# IntegratedGaussianPRF¶

class photutils.psf.IntegratedGaussianPRF[source]

Circular Gaussian model integrated over pixels. Because it is integrated, this model is considered a PRF, not a PSF (see Terminology for more about the terminology used here.)

This model is a Gaussian integrated over an area of 1 (in units of the model input coordinates, e.g. 1 pixel). This is in contrast to the apparently similar astropy.modeling.functional_models.Gaussian2D, which is the value of a 2D Gaussian at the input coordinates, with no integration. So this model is equivalent to assuming the PSF is Gaussian at a sub-pixel level.

Parameters: sigma : float Width of the Gaussian PSF. flux : float (default 1) Total integrated flux over the entire PSF x_0 : float (default 0) Position of the peak in x direction. y_0 : float (default 0) Position of the peak in y direction.

Notes

This model is evaluated according to the following formula:

$f(x, y) = \frac{F}{4} \left[ {\rm erf} \left(\frac{x - x_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{x - x_0 - 0.5} {\sqrt{2} \sigma} \right) \right] \left[ {\rm erf} \left(\frac{y - y_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{y - y_0 - 0.5} {\sqrt{2} \sigma} \right) \right]$

where erf denotes the error function and F the total integrated flux.

Attributes Summary

Methods Summary

 evaluate(x, y, flux, x_0, y_0, sigma) Model function Gaussian PSF model.

Attributes Documentation

fit_deriv = None
flux
param_names = ('flux', 'x_0', 'y_0', 'sigma')
sigma
x_0
y_0

Methods Documentation

evaluate(x, y, flux, x_0, y_0, sigma)[source]

Model function Gaussian PSF model.