Maximum-likelihood curve-fitting scheme for experiments with pulsed lasers subject to intensity fluctuations

Area of Science:

• Physics
• Spectroscopy
• Data Science

Background:

• Standard data evaluation schemes like least-squares fitting are not universally applicable.
• Improperly derived schemes can lead to reduced accuracy and precision in experimental results.
• Pulsed laser experiments exhibit correlated variations due to pulse-to-pulse power fluctuations.

Purpose of the Study:

• To outline a general method for deriving statistical data evaluation schemes applicable to all experiments.
• To demonstrate a new fitting scheme for laser-spectroscopic experiments using the maximum likelihood method.
• To improve the accuracy and precision of data analysis in pulsed laser experiments.

Main Methods:

• Development of a measurement model incorporating statistical variations of all variables.
• Derivation of a data evaluation scheme using the maximum likelihood method.
• Characterization of the new scheme's accuracy and precision against theoretical limits.

Main Results:

• The derived fitting scheme for pulsed laser experiments shows up to three times better precision than simple least-squares fitting.
• The new method effectively suppresses bias in estimated model parameters.
• The scheme maintains accuracy and precision close to the theoretical limits.

Conclusions:

• A statistically robust data evaluation scheme, derived from a proper measurement model, is crucial for accurate experimental analysis.
• The maximum likelihood-based fitting scheme offers superior performance for pulsed laser experiments, particularly in nonlinear spectroscopy.
• This approach provides a more reliable and precise method for analyzing experimental data across various scientific disciplines.