Direct exit-wave reconstruction from a single defocused image

• Published in: Ultramicroscopy 2011-08, Vol.111 (9-10), p.1455-1460
• Main Authors: Morgan, A.J., Martin, A.V., D'Alfonso, A.J., Putkunz, C.T., Allen, L.J.
• Format: Article
• Language: English
• Subjects: Autocorrelation functions; Diagnostic Imaging - methods; Exit-wave reconstruction; Fourier Analysis; Fourier transforms; Fresnel coherent diffractive imaging; Illumination; Image Processing, Computer-Assisted - methods; Inverse; Lasers; Lighting; Linear equations; Nuclear Magnetic Resonance, Biomolecular; Plane waves; Single defocused image
• ISSN: 0304-3991; 1879-2723
• DOI: 10.1016/j.ultramic.2011.07.005

We propose a direct, non-iterative method for the exact recovery of the complex wave in the exit-surface plane of a coherently illuminated object from a single defocused image. The method is applicable for a wide range of illumination conditions. The defocus range is subject to certain conditions, which if satisfied allow the complex exit-surface wave to be directly recovered by solving a set of linear equations. These linear equations, whose coefficients depend on the incident illumination, are obtained by analyzing the autocorrelation function of an auxiliary wave which is related to the exit-surface wave in a simple way. This autocorrelation is constructed by taking the inverse Fourier transform of the defocused image. We present an experimental proof of concept by recovering the exit-surface wave of a microfiber illuminated by a plane wave formed using a HeNe laser. ► Direct, exact recovery of an exit-surface wave from a single defocused image. ► An experimental proof of concept is given by illuminating a microfiber with a laser. ► Method is applicable for a wide range of illumination conditions. ► This approach is applicable to both coherent X-ray and electron sources.