1. An apparatus for generating a mosaic picture of an object plane, comprising a capturing device for portion-by-portion capturing of the object plane at a two-dimensional distribution of capturing positions so as to acquire subimages which represent pictures of portions of the object plane which mutually overlap, while allocating the capturing positions to the subimages, the capturing device being configured such that the capturing positions allocated to the subimages deviate from actual capturing positions in accordance with error statistics; and a processor for determining offset vectors between pairs of mutually overlapping subimages by means of a similarity analysis of the overlapping subimages and for solving an optimization problem for finding an optimum set of capturing position variables for the subimages for minimizing a measure of a deviation between the offset vectors of the pairs of mutually overlapping subimages, on the one hand, and differences of the capturing position variables of the pairs of mutually overlapping subimages, on the other hand, while complying with a secondary constraint for the capturing position variables which depends on the error statistics, wherein the capturing device is configured to sequentially cycle through the two-dimensional distribution of capturing positions in a capturing path, the processor being configured such that the secondary constraint limits, in dependence on the error statistics, the difference of capturing position variables for pairs of subimages which immediately follow one another along the capturing path.