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Features of the meridional ray invariant in a Focon as functions of the position of the first reflection point
Abstract
Expressions for the meridional ray invariant were derived and its features were studied for mutually opposite positions of the first reflection point relative to the focon axis. It was found that if the focon is tapering for the forward ray, it becomes expanding for the opposing ray. The parameters of the focons and meridional rays in these guides were calculated under the approximation of small taper β. The results obtained will further be used to derive design formulae for calculating parameters of the focons and the meridional rays propagating in these devices.
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Conical light pipes to condense radiation are attractive in their simplicity and low cost.
In addition, when using detectors having non-uniform surface response, the non-image forming characteristics of such channels are desirable. Through the use of a field lens, channels may be designed which condense the radiation through a given area to the smallest possible size. As viewed from the output end of the channel, this corresponds to achievement of the optimum f/number of 0.6. Reflection losses in the experimental model described increased the f/number to 0.77. The cone channel described has the further advantage that it is not receptive to stray light.
New formulas were obtained for the cases most frequently encountered in practice that allow one to find the number of reflections and the path length of a meridional ray in a hollow focon with a linear generatrix and a specular-reflecting inner side surface. By using a meridional-ray invariant, formulas were obtained that are free of any restrictions usually imposed on the focon conicity.