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Reflecting anastigmatic optical systems hold several inherent advantages over refracting equivalents, such as compactness, absence of color, high “refractive efficiency,” wide bandwidth, and size scalability to enormous apertures. Such advantages have led to these systems becoming, increasingly since their first deliberate development in 1905, the “go-to” solution for various classes of optical design problems. This paper describes in broad terms the history of the development of this class of optical system, with an emphasis on the early history.
When symmetry is broken, the wave-aberration function generalizes to have not only odd-orders but also even-orders. Geometric interpretation of the lowest-order coefficients (i.e., second) and insights offered by consideration of these terms are presented.
A glass selection optimization algorithm is developed for primary and secondary color correction in thick lens systems. The approach is based on the downhill simplex method and requires manipulation of the surface color equations to obtain a single glass-dependent parameter for each lens element. Linear correlation is used to relate this parameter to all other glass-dependent variables. The algorithm provides a statistical distribution of Abbe numbers for each element in the system. Examples of several lenses, from two- to six-element systems, are performed to verify this approach. The optimization algorithm proposed is capable of finding glass solutions with high color correction without requiring an exhaustive search of the glass catalog.
A systematic method for the design of nonaxially symmetric optical systems is described. Free-form optical surfaces are constructed by superposition of a conic segment and a polynomial, and successfully applied to design relatively fast wide field-of-view optical systems.