3D quantitative phase (refractive index) microscopy reveals volumetric structure of biological specimens. Optical diffraction tomography (ODT) is a common technique for 3D phase imaging. By angularly scanning a spatially coherent light source and measuring scattered fields on the imaging plane, 3D refractive index (RI) is recovered by solving an inverse problem. However, ODT often linearizes the process by using a weakly scattering model, e.g. the first Born approximation or Rytov approximation, which underestimate the RI and fail to reconstruct realistic shape of high RI contrast multiple scattering objects. On the other hand, non-linear models such as the multi-slice or beam propagation methods mitigate artifacts by modeling multiple scattering. However, they ignore back-scattering and intra-slice scattering and make a paraxial approximation by assuming each slice is infinitesimally thin. In this work, we propose a new 3D scattering model Multi-layer Born (MLB), which treats the object as thin 3D slabs with finite thickness and applies the first Born approximation on each slab as the field propagates through the object, increasing the accuracy significantly. In the meantime, a similar computation complexity is achieved comparing to the previously proposed multi-slice models. Therefore, MLB can achieve accuracy similar to that of FDTD or SEAGLE, a frequency domain solver, with orders of magnitude less computation time. In addition to forward scattering, multiple back-scattering effects are also captured by MLB unlike existing models. We apply MLB to recover the RI distribution of 3D phantoms and biological samples with intensity-only measurements from an LED array microscope and show that the results are superior to existing methods.
KEYWORDS: 3D image processing, 3D metrology, Microscopy, Coded apertures, 3D modeling, Coded aperture imaging, Stereoscopy, Data modeling, Reconstruction algorithms, Luminescence
Coded aperture imaging for 3D reconstructions have been applied in both photography and microscopy to successfully recover depth information from images captured with a patterned pupil plane. Generally, single-shot coded aperture microscopy methods require the 3D sample to be extremely sparse and with no overlapping features. Here, we extend coded aperture microscopy methods to multi-shot 3D fluorescent imaging with wave-optical forward models, enabling thicker and denser 3D samples to be faithfully reconstructed with efficient data capture via compressed sensing and advanced inverse algorithms.. We demonstrate successful reconstruction of a 500um thick brine shrimp sample. We further study the minimum required number of codes to capture full fluorescent information under wide-field illumination The experiments are carried out with a 4f system and a spatial light modulator in the Fourier (aperture) domain to display the codes.
Phase-space refers to simultaneous space-frequency information (e.g. Wigner functions, light fields), which is directly related to spatial coherence properties (e.g. Mutual Intensity). We introduce a binary pupil masking technique that allows us to computationally reconstruct the phase space distribution of optical beams from a series of images. Previous work has shown phase space to be useful for 3D imaging and localization in a multiple scattering environment. Binary masks are easy to implement compared to gray masks or phase masks and the proposed scheme requires no interferometry. After designing the masks with nonredundant arrays, we measure an intensity image for each aperture mask and reconstruct the phase space through an auxiliary coherence function. We demonstrate experimentally the reconstruction of the phase space of a collection of 3D incoherent sources.
Phase-space measurements enable characterization of second-order spatial coherence properties and can be used for digital aberration removal or 3D position reconstruction. Previous methods use a scanning aperture to measure the phase space spectrogram, which is slow and light inefficient, while also attenuating information about higher-order correlations. We demonstrate a significant improvement of speed and light throughput by incorporating multiplexing techniques into our phase-space imaging system. The scheme implements 2D coded aperture patterning in the Fourier (pupil) plane of a microscope using a Spatial Light Modulator (SLM), while capturing multiple intensity images in real space. We compare various multiplexing schemes to scanning apertures and show that our phase-space reconstructions are accurate for experimental data with biological samples containing many 3D fluorophores.
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