From the van Cittert-Zernicke theorem, the relationship between observed
visibility function and source brightness in
synthesis imaging is given by

(1) |

But the visibility function is sampled only at discrete points (finite sampling), so only an approximation to , called the ``dirty map'' and denoted , is measured. It is given by

(2) |

where is the sampling function and is the observed visibility function. Let denote Convolution and rearrange the Convolution Theorem,

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

© 1996-9

1999-05-24