FourierODT

Overview

FourierODT is a Matlab toolbox for optical diffraction tomography (ODT). It implements reconstruction algorithms and phase retrieval methods for optical diffraction tomography.

Reconstruction Methods

• Filtered backpropagation algorithm
• Inverse NDFT (nonuniform discrete Fourier transform) with the conjugate gradients method (CGNE)
• TV regularization with a forward-backward primal-dual algorithm (FBPD)

Phase Retrieval Methods

• Error reduction algorithm (ER)
• Hybrid input-output algorithm (HIO)
• Free space propagation approach by Maleki & Devaney (MD)

References

When you are using this code, please cite the paper

Robert Beinert, Michael Quellmalz: Total variation-based phase retrieval for diffraction tomography. SIAM Journal on Imaging Sciences 15(3), p. 1373-1399 (2022). doi:10.1137/22M1474382. (ArXiv Preprint 2201.11579)

This paper also explains the algorithms in more detail.

The code for an arbitrary movement of the object (with possible time dependent axis of rotation) is described in the paper

Robert Beinert, Michael Quellmalz: Total variation-based reconstruction and phase retrieval for diffraction tomography with an arbitrarily moving object. Proceedings in Applied Mathematics & Mechanics 22(1), e202200135 (2023). doi:10.1137/22M1474382.

Installation

This software requires an installation of the NFFT3 Matlab interface in the Matlab path (by default add ../nfft). This folder should contain nfft.m and nfftmex.mexw64. The NFFT3 Matlab inteface is availabe at https://tu-chemnitz.de/~potts/nfft/download.php. Then run startup.m in Matlab and you can execute the srcipts from examples.

Directory structure

File/Folder | Purpose ------------------:| ------------------------------------------------------ data_sets (dir) | Contains data sets that matlab creates (initially empty) examples (dir) | Code for creating the figures in the paper src (dir) | Source code COPYING | License information README.md | This file startup.m | Startup Matlab script

Feedback

Your comments are welcome! This is the first version of the library and may not be as robust or well documented as it should be. Please keep track of bugs or missing/confusing instructions in Guthub Issues. Alternatively, you might contact Robert Beinert or Michael Quellmalz.

Legal Information & Credits

Copyright (c) 2022 Robert Beinert and Michael Quellmalz

This software was written by Robert Beinert and Michael Quellmalz. It was developed at the Institute of Mathematics, TU Berlin. The second mentioned author acknowledges support by the German Research Foundation within the SFB Tomography Across the Scales.

FourierODT is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. If not stated otherwise, this applies to all files contained in this package and its sub-directories.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA