Figure 3

Numerical experiment in FINCH: Reconstruction of 3 different object depth planes of a 3D scene.

Project Description

Incoherent holography has recently attracted significant research interest due to its flexibility for a wide variety of light sources. In this paper, we use compressive sensing to reconstruct a three-dimensional volumetric object from its two-dimensional Fresnel incoherent correlation hologram. We show how compressed sensing enables reconstruction without out-of-focus artifacts, when compared to conventional back-propagation recovery. Finally, we analyze the reconstruction guarantees of the proposed approach both numerically and theoretically and compare that with coherent holography.

Publication

"Compressive Reconstruction for 3D Incoherent Holographic Microscopy"
O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas and S. Yoo
IEEE International Conference on Image Processing (ICIP), September 2016
[PDF]

Images

Finch1

A generalized diagram of a 4f FINCH system.


The real part of the PSF in x − z direction in FINCH.

The real part of the PSF in x−z direction.


The PSF’s width along the x axis varies for different depths due to the limited physical aperture of the system.

Reconstruction of 3 different object depth planes of a 3D scene in FINCH.

Numerical experiment in FINCH: Reconstruction of 3 different object depth planes of a 3D scene.


This figure shows the reconstruction results for the simulated 3D scene. Figure (a) depicts the original object consisting of three different depth planes, while Figures (b) and (c) present reconstruction results using the standard back-propagation and the proposed CS approach, respectively.
We can clearly see that each reconstructed plane by back-propagation (or refocusing) is distorted by out-of-focus artifacts (blurry images from adjacent depth planes), while
CS provides better optical sectioning of the scene.

finch4

Performance comparison of the FINCH system with coherent holography for different values of δ. The coherence parameter μ is computed both using the gram matrix (through eq. (11)) as well as directly through eq. (17).


This figure shows the performance of our FINCH system for large and small δ values and compare that with the coherent holography system in [7] given z0 = 0,M = −1.
We can see that our FINCH system has similar performance as the coherent system when δ is much larger than Lz, and much better performance for smaller δ.

finch5

Simulation results showing the normalized number of reconstructed 3D object's particles as a function of number of object planes, for a constant volume length, Lz=1mm, given a sensor with 512×512 pixels.


As z axial resolution becomes finer (or equivalently Nz become bigger for a constant volume length Lz), fewer 3D points can be reconstructed using CS, which is consistent with the theoretical predication of Eq. (18).

Acknowledgements

 This work was supported in part 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. The work was also supported in part by funding from NSF CAREER grant IIS-1453192 and ONR award N00014-15-1-2735.