Synthetic Wavelength Holography: An Extension of Gabor's Holographic Principle to Imaging with Scattered Wavefronts

Scattering of light is an elementary process that makes it possible to see the objects around us. However, when light is scattered between object and observer (e.g., due to fog), it poses a serious problem to optical imaging. In this work, we demonstrate how to circumvent the deleterious effects of scattering by exploiting spectral correlations of scattered wavefronts. This allows us to extend the use of optical imaging to conditions where strong scattering would otherwise obstruct a clear view. Our method draws inspiration from Gabor's attempts to improve the resolving power of electron microscopes. Gabor's method was to record aberrated wavefronts at electron wavelengths, play this recording back at optical wavelengths, then finally perform an optical aberration correction. Similar to Gabor's approach, we transfer the problem of aberration correction to a larger 'Synthetic Wavelength' by interpreting the wavefront distortion of scattered light as uncharacterized stochastic aberrations. We computationally mix speckle fields recorded at two closely spaced optical wavelengths and uncover object information by playing back the computationally assembled wavefront at a 'Synthetic Wavelength'. An attractive feature of our method is that it generalizes well to many different types of scattering. Moreover, we show that our method works at the fundamental limits of imaging performance in the presence of scattering. Our findings are applicable to a wide range of wave phenomena, opening up new avenues for imaging with scattered wavefronts.