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

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:

[8]:

#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.

[9]:

#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

[10]:

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

INFO - Calculated thin spline correction based on the following landmarks:
pouter_ord: [[203.00551295 342.984878  ]
 [299.87829131 346.19872528]
 [350.95565439 244.78406823]
 [305.64905139 150.19808761]
 [199.53391013 152.77528894]
 [153.41121185 243.04165814]]
pcent: (249.22689776953152, 249.25949630821563)

Optional (Step 3a):#

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

[11]:

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

INFO - 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.

[12]:

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

INFO - Applied translation with (xtrans=8.0, ytrans=7.0).
INFO - Applied rotation with angle=-4.0.

5. Step:#

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

[13]:

sp.apply_momentum_correction()

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

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.

[14]:

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:

[15]:

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

INFO - Saved momentum calibration parameters to sed_config.yaml

2. Step:#

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

[16]:

sp.apply_momentum_calibration()

INFO - Adding kx/ky columns to dataframe:
INFO - Using momentum calibration parameters generated on 05/11/2025, 22:12:10
INFO - 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

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.

[17]:

#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:

[18]:

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

INFO - Saved energy correction parameters to sed_config.yaml

2. Step#

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

[19]:

sp.apply_energy_correction()

INFO - Applying energy correction to dataframe...
INFO - Using energy correction parameters generated on 05/11/2025, 22:12:11
INFO - 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

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.

[20]:

# 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)])

WARNING - Entry "KTOF:Lens:Sample:V" for channel "sampleBias" not found. Skipping the channel.

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.

[21]:

# 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)

INFO - Use feature ranges: [(64638.0, 65386.0), (64913.0, 65683.0), (65188.0, 65991.0), (65474.0, 66310.0), (65782.0, 66651.0), (66101.0, 67003.0), (66442.0, 67388.0), (66794.0, 67795.0), (67190.0, 68213.0), (67575.0, 68664.0), (67993.0, 69148.0)].
INFO - Extracted energy features: [[6.51330000e+04 9.43293095e-01]
 [6.54080000e+04 9.52672958e-01]
 [6.57050000e+04 9.47981834e-01]
 [6.60130000e+04 9.46402431e-01]
 [6.63430000e+04 9.50330198e-01]
 [6.66730000e+04 9.63564813e-01]
 [6.70360000e+04 9.59838033e-01]
 [6.73990000e+04 9.67203319e-01]
 [6.78060000e+04 9.55975950e-01]
 [6.82130000e+04 9.56439197e-01]
 [6.86750000e+04 9.70683038e-01]].

3. Step:#

Next, the detected peak positions and bias voltages are used to determine the calibration function. Essentially, the functional Energy(TOF) is being determined by either least-squares fitting of the functional form d^2/(t-t0)2 via lmfit (method: “lmfit”), or by analytically obtaining a polynomial approximation (method: “lstsq” or “lsqr”). The parameter ref_energy is used to define the absolute energy position of the feature used for calibration in the calibrated energy scale. 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, and the calibration function (Energy(TOF)) together with the extracted features is being plotted.

[22]:

# Eref can be used to set the absolute energy (kinetic energy, E-EF, etc.) of the feature used for energy calibration (if known)
Eref=-1.3
# 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_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},
)

INFO - [[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

Optional (Step 3a):#

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

[23]:

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

INFO - Saved energy calibration parameters to "sed_config.yaml".

4. Step:#

Finally, the the energy axis is added to the dataframe. Here, the applied bias voltages of the measurement is taken into account to provide the correct energy offset. If the bias cannot be read from the file, it can be provided manually.

[24]:

sp.append_energy_axis(bias_voltage=16.8)

INFO - Adding energy column to dataframe:
INFO - Using energy calibration parameters generated on 05/11/2025, 22:12:21
INFO - 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, 243 graph layers