TIE - transport of intensity equation calculator

Description

Transport of Intensity Equation (TIE) is an experiemental open source julia package that solves the so-called transport of intensity equation (i.e., continuity equation of the scalar paraxial wave equation) for the phase of a fast electron wave function pertaining to an electron beam in transmission electron microscope (with minor adaptions it also work with optical data,x-ray date, etc.). The solver is based on a finite difference scheme and incorporates an iterative determination of the unkown boundary conditions. Poisson-like approximations to the TIE are also solved for comparison. Input data are two or three slighly defocused images provided as numpy arrays and a json file containing some metadata.

Installation

The package can be installed into the local julia environment by calling

add https://gitlab.mn.tu-dresden.de/amem-group/tie"

in the built in package manager "Pkg", available from the julia REPL by typing "]".

Usage

An illustrative test example containing a (de)focused images of a Landau pattern can be carried out via

calculate_TIE("path_to_input_files_folder","Py_on_C.json")

that is in the test folder together with the numpy arrays of the (de)focused image intensities. The image intensity files and the json files should reside in the same path_to_input_files_folder. Output containing reconstructed phase and boundary function is also written into that folder. In the json file, the following metadata has to be supplied:

• Uacc: acceleration voltage of the electrons [V]
• dz: defocus magnitude between in-focus and over-focused images [m]
• px: pixel size in x-direction [m]
• py: pixel size in y-direction [m]
• Io: over-focused image intensity numpy array file name
• Iu: under-focused images intensity numpy array file name
• If: focused images intensity numpy array file name
• thick: sample thickness [m]
• maxiter: maximal number of iterations of global optimizer
• bandlim: number of refined Fourier componenents of boundary function
• save: saving data yes / no
• poi: computing poisson reference solutions yes / no

Support

Questions about the library and its use can be asked to a.lubk@ifw-dresden.de.

Roadmap

A python implementation of this script is in progress.

Authors and acknowledgment

Credit for the code and underlying research goes to R. Kyrychenko, O. Zaiets, M. Wegner, D. Wolf, and A. Lubk

License

TIE is licensed under an MIT licence. When publishing results obtained with the help of the package please cite