  Recently introduced speckle-correlations based techniques enable noninvasive
imaging of objects hidden behind scattering layers. In these techniques the
hidden object Fourier amplitude is retrieved from the scattered light
autocorrelation, and the lost Fourier phase is recovered via iterative
phase-retrieval algorithms, which suffer from convergence to wrong local-minima
solutions and cannot solve ambiguities in object-orientation. Here, inspired by
notions used in astronomy, we experimentally demonstrate that in addition to
Fourier amplitude, the object phase information is naturally and inherently
encoded in scattered light bispectrum (the Fourier transform of
triple-correlation), and can also be extracted from a single high-resolution
speckle pattern, based on which we present a single-shot imaging scheme to
deterministically and unambiguously retrieve diffraction-limited images of
objects hidden behind scattering layers.

Optics