Determination of the shape of a binary object of a square with a square hole by means of chosen initial phases

摘要

The binary object treated is a square with a square hole. We first use a set of initial phases to determine the symmetry of the object. The initial image has the gross shape of a square with a square hole, and preserves symmetry of the object. With another set of initial phases, the initial image has gross shape of a square with a hole. Sayre's equation is applied to refine this gross shape. After iterations, the result shows a square with a distorted square hole. These three squares have approximately same edge lengths. These squares are larger than the object. The holes are smaller than the hole of the object. The initial phases or the gross shapes can be used as starting phases or starting envelopes in other iterative algorithms.