We demonstrate that decompressive inference enables 3D tomography from a single 2D monochromatic digital hologram. In compressive sensing, sparse signals in some basis, sampled by multiplex encodings, may be accurately infered with high probability using many fewer measurements than suggested by Shannons sampling theorem. Holography has general advantages in compressive optical imaging since it is an interferometric modality in which both the amplitude and the phase of a field can be obtained. The complex-valued encodings may provide a more direct application of compressive sensing.
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. Experimental results demonstrate and verify the performance of our estimates.
This project investigates dynamic 3D imaging of microscopic objects using compressive holography. Compressive holography enables an accurate 3D reconstruction from a single 2D holographic snapshot for objects that can be sparsely represented in some basis. The snapshot mode enables fast acquisition while achieving tomographic imaging of microscopic moving objects. We demonstrate video-rate tomographic reconstruction of two live water cyclopses with 5.2 micron spatial resolution and 60 micron axial resolution.
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 63.4 mm aperture synthesized by scanning a 5.28 mm subaperture over 144 transverse positions. We demonstrate 60 micron resolution at 2 m range.