Abstract
Intensity interferometry is a well known method in astronomy. Recently, a related method called incoherent diffractive imaging (IDI) was proposed to apply intensity correlations of x-ray fluorescence radiation to determine the 3D arrangement of the emitting atoms in a sample. Here we discuss inherent sources of noise affecting IDI and derive a model to estimate the dependence of the signal to noise ratio (SNR) on the photon counts per pixel, the temporal coherence (or number of modes), and the shape of the imaged object. Simulations in two- and three-dimensions have been performed to validate the predictions of the model. We find that contrary to coherent imaging methods, higher intensities and higher detected counts do not always correspond to a larger SNR. Also, larger and more complex objects generally yield a poorer SNR despite the higher measured counts. The framework developed here should be a valuable guide to future experimental design.
Highlights
The scattering of a spatially and temporally coherent beam from an object gives rise to a far-field diffraction pattern consisting of constructive and destructive interference that encodes that object’s structure, an effect that is utilised to obtain atomic-resolution images of the electron density of crystals with x-rays, for example
This speckle pattern would change each time it is measured due to random fluctuations of the phases of the emitters, the integrated intensities retain correlations. This is the basis for intensity interferometry of Hanbury Brown and Twiss, in which the signals measured in independent detectors are correlated
The situation for incoherent diffractive imaging (IDI) can be compared with coherent diffractive imaging (CDI) based on elastic scattering, where for a well-designed experiment the noise in the measured integrated intensities is dominated by the Poisson statistics of the photons and so higher measured counts yields a higher signal to noise ratio (SNR)
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Keywords: incoherent diffractive imaging, SNR analysis for IDI, intensity correlation imaging, x-ray free-electron laser, Hanbury-Brown and Twiss, coherence, x-ray imaging
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