4.4 Numerical Implementation

**Forward Transform.**The Fourier coefficientsof the mask transmission function*T*_{nm}have to be calculated. As in our model*t*(*x*,*y*)consists of piecewise constant regions with ideal sharp transitions, a simple sampling is not adequate because*t*(*x*,*y*)is definitely no low-pass function. Hence, we developed a semi-analytical method to avoid errors arising from aliasing.*t*(*x*,*y*)**Backward Transform.**The Fourier coefficientsare weighted with the pupil function and have then to be transformed back to the spatial domain to obtain the image field. As the projection lens acts as a low-pass filter due to the finite extent of the pupil function the image has only spectral components up to a certain order. Therefore sampling can be employed for the backward transform without introducing any aliasing.*T*_{nm}

1998-04-17