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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.
Driven by the development of freeform four-mirror solutions, we review and compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined. We have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces in these starting point designs are described as base off-axis conics that image stigmatically for the central field point, also known as Cartesian reflectors, with an aspheric departure “cap” (quartic with the aperture) added to the Cartesian reflectors. Tilt angles are chosen to cancel field-asymmetric field-linear astigmatism and unobscure the system. Paraxial data from an equivalent on-axis system are used to solve a system of linear equations to determine the magnitude of the aspheric departure “caps” that are placed on top of the base Cartesian reflectors, in order to eliminate the remaining third-order image degrading aberrations. In this approach, each aspheric departure “cap” is centered about the intersection of the optical-axis-ray, also known as the base ray, with the base surface, rather than being centered about the axis of rotational invariance.
Gabor’s 1941 catadioptric design can be modified to give much higher performance versions. Some designs are shown that are 0.999 NA in air over a wide field with diffraction-limited correction on a curved image.