Background Removal
The background command removes a model background from the EXAFS signal (\(\chi(k)\)) and stores the computed background as a new column. It supports three fitting methods: polynomial, spline, and Fourier.
After background removal, the chi column is updated to subtract the modeled background:
Basic Usage
background <method> [range] [method-options]
where:
<method>is one of:polynomial,spline, orfourier[range]is an optional k-space range (default: full range)[method-options]are method-specific parameters
Command Options
| Option | Description |
|---|---|
[range] | Optional range in k-space where the background model is fit. Accepts k units (default: 0k to +∞). See range specification for details. |
Background Methods
Polynomial
Fits a single polynomial across the selected k range.
background polynomial [range] [options]
| Option | Description |
|---|---|
--degree <n> -d <n> | Polynomial degree (default: 3) |
--linear -l | Use degree 1 |
--quadratic -q | Use degree 2 |
--cubic -c | Use degree 3 (default) |
--kweight <value> | k-weighting exponent (default: 2.0). The fit is performed on k-weighted data to emphasize higher-k features. |
When to use: For smooth, quasi-monotonic backgrounds across the entire scan range.
Spline
Fits a piecewise spline with nodal control points. More flexible than polynomial for irregular background shapes.
background spline [range] --nodes <node1> [<node2> ...] --degrees <deg1> [<deg2> ...] [options]
| Option | Description |
|---|---|
--nodes <n1> [<n2> ...] | Knot positions or number of equidistant knots (required). If a single dimensionless number is given, that many equidistant knots are generated in the selected range. Otherwise, provide explicit position(s) in k units. |
--degrees <d1> [<d2> ...] | Spline degree(s) for each piece (required). If one node and one degree given, a single spline with that degree is fit. |
--kweight <value> | k-weighting exponent (default: 2.0). |
--fixed-points <k,y> [<k,y> ...] | Force the spline to pass through specific (k, χ) points (optional). Format: k_value,y_value (comma-separated). |
--continuity <n> | Continuity order at knots (default: 1). Use -1 for full continuity (up to degree-1). |
When to use: For backgrounds with multiple features or variable slope, when polynomial fitting is insufficient.
Fourier
Uses Fourier filtering to isolate low-frequency background. The method transforms to r-space, applies a window to exclude the signal region, then inverse-Fourier transforms.
background fourier [range] [options]
| Option | Description |
|---|---|
--rmax <distance> | Radius cutoff in real space (default: 1.0 Å). Signals beyond this distance are removed, leaving only long-range background. |
--kweight <value> | k-weighting exponent (default: 2.0). |
--forward-pad <value> | Padding before the fitted range in k-space (default: 0.1 k). Suppresses ringing. |
--forward-width <value> | Width of the edge window in k-space (default: 1.0 k). Controls transition steepness. |
--backward-pad <value> | Padding beyond the cutoff in r-space (default: 0.1 Å). |
--backward-width <value> | Width of the edge window in r-space (default: 0.2 Å). |
--epsilon <value> | Small regularization constant (default: 1e-30) to avoid division by zero in k-weighting. |
When to use: When you need automatic, physically-motivated separation of signal from background based on real-space locality.
Examples
# Simple cubic polynomial background
background polynomial
# Quadratic polynomial fit in the 3-14 k range
background polynomial 3k 14k --quadratic
# Spline with 5 equidistant knots
background spline --nodes 5 --degrees 3
# Spline with explicit knots at 3.5 and 8.5
background spline --nodes 3.5k 8.5k --degrees 3 3 3
# Fourier background with 2 Å cutoff
background fourier --rmax 2.0A
# Combined: polynomial for range 0-3, Fourier for the scan region
background polynomial 0k 3k --linear
background fourier 3k 15k --rmax 1.5A
Results
After execution, the command:
- creates a
bkgcolumn containing the computed background - updates
chitochi - bkg(EXAFS signal with background removed)
See also: