Noniterative Phase Retrieval from a Single Diffraction Intensity Pattern by Use of an Aperture Array

A noniterative method for retrieving the phase of a wave field from a diffraction intensity measurement in a coherent wave field is proposed. In this method, the phase can be calculated from analytic equations based on the properties of entire functions by use of Fourier transforms. This method requires only a single measurement of the intensity of a diffracted wave through an array filter of rectangular apertures and then does not need to use any lens systems and coherent reference waves. Therefore, it provides a potentially useful means for coherent imaging in a wide class of wave fields such as optical, x ray, electron, and atomic waves.

Figure 1

Schematic diagram of the measurement system for the object reconstruction by the phase-retrieval method. The object function is reconstructed from a single intensity distribution of a diffracted wave through an array of rectangular apertures.

Figure 2

Reconstruction of a complex-valued object from a single intensity distribution by the phase-retrieval method: (a) modulus and (b) phase of the original object (where the values of the phase are in the range of $-2.52$ to 2.51 rad), and (c) modulus in the detector plane of Fig. 1. (d) and (e) [or (f) and (g)] are the modulus and phase, respectively, of a reconstructed object from the noiseless (or noisy) modulus of (c).