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Relationship between two analytic inversion formulae for multispectral extinction data
Applied Optics
|March 11, 2010
Summary
This study examines analytic inversion formulas for multispectral extinction data within the anomalous diffraction approximation. It derives power series and asymptotic expansions for extinction, clarifying relationships between existing formulas.
Area of Science:
- Optics and light scattering
- Mathematical physics
Background:
- Analytic inversion formulas for multispectral extinction data have been presented by Box and McKellar, and by Fymat.
- These formulas are based on the anomalous diffraction approximation.
Purpose of the Study:
- To examine the relationship between the analytic inversion formulas presented by Box and McKellar, and by Fymat.
- To derive power series and asymptotic expansions for extinction within the anomalous diffraction approximation.
Main Methods:
- Comparative analysis of existing analytic inversion formulas.
- Derivation of power series expansion for extinction.
- Derivation of asymptotic expansion for extinction.
Main Results:
- Established the relationship between the Box and McKellar formula and the Fymat formula.
- Successfully derived the power series expansion for extinction.
- Successfully derived the asymptotic expansion for extinction.
Conclusions:
- The study provides a unified understanding of analytic inversion formulas in anomalous diffraction.
- The derived expansions offer new tools for analyzing multispectral extinction data.
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