Recent advances in computational photography techniques have enabled the capture of incoherent holograms. This process now allows for the snapshot 3D imaging of fluorescent biological samples. Open questions in plant biology, such as the role of bacteria in nutrient transport into plant roots, can now be explored using 3D volumetric capture in motion.
In the past, 3D microscopic capture required scanning of the volume with techniques such as confocal microscopy or focal sweep. The slow, sequential nature of these techniques, taking minutes or even hours, prevented scientists from view moving, live samples at all (in fact the samples had to be preserved before imaging). Coherent 3D imaging is not possible in these applications because the fluorescent tags used to identify known locations on or within bacteria are necessarily incoherent sources. Now, with incoherent holographic microscopy, moving 3D images are possible.
An incoherent volume of point sources passes through the incoherent holographic system. The response of this system is modeled as a 3D complex point spread function. The resulting complex field is sampled at the sensor plane. Using phase shifting, three magnitude-only images are captured.
Using sparse optimization techniques, the highly under-constrained problem of recovering a 3D volume from complex 2D measurements can be achieved by enforcing spatial sparsity on the resulting volume. In this case, L1 regularization is added to a quadratic optimization problem minimizing the difference between the forward model of the recovered volume and the captured measurements.
A 128x128x128 volume was seeded with 64 randomly generated points, passed through the forward model, then reconstructed to produce the comparison on the left. This early stage result will benefit from further tuning of reconstruction parameters. but demonstrates the ability of this technique to recover volumetric information with surprising accuracy given few measurements.
This work was supported by funding through the Biological Systems Science Division, Office of Biological and Environmental Research, Office of Science, U.S. Dept. of Energy, under Contract DE-AC02-06CH11357.