Wavelength Calibration¶
The spectral calibration stands as a cornerstone of our research, ensuring the fidelity of the data we analyze. The precision of our cosmological findings depends on accurate calibration, a process where raw instrument data is transformed into scientifically meaningful spectral information.
Challenges in Spectral Calibration¶
Euclid's Near Infrared Spectro-Photometer (NISP) uses slitless spectroscopy to capture the spectra of distant galaxies. Slitless spectroscopy is a technique where the spectra of multiple objects are captured simultaneously. This technique is ideal for large-scale surveys, allowing astronomers to observe thousands of galaxies in a single exposure.
However, slitless spectroscopy poses unique challenges in spectral calibration. The spectra of different objects overlap, making it difficult to distinguish between them. This overlap is further complicated by the presence of instrumental effects that distort the spectra, making it challenging to identify the spectral features of individual objects.
Our Approach¶
The NISP grisms are a combination of a dispersion grating and a prism to compensate for the light deviation caused by the diffraction of the grating. This design allows the NISP to images the sky on both spectroscopic and photometric channel onto the same focal plane. However, as the dispersion induced by the grating and the prism are superimposed, the overall dispersion of the NISP’s grisms is not linear. To add to complexity, to ensure a decent quality across the large field of view of the NISP instrument, NISP’s grisms have focusing power as well as a grating groove which varies across their surface. Up to now, the technique used to characterize the spectral dispersion of the NISP instrument is to use parametric models which parameters are tuned against data. One drawback of this approach is that the parameters are correlated to each other and degenerated between several physical parameters. Any modification of the instrument response induced by stresses (mechanic or thermal stresses) or change in instrument configuration are not easily reproduced by those parametric models unless the model’s parameters are re-calibrated.
A better description of the optical response of the instrument is to describe the instrument response as a transformation that map physical parameters (grating groove steps, focal length of the optics, lenses surface curvature, …) to the image characteristics. The aim is then to obtain the reverse transformation, linking image properties to physical parameters, directly from the data to evaluate the physical parameters that play a role in the imaging. When considering grisms, one can simplify the imaging as being the convolution of the spectral trace with the PSF. The aim of this work package will therefore be to identify and evaluate the physical parameters of the instrument and its optic that shape the spectral trace. To do so, we propose developing an instrument model combining physical parameters of the main optical components of the system with ML models.
The approach will be first to derive a restricted number of physically motivated parameters with a simplified ray-tracing model of the key optical elements of the instrument (telescope, collimator, grism, filter, camera lens). Preliminary analysis of the full ray tracing data using a geometrical model of the light propagation was performed by Y. Copin with the software spectrogrism. Initially implemented for the data-reduction pipelines of the SAURON Bacon et al. 2001 and SNIFS Lantz et al. 2003 spectrometer, the model was adapted to the optical setup of the NISP. This simplified model provides a mapping between a wavelength and a position in the telescope coordinates to a position in the detector plan. This model cannot reach the accuracy we aim to achieve without any additional tuning and our preliminary analysis gave an accuracy of the position in the detector plan about 10 pixels rms, far from the 0.1 pixels accuracy required, but it provides parameters we can interpret and adapt like the grism tilt that changes between each exposure due to the wheel positioning accuracy.
The second step of the approach will be to insert between the optical elements of the simplified ray-tracing model, ML regression models to significantly improve the prediction accuracy. The overall model will be trained on the ground calibration datasets and several types of ML models will be tested to find the best algorithm to represent the instrument. One of the challenges of this work will be to perform the optimization of both the physically motivated parameters and the ML parameters in ensuring the stability of the model. Once the architecture of the ground model is fixed, the next step will then be to train this ground model on the in-flight calibration data. We will set up a transfer learning strategy to limit the parameters to be optimized; because we are expecting the NISP optical elements to be very stable between the ground and the flight condition, we will focus first on tunning the parameters of the model that represent the telescope.
The final stage of this work package is to exploit ML recurrent approaches by making use of the feedback from peculiar features present in images, like star traces or bright sources with known spectral energy distribution in the field, to improve calibration errors by tuning the physical parameters of the instrument and by exploring the possibilities of the Recurrent Neural Networks (RNN).
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.