It is known that one-dimensional phase problem in optics can be reduced to a search of zero positions of the analytic continuation of a light field complex amplitude. Usually this procedure is executed by means of numerical methods based on the measurement of the field intensity on several planes. In this work it is shown that the analytic continuation can be realized by optical way. Namely, two-dimensional Fourier transform with an additional astigmatic phase converts a one- dimensional object field into a singular wavefield. The field zeros are the same as that of the analytic continuation of one-dimensional Fourier transform of the initial field. Thus, it is possible to restore the object field through one measurement. Results of computer simulations are presented.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.