Sampling and processing for compressive holography [Invited].

Compressive holography applies sparsity priors to data acquired by digital holography to infer a small number of object features or basis vectors from a slightly larger number of discrete measurements. Compressive holography may be applied to reconstruct three-dimensional (3D) images from two-dimensional (2D) measurements or to reconstruct 2D images from sparse apertures. This paper is a tutorial covering practical compressive holography procedures, including field propagation, reference filtering, and inverse problems in compressive holography.

Thin holographic camera with integrated reference distribution.

Off-axis digital holography typically uses a beam splitter to combine reference and object waves at an angle matched to the sampling period of the sensor array. The beam splitter determines the thickness of the recording system. This paper describes and demonstrates a total internal reflection hologram that replaces the beam splitter and enables hologram recording over a large aperture with a thin camera.

Image-based registration for synthetic aperture holography.

High pixel count apertures for digital holography may be synthesized by scanning smaller aperture detector arrays. Characterization and compensation for registration errors in the detector array position and pitch and for phase instability between the reference and object field is a major challenge in scanned systems. We use a secondary sensor to monitor phase and image-based registration parameter estimators to demonstrate near diffraction-limited resolution from a 63.

Video-rate compressive holographic microscopic tomography.

Compressive holography enables 3D reconstruction from a single 2D holographic snapshot for objects that can be sparsely represented in some basis. The snapshot mode enables tomographic imaging of microscopic moving objects. We demonstrate video-rate tomographic image acquisition of two live water cyclopses with 5.

Compressive holography of diffuse objects.

We propose an estimation-theoretic approach to the inference of an incoherent 3D scattering density from 2D scattered speckle field measurements. The object density is derived from the covariance of the speckle field. The inference is performed by a constrained optimization technique inspired by compressive sensing theory.

Compressive holography.

Compressive sampling enables signal reconstruction using less than one measurement per reconstructed signal value. Compressive measurement is particularly useful in generating multidimensional images from lower dimensional data. We demonstrate single frame 3D tomography from 2D holographic data.