Beam propagation method | EPFL Graph Search

The beam propagation method (BPM) is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. It is essentially the same as the so-called parabolic equation (PE) method in underwater acoustics. Both BPM and the PE were first introduced in the 1970s. When a wave propagates along a waveguide for a large distance (larger compared with the wavelength), rigorous numerical simulation is difficult. The BPM relies on approximate differential equations which are also called the one-way models. These one-way models involve only a first order derivative in the variable z (for the waveguide axis) and they can be solved as "initial" value problem. The "initial" value problem does not involve time, rather it is for the spatial variable z. The original BPM and PE were derived from the slowly varying envelope approximation and they are the so-called paraxial one-way models. Since then, a number of improved one-way models are introduced. They come from a

3D Reconstruction of Optical Diffraction Tomography Based on a Neural Network Model

Morteza Hasani Shoreh

Optical tomography has been widely investigated for biomedical imaging applications. In recent years, it has been combined with digital holography and has been employed to produce high quality images of phase objects such as cells. In this Thesis, we look into some of the newest optical Diffraction Tomography (DT) based techniques to solve Three-Dimensional (3D) reconstruction problems and discuss and compare some of the leading ideas and papers. Then we propose a neural-network-based algorithm to solve this problem and apply it on both synthetic and biological samples. Conventional phase tomography with coherent light and off axis recording is performed. The Beam Propagation Method (BPM) is used to model scattering and each x-y plane is modeled by a layer of neurons in the BPM. The network's output (simulated data) is compared to the experimental measurements and the error is used for correcting the weights of the neurons (the refractive indices of the nodes) using standard error back-propagation techniques. The proposed algorithm is detailed and investigated. Then, we look into resolution-conserving regularization and discuss a method for selecting regularizing parameters. In addition, the local minima and phase unwrapping problems are discussed and ways of avoiding them are investigated. It is shown that the proposed learning tomography (LT) achieves better performance than other techniques such as, DT especially when insufficient number or incomplete set of measurements is available. We also explore the role of regularization in obtaining higher fidelity images without losing resolution. It is experimentally shown that due to overcoming multiple scattering, the LT reconstruction greatly outperforms the DT when the sample contains two or more layers of cells or beads. Then, reconstruction using intensity measurements is investigated. 3D reconstruction of a live cell during apoptosis is presented in a time-lapse format. At the end, we present a final comparison with leading papers and commercially available systems. It is shown that -compared to other existing algorithms- the results of the proposed method have better quality. In particular, parasitic granular structures and the missing cone artifact are improved. Overall, the perspectives of our approach are pretty rich for high-resolution tomographic imaging in a range of practical applications.

EPFL2018

Learning approaches to high-fidelity optical diffraction tomography

Joowon Lim

Optical diffraction tomography (ODT) provides us 3D refractive index (RI) distributions of transparent samples. Since RI values differ across different materials, they serve as endogenous contrasts. It, therefore, enables us to image without pre-processing of labeling which can disturb samples during measurement. It has been utilized in various applications to study hematology, morphological parameters, biochemical information, and so on. The fundamental principle of ODT reconstruction is to recover the 3D information from multiple 2D measurements. While we require 2D measurements acquired by fully scanning a sample, there exist missing measurements that we are not able to access due to the limited numerical apertures (NAs) in the optical system. This is called the missing cone problem since the parts which are not covered by the NAs form cone shapes. The missing cone problem degrades the final reconstruction by underestimating RI values and more severely elongating images along the optical axis. Another challenge in ODT reconstruction is to model the nonlinear relationship between a sample and the measurements. The first order of scattering is commonly considered while neglecting the other higher orders to linearize the relationship, however, this results in degradation of the final reconstruction as the higher orders of scattering become more pronounced. In this thesis, we aim at solving the challenges in ODT reconstruction to provide more accurate quantitative information, namely, RI distributions. The first approach is based on model-based iterative reconstruction schemes. We choose the beam propagation method (BPM) for the forward model in order to capture the high orders of scattering. Due to the similarity of the multi-layer structure of the BPM with that of neural networks used in deep learning, we call this scheme learning tomography (LT). We rigorously investigate the performance of LT over the conventional linear model-based reconstruction scheme. Furthermore, by applying a more advanced BPM for the forward model, we even improve the LT and demonstrate the dramatically improved performance by both simulations and experiments. The second approach is based on statistically learning artifacts present in final reconstructions using a deep neural network (DNN) from a large dataset. Unlike the previous approaches which require iterations, the DNN approach instantly reconstructs RI distributions. We demonstrate the use of DNN using red blood cells which are highly distorted by the missing cone problem. In order to overcome the lack of ground truth in 3D ODT reconstruction, we digitally generate a synthetic dataset. The reconstruction results from the network present highly accurate results for the synthetic test set. Most importantly, we obtain high-fidelity reconstructions of experimental data using the network trained only on the synthetic data. Unlike other imaging modalities, ODT provides 3D quantitative information without labeling. To fully benefit from the capacity of quantitative imaging, it is critical to solve the existing challenges in ODT reconstruction to produce high-fidelity reconstructions. In this contribution, we aim to resolve the major challenges in ODT reconstruction using various learning approaches, and we believe that it can further improve ODT as a powerful tool for various applications.

EPFL2020