# Precision and informational limits in inelastic optical spectroscopy

## TL;DR

This paper analyzes the fundamental precision limits in inelastic optical spectroscopy using Fisher information, deriving formulas that account for instrument response and practical factors to optimize spectral parameter measurement.

## Contribution

It introduces general analytic formulas for precision limits in inelastic optical spectroscopy, considering instrument response and practical aberrations, advancing the understanding of measurement accuracy.

## Key findings

- Derived formulas for precision limits in spectral parameter estimation.
- Identified optimal configurations for Lorentzian and Voigt lineshapes.
- Analyzed effects of aberrations and detector limitations on measurement accuracy.

## Abstract

Using Fisher information and the Cram\'er-Rao lower bound, we analyse fundamental precision limits in the determination of spectral parameters in inelastic optical scattering. General analytic formulae are derived which account for the instrument response functions of the dispersive element and relay optics found in practical Raman and Brillouin spectrometers. Limiting cases of dispersion and diffraction limited spectrometers, corresponding to measurement of Lorentzian and Voigt lineshapes respectively, are discussed in detail allowing optimal configurations to be identified. Effects of defocus, spherical aberration, detector pixellation and a finite detector size are also considered.