finesse.utilities.maps.overlap_1D_tilt_coefficients¶
- finesse.utilities.maps.overlap_1D_tilt_coefficients(x, z, weight_spot: float)[source]¶
Computes the amount of spot size weighted linear x term there is present in some 1D data.
- Parameters
- xndarray(dtype=float)
Sample points, ideally should be symmetric about 0.
- zndarray(dtype=float)
function at sample points x
- weight_spotfloat
Spot size to use as weighting
- Returns
- linear_termdouble
Weighted linear term of z
Notes
This function is essentially evaluating a weighted Hermite polynomial overlap integral with z(x) to determine the linear term.
\[\int_{\min(x)}^{\max(x)} H_{1}(x) z(x) W(x) dx\]Where the weighting function is \(W(x) = exp(-x**2)\).