Point Spread Functions (PSF) Models

The PSF characterizes how a telescope blurs a point-like source into an extended image on the detector. PSF plays a vital role in astronomical observations, influencing the precision of object detection, flux measurements, source deblending, shape measurement, and ultimately, scientific interpretations.

Challenges in PSF Modeling

Modeling the PSF accurately is complex, especially in the context of slitless spectroscopy. In space telescopes, the PSF is a function of multiple factors, including the telescope's optical design, thermal environment, and observational parameters. The PSF's behavior is also wavelength-dependent, varying across the instrument's spectral range. These complexities are further compounded by the presence of instrumental effects, such as detector characteristics and spectral dependencies.

Our Approach

The aim of this work package will be to develop the PSF model based on the state of the art of the PSF generation and interpolation with ML methods. The extremely low sampling of the NISP’s PSF makes the exploitation of the data available very tricky. For this study, the acquisition data set will be enlarged with ray tracing simulations, as Zemax simulation of the NISP instruments, to obtain a higher resolution dataset. For what concerns the NISP spectroscopic channel, the total energy of the PSF is distributed between the different order of the dispersion pattern produced by the NISP grisms. The NISP instrument is designed such that maximum energy, up to 95 %, falls into the 1st order while the remaining energy is mostly distributed between the 0th order (almost 5 %) and higher order (< 1 %). The challenge of this work package will be to adapt recent development used in photometry to model realistic PSF with ML Herbel et al. 2018 to the simulation of the NISP’s under-sampled spectroscopic PSF for each of the relevant order of the spectra that produced by NISP grisms.

The low sampling of the PSF on the instrument detector reduce drastically the capacity to identify the principal features of the PSF only based on the acquired PSF image. Based on the ray tracing simulation, we already started to generate a high-sampled PSF library from which we seek to perform a principal component analysis (PCA) to find the main modes of variation of the PSF and incorporate these characteristics into a parametric model. As in Smith el al. 2019 we aim to build and train a Convolutional Neural Network (CNN) to predict the model parameters for each of the measured PSF in the ground test campaigns and map the parameter values as function of the position in the field of view and the wavelength.

At this stage, the parametric model could already be used by the simulation, and considering the sampling of the PSF, this would be sufficient for the purpose of the PV-phase. But a second approach could be explored to significantly improve the variety of the PSF by generating PSF images directly from the model. Lanusse et al. 2020 shown that generative models can be a powerful solution for building fully data-driven simulation of the galaxy morphology, and this is a method investigated in the Euclid consortium. We will take advantage of the results obtained at the previous step, and we will develop a fast generator of simulated PSF based on a Generative Adversarial Network (GAN). The strategy will be to use the source images in the photometric bands of the NISP to predict the source profile in the spectroscopic channels. This strategy has the advantage of also addressing the case of the resolve sources without having to develop an additional tool to convolve the source profile with the PSF.

Finally, as in WP1, most of the ground data we have and we will use for the initial training described above, have no telescope, or a degraded telescope under gravity that will affect the PSF size and shape (we expect mostly astigmatism and coma). We will have to retrain, at least partially, the model on the in-flight data. The strategy for transfer learning will strongly depend on the ML model we obtain in the previous steps. We will try to identify some layers that have a significant impact on the PSF, with the goal of fixing the rest of the model and focusing the training on those layers only. In the case of the GAN model, we will also study the latent space and look for the parameters that may impact significantly the PSF size.