Abstract
Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.
Highlights
A prime example and an important application for phase retrieval is coherent diffraction imaging (CDI)[1,2,3,4,5,6] where an object is algorithmically reconstructed from measurements of the freely diffracting intensity pattern image that corresponds to the spatial spectrum of the object
As we have shown recently, using sparsity as the prior can be very powerful in CDI29,39
It was proposed in numerical simulations that sparsity can remove the ambiguity associated with 1D phase retrieval[25,28,30,41]
Summary
A prime example and an important application for phase retrieval is coherent diffraction imaging (CDI)[1,2,3,4,5,6] where an object is algorithmically reconstructed from measurements of the freely diffracting intensity pattern image that corresponds to the spatial spectrum (that is, the square of the Fourier amplitude) of the object. As shown in the Supplementary Note 1 and Supplementary Figs 1–2, the problem of reconstructing the original 1D object from the power spectrum suffers from ambiguity that cannot be removed by prior information about the support of the object.
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