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This study analyzes precision limits in spectral parameter determination for inelastic optical scattering using Fisher information. It provides formulas for Raman and Brillouin spectrometers, considering various optical and detector effects to identify optimal configurations.

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Area of Science:

  • Spectroscopy
  • Optical Physics
  • Metrology

Background:

  • Accurate determination of spectral parameters is crucial in inelastic optical scattering techniques like Raman and Brillouin spectroscopy.
  • Existing methods may not fully account for instrumental limitations affecting measurement precision.
  • Understanding fundamental precision limits is key to optimizing spectrometer design and performance.

Purpose of the Study:

  • To analyze the fundamental precision limits in determining spectral parameters in inelastic optical scattering.
  • To derive general analytic formulae for precision limits, incorporating instrument response functions.
  • To identify optimal spectrometer configurations by considering various optical and detector effects.

Main Methods:

  • Application of Fisher information and the Cramér-Rao lower bound to analyze precision limits.
  • Derivation of general analytic formulae accounting for dispersive element and relay optics response functions.
  • Analysis of limiting cases for dispersion-limited (Lorentzian) and diffraction-limited (Voigt) spectrometers.

Main Results:

  • General analytic formulae for fundamental precision limits in spectral parameter determination were derived.
  • The formulae explicitly include the effects of instrument response functions.
  • Optimal configurations for spectrometers measuring Lorentzian and Voigt lineshapes were identified, considering aberrations and detector properties.

Conclusions:

  • The study provides a theoretical framework for understanding and improving precision in inelastic optical scattering measurements.
  • Consideration of optical aberrations and detector characteristics is essential for achieving optimal spectral parameter determination.
  • The derived formulae can guide the design and optimization of Raman and Brillouin spectrometers.