Single-shot incoherent three-dimensional imaging for various in-focus situations

Incoherent digital holography (IDH) has made 3D imaging possible under fluorescent and other thermal light sources. Typically, different transverse planes can be reconstructed from a single IDH, each plane at a time. However, is it possible to reconstruct a single transverse plane or multiple planes from the same IDH? We herein introduce a novel, to our knowledge, technique for 3D imaging that enables the reconstruction of only a specific transverse plane or multiple planes at a time from the same single-shot recorded pattern according to the user's wishes and by postprocessing this pattern. An object hologram (OH) is recorded while keeping <i>N</i> object subspaces in focus with a phase mask introduced in the system's aperture. The phase mask is a multiplexing of <i>N</i> sets of unique scattering phases multiplied by unique quadratic phases (diffractive lenses) such that each set has a unique focal length. Each set is assigned to a specific subspace of the object space. Each scattering phase is intended to yield a unique pattern of randomly distributed dots on the camera. Any of the <i>n</i>th (1 ≤ <i>n</i> <i>≤</i> <i>N</i>) subspace can be reconstructed by deconvolving OH with the corresponding pattern of random dots. Simultaneous reconstruction of 1 ≤ <i>n</i> <i>≤</i> <i>N</i> planes in the volume can be obtained by deconvolving OH with the combined pattern of random dots. The multiple features of this single-shot technique make it cost-effective and time-efficient since different situations of the observed scene can be reconstructed from the same IDH without the need to record another IDH. The experimental results for two transverse planes (<b><i>N</i></b> = 2) separated along the <i>Z</i> axis are presented in this work.