Optimal extraction of echelle spectra: Getting the most out of observations

Context. The price of instruments and observing time on modern telescopes is quickly increasing. Therefore, it is worth revisiting the data reduction algorithms to extract every bit of scientific information from available observations. Echelle spectrographs are typical instruments used in high-resolution spectroscopy, but attempts to improve the wavelength coverage and versatility of these instruments has resulted in a complicated and variable footprint of the entrance slit projection onto the science detector. Traditional spectral extraction methods generally fail to perform a truly optimal extraction when the slit image is not aligned with the detector columns and, instead, is tilted or even curved.Aims. Here, we present the mathematical algorithms and examples of their application to the optimal extraction and the following reduction steps for echelle spectrometers equipped with an entrance slit that is imaged with various distortions. The new method minimises the loss of spectral resolution, maximises the signal-to-noise ratio, and efficiently identifies local outliers. In addition to the new optimal extraction, we present order splicing and a more robust continuum normalisation algorithm.Methods. We developed and implemented new algorithms that create a continuum-normalised spectrum. In the process, we account for the (variable) tilt or curvature of the slit image on the detector and achieve optimal extraction without prior assumptions about the slit illumination. Thus, the new method can handle arbitrary image slicers, slit scanning, and other observational techniques aimed at increasing the throughput or dynamic range.Results. We compare our methods with other techniques for different instruments to illustrate the superior performance of the new algorithms compared to commonly used procedures.Conclusions. Advanced modelling of the focal plane requires significant computational effort but it has proven worthwhile thanks to the retrieval of a greater store of science information from every observation. The described algorithms and tools are freely available as part of our PyReduce package.

Automated summary

The article presents mathematical algorithms for optimal extraction of echelle spectrometers with distorted entrance slits, minimizing loss of spectral resolution, maximizing signal-to-noise ratio, and identifying local outliers efficiently. The new method also includes order splicing and a robust continuum normalization algorithm, offering superior performance compared to commonly used procedures, and is freely available in the PyReduce package.