In-Flight Estimation of Instrument Spectral Response Functions Using Sparse Representations

TL;DR

This work tackles the challenge of in‑flight ISRF estimation for high‑resolution spectrometers by replacing traditional parametric fits with SPIRIT, a sparse dictionary‑based approach. ISRFs are modeled as sparse combinations of learned atoms, with dictionaries built from ground ISRFs via SVD or K‑SVD and sparse codes computed by OMP or LASSO; this yields substantially lower ISRF estimation errors than Gaussian or super‑Gaussian models across six spaceborne instruments. Across Avantes, GOME‑2, OMI, TROPOMI, OCO‑2, and MicroCarb data, SPIRIT consistently achieves sub‑1% normalized ISRF errors and improved spectral residuals, while remaining robust to noise and scene‑dependent ISRF changes. The results support using a dictionary‑based SPIRIT framework (SVD dictionary with OMP coding) for fast, accurate in‑flight ISRF estimation and real‑time recalibration of remote sensing instruments.

Abstract

Accurate estimates of Instrument Spectral Response Functions (ISRFs) are crucial in order to have a good characterization of high resolution spectrometers. Spectrometers are composed of different optical elements that can induce errors in the measurements and therefore need to be modeled as accurately as possible. Parametric models are currently used to estimate these response functions. However, these models cannot always take into account the diversity of ISRF shapes that are encountered in practical applications. This paper studies a new ISRF estimation method based on a sparse representation of atoms belonging to a dictionary. This method is applied to different high-resolution spectrometers in order to assess its reproducibility for multiple remote sensing missions. The proposed method is shown to be very competitive when compared to the more commonly used parametric models, and yields normalized ISRF estimation errors less than 1%.

Figures (11)

• Figure 1: Examples of MicroCarb ISRFs.
• Figure 2: Representation of the four first atoms of the dictionary constructed using one SVD (top) or using the K-SVD algorithm (bottom) for the MicroCarb spectrometer (band B1).
• Figure 3: Examples of ISRFs and their estimates using parametric methods and SPIRIT for ISRFs centered at 404.25 nm for Avantes (a), centered at 430 nm for GOME-2 (b), OMI (c) and TROPOMI (d) and centered at 763.01 nm for OCO-2 (e) and MicroCarb (f).
• Figure 4: Avantes (a) and GOME-2 (b) ISRF estimates using different methods (Gauss, Super-Gauss, OMP and LASSO, SVD and K-SVD).
• Figure 5: OMI (a) and TROPOMI (b) ISRF estimates using different methods (Gauss, Super-Gauss, OMP and LASSO, SVD and K-SVD).