Abstract
BackgroundAnalyzing the three-dimensional (3D) refractive index distribution of a single cell makes it possible to describe and characterize its inner structure in a marker-free manner. A dense, full-view tomographic data set is a set of images of a cell acquired for multiple rotational positions, densely distributed from 0 to 360 degrees. The reconstruction is commonly realized by projection tomography, which is based on the inversion of the Radon transform. The reconstruction quality of projection tomography is greatly improved when first order scattering, which becomes relevant when the imaging wavelength is comparable to the characteristic object size, is taken into account. This advanced reconstruction technique is called diffraction tomography. While many implementations of projection tomography are available today, there is no publicly available implementation of diffraction tomography so far.ResultsWe present a Python library that implements the backpropagation algorithm for diffraction tomography in 3D. By establishing benchmarks based on finite-difference time-domain (FDTD) simulations, we showcase the superiority of the backpropagation algorithm over the backprojection algorithm. Furthermore, we discuss how measurment parameters influence the reconstructed refractive index distribution and we also give insights into the applicability of diffraction tomography to biological cells.ConclusionThe present software library contains a robust implementation of the backpropagation algorithm. The algorithm is ideally suited for the application to biological cells. Furthermore, the implementation is a drop-in replacement for the classical backprojection algorithm and is made available to the large user community of the Python programming language.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0764-0) contains supplementary material, which is available to authorized users.
Highlights
Analyzing the three-dimensional (3D) refractive index distribution of a single cell makes it possible to describe and characterize its inner structure in a marker-free manner
We investigate the contribution of several physical parameters to the overall reconstruction quality, complement previously conducted two-dimensional (2D) studies [7, 10, 11] with 3D data, and draw conclusions concerning the validity of the backpropagation algorithm in three dimensions
To make the reconstruction process more transparent and to allow user-defined modifications of the reconstruction, we split the reconstruction process into three steps: a) apply a filter to the complex wave sinogram that corresponds to the required approximation (Born, Radon, or Rytov), b) reconstruct the object data from the sinogram, c) compute the refractive index distribution from the obtained object data
Summary
We present a Python library that implements the backpropagation algorithm for diffraction tomography in 3D. By establishing benchmarks based on finite-difference time-domain (FDTD) simulations, we showcase the superiority of the backpropagation algorithm over the backprojection algorithm. We discuss how measurment parameters influence the reconstructed refractive index distribution and we give insights into the applicability of diffraction tomography to biological cells
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