text{PAT}} e^{-j2\pi(nx/a+my/b)}\,dxdy$$ (B.1)

for the elementary triangular- and rectangular-shaped patterns. Additionally, the stability of the numerical evaluation of the derived formulae is investigated.