Proceedings PaperExplicit design of equiripple edge filters
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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.