E.3 Rectangular Aperture

(E.54) |

The area of the aperture is given by . The FOURIER transform can be calculated from (E.27) and splitted into two integrals

One stripe in Figure E.6 is thereby given by

(E.56) |

Integration of (E.55) is simple and straightforward

The rightmost term can be defined as a new function

(E.58) |

With this substitution (E.57) yields

(E.59) |

and

(E.60) |

in an analogous way. Therefore in Point the electric field is according to (E.29)

(E.61) |

and the intensity as the square of the electrical field is then

For the special case of the source being located on the z-axis, the coordinates are zero and the coordinates are the following functions of

For and (the direct beam) the coordinates are and according to (E.63) . The direct beam is therefore in the z-axis and can be written as

Together with (E.14) and (E.64) the square of the fraction in (E.62) gives

(E.65) |

Therefore this fraction can be set to unity if . This assumption yields finally for the intensity behind a rectangular aperture

R. Minixhofer: Integrating Technology Simulation into the Semiconductor Manufacturing Environment