ComaPSFModel

class ctapipe.instrument.optics.ComaPSFModel(**kwargs: Any)

Bases: PSFModel

PSF model describing pure coma aberrations PSF effect.

The PSF is described by a product of an asymmetric Laplacian for the radial part and a symmetric Laplacian in the polar direction. Explicitly, the radial part is given by

\[\begin{split}f_{R}(r, K) = \begin{cases}\frac{1}{S_{R}(K+K^{-1})}e^{-K\frac{r-r_0}{S_{R}}}, r\ge r_0\\ \frac{1}{S_{R}(K+K^{-1})}e^{\frac{r-r_0}{KS_{R}}}, r < r_0\end{cases}\end{split}\]

and the polar part is given by

\[f_{\Phi}(\phi) = \frac{1}{2S_\phi}e^{-|\frac{\phi-\phi_0}{S_\phi}|}\]

The parameters \(K\), \(S_{R}\), and \(S_{\phi}\) are functions of the distance \(r\) to the optical axis. Their detailed description is provided in the attributes section.

Parameters:

subarrayctapipe.instrument.SubarrayDescription

Description of the subarray.

Attributes:

asymmetry_paramslist

Describes the dependency of the PSF on the distance to the center of the camera. Used to calculate a PDF asymmetry parameter K of the asymmetric radial Laplacian of the PSF as a function of the distance r to the optical axis.

\[K(r) = 1 - c_0 \tanh(c_1 r) - c_2 r\]

radial_scale_paramslist

Describes the dependency of the radial scale on the distance to the center of the camera. Used to calculate width Sr of the asymmetric radial Laplacian in the PSF as a function of the distance \(r\) to the optical axis.

\[S_{R}(r) = b_1 + b_2\,r + b_3\,r^2 + b_4\,r^3\]

phi_scale_paramslist

Describes the dependency of the polar angle (\(\phi\)) scale on the distance to the center of the camera. Used to calculate the width Sf of the polar Laplacian in the PSF as a function of the distance \(r\) to the optical axis.

\[S_{\phi}(r) = a_1\,\exp{(-a_2\,r)}+\frac{a_3}{a_3+r}\]

References

For reference, see [A+23]

Attributes Summary

asymmetry_params	Describes the dependency of the PSF on the distance to the center of the camera.
phi_scale_params	Describes the dependency of the polar scale on the distance to the center of the camera.
pixel_width	Width of a pixel of the camera in meters
radial_scale_params	Describes the dependency of the radial scale on the distance to the center of the camera.

Methods Summary

pdf(x, y, x0, y0)

Calculates the value of the psf at a given location

Attributes Documentation

asymmetry_params

Describes the dependency of the PSF on the distance to the center of the camera. Used to calculate a PDF asymmetry parameter \(K\) of the asymmetric radial Laplacian of the PSF as a function of the distance r to the optical axis

phi_scale_params

Describes the dependency of the polar scale on the distance to the center of the camera. Used to calculate the width \(S_\phi\) of the polar Laplacian in the PSF as a function of the distance r to the optical axis

pixel_width

Width of a pixel of the camera in meters

radial_scale_params

Describes the dependency of the radial scale on the distance to the center of the camera. Used to calculate width \(S_R\) of the asymmetric radial Laplacian in the PSF as a function of the distance r to the optical axis

Methods Documentation

pdf(x, y, x0, y0) → ndarray

Calculates the value of the psf at a given location

Parameters:

xu.Quantity[length]

x-coordinate of the point on the focal plane where the psf is evaluated

yu.Quantity[length]

y-coordinate of the point on the focal plane where the psf is evaluated

x0u.Quantity[length]

x-coordinate of the point source on the focal plane

y0u.Quantity[length]

y-coordinate of the point source on the focal plane

Returns

———-

psfnp.ndarray

value of the PSF at the specified location with the specified position of the point source