Add PSF model based on Zernike coefficients

[mexanick]

Summary

Adds ZernikePSFModel, to ctapipe.instrument.optics alongside the existing ComaPSFModel.

Unlike ComaPSFModel's parametric radial/polar scaling approach, this model reconstructs the optical wavefront directly from Zernike coefficients (using Noll indexing) and propagates it through Fraunhofer diffraction (FFT of the aberrated pupil).

Implementation details

• Builds a circular pupil grid (pupil_size, pupil_diameter_fraction) with a soft-edged aperture (pupil_edge_softness) to avoid FFT ringing.
• Reconstructs the wavefront from per-telescope Zernike coefficients z2–z11 (tilt, defocus, astigmatism, coma, trefoil, spherical), using the zernike package's RZern for polynomial evaluation.
• Adds off-axis aberration growth: coma grows linearly with field angle θ (z7_theta, z8_theta), astigmatism grows quadratically with θ² (z5_theta2, z6_theta2).
• Computes the focal-plane intensity via FFT of the complex pupil function, averaged over wavelength_samples wavelengths between wavelength_min and wavelength_max, weighted by a cherenkov_spectrum_index power law (dN/dλ ∝ λ^-index).
• Applies Gaussian smoothing (focal_plane_smoothing_sigma_pix) to the resulting intensity to approximate pixel/light-guide response.
• Exposes the standard pdf(tel_id, lon, lat, lon0, lat0) interface shared with ComaPSFModel, interpolating the precomputed PSF grid via scipy.ndimage.map_coordinates and normalizing to unit integral.

[kosack]

Looks good, but a couple of small requests:

• Can you add a citation to the docs to where the "Zernike" coefficients are defined?
• Just a question: you make all the parameters generic names like "z2-z6", but they could have nicer names, e.g. z2 could be tilt_x, etc. Maybe that is because of how they are defined in the reference paper? If so, then adding the citation is fine, but otherwise, why not use human-readable names?

[mexanick]

• Can you add a citation to the docs to where the "Zernike" coefficients are defined?

I've added a reference to Wikipedia. The original Zernike article is in German, and Noll's article is behind a paywall, but Wikipedia provides all the necessary information.

• Just a question: you make all the parameters generic names like "z2-z6", but they could have nicer names, e.g. z2 could be tilt_x, etc. Maybe that is because of how they are defined in the reference paper? If so, then adding the citation is fine, but otherwise, why not use human-readable names?

I would like to keep them as is (Zi), as this is the industry standard. For example, Ansys Zemax uses this notation, which makes it easy to copy or cross-check coefficient values directly from ray-tracing software. The docstrings for each parameter already contain the human-readable descriptions, so I think it's a good compromise between readability and standardization.

[Voutsi]

According to wikipedia link, the Noll coefficient z7 is the vertical and z8 the horizontal. I think then you need to swap the comas, I mean add coma_x to z8 and coma_y to z7

[mexanick]

This was an artifact of some experimenting with the internal to the model coordinate transforms, I've simplified it.

[Voutsi]

The angular coordinates depend on the wavelength. I think here we ignore this dependence, it should be accounted for before the final summation.

[Voutsi]

Hi @mexanick , thanks a lot for this. I asked for one more thing to be clarified. Other than that looks good to me.

[mexanick]

Hi @mexanick , thanks a lot for this. I asked for one more thing to be clarified. Other than that looks good to me.

Thanks, it is fixed now. I also found and fixed an error in the astigmatism application. An updated PSF map:

[maxnoe]

Thanks, this looks very good.

Aside from the comment by @Voutsi, I'd just request that we add the new package only as an optional dependency.

[ctao-sonarqube]

Quality Gate passed

Issues
0 New issues
0 Fixed issues
0 Accepted issues

Measures
0 Security Hotspots
94.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube