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Identification of appropriate primitive polynomials to avoid cross-contamination in multifocal electroretinogram
J M Ireland1, D Keating, S G Hoggar
1Department of Mathematics, University of Glasgow, Scotland. Jillian.Ireland@jillber.freeserve.co.uk
Medical & Biological Engineering & Computing
|September 14, 2002
Summary
This study introduces a method using finite field theory to select optimal primitive polynomials for multifocal electroretinography (mfERG). This approach minimizes cross-contamination in mfERG signals, improving visual pathway response analysis.
Area of Science:
- Ophthalmology
- Neuroscience
- Signal Processing
Background:
- Multifocal electroretinography (mfERG) uses decimated m-sequences for simultaneous visual pathway stimulation.
- Investigating higher-order response cross-contamination is crucial for mfERG accuracy.
Purpose of the Study:
- To investigate cross-contamination effects from higher-order responses in mfERG.
- To identify optimal primitive polynomials for generating m-sequences in mfERG.
Main Methods:
- Generated primitive polynomials using finite field theory.
- Analyzed cross-contamination using Zech logarithms.
- Correlated m-sequences with physiological responses to form first and second-order ERG responses.
- Experimentally validated findings using a photodiode and trace arrays.
Main Results:
- Cross-contamination decreased with higher-degree primitive polynomials (degree 16 showed 5.6% contamination).
- "Bad" primitive polynomials introduced additional waveforms in experimental trace arrays.
- Theoretical analysis using finite fields and Zech logarithms predicted suitable polynomials.
Conclusions:
- Finite field theory and Zech logarithm analysis effectively predict suitable primitive polynomials for mfERG.
- This method enhances the generation of m-sequences, reducing cross-contamination.
- Findings have significant implications for the development of multifocal electrophysiology systems.