Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements

Abstract

The general problem of reconstructing two unknown functions from a number of measurements of the intensity of the Fourier transform of the product of the functions, where the functions are displaced relative to one another by a different amount for each measurement, is examined. It is shown that this problem is equivalent to a blind deconvolution problem, which suggests that a unique solution exists for functions of any number of dimensions. Such a problem arises when attempts are made to recover the specimen and probe functions from microdiffraction plane intensity measurements in a scanning transmission electron microscope. An iterative algorithm capable of recovering these functions is described, and examples of the operation of the algorithm are presented for simulated data involving one- and two-dimensional functions.