Two-dimensional phase retrieval using a window function

Two-dimensional phase retrieval by use of a window function is considered. First the uniqueness and the reconstruction of a two-dimensional signal from the Fourier intensities of the three signals, an original signal, the signal windowed by a window w(m, n) , and the signal windowed by its complementary window w(c)(m, n) = 1 - w(m, n) , are addressed. Then phase retrieval without a complementary window is considered. Conditions under which a signal can be uniquely specified from the Fourier intensities of the original signal and the windowed signal by w(m, n) are developed, and a reconstruction algorithm is presented.