Explicit design of equiripple edge filters

John S. Seeley

doi:10.1117/12.192128

4 November 1994 Explicit design of equiripple edge filters

John S. Seeley

Proceedings Volume 2253, Optical Interference Coatings; (1994) https://doi.org/10.1117/12.192128
Event: 1994 International Symposium on Optical Interference Coatings, 1994, Grenoble, France

Abstract

When a dielectric multilayer is restricted in refractiveindex to the classic Hi/Lo practicable stack,extraction of edge filter design becomes a choice between these:- i) sufficient Herpin equivalent-layer "periods" matched to the substrate, as taught by Thelen, ii) exact prototypes due to Riblet, Young (1962) and Levy (1965), modified to make their inherent index "steps" more practicable, iii) explicit near-exact formulas, deriving from the equiripple polynomial, and particularly:for index steps (Rhodes (1976)), for Fresnel reflectance (Seeley (1961)), for layer thickness (Seeley (1965)). None are exact when compared with the Chebyshev equiripple polynomial (used as spectral target). Accuracy can be improved in iii) however by including the adjacent p and r in a better formula for thickness (q), thus:( (tp+tr) ) Sin (q) = ( Imped(q) g(q) I)ISQR((1-LofHi.tp"2).(1-LoMi.tr"2)) ( Admit(p,r) ) where tØ is the adjacent half-tangent. Motivation for revisiting this problem remains a need to know "optimum" performance" for a Chebyshev Stack and how it may be designed explicitly without computer refinement. The improved stack is presumed matched to air with exact antirefiection (extrapolated from Levy) to be certain.

Citation Download Citation

John S. Seeley "Explicit design of equiripple edge filters", Proc. SPIE 2253, Optical Interference Coatings, (4 November 1994); https://doi.org/10.1117/12.192128

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KEYWORDS

Prototyping

Transformers

Optical filters

Linear filtering

Refractive index

Dielectric filters

Lanthanum

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