Transformations and filtering

Use these guides to rotate maps and volumes, shift spectra to correct drift, apply known symmetries, add Gaussian broadening to simulations, and visualize dispersive features.

Rotate maps and volumes

Determine the rotation angle and center from the experimental geometry or a visible reference feature. Rotate the two evenly sampled momentum dimensions while preserving the remaining dimensions:

import erlab.analysis as era

rotated = era.transform.rotate(
    data,
    angle=25.0,
    axes=("ky", "kx"),
    center={"ky": 0.0, "kx": 0.0},
    reshape=True,
)

(Source code)

Set reshape=False when the output must keep the original extent. Determine the rotation center and angle before using the result. Rotation requires interpolation when the new grid does not coincide with the measured points. Repeated rotations can compound this effect. See erlab.analysis.transform.rotate() for interpolation, reshape, and fill-value arguments.

Shift spectra to correct drift

Use erlab.analysis.transform.shift() when energy_offsets contains a verified energy offset for every value of another coordinate. The offset DataArray broadcasts across the remaining dimensions:

import erlab.analysis as era

aligned = era.transform.shift(
    spectra,
    shift=-energy_offsets,
    along="eV",
)

(Source code)

The fitted edge must follow the displacement before alignment. After the shift, the edge must coincide with 0 eV in both endpoint spectra and across the \(h\nu\) series.

Ensure that energy_offsets uses the same energy units and compatible coordinates as spectra. Derive the offsets from an appropriate reference edge or another established energy reference. Do not infer the energy correction from dispersing bands in the sample data.

If the shifts would remove valid data at the original coordinate bounds, expand the output coordinate range:

aligned = era.transform.shift(
    spectra,
    shift=-energy_offsets,
    along="eV",
    shift_coords=True,
)

(Source code)

The fitted offsets record a displacement. They do not establish its physical cause. See erlab.analysis.transform.shift() for coordinate and interpolation arguments.

Reflection symmetrization

Use reflection symmetrization when the data must be combined with its reflection about a known coordinate:

import erlab.analysis as era

symmetrized = era.transform.symmetrize(
    data,
    dim="kx",
    center=0.0,
)
antisymmetrized = era.transform.symmetrize(
    data,
    dim="kx",
    center=0.0,
    subtract=True,
)

(Source code)

Use a symmetry center established independently from the transformation. Do not use symmetrized intensity to determine normal emission or to justify a reflection symmetry that is not known for the measured system.

By default, the outputs contain the sum or difference of the original and reflected values. Set average=True to divide the result by two where both coordinate ranges overlap.

See erlab.analysis.transform.symmetrize() for coordinate and output-range arguments.

Rotational n-fold symmetrization

Use rotational symmetrization when a map or volume must be averaged over equivalent in-plane rotations. Supply the symmetry order, momentum dimensions, and rotation center:

import erlab.analysis as era

symmetrized = era.transform.symmetrize_nfold(
    data,
    6,
    axes=("kx", "ky"),
    center={"kx": 0.0, "ky": 0.0},
    reshape=True,
)

(Source code)

Set reshape=False when the output must keep the original grid. Determine the rotation center and symmetry order independently. Compare the result with the measured map. Do not use the averaged result to establish the symmetry that you supplied.

See erlab.analysis.transform.symmetrize_nfold() for coordinate, interpolation, and output-range arguments.

Gaussian convolution

Supply the Gaussian standard deviation in the units of each coordinate:

import erlab.analysis as era

broadened = era.image.gaussian_filter(
    simulated_data,
    sigma={"eV": 0.01, "alpha": 0.2},
)

(Source code)

See erlab.analysis.image.gaussian_filter() for dimension selection and boundary handling.

Visualizing dispersive features

Open the two-dimensional cut in dtool:

import erlab.interactive as eri

eri.dtool(data)

Use the interpolation and smoothing controls before you select a derivative-based method. Compare the processed result with the source intensity in the same window. After you select the parameters, copy the generated calculation code or open the result in ImageTool from the plot context menu.

See erlab.interactive.dtool() for the Python entry point. See dtool for its methods, controls, and ImageTool integration.