finesse.utilities.maps.overlap_1D_tilt_coefficients

finesse.utilities.maps.overlap_1D_tilt_coefficients(x, z, weight_spot: float)

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 $W(x) = exp(-x**2)$.