neutronpy.functions.gaussian_ring

neutronpy.functions.gaussian_ring(p, q)

Returns a two dimensional gaussian ellipse profile.

Parameters:

p : ndarray

Parameters for the gaussian ellipse function, in the following format:

p[0]	Constant background
p[1]	Linear background slope
p[2]	Volume under first ellipse
p[3]	X position of first ellipse
p[4]	Y position of first ellipse
p[5]	Radius of first ellipse
p[6]	Eccentricity of first ellipse
p[7]	FWHM of first ellipse
p[8]	Volume under second ellipse
p[…]	etc.

q : tuple of ndarray

Two input arrays of equivalent size and shape, e.g. formed with numpy.meshgrid.

Returns:

out : ndarray

Two dimensional gaussian ellipse profile.

Notes

A gaussian ellipse profile is defined as

$$f(x,y) = \frac{1}{N} e^{-\frac{1}{2}\frac{(\sqrt{(x-x_0)^2 + \alpha^2(y-y_0)^2}-r_0)^2}{2 \sigma}},$$

where $FWHM = 2\sqrt{2\ln(2)}\sigma$, and N is the normalization pre-factor given by

$$N = \frac{2\pi}{\alpha} \left(\sigma^2 e^{-\frac{r_0^2}{2\sigma^2}} + \sqrt{\frac{\pi}{2}} r_0 \sigma \left(1 + \mathrm{Erf}\left(\frac{r_0}{\sqrt{2}\sigma}\right)\right)\right).$$