Information flow in diffractive imaging with subwavelength resolution

Optical microscopy provides unparalleled tools for understanding and characterization of small-scale objects. We have recently developed an approach that combines diffractive imaging and machine learning to characterize wavelength-scale objects with subwavelength resolution based on few (or, often, single) measurement. The technique relies on the diffraction interaction between finite-sized diffraction grating and an object to outcouple information about both sub-wavelength and wavelength-scale features of the object into the far field and on machine learning to characterize the object based on its diffractive signature. In this work we aim to understand the flow of information through the image recognition process. We parameterize the diffractive signatures in Bessel and Fourier representations and analyze the performance of the recovery routines dependent on the choice of the harmonics in these expansions. Separately, we analyze the subset of the harmonics that are used by the machine learning algorithms in identifying the objects. Performance of the recovery routines as a function of noise is also analyzed. Our study provides an insight into the dynamics of machine learning and it helps identify the information channels that are crucial for optimal recovery of complex objects with high resolution, fidelity, and speed.