Model
- 2D Gaussian:
[math]\displaystyle{ G(x,y)=B+A e^{-\left( \frac{(x-x_0)^2}{2\sigma^2_x} + \frac{(y-y_0)^2}{2\sigma^2_y} \right)} }[/math]
- Parameters:
- [math]\displaystyle{ B }[/math]: The average local background in the [0, 1] range.
- [math]\displaystyle{ A }[/math]: The maximal intensity of the star in the [0, 1] range: this is the peak value of the fitted function, located at the centroid coordinates x0 and y0.
- [math]\displaystyle{ x_0 }[/math] and [math]\displaystyle{ y_0 }[/math]: The centroid coordinates in pixel units, which is the position of the center of symmetry of the fitted PSF.
- [math]\displaystyle{ \text{FWHM}_X }[/math] and [math]\displaystyle{ \text{FWHM}_Y }[/math]: The Full Width Half Maximum on the X and Y axis in pixel units. These parameters are calculated as follow :
- [math]\displaystyle{ \text{FWHM}_X = 2\sigma_x\sqrt{2\log{2}} }[/math]
- [math]\displaystyle{ \text{FWHM}_Y = 2\sigma_y\sqrt{2\log{2}} }[/math]
- It is possible to obtain the FWHM parameters in arcseconds units. This requires you fill all fields corresponding to your camera and lens/telescope focal in the setting parameter window. If standard FITS keywords FOCALLEN, XPIXSZ, YPIXSZ, XBINNING and YBINNING are read in the FITS HDU, the PSF will also compute the image scale in arcseconds per pixel.
- [math]\displaystyle{ r }[/math]: The roundness parameter. It is expressed as [math]\displaystyle{ \text{FWHM}_Y/\text{FWHM}_X }[/math], with [math]\displaystyle{ \text{FWHM}_X\gt \text{FWHM}_Y }[/math] the symmetry condition.
- Angle: The rotation angle of the X axis with respect to the centroid coordinates in the [-90, 90] range. The angle [math]\displaystyle{ \theta }[/math] is computed as follow:
- [math]\displaystyle{ x' = +x cos \theta + y sin \theta }[/math]
- [math]\displaystyle{ y' = -x sin \theta + y cos \theta }[/math]
- RMSE: This is an estimation of fitting quality. The smaller the RMSE is, the better the function is fitted.