# Modeling the Echelle Spectra Continuum with Alpha Shapes and Local Regression Fitting

## TL;DR

This paper introduces two novel, data-driven algorithms for continuum normalization of echelle spectra, improving accuracy over polynomial fitting and addressing detector artifacts in high-precision spectrometry.

## Contribution

The paper presents two new algorithms, AFS and ALSFS, for spectrum continuum normalization that outperform polynomial methods and incorporate lab reference data.

## Key findings

- Improved continuum normalization accuracy over polynomial fitting.
- Effective mitigation of CCD detector artifacts.
- Validated on simulated spectra and real spectrometer data.

## Abstract

Continuum normalization of echelle spectra is an important data analysis step that is difficult to automate. Polynomial fitting requires a reasonably high order model to follow the steep slope of the blaze function. However, in the presence of deep spectral lines, a high order polynomial fit can result in ripples in the normalized continuum that increase errors in spectral analysis. Here, we present two algorithms for flattening the spectrum continuum. The Alpha-shape Fitting to Spectrum algorithm (AFS) is completely data-driven, using an alpha shape to obtain an initial estimate of the blaze function. The Alpha-shape and Lab Source Fitting to Spectrum algorithm (ALSFS) incorporates a continuum constraint from a lab source reference spectrum for the blaze function estimation. These algorithms are tested on a simulated spectrum, where we demonstrate improved normalization compared to polynomial regression for continuum fitting. We show an additional application, using the algorithms for mitigation of spatially correlated quantum efficiency variations and fringing in the CCD detector of the EXtreme PREcision Spectrometer (EXPRES).