Calibrate a new Detector for EDS fit and quantification

This guide explains how to calibrate the detector model used by AutoEMX to fit and quantify EDS spectra, for a new detector or microscope.

AutoEMX models each spectrum with peak shapes and a background whose parameters depend on the detector. These parameters are fixed during fitting, as functions of the X-ray energy or of the atomic number, calibrated once per detector on spectra of standards. The calibration of the Phenom XL is shipped with AutoEMX and described in the Supplementary Information of Giunto et al., Nature Communications 17, 9735 (2026), https://doi.org/10.1038/s41467-026-76633-x (Supplementary Notes Parameter calibration for peak shape modeling and Calibration of P, F and β background model parameters).

Note

Calibration is required for optimal accuracy, not to use AutoEMX: the parameters of the Phenom XL generalize reasonably well to other detectors.

The energy calibration of the detector (offset and gain) is a separate, regular calibration: see EDS Detector Calibration.

The detector model

The detector model of each microscope is saved in the package, in autoemx/calibrations/<microscope_ID>/:

detector_model.json: the values of the model, validated when loaded (see autoemx/config/schema_models/detector_model.py for the meaning of each value). It contains:
- detector characteristics: number of channels, emergence (take-off) angle, Si density, undetectable elements, available measurement modes;
- peak width: Fano factor F, electronic noise elec_noise, conversion efficiency conv_eff;
- peak shape (peak_shape): parameters of the low-energy tailing and incomplete charge collection (ICC), gamma, f_tail, R_e and F_loss, each a sigmoid of the line energy;
- background (background): functions of the atomic number P(Z), F(Z) and β(Z) of the modified Duncumb model of the generated background;
- fine-tuning factors: upper bounds of escape and pileup peaks, Ll/Kα ratio, background and strobe peak scaling.
detector_efficiency.msa: the detector efficiency as a function of energy, as provided by the manufacturer.

To add a new microscope, create a folder named with its microscope ID, starting from a copy of the files of a similar microscope, and set the detector characteristics. The microscope also needs a driver (see Add new Electron Microscope Driver): by default, the driver named as the microscope ID. For a second instrument of a supported model, with its own calibrated detector, set "driver" in its detector_model.json to the driver of the model (e.g. "driver": "PhenomXL").

Note

The detector model is read from the package. To calibrate it, work in a git checkout of AutoEMX installed in editable mode (pip install -e .), edit detector_model.json there, and consider contributing the calibration of your microscope to AutoEMX.

Calibration procedure

The parameters of the model are correlated: the fitted value of each depends on the values of the others. Calibrate one parameter at a time, updating detector_model.json after each step, in the following order, and repeat the sequence until the values no longer change significantly.

Energy calibration. Calibrate the detector channel parameters (EDS Detector Calibration).
Spectra of standards. Acquire high-count spectra of bulk, polished standards, ideally pure elements, spanning the energy range of the X-ray lines (peak shape) and the atomic numbers of your samples (background), e.g. with Run_Experimental_Standard_Collection.py and update_std_library = False (EDS Experimental Standard Collection). The paper used ten to fifteen spectra of 250,000 counts per standard. Acquire them at the acceleration voltage of your measurements: the background functions, β in particular, are expected to depend on it.
Peak width: Calibrate_Peak_Sigma_Params.py (below).
Peak shape: Calibrate_Peak_Shape_Params.py, one parameter at a time (below).
Background: Calibrate_Background_Params.py, in the order P, β, F (below).
Reference P/B values. Once the model is calibrated, refit the standards with Refit_Experimental_Standards.py and update_std_library = True (or collect new ones), since the reference values depend on the spectral fit.

All calibration scripts are in autoemx/scripts/Microscope calibration/. They print the fitted values with the current ones, plot them, and print the new values to paste into detector_model.json: they never change the model themselves. After changing the model, refit the standards before calibrating the next parameter. The detector response matrices computed from the model are recomputed automatically (about 10 s, then cached in ~/.autoemx/cache).

Tip

Fitted values at the bounds allowed during fitting are flagged (⚠️ at fit bound). They mean that the current model is far from the measured value: update the model, refit, and calibrate again.

Peak width

The Gaussian width of the peaks depends on the line energy E (keV) as

\[\sigma = \mathrm{conv\_eff} \sqrt{\mathrm{elec\_noise}^2 + E \cdot F / \mathrm{conv\_eff}}\]

with the Fano factor F fixed (0.12). Calibrate_Peak_Sigma_Params.py reads the peak widths fitted in the spectra of the standards from their ledgers (Kα₁, Lα₁ and Mα₁ lines, or the lines you list), and fits conv_eff and elec_noise.

samples = {
    '/path/to/Std_measurements/Al': None,                 # Ka1, La1, Ma1 lines
    '/path/to/Std_measurements/Cu': ['Cu_Ka1', 'Cu_La1'],
}

Widths can only vary between 0.93 and 1.1 times the current model during fitting: if many are at these bounds, update the model, refit the standards, and calibrate again.

Peak shape

The peaks of lines below 1.84 keV have a low-energy tail (gamma: skewness, f_tail: tail fraction), and those between 1.18 and 5 keV are broadened by incomplete charge collection (R_e: charge cloud radius, F_loss: fraction of X-rays lost at the detector surface); between 1.18 and 1.84 keV, both apply. Each parameter is a sigmoid of the line energy E, c + L / (1 + exp(-k (E - x0))), with coefficients offset (c), amplitude (L), center (x0) and steepness (k).

Calibrate_Peak_Shape_Params.py refits the spectra of the standards with the chosen parameters fitted freely for the chosen elements, averages the fitted values of each line, and fits the chosen sigmoid coefficients:

samples = {
    '/path/to/Std_measurements/C': ['C'],     # elements whose peak shapes are fitted
    '/path/to/Std_measurements/Al': ['Al'],
}
params = ['gamma']                            # parameters fitted freely
sigmoid_coeffs = ['offset', 'amplitude', 'center', 'steepness']

A sigmoid is fitted only with more lines than coefficients. With few standards, fit fewer coefficients (e.g. only offset, to shift the current function).

Calibrate the parameters one at a time, for example gamma and f_tail first, on lines below 1.18 keV where only the tail applies, then R_e and F_loss on lines between 1.84 and 5 keV where only the ICC applies. Then check the lines between 1.18 and 1.84 keV, where both apply.

Background

The generated background (modified Duncumb model) depends on three functions of the atomic number Z: the shape factor P(Z) (a quadratic polynomial), which sets the curvature of the continuum, the attenuation factor β(Z) (a sigmoid plus a Gaussian), and the intensity factor F(Z) = 1 - exp(-(Z + z_offset) / z_scale). For compounds, P and F are evaluated at the mean atomic number of the sample, and β is the mass-weighted average of the elemental values: calibrate with pure elements, spanning the atomic numbers of your samples (C to Bi in the paper).

Calibrate_Background_Params.py refits the spectra with the chosen parameters fitted freely (params), the others being set by the detector model, and fits the functions of the chosen parameters (fit_functions). Follow the order of the paper:

params = ['P', 'F', 'beta'], fit_functions = ['P']: all three free, fit P(Z). Update the model.
params = ['beta'], fit_functions = ['beta']: with P fixed, fit β(Z). Update the model.
params = ['F'], fit_functions = ['F']: with P and β fixed, fit F(Z). Update the model.

Optionally, fit only some coefficients of a function with coeffs, e.g. {'P': ['a0']}. A function is fitted only with more standards than coefficients (P: 3, F: 2, β: 7).

Fine-tuning factors

The remaining factors (escape_peak_probability, pileup_peak_probability, weight_Ll_ref_Ka1, gen_background_time_scaling_factor, strobe_peak_int_factor, zero_strobe_peak_sigma) are upper bounds or initial guesses for parameters fitted in each spectrum, and are not critical: reasonable estimates suffice. To check them, compare with the values fitted in a few high-count spectra of standards.