Demonstration of the conversion pipeline using time-resolved ARPES data stored on Zenodo

In this example, we pull some time-resolved ARPES data from Zenodo, and load it into the sed package using functions of the mpes package. Then, we run a conversion pipeline on it, containing steps for visualizing the channels, correcting image distortions, calibrating the momentum space, correcting for energy distortions and calibrating the energy axis. Finally, the data are binned in calibrated axes. For performance reasons, best store the data on a locally attached storage (no network drive). This can also be achieved transparently using the included MirrorUtil class.

%load_ext autoreload
%autoreload 2
import numpy as np
import matplotlib.pyplot as plt
import sed
from sed.dataset import dataset

%matplotlib widget

Load Data

dataset.get("WSe2") # Put in Path to a storage of at least 20 GByte free space.
data_path = dataset.dir # This is the path to the data
scandir, caldir = dataset.subdirs # scandir contains the data, caldir contains the calibration files

INFO - Not downloading WSe2 data as it already exists at "/home/runner/work/sed/sed/docs/tutorial/datasets/WSe2".
Set 'use_existing' to False if you want to download to a new location.
INFO - Using existing data path for "WSe2": "/home/runner/work/sed/sed/docs/tutorial/datasets/WSe2"
INFO - WSe2 data is already present.

# create sed processor using the config file:
sp = sed.SedProcessor(folder=scandir, config="../sed/config/mpes_example_config.yaml", verbose=True)

Configuration loaded from: [/home/runner/work/sed/sed/docs/sed/config/mpes_example_config.yaml]
Folder config loaded from: [/home/runner/work/sed/sed/docs/tutorial/sed_config.yaml]
Default config loaded from: [/home/runner/work/sed/sed/sed/config/default.yaml]

# Apply jittering to X, Y, t, ADC columns.
# Columns are defined in the config, or can be provided as list.
sp.add_jitter()

# Plot of the count rate through the scan
rate, secs = sp.loader.get_count_rate(range(100))
plt.plot(secs, rate)

[<matplotlib.lines.Line2D at 0x7fbb00391af0>]

# The time elapsed in the scan
sp.loader.get_elapsed_time()

2588.4949999999994

# Inspect data in dataframe Columns:
# axes = ['X', 'Y', 't', 'ADC']
# bins = [100, 100, 100, 100]
# ranges = [(0, 1800), (0, 1800), (130000, 140000), (0, 9000)]
# sp.view_event_histogram(dfpid=1, axes=axes, bins=bins, ranges=ranges)
sp.view_event_histogram(dfpid=2)

Distortion correction and Momentum Calibration workflow

Distortion correction

1. step:

Bin and load part of the dataframe in detector coordinates, and choose energy plane where high-symmetry points can well be identified. Either use the interactive tool, or pre-select the range:

#sp.bin_and_load_momentum_calibration(df_partitions=20, plane=170)
sp.bin_and_load_momentum_calibration(df_partitions=100, plane=33, width=10, apply=True)

2. Step:

Next, we select a number of features corresponding to the rotational symmetry of the material, plus the center. These can either be auto-detected (for well-isolated points), or provided as a list (these can be read-off the graph in the cell above). These are then symmetrized according to the rotational symmetry, and a spline-warping correction for the x/y coordinates is calculated, which corrects for any geometric distortions from the perfect n-fold rotational symmetry.

#features = np.array([[203.2, 341.96], [299.16, 345.32], [350.25, 243.70], [304.38, 149.88], [199.52, 152.48], [154.28, 242.27], [248.29, 248.62]])
#sp.define_features(features=features, rotation_symmetry=6, include_center=True, apply=True)
# Manual selection: Use a GUI tool to select peaks:
#sp.define_features(rotation_symmetry=6, include_center=True)
# Autodetect: Uses the DAOStarFinder routine to locate maxima.
# Parameters are:
#   fwhm: Full-width at half maximum of peaks.
#   sigma: Number of standard deviations above the mean value of the image peaks must have.
#   sigma_radius: number of standard deviations around a peak that peaks are fitted
sp.define_features(rotation_symmetry=6, auto_detect=True, include_center=True, fwhm=10, sigma=12, sigma_radius=4, apply=True)

3. Step:

Generate nonlinear correction using splinewarp algorithm. If no landmarks have been defined in previous step, default parameters from the config are used

# Option whether a central point shall be fixed in the determination fo the correction
sp.generate_splinewarp(include_center=True)

Calculated thin spline correction based on the following landmarks:
pouter: [[153.40464026 243.07041743]
 [199.54049591 152.77697099]
 [203.00793508 342.98660563]
 [299.87451482 346.19873685]
 [305.63374558 150.17725745]
 [350.94684854 244.78960163]]
pcent: (249.22391328272423, 249.25212721013787)
Original slice with reference features

Corrected slice with target features

Original slice with target features

Optional (Step 3a):

Save distortion correction parameters to configuration file in current data folder:

# Save generated distortion correction parameters for later reuse
sp.save_splinewarp()

Saved momentum correction parameters to "sed_config.yaml".

4. Step:

To adjust scaling, position and orientation of the corrected momentum space image, you can apply further affine transformations to the distortion correction field. Here, first a potential scaling is applied, next a translation, and finally a rotation around the center of the image (defined via the config). One can either use an interactive tool, or provide the adjusted values and apply them directly.

#sp.pose_adjustment(xtrans=14, ytrans=18, angle=2)
sp.pose_adjustment(xtrans=8, ytrans=7, angle=-4, apply=True)

5. Step:

Finally, the momentum correction is applied to the dataframe, and corresponding meta data are stored

sp.apply_momentum_correction()

Adding corrected X/Y columns to dataframe:
Calculating inverse deformation field, this might take a moment...
Dask DataFrame Structure:
                       X        Y        t      ADC       Xm       Ym
npartitions=100
                 float64  float64  float64  float64  float64  float64
                     ...      ...      ...      ...      ...      ...
...                  ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...
Dask Name: apply_dfield, 206 graph layers

Momentum calibration workflow

1. Step:

First, the momentum scaling needs to be calibrated. Either, one can provide the coordinates of one point outside the center, and provide its distance to the Brillouin zone center (which is assumed to be located in the center of the image), one can specify two points on the image and their distance (where the 2nd point marks the BZ center),or one can provide absolute k-coordinates of two distinct momentum points.

If no points are provided, an interactive tool is created. Here, left mouse click selects the off-center point (brillouin_zone_centered=True) or toggle-selects the off-center and center point.

k_distance = 2/np.sqrt(3)*np.pi/3.28 # k-distance of the K-point in a hexagonal Brillouin zone
#sp.calibrate_momentum_axes(k_distance = k_distance)
point_a = [308, 345]
sp.calibrate_momentum_axes(point_a=point_a, k_distance = k_distance, apply=True)
#point_b = [247, 249]
#sp.calibrate_momentum_axes(point_a=point_a, point_b = point_b, k_coord_a = [.5, 1.1], k_coord_b = [0, 0], equiscale=False)

Optional (Step 1a):

Save momentum calibration parameters to configuration file in current data folder:

# Save generated momentum calibration parameters for later reuse
sp.save_momentum_calibration()

Saved momentum calibration parameters to sed_config.yaml

2. Step:

Now, the distortion correction and momentum calibration needs to be applied to the dataframe.

sp.apply_momentum_calibration()

Adding kx/ky columns to dataframe:
Dask DataFrame Structure:
                       X        Y        t      ADC       Xm       Ym       kx       ky
npartitions=100
                 float64  float64  float64  float64  float64  float64  float64  float64
                     ...      ...      ...      ...      ...      ...      ...      ...
...                  ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...
Dask Name: assign, 216 graph layers

Energy Correction and Calibration workflow

Energy Correction (optional)

The purpose of the energy correction is to correct for any momentum-dependent distortion of the energy axis, e.g. from geometric effects in the flight tube, or from space charge

1st step:

Here, one can select the functional form to be used, and adjust its parameters. The binned data used for the momentum calibration is plotted around the Fermi energy (defined by tof_fermi), and the correction function is plotted ontop. Possible correction functions are: “spherical” (parameter: diameter), “Lorentzian” (parameter: gamma), “Gaussian” (parameter: sigma), and “Lorentzian_asymmetric” (parameters: gamma, amplitude2, gamma2).

One can either use an interactive alignment tool, or provide parameters directly.

#sp.adjust_energy_correction(amplitude=2.5, center=(730, 730), gamma=920, tof_fermi = 66200)
sp.adjust_energy_correction(amplitude=2.5, center=(730, 730), gamma=920, tof_fermi = 66200, apply=True)

Optional (Step 1a):

Save energy correction parameters to configuration file in current data folder:

# Save generated energy correction parameters for later reuse
sp.save_energy_correction()

Saved energy correction parameters to sed_config.yaml

2. Step

After adjustment, the energy correction is directly applied to the TOF axis.

sp.apply_energy_correction()

Applying energy correction to dataframe...
Using energy correction parameters generated on 02/05/2025, 21:14:12
Dask DataFrame Structure:
                       X        Y        t      ADC       Xm       Ym       kx       ky       tm
npartitions=100
                 float64  float64  float64  float64  float64  float64  float64  float64  float64
                     ...      ...      ...      ...      ...      ...      ...      ...      ...
...                  ...      ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...      ...
Dask Name: assign, 230 graph layers

Energy calibration

For calibrating the energy axis, a set of data taken at different bias voltages around the value where the measurement was taken is required.

1. Step:

In a first step, the data are loaded, binned along the TOF dimension, and normalized. The used bias voltages can be either provided, or read from attributes in the source files if present.

# Load energy calibration EDCs
energycalfolder = caldir
scans = np.arange(1,12)
voltages = np.arange(12,23,1)
files = [energycalfolder + r'/Scan' + str(num).zfill(3) + '_' + str(num+11) + '.h5' for num in scans]
sp.load_bias_series(data_files=files, normalize=True, biases=voltages, ranges=[(64000, 75000)])

2. Step:

Next, the same peak or feature needs to be selected in each curve. For this, one needs to define “ranges” for each curve, within which the peak of interest is located. One can either provide these ranges manually, or provide one range for a “reference” curve, and infer the ranges for the other curves using a dynamic time warping algorithm.

# Option 1 = specify the ranges containing a common feature (e.g an equivalent peak) for all bias scans
# rg = [(129031.03103103103, 129621.62162162163), (129541.54154154155, 130142.14214214214), (130062.06206206206, 130662.66266266267), (130612.61261261262, 131213.21321321322), (131203.20320320321, 131803.8038038038), (131793.7937937938, 132384.38438438438), (132434.43443443443, 133045.04504504506), (133105.10510510512, 133715.71571571572), (133805.8058058058, 134436.43643643643), (134546.54654654654, 135197.1971971972)]
# sp.find_bias_peaks(ranges=rg, infer_others=False)
# Option 2 = specify the range for one curve and infer the others
# This will open an interactive tool to select the correct ranges for the curves.
# IMPORTANT: Don't choose the range too narrow about a peak, and choose a refid
# somewhere in the middle or towards larger biases!
rg = (66100, 67000)
sp.find_bias_peaks(ranges=rg, ref_id=5, infer_others=True, apply=True)

3. Step:

Next, the detected peak positions and bias voltages are used to determine the calibration function. This can be either done by fitting the functional form d^2/(t-t0)2 via lmfit (“lmfit”), or using a polynomial approximation (“lstsq” or “lsqr”). Here, one can also define a reference id, and a reference energy. Those define the absolute energy position of the feature used for calibration in the “reference” trace, at the bias voltage where the final measurement has been performed. The energy scale can be either “kinetic” (decreasing energy with increasing TOF), or “binding” (increasing energy with increasing TOF).

After calculating the calibration, all traces corrected with the calibration are plotted ontop of each other, the calibration function together with the extracted features is plotted.

# use the refid of the bias that the measurement was taken at
# Eref can be used to set the absolute energy (kinetic energy, E-EF) of the feature used for energy calibration (if known)
refid=4
Eref=-0.5
# the lmfit method uses a fit of (d/(t-t0))**2 to determine the energy calibration
# limits and starting values for the fitting parameters can be provided as dictionaries
sp.calibrate_energy_axis(
    ref_id=refid,
    ref_energy=Eref,
    method="lmfit",
    energy_scale='kinetic',
    d={'value':1.0,'min': .7, 'max':1.2, 'vary':True},
    t0={'value':8e-7, 'min': 1e-7, 'max': 1e-6, 'vary':True},
    E0={'value': 0., 'min': -100, 'max': 0, 'vary': True},
    verbose=True,
)

[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 43
    # data points      = 11
    # variables        = 3
    chi-square         = 0.00218781
    reduced chi-square = 2.7348e-04
    Akaike info crit   = -87.7502612
    Bayesian info crit = -86.5565754
[[Variables]]
    d:   1.09544523 +/- 0.03646409 (3.33%) (init = 1)
    t0:  7.6073e-07 +/- 7.5361e-09 (0.99%) (init = 8e-07)
    E0: -46.6158341 +/- 0.79487877 (1.71%) (init = 0)
[[Correlations]] (unreported correlations are < 0.100)
    C(d, t0)  = -0.9997
    C(d, E0)  = -0.9988
    C(t0, E0) = +0.9974
Quality of Calibration:

E/TOF relationship:

Optional (Step 3a):

Save energy calibration parameters to configuration file in current data folder:

# Save generated energy calibration parameters for later reuse
sp.save_energy_calibration()

Saved energy calibration parameters to "sed_config.yaml".

4. Step:

Finally, the the energy axis is added to the dataframe.

sp.append_energy_axis()

Adding energy column to dataframe:
Using energy calibration parameters generated on 02/05/2025, 21:14:20
Dask DataFrame Structure:
                       X        Y        t      ADC       Xm       Ym       kx       ky       tm   energy
npartitions=100
                 float64  float64  float64  float64  float64  float64  float64  float64  float64  float64
                     ...      ...      ...      ...      ...      ...      ...      ...      ...      ...
...                  ...      ...      ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...      ...      ...
                     ...      ...      ...      ...      ...      ...      ...      ...      ...      ...
Dask Name: assign, 240 graph layers

4. Delay calibration:

The delay axis is calculated from the ADC input column based on the provided delay range. ALternatively, the delay scan range can also be extracted from attributes inside a source file, if present.

#from pathlib import Path
#datafile = "file.h5"
#print(datafile)
#sp.calibrate_delay_axis(datafile=datafile)
delay_range = (-500, 1500)
sp.calibrate_delay_axis(delay_range=delay_range, preview=True)

Adding delay column to dataframe:
Append delay axis using delay_range = [-500, 1500] and adc_range = [475.0, 6400.0]
             X            Y             t          ADC           Xm  \
0     0.473214     0.473214      0.473214     0.473214   -12.738235
1   365.458604  1002.458604  70101.458604  6317.458604   356.025674
2   760.590267   817.590267  75614.590267  6315.590267   790.992877
3   692.361324   971.361324  66455.361324  6317.361324   713.946785
4   670.979661   711.979661  73025.979661  6316.979661   696.945018
5   298.881130  1163.881130  68458.881130  6315.881130   282.119991
6   570.507782   664.507782  73902.507782  6315.507782   589.459563
7   821.532098   544.532098  72631.532098  6317.532098   847.576573
8   817.892378   415.892378  72421.892378  6316.892378   838.367701
9  1005.816779   666.816779  72801.816779  6316.816779  1039.835403

            Ym        kx        ky            tm     energy        delay
0    87.761377 -2.094240 -1.824661    -47.709950 -25.209439  -660.177818
1  1032.588835 -1.105073  0.709729  70084.453139  -9.301534  1472.137925
2   839.207790  0.061676  0.191007  75613.719453 -16.702493  1471.507263
3   985.330516 -0.144991  0.582964  66449.664800  -0.819935  1472.105088
4   741.351151 -0.190597 -0.071482  73025.592234 -13.802723  1471.976257
5  1185.105713 -1.303317  1.118838  68432.367734  -5.957558  1471.605445
6   700.814848 -0.478914 -0.180216  73899.572929 -14.872918  1471.479420
7   586.477024  0.213455 -0.486914  72627.370891 -13.279648  1472.162733
8   466.547698  0.188753 -0.808611  72412.234069 -12.987126  1471.946794
9   709.020925  0.729167 -0.158205  72794.341525 -13.501820  1471.921276

5. Visualization of calibrated histograms

With all calibrated axes present in the dataframe, we can visualize the corresponding histograms, and determine the respective binning ranges

axes = ['kx', 'ky', 'energy', 'delay']
ranges = [[-3, 3], [-3, 3], [-6, 2], [-600, 1600]]
sp.view_event_histogram(dfpid=1, axes=axes, ranges=ranges)

Define the binning ranges and compute calibrated data volume

axes = ['kx', 'ky', 'energy', 'delay']
bins = [100, 100, 200, 50]
ranges = [[-2, 2], [-2, 2], [-4, 2], [-600, 1600]]
res = sp.compute(bins=bins, axes=axes, ranges=ranges, normalize_to_acquisition_time="delay")

Calculate normalization histogram for axis 'delay'...

Some visualization:

fig, axs = plt.subplots(4, 1, figsize=(6, 18), constrained_layout=True)
res.loc[{'energy':slice(-.1, 0)}].sum(axis=(2,3)).T.plot(ax=axs[0])
res.loc[{'kx':slice(-.8, -.5)}].sum(axis=(0,3)).T.plot(ax=axs[1])
res.loc[{'ky':slice(-.2, .2)}].sum(axis=(1,3)).T.plot(ax=axs[2])
res.loc[{'kx':slice(-.8, -.5), 'energy':slice(.5, 2)}].sum(axis=(0,1)).plot(ax=axs[3])

<matplotlib.collections.QuadMesh at 0x7fbb352051c0>

fig, ax = plt.subplots(1,1)
(sp._normalization_histogram*90000).plot(ax=ax)
sp._binned.sum(axis=(0,1,2)).plot(ax=ax)
plt.show()