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

The presence of a scattering medium in the imaging path between an object and an observer is known to severely limit the visual acuity of the imaging system. We present an approach to circumvent the deleterious effects of scattering, by exploiting spectral correlations in scattered wavefronts. Our method draws inspiration from Gabor's attempts to improve the resolving power of electron microscopes by recording aberrated wavefronts at electron wavelengths, followed by aberration correction and playback at optical wavelengths. We extend the notion to scattered wavefronts, by interpreting the scattering of light as a source of randomized aberration. We compensate for these aberrations by mixing speckle fields recorded at two closely spaced optical wavelengths, and replaying the computationally assembled wavefront at a 'Synthetic Wavelength'. An attractive feature of our method is that it accommodates a wide variety of scattering mechanisms and operates at the physical limits of imaging in the presence of scatter. Moreover, our findings are applicable to other wave phenomena, opening up new avenues for imaging with scattered wavefronts.