Accuracy optimization of combined multiparameter measuring systems with application to polarized light microscopy

Area of Science:

• Metrology and Measurement Science
• Optical Physics
• Materials Science

Background:

• Combined multiparameter measuring systems (CMPMSs) determine multiple unknown quantities from single-variable measurements under varying control parameters.
• Inaccuracies in CMPMSs can arise from the selection of these control parameters.
• Optimizing control parameters is crucial for improving the accuracy of determined quantities.

Purpose of the Study:

• To develop a mathematical method for selecting optimal control parameters in CMPMSs.
• To minimize the upper bound of the error function for determined quantities.
• To enhance the accuracy and reliability of measurements in CMPMSs.

Main Methods:

• Utilizing the submultiplicativity of spectral and Frobenius matrix norms to construct an error function upper bound.
• Minimizing the derived upper bound to determine the optimal set of control parameters.
• Applying the method to the LC-PolScope technique for validating its effectiveness.

Main Results:

• A novel mathematical method for selecting optimal control parameters in CMPMSs was developed.
• The method successfully minimized the error bound, leading to improved accuracy.
• Application to the LC-PolScope demonstrated superior or comparable performance to existing parameter sets.

Conclusions:

• The proposed method offers a robust approach for optimizing control parameters in CMPMSs.
• This technique enhances measurement accuracy irrespective of specific system features or error distributions.
• The method is broadly applicable to various CMPMSs, including optical metrology applications.