diff --git a/src/ctapipe/instrument/optics.py b/src/ctapipe/instrument/optics.py index bdbb6c28031..d14783dc33e 100644 --- a/src/ctapipe/instrument/optics.py +++ b/src/ctapipe/instrument/optics.py @@ -313,15 +313,17 @@ class ComaPSFModel(PSFModel): r""" PSF model describing pure coma aberrations PSF effect. - The PSF is described by a combination of an asymmetric Laplacian for the radial part and a symmetric Laplacian in the polar direction. - It uses an asymmetric Laplacian for the radial part + 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 - .. math:: f_{R}(r, K) = \begin{cases}\frac{1}{S_{R}(K+K^{-1})}e^{-K\frac{r-L}{S_{R}}}, r\ge L\\ \frac{1}{S_{R}(K+K^{-1})}e^{\frac{r-L}{KS_{R}}}, r < L\end{cases} + .. math:: 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} - and a symmetric Laplacian in polar direction + and the polar part is given by .. math:: f_{\Phi}(\phi) = \frac{1}{2S_\phi}e^{-|\frac{\phi-\phi_0}{S_\phi}|} + The parameters :math:`K`, :math:`S_{R}`, and :math:`S_{\phi}` are functions of the distance :math:`r` to the optical axis. + Their detailed description is provided in the attributes section. Attributes ---------- @@ -330,7 +332,7 @@ class ComaPSFModel(PSFModel): 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. - .. math:: K(r) = 1 - \text{asym}_0 \tanh(\text{asym}_1 r) - \text{asym}_2 r + .. math:: K(r) = 1 - c_0 \tanh(c_1 r) - c_2 r radial_scale_params : list Describes the dependency of the radial scale on the distance to the center of the camera.