Fourier magnitude of the field incident on a random scattering medium from spatial speckle intensity correlations

Spatial speckle intensity correlations are used to determine the spatial Fourier magnitude of a field incident on a random scattering medium. The patterned beam is scanned across the scattering medium, and the speckle pattern on the opposite side is imaged at each beam position. A theory based on a Green's function representation is used to reconstruct the spatial Fourier magnitude of the patterned incident field.