ComaPSFModel#

class ctapipe.instrument.optics.ComaPSFModel(*args: t.Any, **kwargs: t.Any)[source]#

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, configured via telescope traitlets:

  • Asymmetry parameters (\(K\)):

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

  • Radial scale parameters (\(S_R\)):

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

  • Polar scale parameters (\(S_\phi\)):

    \[S_{\phi}(r) = a_1\,\exp{(-a_2\,r)}+\frac{a_3}{a_3+r}\]
Parameters:
subarrayctapipe.instrument.SubarrayDescription

Description of the subarray.

Notes

Model Limitations:

  • For sources within the central pixel (r0 < pixel_width), the PSF is approximated as a uniform distribution over the pixel area. This avoids singularities at the origin and provides a numerically stable approximation for sub-pixel sources.

  • The angular distribution is limited to a chord around the radial axis based on the approximation that the polar axis is orthogonal to the radial axis. This limits its validity to the inner camera region.

  • This PSF model is designed for pointing determination via star tracking. As the telescope tracks celestial coordinates, stars rotate around the camera center. Their reconstructed positions provide information about the telescope pointing direction. To achieve good pointing accuracy, stars should be located away from the camera center to provide a sufficient lever arm for the pointing solution.

References

For reference, see [A+23]

Attributes Summary

asymmetry_decay_rate

Tanh saturation rate of the asymmetry parameter K with distance to the optical axis (\(c_1\)).

asymmetry_linear_term

Linear term for the asymmetry parameter K with distance to the optical axis (\(c_2\)).

asymmetry_max

Maximum asymmetry parameter K at large distance from the optical axis (\(c_0\)).

polar_scale_amplitude

Initial width \(S_\phi\) at the center of the camera (r=0) (\(a_1\)).

polar_scale_decay

Exponential decay of the polar scale \(S_\phi\) with distance to the optical axis (\(a_2\)).

polar_scale_offset

Offset controlling width \(S_\phi\) at large distance from the optical axis (\(a_3\)).

radial_scale_cubic

Cubic growth of the radial scale \(S_R\) with distance to the optical axis (\(b_4\)).

radial_scale_linear

Linear growth of the radial scale \(S_R\) with distance to the optical axis (\(b_2\)).

radial_scale_offset

Offset of the radial scale \(S_R\) (\(b_1\)).

radial_scale_quadratic

Quadratic growth of the radial scale \(S_R\) with distance to the optical axis (\(b_3\)).

Methods Summary

pdf(tel_id, lon, lat, lon0, lat0)

Calculates the value of the psf at a given location.

Attributes Documentation

asymmetry_decay_rate#

Tanh saturation rate of the asymmetry parameter K with distance to the optical axis (\(c_1\)).

asymmetry_linear_term#

Linear term for the asymmetry parameter K with distance to the optical axis (\(c_2\)).

asymmetry_max#

Maximum asymmetry parameter K at large distance from the optical axis (\(c_0\)).

polar_scale_amplitude#

Initial width \(S_\phi\) at the center of the camera (r=0) (\(a_1\)).

polar_scale_decay#

Exponential decay of the polar scale \(S_\phi\) with distance to the optical axis (\(a_2\)).

polar_scale_offset#

Offset controlling width \(S_\phi\) at large distance from the optical axis (\(a_3\)).

radial_scale_cubic#

Cubic growth of the radial scale \(S_R\) with distance to the optical axis (\(b_4\)).

radial_scale_linear#

Linear growth of the radial scale \(S_R\) with distance to the optical axis (\(b_2\)).

radial_scale_offset#

Offset of the radial scale \(S_R\) (\(b_1\)).

radial_scale_quadratic#

Quadratic growth of the radial scale \(S_R\) with distance to the optical axis (\(b_3\)).

Methods Documentation

pdf(tel_id, lon, lat, lon0, lat0)[source]#

Calculates the value of the psf at a given location.

Parameters:
tel_idint

ID of the telescope for which the PSF is evaluated

lonu.Quantity[angle]

longitude coordinate of the point on the focal plane where the psf is evaluated

latu.Quantity[angle]

latitude coordinate of the point on the focal plane where the psf is evaluated

lon0u.Quantity[angle]

longitude coordinate of the point source on the focal plane

lat0u.Quantity[angle]

latitude 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