Folding

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Folding of Mössbauer spectra

Module: core/folding.py (pure functions, no GUI)

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Why folding is needed

A constant-acceleration Mössbauer spectrometer records two symmetric half-spectra: the detector sees the same sequence of velocities in the forward sweep and in the return sweep. A file of $N$ channels (typically 512) contains two copies of the spectrum, one reflected with respect to the other about a symmetry point (the folding point). Folding (averaging the two half-spectra) produces a single spectrum of $N/2$ points with a signal/noise ratio $\sqrt{2}$ better and removes the duplication.

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Folding point

The folding point is the symmetry channel $c$ that minimizes the difference between the two half-spectra. For each candidate $c$ the following is computed:

$$\chi^2(c) = \sum_{\text{pares}} \bigl[C(c - d) - C(c + d)\bigr]^2$$

where $d = j + 0.5$ runs through the distances to the center and $C(\cdot)$ is the interpolated count (channels numbered 1..N). The minimum is first searched on a grid of half-channels and then parabolically interpolated to obtain subchannel precision (find_best_integer_or_half_center).

Normos convention. Fitbauer internally uses the symmetry center (≈ 255.77 for a Normos upper folding point ≈ 511.55 in 512 channels). The number Normos reports is approximately twice the internal center. read_normos_folding_point reads the "Final folding point" from the .RES sidecar and converts it: if the value is ≥ 400 it is interpreted as full-spectrum convention (÷2); if it is < 400, as a half-spectrum.

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Channel interpolation (interp_channel_1based)

The folding point rarely falls on an integer channel. The function folds into $N/2$ points in the Normos style, obtaining each count by linear interpolation between adjacent channels. At the edges (channels outside the range 1..N), minimal linear extrapolation is used, which avoids losing a channel for half-integer centers such as 255.5 in 512-channel spectra.

For each folded point $j$ (with $j = 0..N/2-1$):

$$F_j = \tfrac{1}{2}\bigl[C(c - (j{+}0.5)) + C(c + (j{+}0.5))\bigr]$$

The result is sorted from negative to positive velocity.

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Edge trimming and normalization (fold_and_normalize)

After folding, the edge channels (first and last) are less reliable because they come from extrapolation. By default, EDGE_TRIM_DEFAULT = 1 channel is trimmed at each end.

Normalization brings the baseline to ≈ 1.0 using the 90th percentile of the folded spectrum (robust against the absorption peaks, which are minima):

$$\mathrm{norm} = P_{90}(F), \qquad y_i = \frac{F_i}{\mathrm{norm}}$$

Poisson noise is propagated taking into account that each folded point is the mean of two Poisson channels:

$$\sigma_i = \frac{\sqrt{\max(F_i / 2,; 1)}}{\mathrm{norm}}$$

The function returns the tuple (folded, sigma, y, norm).

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Velocity axis (velocity_axis)

The velocity axis goes from $-v_{\max}$ to $+v_{\max}$ with $N/2$ points:

$$v = \mathrm{linspace}(-v_{\max},; +v_{\max},; N/2)$$

Important: the axis is trimmed at the same positions as the spectrum ([edge_trim:-edge_trim]), it is not rescaled. Rescaling the axis after trimming would stretch the velocity scale and bias the fitted BHF.

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Pre-folded CSV/velocity format (load_velocity_csv)

For spectra already folded in velocity space (e.g. ESRF synchrotron data), a two-column velocity, counts CSV/TXT/DAT/EXP format is supported:

• Separators: comma, tab or spaces.
• Comment lines (#) or non-numeric header are ignored.
• If all values in column 2 are ≤ 1.0, they are interpreted as normalized transmission and scaled to counts (round(2_000_000 · col2)).
• Inverted-column detection: if col0 has everything > 100 and col1 everything in [−20, 20], an error is raised suggesting that the columns be inverted.
• Deduplication: velocities closer than $10^{-9}$ are averaged.
• Validations: ≥ 10 points, velocity range ≥ 1 mm/s.

These files are not folded (they already come folded); they are loaded directly onto the velocity axis.

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Normos sidecars

When there are Normos sidecar files next to the spectrum, Fitbauer reads them to inherit parameters:

Sidecar	Function	What it extracts
.RES	read_normos_folding_point, read_normos_sidecar_params	Final folding point; final values WID/ARE/ISO/QUA/BHF
.PLT	read_normos_plt_velocity	$V_{\max}$ of the axis
.JOB	read_normos_sidecar_params	Fixed VMAX and QUA(1)

The final Normos values are translated into internal parameters (s1_delta, s1_bhf, s1_quad, s1_gamma1, s1_depth) as a starting point.

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Flow summary

counts (N canales)
   ↓ find_best_integer_or_half_center  →  center (subcanal)
   ↓ fold_integer_or_half              →  N/2 puntos doblados
   ↓ fold_and_normalize (edge_trim)    →  (folded, sigma, y, norm)
   ↓ velocity_axis (mismo recorte)     →  eje de velocidad -vmax..vmax
espectro listo para ajuste