Direct Inversion of Digital 3D Fraunhofer Holography Maps

The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in many experiments to obtain amplitude and phase information about two-dimensional (2D) images. In this article we demonstrate numerically the possibility to apply the DFH also for investigation of unknown 3D Objects. The first simulation is made for a double-spiral structure plus a line as a reference object

Mask-assisted deterministic phase-amplitude retrieval from a single far-field intensity diffraction pattern: Two experimental proofs of principle using visible light

We recently developed a simple closed-form algorithm, which allows one to reconstruct the complex scalar wavefield at the exit surface of a sample, from the intensity of its far-field coherent diffraction pattern which is obtained in the presence of a suitable object-plane mask. In the first variant of this algorithm, the sample is contained within a uniformly illuminated sharp rectangular aperture in which at least one transverse dimension is at least twice that of the object. In the second variant, the sample is uniformly illuminated and is transversely displaced from an opaque rectangular mask in the object plane. For both variants, the far-field diffraction pattern is first Fourier transformed and then differentiated with respect to both transverse coordinates, in order to deterministically yield a series of independent reconstructions of the sample. Here we give an experimental demonstration of each of these two variants of our technique, using visible light