Far-field intensity signature of sub-wavelength microscopic objects

Abstract: Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically depends on the level of noise. This new path to superresolution has been recently investigated with the use of compressed sensing and machine learning. We demonstrate a two-stage technique based on deconvolution and genetic optimization which enables the recovery of objects with features of 1/10 of the wavelength. We indicate that l1-norm based optimization in the Fourier domain unrelated to sparsity is more robust to noise than its l2-based counterpart. We also introduce an extremely fast general-purpose restricted domain calculation method for Fourier transform based iterative algorithms operating on sparse data.