In optical tomography, there exist certain spatial frequency components that cannot be measured due to the limited projection angles imposed by the numerical aperture of objective lenses. This limitation, often called as the missing cone problem, causes the under-estimation of refractive index (RI) values in tomograms and results in severe elongations of RI distributions along the optical axis. To address this missing cone problem, several iterative reconstruction algorithms have been introduced exploiting prior knowledge such as positivity in RI differences or edges of samples. In this paper, various existing iterative reconstruction algorithms are systematically compared for mitigating the missing cone problem in optical diffraction tomography. In particular, three representative regularization schemes, edge preserving, total variation regularization, and the Gerchberg-Papoulis algorithm, were numerically and experimentally evaluated using spherical beads as well as real biological samples; human red blood cells and hepatocyte cells. Our work will provide important guidelines for choosing the appropriate regularization in ODT.
We propose an iterative reconstruction scheme for optical diffraction tomography that exploits the split-step non-paraxial (SSNP) method as the forward model in a learning tomography scheme. Compared with the beam propagation method (BPM) previously used in learning tomography (LT-BPM), the improved accuracy of SSNP maximizes the information retrieved from measurements, relying less on prior assumptions about the sample. A rigorous evaluation of learning tomography based on SSNP (LT-SSNP) using both synthetic and experimental measurements confirms its superior performance compared with that of the LT-BPM. Benefiting from the accuracy of SSNP, LT-SSNP can clearly resolve structures that are highly distorted in the LT-BPM. A serious limitation for quantifying the reconstruction accuracy for biological samples is that the ground truth is unknown. To overcome this limitation, we describe a novel method that allows us to compare the performances of different reconstruction schemes by using the discrete dipole approximation to generate synthetic measurements. Finally, we explore the capacity of learning approaches to enable data compression by reducing the number of scanning angles, which is of particular interest in minimizing the measurement time.
Quantitative phase imaging has gained popularity in bioimaging because it can avoid the need for cell staining, which, in some cases, is difficult or impossible. However, as a result, quantitative phase imaging does not provide the labelling of various specific intracellular structures. Here we show a novel computational segmentation method based on statistical inference that makes it possible for quantitative phase imaging techniques to identify the cell nucleus. We demonstrate the approach with refractive index tomograms of stain-free cells reconstructed using tomographic phase microscopy in the flow cytometry mode. In particular, by means of numerical simulations and two cancer cell lines, we demonstrate that the nucleus can be accurately distinguished within the stain-free tomograms. We show that our experimental results are consistent with confocal fluorescence microscopy data and microfluidic cyto-fluorimeter outputs. This is a remarkable step towards directly extracting specific three-dimensional intracellular structures from the phase contrast data in a typical flow cytometry configuration.
Maxwell’s equations govern light propagation and its interaction with matter. Therefore, the solution of Maxwell’s equations using computational electromagnetic simulations plays a critical role in understanding light–matter interaction and designing optical elements. Such simulations are often time-consuming, and recent activities have been described to replace or supplement them with trained deep neural networks (DNNs). Such DNNs typically require extensive, computationally demanding simulations using conventional electromagnetic solvers to compose the training dataset. In this paper, we present a novel scheme to train a DNN that solves Maxwell’s equations speedily and accurately without relying on other computational electromagnetic solvers. Our approach is to train a DNN using the residual of Maxwell’s equations as the physics-driven loss function for a network that finds the electric field given the spatial distribution of the material property. We demonstrate it by training a single network that simultaneously finds multiple solutions of various aspheric micro-lenses. Furthermore, we exploit the speed of this network in a novel inverse design scheme to design a micro-lens that maximizes a desired merit function. We believe that our approach opens up a novel way for light simulation and optical design of photonic devices.
Polarization of light has been widely used as a contrast mechanism in two-dimensional (2D) microscopy and also in some three-dimensional (3D) imaging modalities. In this paper, we report the 3D tomographic reconstruction of the refractive index (RI) tensor using 2D scattered fields measured for different illumination angles and polarizations. Conventional optical diffraction tomography (ODT) has been used as a quantitative, label-free 3D imaging method. It is based on the scalar formalism, which limits its application to isotropic samples. We achieve imaging of the birefringence of 3D objects through a reformulation of ODT based on vector diffraction theory. The off-diagonal components of the RI tensor reconstruction convey additional information that is not available in either conventional scalar ODT or 2D polarization microscopy. Finally, we show experimental reconstructions of 3D objects with a polarization-sensitive contrast metric quantitatively displaying the true birefringence of the samples.
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