Distribution fitting

⚙️ Generated page — do not edit here. Source: BHF_DISTRIBUTION_EN.md. Edit it in the repository and the wiki rebuilds itself.

Distributions in Mössbauer Spectra

Continuous distribution engine integrated in the GUI and available via CLI and Python API.

Main files

• mossbauer_distribution.py: Hesse–Rübartsch engine (P(BHF) ≥ 0 + Tikhonov/TV regularization).
• mossbauer_ws5.py: reading/folding of .ws5 files and Normos sidecars.
• mossbauer_bhf_pipeline.py: high-level function for the web endpoint.
• fit_bhf_distribution_cli.py: CLI script for testing and generating .dat/.png files.

Distribution modes available in the GUI

Mode	Distributed variable	Typical use
P(BHF)	Hyperfine field $B_{hf}$	Ferrites, oxides with magnetic disorder
P(ΔEQ)	Quadrupole splitting	Silicates, glasses, paramagnetic amorphous phases
P(δ)	Isomer shift	Distribution of electronic environments
P(BHF, ΔEQ) 2D	Field + quadrupole	Nanoparticles with $B$–$Q$ coupling
P(δ, ΔEQ) 2D	IS + quadrupole	Wide doublets with simultaneous variation of centre and separation
P(BHF, δ) 2D	Field + IS	Magnetic phases with environmental distribution (sensitive to calibration)

All modes support simultaneous sharp components (sextets, doublets or singlets with free non-negative amplitude fitted jointly with the distribution).

Regularization

Tikhonov (second difference, default)

Penalizes the curvature of the distribution:

$$\Phi(\mathbf{p}) = |W^{1/2}(X\mathbf{z} - \mathbf{y})|^2 + \alpha |L\mathbf{p}|^2$$

where $L$ is the second-difference operator. Favours smooth distributions. The alpha selector is available in the GUI; preset buttons (fine / medium / smooth) and L-curve α for automatic estimation by maximum curvature or GCV.

Total Variation (L1, for discrete phases)

Penalizes the total variation of the distribution:

$$\Phi(\mathbf{p}) = |W^{1/2}(X\mathbf{z} - \mathbf{y})|^2 + \alpha |D_1\mathbf{p}|_1$$

Favours distributions with sharp transitions (mixture of a few well-defined phases), unlike Tikhonov which smooths. Selectable in the distribution mode options panel.

Basic CLI usage

python3 fit_bhf_distribution_cli.py sample.ws5 \
  --bmin 0 --bmax 50 --nbins 50 \
  --gamma 0.18 --alpha 0.01 \
  --plot --scan-alpha

Outputs:

• *_bhf_spectrum.dat: velocity, data, fit, residual, folded counts.
• *_bhf_distribution.dat: BHF, P, normalized P.
• *_bhf_summary.json: parameters and metrics.
• *_bhf_plot.png: spectrum + residual + P(BHF).
• *_bhf_alpha_scan.dat/.png: L-curve if --scan-alpha --plot is used.

Mixing with sharp components

In the GUI, with P(BHF) mode active, you can enable sum active sharp components. Active components 1–3 are added to the distribution as a singlet, doublet or sextet. The fit recalculates P(BHF) and the amplitude of each sharp component simultaneously.

To add a residual metallic-Fe-type phase with a fixed BHF from the CLI:

python3 fit_bhf_distribution_cli.py sample.ws5 \
  --bmin 15 --bmax 45 --nbins 50 \
  --alpha 0.1 --gamma 0.18 \
  --sharp-bhf 33 --sharp-gamma 0.14 \
  --plot --scan-alpha

Thickness correction with distributions

When the sample is thick (absorption > ~15 %), thickness correction can also be enabled in distribution mode. Distribution mode uses an inverse transform that recovers linearity in the weights:

$$A_\text{obs}(v) = -C \ln!\left(1 - \frac{b + sv - y(v)}{C}\right)$$

The regularized solver works on $A_\text{obs}$ (linear in $P$) and the model is re-saturated to compute residuals. An external VARPRO loop refines $(b, s, C)$ while the internal solver recovers $P$ at each iteration. See docs/correccion_espesor.tex for the full derivation.

Usage from Python / endpoint

from mossbauer_bhf_pipeline import fit_ws5_bhf_distribution

payload = fit_ws5_bhf_distribution(
    "sample.ws5",
    bmin=0,
    bmax=50,
    nbins=50,
    alpha=1e-2,
    gamma=0.18,
    sharp_bhf=[33.0],   # optional
)

print(payload["BHF_centers"])
print(payload["probability"])
print(payload["fitted_curve"])

Practical notes

• alpha is the critical parameter: use --scan-alpha or the GUI's L-curve α button to choose it.
• If B_min=0, the fit may use low-field values to absorb non-magnetic contributions. For a purely magnetic distribution, try --bmin 15 or --bmin 20.
• delta, quad and gamma are global/fixed for the entire distribution in 1D mode.
• For 2D distributions: the grid can be large ($N_x \times N_y$ bins); use independent regularizations $\alpha_x$, $\alpha_y$ and verify stability by varying both. See docs/distribuciones_2d_mossbauer.tex.
• Distributions with IS (P(δ), P(δ, ΔEQ)): very sensitive to velocity calibration and folding point. See docs/distribuciones_is_mossbauer.tex.