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A priori information and optimisation in polarimetry
Matthew R Foreman1, Carlos Macias Romero, Peter Török
1Department of Physics, Blackett Laboratory, Imperial College London, Prince Consort Road, London, UK.
Optics Express
|September 17, 2008
Summary
This study introduces a new framework using Fisher information to improve polarimetric measurements by incorporating prior knowledge, enhancing precision beyond traditional methods. It also provides new insights into error analysis for Mueller matrix decomposition.
Area of Science:
- Physics
- Optical Engineering
- Information Theory
Background:
- Polarimetric measurements are crucial for system analysis but are limited by noise, affecting data precision.
- Existing methods for optimizing polarimetric systems often neglect valuable a priori information.
Purpose of the Study:
- To develop a novel framework for designing and optimizing polarimetric systems using Fisher information.
- To provide a more comprehensive figure of merit than the conventional condition number.
- To analyze error distributions in Mueller matrix polar decomposition for improved noise analysis.
Main Methods:
- Utilizing the Fisher information matrix to incorporate a priori knowledge into system design.
- Comparing the proposed figure of merit with the condition number using various scenarios.
- Deriving analytic results for error distribution in Mueller matrix polar decomposition.
Main Results:
- The Fisher information-based framework offers superior precision by integrating prior knowledge.
- The proposed figure of merit demonstrates advantages over the condition number in general cases.
- Bounds for informational gains using multiple polarimeter arms were established.
- Analytic results for error distribution in Mueller matrix polar decomposition were obtained.
Conclusions:
- The proposed framework enhances the precision of polarimetric measurements by effectively utilizing a priori information.
- The new figure of merit provides a more complete assessment of polarimetric system performance.
- The derived error analysis aids in more accurate noise assessment in polarimetric experiments.
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