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Drive nonlinearities: their effects in Fourier spectroscopy
Applied Optics
|February 20, 2010
Summary
This study analyzes spectrum errors in Michelson interferometers caused by drive nonlinearities. It reveals that fringe-reference sampling with minimal distortion filters results in random errors comparable to drive speed errors, varying with spectral interval.
Area of Science:
- Optical Physics
- Spectroscopy
- Metrology
Background:
- Michelson interferometers are crucial for spectroscopy, but their accuracy can be compromised by drive nonlinearities.
- Understanding and quantifying spectrum errors is essential for reliable interferometric measurements.
Purpose of the Study:
- To comprehensively analyze spectrum errors arising from drive nonlinearities in a Michelson interferometer.
- To evaluate these errors for both repeatable and random nonlinearities under fringe-reference sampling.
- To provide a framework for numerical evaluation of spectrum errors for various system parameters.
Main Methods:
- Development of theoretical equations for actual (mean-square) spectrum error.
- Analysis of fringe-reference sampling and partial results for equal-time sampling.
- Derivation of closed-form solutions for special cases to understand qualitative features and bounds.
- Numerical evaluation of derived equations using parameters like drive speed variation, input spectrum, apodization, and filter characteristics.
Main Results:
- Quantification of spectrum errors for repeatable and random drive nonlinearities in Michelson interferometers.
- Demonstration that fringe-reference sampling with minimal distortion filters leads to relative rms random errors in intensity similar to relative rms drive speed errors under specific resolving power conditions.
- Establishment that the spectrum error magnitude varies with the square root of the resolved spectral interval.
Conclusions:
- Drive nonlinearities significantly impact spectral accuracy in Michelson interferometers.
- Fringe-reference sampling offers a method to manage spectrum errors, with error magnitudes predictable based on system parameters.
- The findings provide a basis for optimizing interferometer design and operational parameters to minimize spectral measurement uncertainties.
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