erlab.io.exampledata

Generates simple simulated ARPES data for testing and demonstration.

Functions

generate_data([shape, krange, Erange, temp, ...])	Generate simulated data for a given shape in momentum space.
generate_data_angles([shape, angrange, ...])	Generate simulated data for a given shape in angle space.
generate_data_dirac([shape, angrange, ...])	Generate simulated topological surface-state ARPES data in angle space.
generate_gold_edge([shape, a, b, c, temp, ...])	Generate a curved Fermi edge with a linear density of states.
generate_hvdep_cuts([shape, angrange, ...])	Generate simulated hv-dependent cuts.
make_mesh_pattern(shape, *[, pitch, duty, ...])	Simulate an ARPES mesh pattern using step edges broadened by Gaussians.

erlab.io.exampledata.generate_data(shape=(250, 250, 300), *, krange=0.89, Erange=(-0.45, 0.09), temp=20.0, a=6.97, t=0.43, bandshift=0.0, Sreal=0.0, Simag=0.03, kres=0.01, Eres=2.0e-3, noise=True, seed=None, count=100000000, ccd_sigma=0.6, const_bkg=1e-3)

Generate simulated data for a given shape in momentum space.

Generates simulated ARPES data based on a simple graphene-like tight-binding model.

Parameters:

• shape (tuple[int, int, int], default: (250, 250, 300)) – The shape of the generated data, by default (250, 250, 300)

• krange (float | tuple[float, float] | dict[str, tuple[float, float]], default: 0.89) – Momentum range in inverse angstroms. Can be a single float, a tuple of floats representing the range, or a dictionary with kx and ky keys mapping to tuples representing the range for each dimension, by default 0.89

• Erange (tuple[float, float], default: (-0.45, 0.09)) – Binding energy range in electronvolts, by default (-0.45, 0.09)

• temp (float, default: 20.0) – The temperature in Kelvins for the Fermi-Dirac cutoff. If 0, no cutoff is applied, by default 20.0

• a (float, default: 6.97) – Tight binding parameter \(a\), by default 6.97

• t (float, default: 0.43) – Tight binding parameter \(t\), by default 0.43

• bandshift (float, default: 0.0) – The rigid energy shift in eV, by default 0.0

• Sreal (float, default: 0.0) – The real part of the self energy, by default 0.0

• Simag (float, default: 0.03) – The imaginary part of the self energy, by default 0.03

• kres (float, default: 0.01) – Broadening in momentum in inverse angstroms, by default 0.01

• Eres (float, default: 2.0e-3) – Broadening in energy in electronvolts, by default 2.0e-3

• noise (bool, default: True) – Whether to add noise to the generated data, by default True

• seed (int | None, default: None) – Seed for the random number generator for the noise. Default is None.

• count (int, default: 100000000) – Determines the signal-to-noise ratio when noise is True, by default 1e+8

• ccd_sigma (float, default: 0.6) – The sigma value for CCD noise generation when noise is True, by default 0.6

• const_bkg (float, default: 1e-3) – Constant background as a fraction of the count, by default 1e-3

Returns:

xarray.DataArray – The generated data with coordinates for kx, ky, and eV.

Return type:

DataArray

erlab.io.exampledata.generate_data_angles(shape=(500, 60, 500), *, angrange=15.0, Erange=(-0.45, 0.12), hv=50.0, configuration=erlab.constants.AxesConfiguration.Type1, temp=20.0, a=6.97, t=0.43, bandshift=0.0, Sreal=0.0, Simag=0.03, angres=0.1, Eres=10.0e-3, noise=True, seed=None, count=100000000, ccd_sigma=0.6, const_bkg=1e-3, assign_attributes=False, extended=True, polarization=(0.0, 0.0, 1.0), inner_potential=10.0)

Generate simulated data for a given shape in angle space.

Parameters:

• shape (tuple[int, int, int], default: (500, 60, 500)) – The shape of the generated data, by default (250, 250, 300)

• angrange (float | tuple[float, float] | dict[str, tuple[float, float]], default: 15.0) – Angle range in degrees. Can be a single float, a tuple of floats representing the range, or a dictionary with alpha and beta keys mapping to tuples representing the range for each dimension, by default 15.0

• Erange (tuple[float, float], default: (-0.45, 0.12)) – Binding energy range in electronvolts, by default (-0.45, 0.12)

• hv (float, default: 50.0) – The photon energy in eV. Note that the sample work function is assumed to be 4.5 eV, by default 30.0

• configuration (AxesConfiguration | int, default: erlab.constants.AxesConfiguration.Type1) – The experimental configuration, by default Type1DA

• temp (float, default: 20.0) – The temperature in Kelvins for the Fermi-Dirac cutoff. If 0, no cutoff is applied, by default 20.0

• a (float, default: 6.97) – Tight binding parameter \(a\), by default 6.97

• t (float, default: 0.43) – Tight binding parameter \(t\), by default 0.43

• bandshift (float, default: 0.0) – The rigid energy shift in eV, by default 0.0

• Sreal (float, default: 0.0) – The real part of the self energy, by default 0.0

• Simag (float, default: 0.03) – The imaginary part of the self energy, by default 0.03

• angres (float, default: 0.1) – Broadening in angle in degrees, by default 0.01

• Eres (float, default: 10.0e-3) – Broadening in energy in electronvolts, by default 2.0e-3

• noise (bool, default: True) – Whether to add noise to the generated data, by default True

• seed (int | None, default: None) – Seed for the random number generator for the noise. Default is None.

• count (int, default: 100000000) – Determines the signal-to-noise ratio when noise is True, by default 1e+8

• ccd_sigma (float, default: 0.6) – The sigma value for CCD noise generation when noise is True, by default 0.6

• const_bkg (float, default: 1e-3) – Constant background as a fraction of the count, by default 1e-3

• assign_attributes (bool, default: False) – Whether to assign attributes to the generated data, by default False

• extended (bool, default: True) – Whether to include additional effects such as kz modulation and polarization, by default True

• polarization (Sequence[float], default: (0.0, 0.0, 1.0)) – Photon polarization vector, by default (0.0, 0.0, 1.0). Only used if extended is True

• inner_potential (float, default: 10.0) – Inner potential in eV, by default 10.0. Only used if extended is True.

Returns:

xarray.DataArray – The generated data with coordinates for alpha, beta, and eV.

Return type:

DataArray

erlab.io.exampledata.generate_data_dirac(shape=(500, 60, 500), *, angrange=15.0, Erange=(-0.45, 0.12), hv=50.0, configuration=erlab.constants.AxesConfiguration.Type1, temp=20.0, dirac_velocity=0.3, curvature=0.0, gap=0.0, bandshift=0.0, Sreal=0.0, Simag=0.03, alpha_coeff=1.0, beta_coeff=0.6, branch='both', spin='integrated', angres=0.1, Eres=10.0e-3, noise=True, seed=None, count=100000000, ccd_sigma=0.6, const_bkg=1e-3, assign_attributes=False, extended=True, polarization=(0.0, 0.0, 1.0), inner_potential=10.0)

Generate simulated topological surface-state ARPES data in angle space.

The surface-state dispersion follows a minimal Dirac/Rashba Hamiltonian with an optional quadratic curvature and mass gap. The matrix-element texture follows the spin-integrated and spin-filtered angular factors discussed by Moser for spin-orbit-coupled surface states.

Added in version 3.21.0.

Parameters:

• shape (tuple[int, int, int], default: (500, 60, 500)) – The shape of the generated data as (alpha, beta, eV).

• angrange (float | tuple[float, float] | dict[str, tuple[float, float]], default: 15.0) – Angle range in degrees. Can be a single float, a tuple of floats representing the range, or a dictionary with alpha and beta keys mapping to tuples representing the range for each dimension, by default 15.0.

• Erange (tuple[float, float], default: (-0.45, 0.12)) – Binding energy range in electronvolts, by default (-0.45, 0.12).

• hv (float, default: 50.0) – The photon energy in eV. The sample work function is assumed to be 4.5 eV.

• configuration (AxesConfiguration | int, default: erlab.constants.AxesConfiguration.Type1) – The experimental configuration, by default Type1.

• temp (float, default: 20.0) – The temperature in kelvins for the Fermi-Dirac cutoff. If 0, no cutoff is applied.

• dirac_velocity (float, default: 0.3) – Linear Dirac or Rashba coefficient in eV A.

• curvature (float, default: 0.0) – Quadratic curvature coefficient in eV A^2.

• gap (float, default: 0.0) – Dirac mass term in eV. The full gap at the Dirac point is 2 * gap.

• bandshift (float, default: 0.0) – The rigid energy shift in eV.

• Sreal (float, default: 0.0) – The real part of the self energy.

• Simag (float, default: 0.03) – The imaginary part of the self energy.

• alpha_coeff (float, default: 1.0) – Weight of the out-of-plane spz orbital contribution in the matrix element.

• beta_coeff (float, default: 0.6) – Weight of the in-plane orbital contribution in the matrix element.

• branch (Literal['both', 'upper', 'lower'], default: "both") – Which branch of the surface state to include: "upper", "lower", or "both".

• spin (Literal['integrated', 'up', 'down'], default: "integrated") – Matrix-element channel: spin-integrated (default) or one spin-projected component ("up" or "down").

• angres (float, default: 0.1) – Broadening in angle in degrees.

• Eres (float, default: 10.0e-3) – Broadening in energy in electronvolts.

• noise (bool, default: True) – Whether to add noise to the generated data.

• seed (int | None, default: None) – Seed for the random number generator for the noise.

• count (int, default: 100000000) – Determines the signal-to-noise ratio when noise is True.

• ccd_sigma (float, default: 0.6) – The sigma value for CCD noise generation when noise is True.

• const_bkg (float, default: 1e-3) – Constant background as a fraction of the count.

• assign_attributes (bool, default: False) – Whether to assign attributes to the generated data.

• extended (bool, default: True) – Whether to include the free-electron final-state polarization prefactor.

• polarization (Sequence[float], default: (0.0, 0.0, 1.0)) – Photon polarization vector. Only used if extended is True.

• inner_potential (float, default: 10.0) – Inner potential in eV. Only used if extended is True.

Returns:

xarray.DataArray – The generated data with coordinates for alpha, beta, and eV.

Return type:

DataArray

erlab.io.exampledata.generate_gold_edge(shape=(200, 300), *, a=-0.05, b=0.1, c=1e-3, temp=100.0, Eres=1e-2, angres=0.1, edge_coeffs=(0.04, 1e-5, -3e-4), background_coeffs=(1.0, 0.0, -2e-3), count=1000000000, noise=True, seed=None, ccd_sigma=0.6, add_mesh=False, mesh_params=None)

Generate a curved Fermi edge with a linear density of states.

Parameters:

• shape (tuple[int, int], default: (200, 300)) – Shape of the generated data. Default is (200, 300).

• a (float, default: -0.05) – Slope of the linear density of states. Default is -0.05.

• b (float, default: 0.1) – Intercept of the linear density of states. Default is 0.1.

• c (float, default: 1e-3) – Constant background. Default is 1e-3.

• temp (float, default: 100.0) – Temperature in Kelvin. Default is 100.0.

• Eres (float, default: 1e-2) – Energy resolution in eV. Default is 1e-2.

• angres (float, default: 0.1) – Angular resolution. Default is 0.1.

• edge_coeffs (Sequence[float], default: (0.04, 1e-5, -3e-4)) – Coefficients for the polynomial equation used to calculate the curved Fermi level as a function of angle in degrees. Default is (0.04, 1e-5, -3e-4).

• background_coeffs (Sequence[float], default: (1.0, 0.0, -2e-3)) – Coefficients for the polynomial equation used to calculate the polynomial background of the spectrum as a function of angle in degrees. Negative values are clipped. Default is (1.0, 0.0, -2e-3).

• count (int, default: 1000000000) – Determines the signal-to-noise ratio when noise is True. Default is 1e+8.

• noise (bool, default: True) – Flag indicating whether to add noise to the spectrum. Default is True.

• seed (int | None, default: None) – Seed for the random number generator for the noise. Default is None.

• ccd_sigma (float, default: 0.6) – Standard deviation of the Gaussian filter applied to the spectrum. Default is 0.6.

• add_mesh (bool, default: False) – Whether to multiply the spectrum by a mesh pattern. Default is False.

• mesh_params (dict | None, default: None) – Parameters for the mesh pattern generation. Default is None.

Returns:

data (xarray.DataArray) – Simulated gold edge spectrum.

Return type:

DataArray

erlab.io.exampledata.generate_hvdep_cuts(shape=(50, 250, 300), *, angrange=(-15.0, 15.0), Erange=(-0.45, 0.12), hvrange=(20.0, 69.0), hv_shift=None, configuration=erlab.constants.AxesConfiguration.Type1, temp=20.0, a=6.97, t=0.43, **kwargs)

Generate simulated hv-dependent cuts.

Parameters:

• shape (tuple[int, int, int], default: (50, 250, 300)) – The shape of the generated data, by default (250, 250, 300)

• hvrange (tuple[float, float], default: (20.0, 69.0)) – Photon energy range in eV.

• hv_shift (float | tuple[float, float] | ndarray | None, default: None) – Optional energy shift (in eV) applied across the photon-energy axis. If a float, a linear shift from -hv_shift to +hv_shift is applied across the hν range. If a tuple, the shift is linearly interpolated between the two values across hν. If an array, it must have length shape[0] and provides the shift at each hν value. If None, no shift is applied. The shift is simulated by generating each hν cut on a shifted energy axis and then assigning a common energy coordinate, so the output contains no all-NaN energies.

• angrange (tuple[float, float], default: (-15.0, 15.0)) – Angle range in degrees.

• Erange (tuple[float, float], default: (-0.45, 0.12)) – Binding energy range in electronvolts.

• configuration (AxesConfiguration | int, default: erlab.constants.AxesConfiguration.Type1) – The experimental configuration, by default Type1DA

• temp (float, default: 20.0) – The temperature in Kelvins for the Fermi-Dirac cutoff. If 0, no cutoff is applied, by default 20.0

• a (float, default: 6.97) – Tight binding parameter \(a\), by default 6.97

• t (float, default: 0.43) – Tight binding parameter \(t\), by default 0.43

• **kwargs – Additional keyword arguments to pass to generate_data_angles.

erlab.io.exampledata.make_mesh_pattern(shape, *, pitch=12.4, duty=0.8, amplitude=0.3, rotate=27.0, sigma_edge=0.7)

Simulate an ARPES mesh pattern using step edges broadened by Gaussians.

Parameters:

• shape (tuple[int, int]) – Output image size.

• pitch (float, default: 12.4) – Period of the mesh in pixels.

• duty (float, default: 0.8) – Open fraction along each axis, between 0 and 1.

• amplitude (float, default: 0.3) – Amplitude of the mesh.

• rotate (float, default: 27.0) – Rotation of the mesh relative to detector x-axis.

• sigma_edge (float, default: 0.7) – Gaussian sigma (in pixels) for edge broadening.