Computing arbitrary fractional powers of a transform operator from selected precomputed fractional powers of the operator

摘要

A computer-implemented system and method for correcting misfocus in original particle beam image data by using a fractional Fourier transform operation or an approximation of it. In one embodiment, the particle beam image data is produced by an electron microscope. The approximation of a fractional Fourier transform operation may comprise a portion of a Taylor series expansion, a Hermite function expansion, a perturbation approximation, a singular integral approximation, or an infinitesimal generator. The described embodiments provide for the reconstruction of phase information associated with the original image data, and for the reconstructed phase information to also utilize an approximation of a fractional Fourier transform operation. The focus correction can be selected and controlled by user interaction or an automatic feedback control system that may include optimization.