Noise limits in the assembly of diffraction data

TL;DR

This paper establishes an information theoretic criterion for assembling noisy diffraction data without known tomograph positions, showing that successful assembly is feasible with fewer photons than previously thought, and demonstrates an algorithm reaching this limit.

Contribution

It introduces a new information theoretic criterion for diffraction data assembly and demonstrates an algorithm that achieves this theoretical limit.

Findings

Minimum photons per tomograph grow logarithmically with resolution

Assembly is feasible with fewer photons than previously believed

Algorithm reaches the information theoretic limit

Abstract

We obtain an information theoretic criterion for the feasibility of assembling diffraction signals from noisy tomographs when the positions of the tomographs within the signal are unknown. For shot-noise limited data, the minimum number of detected photons per tomograph for successful assembly is much smaller than previously believed necessary, growing only logarithmically with the number of resolution elements of the diffracting object. We also demonstrate assembly up to the information theoretic limit with a constraint-based algorithm.