Single-shot diffraction-limited imaging through scattering layers via bispectrum analysis.

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 minimums 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 the 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.