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will need Python 3, and following Python packages installed in your computer: numpy matplotlib scipy astropy pip install --upgrade numpy scipy matplotlib astropy jupyterlab I will be using Jupyter notebook to write and execute our python codes. Of course, you can use any other IDE or code editor of your choice. info If you are new to python programming, you can check out my python tutorial.","s":"Prerequisite","u":"/arpespythontools/docs/","h":"#prerequisite","p":1},{"i":5,"t":"You can clone the repository using git: git clone https://github.com/pranabdas/arpespythontools.git Alternatively, you can download the package archive here. Unzip the folder inside your project/ working directory or any other preferred location. You can install the required python packages from the requirements.txt specification: cd arpespythontools pip install --upgrade -r requirements.txt","s":"Getting ARPES Python tools","u":"/arpespythontools/docs/","h":"#getting-arpes-python-tools","p":1},{"i":7,"t":"We can import the module by import arpespythontools as arp so that later in the code we can refer to the module as arp in short. import sys sys.path.append(\"/workspaces/projects/\") # module is path is `/workspaces/projects/arpespythontools` import arpespythontools as arp If you put the library inside your working directory, you don't need the first two lines above.","s":"Importing arpespythontools","u":"/arpespythontools/docs/","h":"#importing-arpespythontools","p":1},{"i":9,"t":"If you want to setup and run python in a container, I have a Dockerfile, please adjust according to your needs. Dockerfile # Start from Ubuntu 22.04 LTS FROM ubuntu:jammy # Update OS RUN apt update && apt upgrade -y # Install software packages RUN apt install -y python3 python3-pip git fonts-open-sans # Install pip packages RUN pip3 install jupyterlab numpy scipy matplotlib # jupyterlab settings RUN mkdir /etc/jupyter && \\ (echo \"c.ServerApp.ip = '0.0.0.0'\" && \\ echo \"c.ServerApp.allow_root = True\" && \\ echo \"c.ServerApp.open_browser = False\") \\ >> /etc/jupyter/jupyter_server_config.py # clone arpespythontools to `/root` directory WORKDIR /root RUN git clone --depth 1 https://github.com/pranabdas/arpespythontools.git # leave in `/home` which we can map with the host WORKDIR /home Build the Docker image (you can specify any name for your image, here arptools): docker build -t arptools . Run Docker (you can either forward a specific port or if are using Linux, map host network): docker run -ti -p 8888:8888 -v ${PWD}:/home arptools bash docker run -ti --net=host -v /host/path:/home arptools bash Launch Jupyterlab inside the container: jupyter-lab Now we can create Python 3 notebook, and start writing our code. To import arpespythontools, include in your notebook: import sys sys.path.append(\"/root\") import arpespythontools as arp","s":"Run Python and Jupyter notebook in Docker container","u":"/arpespythontools/docs/","h":"#run-python-and-jupyter-notebook-in-docker-container","p":1},{"i":11,"t":"You can download the sample dataset used in this tutorial from here.","s":"Sample dataset","u":"/arpespythontools/docs/","h":"#sample-dataset","p":1},{"i":13,"t":"Sometimes our spectra are not well resolved. In such cases, we may perform some post processing to enhance the spectral features. You will need astropy module to be installed: pip install astropy caution Following modules are currently experimental and under development. Please review the codes and use with caution. You may instead use the Igor Macro implemented by Prof. P. Zhang. Here is our original data: url = 'https://pranabdas.github.io/drive/datasets/arpes/sample_spectrum.txt' data, energy, angle = arp.load_ses_spectra(url) plt.imshow(data, origin = 'lower', aspect = 'auto', \\ extent = (angle[0], angle[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show()","s":"Enhancing spectral features","u":"/arpespythontools/docs/enhancements","h":"","p":12},{"i":15,"t":"We can take the double derivative of the spectra in order to enhance the edges: I′=∂2I∂x2+w2∂2I∂y2I' = \\frac{\\partial^2 I}{\\partial x^2} + w^2 \\frac{\\partial^2 I}{\\partial y^2}I′=∂x2∂2I​+w2∂y2∂2I​ Since the xxx and yyy scales represent different quantities (units), we also have a weight factor www. # diff2 = arp.laplacian(data, x, y, bw=5, w=1) diff2 = arp.laplacian(data, energy, angle) plt.imshow(diff2, vmax=0, cmap='terrain_r') plt.axis('off') plt.show()","s":"Laplacian","u":"/arpespythontools/docs/enhancements","h":"#laplacian","p":12},{"i":17,"t":"The curvature method could be more appropriate to enhance spectral features. Two dimensional curvature is given by: I′=[1+Cx(∂I∂x)2]Cy∂2I∂y2−2CxCy∂I∂x∂I∂y∂2I∂x∂y+[1+Cy(∂I∂y)2]Cx∂2I∂x2[1+Cx(∂I∂x)2+Cy(∂I∂y)2]3/2I' = \\frac{\\left[1 + C_x \\left(\\frac{\\partial I}{\\partial x}\\right)^2\\right] C_y \\frac{\\partial^2 I}{\\partial y^2} - 2 C_x C_y \\frac{\\partial I}{\\partial x} \\frac{\\partial I}{\\partial y} \\frac{\\partial^2 I}{\\partial x \\partial y} + \\left[1+ C_y\\left(\\frac{\\partial I}{\\partial y}\\right)^2\\right] C_x \\frac{\\partial^2 I}{\\partial x^2}}{\\left[1 + C_x \\left(\\frac{\\partial I} {\\partial x}\\right)^2 + C_y \\left(\\frac{\\partial I}{\\partial y}\\right)^2 \\right]^{3/2}}I′=[1+Cx​(∂x∂I​)2+Cy​(∂y∂I​)2]3/2[1+Cx​(∂x∂I​)2]Cy​∂y2∂2I​−2Cx​Cy​∂x∂I​∂y∂I​∂x∂y∂2I​+[1+Cy​(∂y∂I​)2]Cx​∂x2∂2I​​ The details about the curvature method can be found here: P. Zhang et. al., A precise method for visualizing dispersive features in image plots, Review of Scientific Instruments 82, 043712 (2011). # cv2d = arp.cv2d(data, x, y, bw=5, c1=0.001, c2=0.001, w=1) cv2d = arp.cv2d(data, energy, angle) plt.imshow(cv2d, vmax=0, cmap='terrain_r') plt.axis('off') plt.show() You may vary various free parameters (CxC_xCx​, CyC_yCy​, www) in order to get the best result specific to your dataset.","s":"2D curvature","u":"/arpespythontools/docs/enhancements","h":"#2d-curvature","p":12},{"i":19,"t":"Full list of arpespythontools modules/ routines in alphabetical order: import arpespythontools as arp","s":"Glossary","u":"/arpespythontools/docs/glossary","h":"","p":18},{"i":21,"t":"data_crop, x_crop, y_crop = arp.crop_2d(data, x, y, x_min, x_max, y_min, y_max) Returns cropped 2D array and corresponding axes scaling vectors defined by [x_min, x_max] and [y_min, y_max]. Inputs: data : 2D array (intensity matrix). x : 1D vector (e.g., angle). y : 1D vector (e.g., energy). x_min and x_max : lower and upper bound of x to crop. y_min and y_max : lower and upper bound of y to crop. Outputs: data_crop : cropped 2D array. x_crop : corresponding x-scaling vector. y_crop : corresponding y-scaling vector.","s":"crop_2d","u":"/arpespythontools/docs/glossary","h":"#crop_2d","p":18},{"i":23,"t":"cv2d = arp.cv2d(data, x, y, bw=5, c1=0.001, c2=0.001, w=1) Calculates two-dimensional curvature. The details about the curvature method can be found here: P. Zhang et. al., A precise method for visualizing dispersive features in image plots, Review of Scientific Instruments 82, 043712 (2011). Inputs: data : 2D spectra. x : 1D array of energy. y : 1D array of theta values. bw : width for box-car smoothing, integer number of points (default value = 5). c1, c2 : free parameters as described in the above reference (optional). w : scaling weight (optional). Default weight is 1. Outputs: cv2d : 2D array of curvature. Output array has the same shape as the input array.","s":"cv2d","u":"/arpespythontools/docs/glossary","h":"#cv2d","p":18},{"i":25,"t":"arp.export_itx(path, data, x=[], y=[], z =[], wave_name='wave', \\ x_label='x-label', y_label='y-label', z_label='z-label') Exports 1D, 2D, or 3D array to Igor text (.itx) file. Inputs: path : Output filename or path of the .itx file. data : Input data array to save. Could be 1D, 2D, or 3D array. x, y, z (optional) : axes scaling for the corresponding input data array. If a value is not provided, default DimOffset=0 and DimDelta=1 would be applied. wave_name (optional) : Igor wave name. x-, y-, z-label (optional) : labels for x, y and z, respectively.","s":"export_itx","u":"/arpespythontools/docs/glossary","h":"#export_itx","p":18},{"i":27,"t":"data, x, y, z = arp.import_itx(name) Loads data and its axes scaling from Igor text (.itx) format. Inputs: name (string) : Input Igor text filename. Outputs: data : 1D, 2D, or 3D array. x, y, z : axes scales. Number of output returned depends on the input wave dimension.","s":"import_itx","u":"/arpespythontools/docs/glossary","h":"#import_itx","p":18},{"i":29,"t":"data_k, e_bin, k = arp.k_conv(data, energy, angle, fermi_energy) Transforms the intensity fromm real space to k-space. Inputs: data : 2D array of intensity values in real space. Dimension 1 is along energy and Dimension 2 is along angle. energy : 1D array of kinetic energy values in eV. angle : 1D array of theta values in degree. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 2D array of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. k : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1.","s":"k_conv","u":"/arpespythontools/docs/glossary","h":"#k_conv","p":18},{"i":31,"t":"data_k, e_bin, kx, ky = arp.k_conv3d(data, energy, theta, phi, fermi_energy) Transforms the Fermi map data from real space to k-space. Inputs: data : 3D matrix of intensity values in real space. Dimension 1 is along kinetic energy, Dimension 2 is along theta, and Dimension 3 along phi. energy : 1D array of kinetic energy values in eV. theta : 1D array of theta values in degree. This is the direction along the slit. phi : 1D array of phi values in degree. This is the direction perpendicular to the slit. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 3D matrix of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. kx, ky : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1 along the slit, and perpendicular to the slit directions, respectively.","s":"k_conv3d","u":"/arpespythontools/docs/glossary","h":"#k_conv3d","p":18},{"i":33,"t":"data_k, e_bin, kx, ky = arp.k_conv3d_mp(data, energy, theta, phi, fermi_energy) Multiprocessing implementation of k_conv3d. Should be up to as many times faster as many processor cores are available. Transforms the Fermi map data from real space to k-space. Inputs: data : 3D matrix of intensity values in real space. Dimension 1 is along kinetic energy, Dimension 2 is along theta, and Dimension 3 along phi. energy : 1D array of kinetic energy values in eV. theta : 1D array of theta values in degree. This is the direction along the slit. phi : 1D array of phi values in degree. This is the direction perpendicular to the slit. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 3D matrix of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. kx, ky : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1 along the slit, and perpendicular to the slit directions, respectively.","s":"k_conv3d_mp","u":"/arpespythontools/docs/glossary","h":"#k_conv3d_mp","p":18},{"i":35,"t":"diff2 = arp.laplacian(data, x, y, bw=5, w=1) Laplacian (second order partial derivatives with respect to both energy and angle) of the spectra. Inputs: data : 2D spectra. x : 1D array of energy. y : 1D array of theta values. bw : width for box-car smoothing, integer number of points (default value = 5). w : scaling weight (optional). Default weight is 1. Outputs: diff2 : 2D array of spectra after taking second order partial derivative w.r.t. both energy and angle. This array has the same shape as input array.","s":"laplacian","u":"/arpespythontools/docs/glossary","h":"#laplacian","p":18},{"i":37,"t":"edc = arp.line_profile(data, y, y_min, y_max) Returns the 1D vector of integrated line profile. The integration is done along the second dimension of data. Inputs: data : 2D array. y : 1D vector of axis scaling along the second dimension of data. y_min, y_max : integration bounds. Outputs: edc : 1D vector of integrated values defined by the width [y_min, y_max] along the first dimension.","s":"line_profile","u":"/arpespythontools/docs/glossary","h":"#line_profile","p":18},{"i":39,"t":"data, energy, theta, phi = arp.load_map_data(name) Loads Fermi map data from output .zip file of Scienta-Omicron SES program. Inputs: name (string) : name or file path of .zip map data file. It could be a local path or URL path. Outputs: data: 3D array of intensity values. Dimension 1 → energy, Dimension 2 → angle theta (along the slit direction), and Dimension 3 → angle phi (azimuth/ perpendicular to the slit direction). energy: 1D vector of kinetic energy points in eV. theta: 1D vector of theta values in degree. phi : 1D vector of phi values in degree.","s":"load_ses_map","u":"/arpespythontools/docs/glossary","h":"#load_ses_map","p":18},{"i":41,"t":"data, angle, energy = arp.load_ses_spectra(name) Loads data from a text file produced by Scienta-Omicron SES program. Inputs: name (string) : name or file path of SES .txt file. It could be a local path or a URL address. Outputs: data : 2D array (numpy ndarry) of intensity values. angle : 1D vector (numpy ndarry) of angle values in degree. energy : 1D vector (numpy ndarry) of kinetic energy values in eV.","s":"load_ses_spectra","u":"/arpespythontools/docs/glossary","h":"#load_ses_spectra","p":18},{"i":43,"t":"surf = arp.plane_slice(data, x, x_min, x_max) Returns the 2D slice along the first dimension of data and integrated in the width [x_min, x_max]. Inputs: data : 3D matrix. x : axes scaling along the first dimension. x_min, x_max : integration bounds. Outputs: surf : 2D array.","s":"plane_slice","u":"/arpespythontools/docs/glossary","h":"#plane_slice","p":18},{"i":45,"t":"data_r, theta_r, phi_r = arp.rotate_2d(data, angle, theta, phi) Rotates 2D array with rotation axis perpendicular to the plane. Center of rotation is at theta=0, phi=0. Inputs: data : 2D array. The data will be rotated perpendicular to the plane. angle : amount of rotation in degree. Positive value rotates clockwise. theta : 1D array of axis scaling along the second dimension of data. phi : 1D array of axis scaling along the third dimension of data. Outputs: data_r : rotated 2D matrix. Data points outside of interpolation range is set to NaN (not a number). theta_r : 1D array of axis scaling along the second dimension of data_r. phi_r : 1D array of axis scaling along the third dimension of data_r.","s":"rotate_2d","u":"/arpespythontools/docs/glossary","h":"#rotate_2d","p":18},{"i":47,"t":"data_r, theta_r, phi_r = arp.rotate_3d(data, angle, theta, phi) Rotates the volume data (3D matrix) with respect to the first dimension. Center of rotation is at theta=0, phi=0. Inputs: data : 3D array. First, second, and third dimensions are along energy, theta, and phi, respectively. The data will be rotated perpendicular to energy, i.e., in the theta-phi plane. angle : amount of rotation in degree. Positive value rotates clockwise. theta : 1D array of axis scaling along the second dimension of data. phi : 1D array of axis scaling along the third dimension of data. Outputs: data_r : rotated 3D matrix. Data points outside of interpolation range is set to NaN (not a number). theta_r : 1D array of axis scaling along the second dimension of data_r. phi_r : 1D array of axis scaling along the third dimension of data_r.","s":"rotate_3d","u":"/arpespythontools/docs/glossary","h":"#rotate_3d","p":18},{"i":49,"t":"arp.save_xps(energy, intensity, \"xps_data.x_y\") Save XPS energy and intensity in two column plaintext file. Inputs: energy : one dimensional vector intensity : one dimensional vector filename : Optional output filename. Two column data is saved in file.","s":"save_xps","u":"/arpespythontools/docs/glossary","h":"#save_xps","p":18},{"i":51,"t":"At the moment, this module can only import data produced by Scienta-Omicron SES program. However, you can implement custom loader specific to your data file, and use other modules. Here is an example of custom loader. For the spectral scans, we will use SES produced plaintext (.txt) output file as input, while in case of Fermi map data, we will need the ZIP files as input format. First thing first, import arpespythontools in your program: import arpespythontools as arp","s":"Loading ARPES data","u":"/arpespythontools/docs/data-import","h":"","p":50},{"i":53,"t":"data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') Here, data is a two dimensional numpy array; x-dimension is along energy and y-dimension is along angle/theta. energy and angle are one dimensional vectors of kinetic energy in eV and angle values are in degree, respectively. tip If you have a workflow to directly work from cloud services like Dropbox or OneDrive, it is possible to import data directly from an URL source instead of local file path. You will require additional code for Dropbox or OneDrive authentication, which is not currently included with arpespythontools. url = \"https://pranabdas.github.io/drive/datasets/arpes/sample_spectrum.txt\" data, energy, angle = arp.load_ses_spectra(url)","s":"Load ARPES Spectra from SES plaintext file","u":"/arpespythontools/docs/data-import","h":"#load-arpes-spectra-from-ses-plaintext-file","p":50},{"i":55,"t":"map_data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') map_data will contain three dimensional array of Fermi map data; x-dimension is along energy, y-dimension is along theta and z-dimension is along phi. energy, theta, and phi are one dimensional vectors of kinetic energy (eV), theta (deg), and phi (deg), respectively. Notice that you do not need to unzip the SES produced .zip file, the program directly reads from .zip file.","s":"Load Fermi Map data from SES ZIP file","u":"/arpespythontools/docs/data-import","h":"#load-fermi-map-data-from-ses-zip-file","p":50},{"i":57,"t":"If you need to work with the Igor Program, arpespythontools provides a way to import and export data in Igor text (.itx) format. import_itx and export_itx functions can import and export 1-dimensionl, 2-dimensionl, and 3-dimensionl data/wave, respectively. import arpespythontools as arp # import itx file data, x = arp.import_itx('path/data.itx') # 1D wave data, x, y = arp.import_itx('path/data.itx') # 2D wave data, x, y, z = arp.import_itx('path/data.itx') # 3D wave # export itx file arp.export_itx(\"path/data.itx\", data, x=[], y=[], z =[], wave_name='wave',\\ x_label='x-label', y_label='y-label', z_label='z-label') While importing, data contains the 1D, 2D or 3D data. x, y, z are the corresponding axis scaling. While exporting, axis scaling is optional. In case x, y, z is not provided the default scaling (DimOffset=0, and DimDelta=1) would be applied. Similarly, you can provide wave name, and axis labels (optional) as well. note If you need to read Igor Binary Waves (.ibw format), you can check out this Python implementation: https://github.com/wking/igor.","s":"Import / export Igor text","u":"/arpespythontools/docs/igor","h":"","p":56},{"i":59,"t":"MIT License Copyright (c) 2019-Present Pranab Das Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.","s":"License","u":"/arpespythontools/docs/license","h":"","p":58},{"i":61,"t":"The electron analyzer records the intensities in angle and kinetic energy. In order to convert convert into k-space we can use the following formula: Ebin+Wϕ+Ekin=hνE_{bin} + W_ϕ + E_{kin} = h\\nuEbin​+Wϕ​+Ekin​=hνk∥=2mℏ2Ekinsin⁡(θ)k_{\\parallel} = \\sqrt{\\frac{2m}{\\hbar^2} E_{kin}} \\sin(\\theta)k∥​=ℏ22m​Ekin​​sin(θ) info In the above expression, photon momentum is ignored, which is good approximation for photon energies in UV range or lower. If high photon energy is used (e.g., soft-x-ray), we will need correction for photon momentum. The input data is in uniform grid of angle (degree) and energy. After point-wise conversion, we no longer have uniform grid in k-space. In order to store the data in uniform grid, we make use of interpolation. The k_conv function can convert two-dimensional Energy vs theta data to binding energy vs kkk (momentum). Here binding energy below the Fermi energy is positive convention used. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') data_k, e_bin, k = arp.k_conv(data, energy, angle, 16.67) # Fermi energy = 16.67 eV # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(data_k, origin = 'lower', aspect = 'auto', \\ extent = (k[0], k[-1], e_bin[0], e_bin[-1])) plt.xlabel(\"k ($\\AA^{-1}$)\") plt.ylabel(\"$E_{bin}$ (eV)\") plt.set_cmap('magma_r') plt.show() Which would produce a plot like this:","s":"k-space conversion","u":"/arpespythontools/docs/k-conv","h":"","p":60},{"i":63,"t":"Similarly, we can convert three dimensional (Energy, theta, phi) Fermi map data to kkk-space by using k_conv3d function. data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') data_k, e_bin, kx, ky = arp.k_conv3d(data, energy, theta, phi, 16.67) # Fermi energy = 16.67 eV caution Depending on the size of data matrix and computing power, the k_conv3d might take several minutes to complete.","s":"k-space conversion for 3D Fermi map data","u":"/arpespythontools/docs/k-conv","h":"#k-space-conversion-for-3d-fermi-map-data","p":60},{"i":65,"t":"There is also a multiprocessing implementation of the k_conv3d, which should be up to as many times faster as many processor cores are available. data_k, e_bin, kx, ky = arp.k_conv3d_mp(data, energy, theta, phi, 16.67)","s":"Multiprocessing version","u":"/arpespythontools/docs/k-conv","h":"#multiprocessing-version","p":60},{"i":67,"t":"We can slice our 3D Fermi map data in order to get a particular plane using the plane_slice function. Say, we need a constant energy cut. import arpespythontools as arp data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') # We want iso-energy surface integrated between energy values 15.6 and 15.8 eV iso_energy_surf = arp.plane_slice(data, energy, 15.6, 15.8) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(iso_energy_surf, origin = 'lower', aspect = 'auto', \\ extent = (theta[0], theta[-1], phi[0], phi[-1])) plt.xlabel(\"$\\\\phi$ (deg)\") plt.ylabel(\"$\\\\theta$ (deg)\") plt.show() This should give you an iso-energy surface like this: How about if we want the slice along another axis? All we need is transpose the data, and provide the correct axis order. # integrating phi values between (-0.5, 0.5) degrees phi_slice = arp.plane_slice(data.transpose([2, 0, 1]), phi, -0.5, 0.5) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(phi_slice, origin = 'lower', aspect = 'auto', \\ extent = (phi[0], phi[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.show()","s":"Slicing volume data","u":"/arpespythontools/docs/plane-slice","h":"","p":66},{"i":69,"t":"If your Fermi map measurement was not done keeping the high symmetry directions along the slit direction (or perpendicular to the slit direction), and you need to rotate the collected data in order to make the high symmetry directions along the x- or y-coordinate, the rotate_2d and rotate_3d functions come handy. Remember positive rotation angle rotates clockwise, and center of rotation is at (kx=0k_x=0kx​=0, ky=0k_y=0ky​=0). rotate_2d can rotate a 2D array with respect to its surface normal. Let's get some Fermi map data first. import arpespythontools as arp import matplotlib.pyplot as plt %matplotlib inline url = 'https://pranabdas.github.io/drive/datasets/arpes/sample_map_data.zip' data, energy, theta, phi = arp.load_ses_map(url) # Plot one slice plt.figure(figsize = (8, 6)) plt.imshow(data[150, :, :], origin = 'lower', aspect = 'auto', \\ extent = (phi[0], phi[-1], theta[0], theta[-1])) plt.show() This is how a constant energy cut looks like before rotation: Now, we can rotate only a single slice first. data_r, theta_r, phi_r = arp.rotate_2d(data[150, :, :], 45, theta, phi) # Plot one slice plt.figure(figsize = (8, 6)) plt.imshow(data_r, origin = 'lower', aspect = 'auto', \\ extent = (phi_r[0], phi_r[-1], theta_r[0], theta_r[-1])) plt.show() Let us plot a slice again. This is what we get after the rotation.","s":"Rotate Fermi map data","u":"/arpespythontools/docs/rotate","h":"","p":68},{"i":71,"t":"Instead of rotating only one slice, we can also rotate the full 3D array. rotate_3d function needs the 3D map data (with first dimension along the energy, second and third dimensions are kxk_xkx​ and kyk_yky​, respectively) as input. It needs kxk_xkx​ and kyk_yky​ vectors as input as well. Provide the required angle to rotate in degree as before. Axis of rotation is the first axis (i.e., energy). The function returns rotated data, new kx′k_x'kx′​ and ky′k_y'ky′​ vectors. Let's see an example: data_r, theta_r, phi_r = arp.rotate_3d(data, 45, theta, phi) # we can plot a slice after rotation to get the above result plt.imshow(data_r[150, :, :], origin = 'lower', aspect = 'auto', \\ extent = (phi_r[0], phi_r[-1], theta_r[0], theta_r[-1])) plt.show()","s":"Rotate 3D Fermi map data","u":"/arpespythontools/docs/rotate","h":"#rotate-3d-fermi-map-data","p":68},{"i":73,"t":"This example provides basic example of image plot using matplotlib. There is a huge list of customization possible using matplotlib. You can consult matplotlib documentation for advanced customizations. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(data, origin = 'lower', aspect = 'auto', \\ extent = (angle[0], angle[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show() You should see a plot like this upon successful execution:","s":"Data visualization","u":"/arpespythontools/docs/visualization","h":"","p":72},{"i":75,"t":"We can crop images (two-dimensionl data) using the crop_2d function. Say, we want to crop and focus only on the Dirac cone part. We want to crop the energy range (16, 16.8) and angle range (-6, 4). # data_crop, x_crop, y_crop = crop_2d(data, x, y, x_min, x_max, y_min, y_max) data_crop, x_crop, y_crop = arp.crop_2d(data, x, y, 16, 16.8, -6, 4) plt.figure(figsize = (8, 8)) plt.imshow(data_crop, origin = 'lower', aspect = 'auto', \\ extent = (y_crop[0], y_crop[-1], x_crop[0], x_crop[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show() That's what we wanted to achieve. tip For advanced 3D visualization of Fermi map data, you may have a look at this example from my Python tutorial.","s":"Crop image","u":"/arpespythontools/docs/visualization","h":"#crop-image","p":72},{"i":77,"t":"X-ray Photoemission Spectroscopy (XPS) data is recorded in the same way as the ARPES spectra. It records two dimensional (energy- and angle- resolved) intensities. Since the energy range for XPS scans are often very large, the data files could be very large (up to several hundred megabytes). Generally, we do not need any angle-resolved information, therefore the spectra can be saved in simple energy vs. intensity two column format. XPS data are generally measured in transmission mode, which has angular range about (-3, 3) degree. Often there are some artifacts on the edge of detector, so we can restrict only to the central part with integration limits for line profile. import arpespythontools as arp import numpy as np data, energy, angle = arp.load_ses_spectra(\"xps_data.txt\") intensity = arp.line_profile(data, angle, -2.5, 2.5) If you require energy in terms of binding energy instead of kinetic energy, you can convert using: Ebin=EF−EkinE_{bin} = E_F - E_{kin}Ebin​=EF​−Ekin​EF=hν−WϕE_F = h\\nu - W_{\\phi}EF​=hν−Wϕ​ where EFE_FEF​ is Fermi energy, and WϕW_{\\phi}Wϕ​ is work function which is about 4.5 eV for our setup. tip If you do not need to specify the integration limits i.e., you want to sum over full angle range, it is simpler to use numpy.sum method instead. import numpy as np intensity = np.sum(data, axis=1)","s":"Working with XPS data","u":"/arpespythontools/docs/xps","h":"","p":76},{"i":79,"t":"xps_data = np.array([energy, intensity]).T np.savetxt(\"xps_data.x_y\", xps_data) In the above example, we have saved the data in two column (.x_y) format, which is suitable for importing to other XPS analysis software (like CasaXPS). We may also use the module save_xps to save data. arp.save_xps(energy, intensity, \"xps_data.x_y\") If you need to load the two column data using python: energy, intensity = np.loadtxt(\"xps_data.x_y\", unpack=True) tip If you only need to obtain integrated intensity from the SES spectra for XPS data analysis, you may try our web application.","s":"Save/export XPS data","u":"/arpespythontools/docs/xps","h":"#saveexport-xps-data","p":76},{"i":81,"t":"How can we extract line profile from our two-dimensional image data? The function line_profile does the work. Let's say we want to extract an energy distribution curve (EDC) from our ARPES spectrum. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') # extract line profile between angles (-3, 3) edc = arp.line_profile(data, angle, -3, 3) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.plot(energy, edc/max(edc)) plt.xlabel('$E_{kin}$ (eV)') plt.ylabel('Intensity (a.u)') plt.show() How about if we want the momentum distribution curve (MDC) instead? That means we have to extract line profile along the other axis, which can be done by transposing the data, and interchanging the axes: # extract line profile between energy values (16.5, 16.7) mdc = arp.line_profile(data.T, energy, 16.5, 16.7) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.plot(angle, mdc/max(mdc)) plt.xlabel('$\\\\theta$ (deg)') plt.ylabel('Intensity (a.u)') plt.show() tip If you do not need to specify the integration limits i.e., you want to sum over full angle (in case of EDC) or energy (in case MDC) range, it is simpler to use numpy.sum method instead. import numpy as np edc = np.sum(data, axis=1) mdc = np.sum(data, axis=0)","s":"Extracting line 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the moment, this module can only import data produced by Scienta-Omicron SES program. However, you can implement custom loader specific to your data file, and use other modules. Here is an example of custom loader. For the spectral scans, we will use SES produced plaintext (.txt) output file as input, while in case of Fermi map data, we will need the ZIP files as input format. First thing first, import arpespythontools in your program: import arpespythontools as arp","s":"Loading ARPES data","u":"/arpespythontools/docs/data-import","h":"","p":1},{"i":4,"t":"data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') Here, data is a two dimensional numpy array; x-dimension is along energy and y-dimension is along angle/theta. energy and angle are one dimensional vectors of kinetic energy in eV and angle values are in degree, respectively. tip If you have a workflow to directly work from cloud services like Dropbox or OneDrive, it is possible to import data directly from an URL source instead of local file path. You will require additional code for Dropbox or OneDrive authentication, which is not currently included with arpespythontools. url = \"https://pranabdas.github.io/drive/datasets/arpes/sample_spectrum.txt\" data, energy, angle = arp.load_ses_spectra(url)","s":"Load ARPES Spectra from SES plaintext file","u":"/arpespythontools/docs/data-import","h":"#load-arpes-spectra-from-ses-plaintext-file","p":1},{"i":6,"t":"map_data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') map_data will contain three dimensional array of Fermi map data; x-dimension is along energy, y-dimension is along theta and z-dimension is along phi. energy, theta, and phi are one dimensional vectors of kinetic energy (eV), theta (deg), and phi (deg), respectively. Notice that you do not need to unzip the SES produced .zip file, the program directly reads from .zip file.","s":"Load Fermi Map data from SES ZIP file","u":"/arpespythontools/docs/data-import","h":"#load-fermi-map-data-from-ses-zip-file","p":1},{"i":9,"t":"You will need Python 3, and following Python packages installed in your computer: numpy matplotlib scipy astropy pip install --upgrade numpy scipy matplotlib astropy jupyterlab I will be using Jupyter notebook to write and execute our python codes. Of course, you can use any other IDE or code editor of your choice. info If you are new to python programming, you can check out my python tutorial.","s":"Prerequisite","u":"/arpespythontools/docs/","h":"#prerequisite","p":7},{"i":11,"t":"You can clone the repository using git: git clone https://github.com/pranabdas/arpespythontools.git Alternatively, you can download the package archive here. Unzip the folder inside your project/ working directory or any other preferred location. You can install the required python packages from the requirements.txt specification: cd arpespythontools pip install --upgrade -r requirements.txt","s":"Getting ARPES Python tools","u":"/arpespythontools/docs/","h":"#getting-arpes-python-tools","p":7},{"i":13,"t":"We can import the module by import arpespythontools as arp so that later in the code we can refer to the module as arp in short. import sys sys.path.append(\"/workspaces/projects/\") # module is path is `/workspaces/projects/arpespythontools` import arpespythontools as arp If you put the library inside your working directory, you don't need the first two lines above.","s":"Importing arpespythontools","u":"/arpespythontools/docs/","h":"#importing-arpespythontools","p":7},{"i":15,"t":"If you want to setup and run python in a container, I have a Dockerfile, please adjust according to your needs. Dockerfile # Start from Ubuntu 22.04 LTS FROM ubuntu:jammy # Update OS RUN apt update && apt upgrade -y # Install software packages RUN apt install -y python3 python3-pip git fonts-open-sans # Install pip packages RUN pip3 install jupyterlab numpy scipy matplotlib # jupyterlab settings RUN mkdir /etc/jupyter && \\ (echo \"c.ServerApp.ip = '0.0.0.0'\" && \\ echo \"c.ServerApp.allow_root = True\" && \\ echo \"c.ServerApp.open_browser = False\") \\ >> /etc/jupyter/jupyter_server_config.py # clone arpespythontools to `/root` directory WORKDIR /root RUN git clone --depth 1 https://github.com/pranabdas/arpespythontools.git # leave in `/home` which we can map with the host WORKDIR /home Build the Docker image (you can specify any name for your image, here arptools): docker build -t arptools . Run Docker (you can either forward a specific port or if are using Linux, map host network): docker run -ti -p 8888:8888 -v ${PWD}:/home arptools bash docker run -ti --net=host -v /host/path:/home arptools bash Launch Jupyterlab inside the container: jupyter-lab Now we can create Python 3 notebook, and start writing our code. To import arpespythontools, include in your notebook: import sys sys.path.append(\"/root\") import arpespythontools as arp","s":"Run Python and Jupyter notebook in Docker container","u":"/arpespythontools/docs/","h":"#run-python-and-jupyter-notebook-in-docker-container","p":7},{"i":17,"t":"You can download the sample dataset used in this tutorial from here.","s":"Sample dataset","u":"/arpespythontools/docs/","h":"#sample-dataset","p":7},{"i":19,"t":"If you need to work with the Igor Program, arpespythontools provides a way to import and export data in Igor text (.itx) format. import_itx and export_itx functions can import and export 1-dimensionl, 2-dimensionl, and 3-dimensionl data/wave, respectively. import arpespythontools as arp # import itx file data, x = arp.import_itx('path/data.itx') # 1D wave data, x, y = arp.import_itx('path/data.itx') # 2D wave data, x, y, z = arp.import_itx('path/data.itx') # 3D wave # export itx file arp.export_itx(\"path/data.itx\", data, x=[], y=[], z =[], wave_name='wave',\\ x_label='x-label', y_label='y-label', z_label='z-label') While importing, data contains the 1D, 2D or 3D data. x, y, z are the corresponding axis scaling. While exporting, axis scaling is optional. In case x, y, z is not provided the default scaling (DimOffset=0, and DimDelta=1) would be applied. Similarly, you can provide wave name, and axis labels (optional) as well. note If you need to read Igor Binary Waves (.ibw format), you can check out this Python implementation: https://github.com/wking/igor.","s":"Import / export Igor text","u":"/arpespythontools/docs/igor","h":"","p":18},{"i":21,"t":"The electron analyzer records the intensities in angle and kinetic energy. In order to convert convert into k-space we can use the following formula: Ebin+Wϕ+Ekin=hνE_{bin} + W_ϕ + E_{kin} = h\\nuEbin​+Wϕ​+Ekin​=hνk∥=2mℏ2Ekinsin⁡(θ)k_{\\parallel} = \\sqrt{\\frac{2m}{\\hbar^2} E_{kin}} \\sin(\\theta)k∥​=ℏ22m​Ekin​​sin(θ) info In the above expression, photon momentum is ignored, which is good approximation for photon energies in UV range or lower. If high photon energy is used (e.g., soft-x-ray), we will need correction for photon momentum. The input data is in uniform grid of angle (degree) and energy. After point-wise conversion, we no longer have uniform grid in k-space. In order to store the data in uniform grid, we make use of interpolation. The k_conv function can convert two-dimensional Energy vs theta data to binding energy vs kkk (momentum). Here binding energy below the Fermi energy is positive convention used. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') data_k, e_bin, k = arp.k_conv(data, energy, angle, 16.67) # Fermi energy = 16.67 eV # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(data_k, origin = 'lower', aspect = 'auto', \\ extent = (k[0], k[-1], e_bin[0], e_bin[-1])) plt.xlabel(\"k ($\\AA^{-1}$)\") plt.ylabel(\"$E_{bin}$ (eV)\") plt.set_cmap('magma_r') plt.show() Which would produce a plot like this:","s":"k-space conversion","u":"/arpespythontools/docs/k-conv","h":"","p":20},{"i":23,"t":"Similarly, we can convert three dimensional (Energy, theta, phi) Fermi map data to kkk-space by using k_conv3d function. data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') data_k, e_bin, kx, ky = arp.k_conv3d(data, energy, theta, phi, 16.67) # Fermi energy = 16.67 eV caution Depending on the size of data matrix and computing power, the k_conv3d might take several minutes to complete.","s":"k-space conversion for 3D Fermi map data","u":"/arpespythontools/docs/k-conv","h":"#k-space-conversion-for-3d-fermi-map-data","p":20},{"i":25,"t":"There is also a multiprocessing implementation of the k_conv3d, which should be up to as many times faster as many processor cores are available. data_k, e_bin, kx, ky = arp.k_conv3d_mp(data, energy, theta, phi, 16.67)","s":"Multiprocessing version","u":"/arpespythontools/docs/k-conv","h":"#multiprocessing-version","p":20},{"i":27,"t":"Sometimes our spectra are not well resolved. In such cases, we may perform some post processing to enhance the spectral features. You will need astropy module to be installed: pip install astropy caution Following modules are currently experimental and under development. Please review the codes and use with caution. You may instead use the Igor Macro implemented by Prof. P. Zhang. Here is our original data: url = 'https://pranabdas.github.io/drive/datasets/arpes/sample_spectrum.txt' data, energy, angle = arp.load_ses_spectra(url) plt.imshow(data, origin = 'lower', aspect = 'auto', \\ extent = (angle[0], angle[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show()","s":"Enhancing spectral features","u":"/arpespythontools/docs/enhancements","h":"","p":26},{"i":29,"t":"We can take the double derivative of the spectra in order to enhance the edges: I′=∂2I∂x2+w2∂2I∂y2I' = \\frac{\\partial^2 I}{\\partial x^2} + w^2 \\frac{\\partial^2 I}{\\partial y^2}I′=∂x2∂2I​+w2∂y2∂2I​ Since the xxx and yyy scales represent different quantities (units), we also have a weight factor www. # diff2 = arp.laplacian(data, x, y, bw=5, w=1) diff2 = arp.laplacian(data, energy, angle) plt.imshow(diff2, vmax=0, cmap='terrain_r') plt.axis('off') plt.show()","s":"Laplacian","u":"/arpespythontools/docs/enhancements","h":"#laplacian","p":26},{"i":31,"t":"The curvature method could be more appropriate to enhance spectral features. Two dimensional curvature is given by: I′=[1+Cx(∂I∂x)2]Cy∂2I∂y2−2CxCy∂I∂x∂I∂y∂2I∂x∂y+[1+Cy(∂I∂y)2]Cx∂2I∂x2[1+Cx(∂I∂x)2+Cy(∂I∂y)2]3/2I' = \\frac{\\left[1 + C_x \\left(\\frac{\\partial I}{\\partial x}\\right)^2\\right] C_y \\frac{\\partial^2 I}{\\partial y^2} - 2 C_x C_y \\frac{\\partial I}{\\partial x} \\frac{\\partial I}{\\partial y} \\frac{\\partial^2 I}{\\partial x \\partial y} + \\left[1+ C_y\\left(\\frac{\\partial I}{\\partial y}\\right)^2\\right] C_x \\frac{\\partial^2 I}{\\partial x^2}}{\\left[1 + C_x \\left(\\frac{\\partial I} {\\partial x}\\right)^2 + C_y \\left(\\frac{\\partial I}{\\partial y}\\right)^2 \\right]^{3/2}}I′=[1+Cx​(∂x∂I​)2+Cy​(∂y∂I​)2]3/2[1+Cx​(∂x∂I​)2]Cy​∂y2∂2I​−2Cx​Cy​∂x∂I​∂y∂I​∂x∂y∂2I​+[1+Cy​(∂y∂I​)2]Cx​∂x2∂2I​​ The details about the curvature method can be found here: P. Zhang et. al., A precise method for visualizing dispersive features in image plots, Review of Scientific Instruments 82, 043712 (2011). # cv2d = arp.cv2d(data, x, y, bw=5, c1=0.001, c2=0.001, w=1) cv2d = arp.cv2d(data, energy, angle) plt.imshow(cv2d, vmax=0, cmap='terrain_r') plt.axis('off') plt.show() You may vary various free parameters (CxC_xCx​, CyC_yCy​, www) in order to get the best result specific to your dataset.","s":"2D curvature","u":"/arpespythontools/docs/enhancements","h":"#2d-curvature","p":26},{"i":33,"t":"MIT License Copyright (c) 2019-Present Pranab Das Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.","s":"License","u":"/arpespythontools/docs/license","h":"","p":32},{"i":35,"t":"How can we extract line profile from our two-dimensional image data? The function line_profile does the work. Let's say we want to extract an energy distribution curve (EDC) from our ARPES spectrum. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') # extract line profile between angles (-3, 3) edc = arp.line_profile(data, angle, -3, 3) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.plot(energy, edc/max(edc)) plt.xlabel('$E_{kin}$ (eV)') plt.ylabel('Intensity (a.u)') plt.show() How about if we want the momentum distribution curve (MDC) instead? That means we have to extract line profile along the other axis, which can be done by transposing the data, and interchanging the axes: # extract line profile between energy values (16.5, 16.7) mdc = arp.line_profile(data.T, energy, 16.5, 16.7) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.plot(angle, mdc/max(mdc)) plt.xlabel('$\\\\theta$ (deg)') plt.ylabel('Intensity (a.u)') plt.show() tip If you do not need to specify the integration limits i.e., you want to sum over full angle (in case of EDC) or energy (in case MDC) range, it is simpler to use numpy.sum method instead. import numpy as np edc = np.sum(data, axis=1) mdc = np.sum(data, axis=0)","s":"Extracting line profile","u":"/arpespythontools/docs/line-profile","h":"","p":34},{"i":37,"t":"We can slice our 3D Fermi map data in order to get a particular plane using the plane_slice function. Say, we need a constant energy cut. import arpespythontools as arp data, energy, theta, phi = arp.load_ses_map('sample_map_data.zip') # We want iso-energy surface integrated between energy values 15.6 and 15.8 eV iso_energy_surf = arp.plane_slice(data, energy, 15.6, 15.8) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(iso_energy_surf, origin = 'lower', aspect = 'auto', \\ extent = (theta[0], theta[-1], phi[0], phi[-1])) plt.xlabel(\"$\\\\phi$ (deg)\") plt.ylabel(\"$\\\\theta$ (deg)\") plt.show() This should give you an iso-energy surface like this: How about if we want the slice along another axis? All we need is transpose the data, and provide the correct axis order. # integrating phi values between (-0.5, 0.5) degrees phi_slice = arp.plane_slice(data.transpose([2, 0, 1]), phi, -0.5, 0.5) # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(phi_slice, origin = 'lower', aspect = 'auto', \\ extent = (phi[0], phi[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.show()","s":"Slicing volume data","u":"/arpespythontools/docs/plane-slice","h":"","p":36},{"i":39,"t":"Full list of arpespythontools modules/ routines in alphabetical order: import arpespythontools as arp","s":"Glossary","u":"/arpespythontools/docs/glossary","h":"","p":38},{"i":41,"t":"data_crop, x_crop, y_crop = arp.crop_2d(data, x, y, x_min, x_max, y_min, y_max) Returns cropped 2D array and corresponding axes scaling vectors defined by [x_min, x_max] and [y_min, y_max]. Inputs: data : 2D array (intensity matrix). x : 1D vector (e.g., angle). y : 1D vector (e.g., energy). x_min and x_max : lower and upper bound of x to crop. y_min and y_max : lower and upper bound of y to crop. Outputs: data_crop : cropped 2D array. x_crop : corresponding x-scaling vector. y_crop : corresponding y-scaling vector.","s":"crop_2d","u":"/arpespythontools/docs/glossary","h":"#crop_2d","p":38},{"i":43,"t":"cv2d = arp.cv2d(data, x, y, bw=5, c1=0.001, c2=0.001, w=1) Calculates two-dimensional curvature. The details about the curvature method can be found here: P. Zhang et. al., A precise method for visualizing dispersive features in image plots, Review of Scientific Instruments 82, 043712 (2011). Inputs: data : 2D spectra. x : 1D array of energy. y : 1D array of theta values. bw : width for box-car smoothing, integer number of points (default value = 5). c1, c2 : free parameters as described in the above reference (optional). w : scaling weight (optional). Default weight is 1. Outputs: cv2d : 2D array of curvature. Output array has the same shape as the input array.","s":"cv2d","u":"/arpespythontools/docs/glossary","h":"#cv2d","p":38},{"i":45,"t":"arp.export_itx(path, data, x=[], y=[], z =[], wave_name='wave', \\ x_label='x-label', y_label='y-label', z_label='z-label') Exports 1D, 2D, or 3D array to Igor text (.itx) file. Inputs: path : Output filename or path of the .itx file. data : Input data array to save. Could be 1D, 2D, or 3D array. x, y, z (optional) : axes scaling for the corresponding input data array. If a value is not provided, default DimOffset=0 and DimDelta=1 would be applied. wave_name (optional) : Igor wave name. x-, y-, z-label (optional) : labels for x, y and z, respectively.","s":"export_itx","u":"/arpespythontools/docs/glossary","h":"#export_itx","p":38},{"i":47,"t":"data, x, y, z = arp.import_itx(name) Loads data and its axes scaling from Igor text (.itx) format. Inputs: name (string) : Input Igor text filename. Outputs: data : 1D, 2D, or 3D array. x, y, z : axes scales. Number of output returned depends on the input wave dimension.","s":"import_itx","u":"/arpespythontools/docs/glossary","h":"#import_itx","p":38},{"i":49,"t":"data_k, e_bin, k = arp.k_conv(data, energy, angle, fermi_energy) Transforms the intensity fromm real space to k-space. Inputs: data : 2D array of intensity values in real space. Dimension 1 is along energy and Dimension 2 is along angle. energy : 1D array of kinetic energy values in eV. angle : 1D array of theta values in degree. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 2D array of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. k : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1.","s":"k_conv","u":"/arpespythontools/docs/glossary","h":"#k_conv","p":38},{"i":51,"t":"data_k, e_bin, kx, ky = arp.k_conv3d(data, energy, theta, phi, fermi_energy) Transforms the Fermi map data from real space to k-space. Inputs: data : 3D matrix of intensity values in real space. Dimension 1 is along kinetic energy, Dimension 2 is along theta, and Dimension 3 along phi. energy : 1D array of kinetic energy values in eV. theta : 1D array of theta values in degree. This is the direction along the slit. phi : 1D array of phi values in degree. This is the direction perpendicular to the slit. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 3D matrix of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. kx, ky : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1 along the slit, and perpendicular to the slit directions, respectively.","s":"k_conv3d","u":"/arpespythontools/docs/glossary","h":"#k_conv3d","p":38},{"i":53,"t":"data_k, e_bin, kx, ky = arp.k_conv3d_mp(data, energy, theta, phi, fermi_energy) Multiprocessing implementation of k_conv3d. Should be up to as many times faster as many processor cores are available. Transforms the Fermi map data from real space to k-space. Inputs: data : 3D matrix of intensity values in real space. Dimension 1 is along kinetic energy, Dimension 2 is along theta, and Dimension 3 along phi. energy : 1D array of kinetic energy values in eV. theta : 1D array of theta values in degree. This is the direction along the slit. phi : 1D array of phi values in degree. This is the direction perpendicular to the slit. fermi_energy (number) : Fermi energy value in eV in terms of kinetic energy. Outputs: data_k : 3D matrix of intensity values in k-space. Intensity values outside the interpolation range is set to NaN (not a number). e_bin : 1D array of Binding energy values in eV. Binding energy below Fermi energy is positive convention is used. kx, ky : 1D array of momentum (k) values in A˚−1\\mathring{A}^{-1}A˚−1 along the slit, and perpendicular to the slit directions, respectively.","s":"k_conv3d_mp","u":"/arpespythontools/docs/glossary","h":"#k_conv3d_mp","p":38},{"i":55,"t":"diff2 = arp.laplacian(data, x, y, bw=5, w=1) Laplacian (second order partial derivatives with respect to both energy and angle) of the spectra. Inputs: data : 2D spectra. x : 1D array of energy. y : 1D array of theta values. bw : width for box-car smoothing, integer number of points (default value = 5). w : scaling weight (optional). Default weight is 1. Outputs: diff2 : 2D array of spectra after taking second order partial derivative w.r.t. both energy and angle. This array has the same shape as input array.","s":"laplacian","u":"/arpespythontools/docs/glossary","h":"#laplacian","p":38},{"i":57,"t":"edc = arp.line_profile(data, y, y_min, y_max) Returns the 1D vector of integrated line profile. The integration is done along the second dimension of data. Inputs: data : 2D array. y : 1D vector of axis scaling along the second dimension of data. y_min, y_max : integration bounds. Outputs: edc : 1D vector of integrated values defined by the width [y_min, y_max] along the first dimension.","s":"line_profile","u":"/arpespythontools/docs/glossary","h":"#line_profile","p":38},{"i":59,"t":"data, energy, theta, phi = arp.load_map_data(name) Loads Fermi map data from output .zip file of Scienta-Omicron SES program. Inputs: name (string) : name or file path of .zip map data file. It could be a local path or URL path. Outputs: data: 3D array of intensity values. Dimension 1 → energy, Dimension 2 → angle theta (along the slit direction), and Dimension 3 → angle phi (azimuth/ perpendicular to the slit direction). energy: 1D vector of kinetic energy points in eV. theta: 1D vector of theta values in degree. phi : 1D vector of phi values in degree.","s":"load_ses_map","u":"/arpespythontools/docs/glossary","h":"#load_ses_map","p":38},{"i":61,"t":"data, angle, energy = arp.load_ses_spectra(name) Loads data from a text file produced by Scienta-Omicron SES program. Inputs: name (string) : name or file path of SES .txt file. It could be a local path or a URL address. Outputs: data : 2D array (numpy ndarry) of intensity values. angle : 1D vector (numpy ndarry) of angle values in degree. energy : 1D vector (numpy ndarry) of kinetic energy values in eV.","s":"load_ses_spectra","u":"/arpespythontools/docs/glossary","h":"#load_ses_spectra","p":38},{"i":63,"t":"surf = arp.plane_slice(data, x, x_min, x_max) Returns the 2D slice along the first dimension of data and integrated in the width [x_min, x_max]. Inputs: data : 3D matrix. x : axes scaling along the first dimension. x_min, x_max : integration bounds. Outputs: surf : 2D array.","s":"plane_slice","u":"/arpespythontools/docs/glossary","h":"#plane_slice","p":38},{"i":65,"t":"data_r, theta_r, phi_r = arp.rotate_2d(data, angle, theta, phi) Rotates 2D array with rotation axis perpendicular to the plane. Center of rotation is at theta=0, phi=0. Inputs: data : 2D array. The data will be rotated perpendicular to the plane. angle : amount of rotation in degree. Positive value rotates clockwise. theta : 1D array of axis scaling along the second dimension of data. phi : 1D array of axis scaling along the third dimension of data. Outputs: data_r : rotated 2D matrix. Data points outside of interpolation range is set to NaN (not a number). theta_r : 1D array of axis scaling along the second dimension of data_r. phi_r : 1D array of axis scaling along the third dimension of data_r.","s":"rotate_2d","u":"/arpespythontools/docs/glossary","h":"#rotate_2d","p":38},{"i":67,"t":"data_r, theta_r, phi_r = arp.rotate_3d(data, angle, theta, phi) Rotates the volume data (3D matrix) with respect to the first dimension. Center of rotation is at theta=0, phi=0. Inputs: data : 3D array. First, second, and third dimensions are along energy, theta, and phi, respectively. The data will be rotated perpendicular to energy, i.e., in the theta-phi plane. angle : amount of rotation in degree. Positive value rotates clockwise. theta : 1D array of axis scaling along the second dimension of data. phi : 1D array of axis scaling along the third dimension of data. Outputs: data_r : rotated 3D matrix. Data points outside of interpolation range is set to NaN (not a number). theta_r : 1D array of axis scaling along the second dimension of data_r. phi_r : 1D array of axis scaling along the third dimension of data_r.","s":"rotate_3d","u":"/arpespythontools/docs/glossary","h":"#rotate_3d","p":38},{"i":69,"t":"arp.save_xps(energy, intensity, \"xps_data.x_y\") Save XPS energy and intensity in two column plaintext file. Inputs: energy : one dimensional vector intensity : one dimensional vector filename : Optional output filename. Two column data is saved in file.","s":"save_xps","u":"/arpespythontools/docs/glossary","h":"#save_xps","p":38},{"i":71,"t":"X-ray Photoemission Spectroscopy (XPS) data is recorded in the same way as the ARPES spectra. It records two dimensional (energy- and angle- resolved) intensities. Since the energy range for XPS scans are often very large, the data files could be very large (up to several hundred megabytes). Generally, we do not need any angle-resolved information, therefore the spectra can be saved in simple energy vs. intensity two column format. XPS data are generally measured in transmission mode, which has angular range about (-3, 3) degree. Often there are some artifacts on the edge of detector, so we can restrict only to the central part with integration limits for line profile. import arpespythontools as arp import numpy as np data, energy, angle = arp.load_ses_spectra(\"xps_data.txt\") intensity = arp.line_profile(data, angle, -2.5, 2.5) If you require energy in terms of binding energy instead of kinetic energy, you can convert using: Ebin=EF−EkinE_{bin} = E_F - E_{kin}Ebin​=EF​−Ekin​EF=hν−WϕE_F = h\\nu - W_{\\phi}EF​=hν−Wϕ​ where EFE_FEF​ is Fermi energy, and WϕW_{\\phi}Wϕ​ is work function which is about 4.5 eV for our setup. tip If you do not need to specify the integration limits i.e., you want to sum over full angle range, it is simpler to use numpy.sum method instead. import numpy as np intensity = np.sum(data, axis=1)","s":"Working with XPS data","u":"/arpespythontools/docs/xps","h":"","p":70},{"i":73,"t":"xps_data = np.array([energy, intensity]).T np.savetxt(\"xps_data.x_y\", xps_data) In the above example, we have saved the data in two column (.x_y) format, which is suitable for importing to other XPS analysis software (like CasaXPS). We may also use the module save_xps to save data. arp.save_xps(energy, intensity, \"xps_data.x_y\") If you need to load the two column data using python: energy, intensity = np.loadtxt(\"xps_data.x_y\", unpack=True) tip If you only need to obtain integrated intensity from the SES spectra for XPS data analysis, you may try our web application.","s":"Save/export XPS data","u":"/arpespythontools/docs/xps","h":"#saveexport-xps-data","p":70},{"i":75,"t":"If your Fermi map measurement was not done keeping the high symmetry directions along the slit direction (or perpendicular to the slit direction), and you need to rotate the collected data in order to make the high symmetry directions along the x- or y-coordinate, the rotate_2d and rotate_3d functions come handy. Remember positive rotation angle rotates clockwise, and center of rotation is at (kx=0k_x=0kx​=0, ky=0k_y=0ky​=0). rotate_2d can rotate a 2D array with respect to its surface normal. Let's get some Fermi map data first. import arpespythontools as arp import matplotlib.pyplot as plt %matplotlib inline url = 'https://pranabdas.github.io/drive/datasets/arpes/sample_map_data.zip' data, energy, theta, phi = arp.load_ses_map(url) # Plot one slice plt.figure(figsize = (8, 6)) plt.imshow(data[150, :, :], origin = 'lower', aspect = 'auto', \\ extent = (phi[0], phi[-1], theta[0], theta[-1])) plt.show() This is how a constant energy cut looks like before rotation: Now, we can rotate only a single slice first. data_r, theta_r, phi_r = arp.rotate_2d(data[150, :, :], 45, theta, phi) # Plot one slice plt.figure(figsize = (8, 6)) plt.imshow(data_r, origin = 'lower', aspect = 'auto', \\ extent = (phi_r[0], phi_r[-1], theta_r[0], theta_r[-1])) plt.show() Let us plot a slice again. This is what we get after the rotation.","s":"Rotate Fermi map data","u":"/arpespythontools/docs/rotate","h":"","p":74},{"i":77,"t":"Instead of rotating only one slice, we can also rotate the full 3D array. rotate_3d function needs the 3D map data (with first dimension along the energy, second and third dimensions are kxk_xkx​ and kyk_yky​, respectively) as input. It needs kxk_xkx​ and kyk_yky​ vectors as input as well. Provide the required angle to rotate in degree as before. Axis of rotation is the first axis (i.e., energy). The function returns rotated data, new kx′k_x'kx′​ and ky′k_y'ky′​ vectors. Let's see an example: data_r, theta_r, phi_r = arp.rotate_3d(data, 45, theta, phi) # we can plot a slice after rotation to get the above result plt.imshow(data_r[150, :, :], origin = 'lower', aspect = 'auto', \\ extent = (phi_r[0], phi_r[-1], theta_r[0], theta_r[-1])) plt.show()","s":"Rotate 3D Fermi map data","u":"/arpespythontools/docs/rotate","h":"#rotate-3d-fermi-map-data","p":74},{"i":79,"t":"This example provides basic example of image plot using matplotlib. There is a huge list of customization possible using matplotlib. You can consult matplotlib documentation for advanced customizations. import arpespythontools as arp data, energy, angle = arp.load_ses_spectra('sample_spectra.txt') # Plot image import matplotlib.pyplot as plt %matplotlib inline # Above line is specific to Jupyter Notebook plt.figure(figsize = (8, 6)) plt.imshow(data, origin = 'lower', aspect = 'auto', \\ extent = (angle[0], angle[-1], energy[0], energy[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show() You should see a plot like this upon successful execution:","s":"Data visualization","u":"/arpespythontools/docs/visualization","h":"","p":78},{"i":81,"t":"We can crop images (two-dimensionl data) using the crop_2d function. Say, we want to crop and focus only on the Dirac cone part. We want to crop the energy range (16, 16.8) and angle range (-6, 4). # data_crop, x_crop, y_crop = crop_2d(data, x, y, x_min, x_max, y_min, y_max) data_crop, x_crop, y_crop = arp.crop_2d(data, x, y, 16, 16.8, -6, 4) plt.figure(figsize = (8, 8)) plt.imshow(data_crop, origin = 'lower', aspect = 'auto', \\ extent = (y_crop[0], y_crop[-1], x_crop[0], x_crop[-1])) plt.xlabel(\"$\\\\theta$ (deg)\") plt.ylabel(\"$E_{kin}$ (eV)\") plt.set_cmap('magma_r') plt.show() That's what we wanted to achieve. tip For advanced 3D visualization of Fermi map data, you may have a look at this example from my Python tutorial.","s":"Crop 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