Ab Initio Spatial Phase Retrieval via Intensity Triple Correlations

TL;DR

This paper introduces a comprehensive method for phase retrieval using third-order intensity correlations, enabling accurate Fourier phase reconstruction and image formation of arbitrary incoherent emitter arrangements.

Contribution

It presents a general ab initio phase retrieval technique from intensity triple correlations, overcoming previous limitations related to emitter configurations and sign ambiguities.

Findings

Simulations show accurate phase retrieval for various emitter clusters.

Method enables direct Fourier inversion and image reconstruction from intensity correlations.

Applicable to imaging stars, fluorescent atoms, and molecules.

Abstract

Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter configurations which simplified an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary configuration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or fluorescent atoms and molecules. With this work, it is now finally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-field intensity correlations alone.