Efficient lineshape estimation by ghost spectroscopy

TL;DR

This paper introduces a method for accurately estimating spectral lineshapes in spectroscopy using a linear inversion approach with moments, validated through a ghost spectroscopy experiment, to achieve optimal precision bounds.

Contribution

It presents a semiparametric model for lineshape estimation that accounts for nuisance parameters, establishing ultimate bounds on estimation precision.

Findings

Experimental confirmation of theoretical precision bounds

Effective linear inversion method for spectral lineshape recovery

Validation through a ghost spectroscopy demonstration

Abstract

Recovering the original spectral lineshapes from data obtained by instruments with extended transmission profiles is a basic tenet in spectroscopy. By using the moments of the measured lines as basic variables, we turn the problem into a linear inversion. However, when only a finite number of these moments are relevant, the rest of them act as nuisance parameters. These can be taken into account with a semiparametric model, which allows us to establish the ultimate bounds on the precision attainable in the estimation of the moments of interest. We experimentally confirm these limits with a simple ghost spectroscopy demonstration.