Since the development of the first achromatic lenses back in the 18th century, dispersion models have been constant companions of optical designers. Various alternatives and extensions to the classical Abbe number and partial dispersion model have been proposed over the years, with the goal of making first- and higher order analysis and correction easier accessible. Hoogland’s reformulation of the classical quantities allowed to visually select glasses and read optical powers for an apochromatic lens from a diagram, and Buchdahl dispersion coefficients have been used as basis for similar work in the infrared spectrum. In both cases however, model parameters must be tuned to arrive at the desired representation. Here we present a model-free approach using principal component analysis of normalized refractive index data at the system wavelengths. We show how it can be applied to understand simultaneously both the dispersion properties and color correction capabilities of a selection of glasses in any part of the optical spectrum, and how to derive favorable glass combinations for apochromatic and superapochromatic lenses including a prediction of residual color.
The evaluation of non-circular test regions poses an unusual but tricky problem to interferometric testing since typical
polynomial decompositions of the measured wavefront like Zernikes are only valid in a circular region. Despite the fact
that of course non-circular polynomial decompositions exist they still rely on regular regions like ellipses or rectangles.
For irregular shapes of test regions no widely accepted general decomposition exists.
Unfortunately it is necessary in some cases to test completely irregularly shaped test regions. May it because the optics
simply is of this shape and needs to be tested in this state or because the used area is irregular and it is undesired to
extend the test region to a larger, but regular shape.
We present a simple method that not only provides a possibility to evaluate any arbitrary shaped test region but also to
have a tolerance model that gives reasonable and uses worldwide accepted specification standards.
Certain interferometer software may be suited for an appropriate data analysis. An overview over some commercially
available interferometer software is given with respect to the requirement of the presented method.
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