Boian A. HRISTOV^*

Institute of Optical Materials and Technology, Bulgarian Academy of Sciences, PO Box 95, Sofia 1113, Bulgaria

(Received August 16, 2012; Revised March 15, 2013; Accepted May 27, 2013)

In the paper we present a new theory designed to overcome the deficiencies of the existing aberration theories. The main advantage is the theory's capacity to perform analytical, direct, and accurate radius, and thickness calculations of aberration corrections for optical components and systems. Methodologically, we derive exact formulas for bilinear transformations from an object to an image space. Next, we introduce relative parameters in the matrix coefficients and by combining bilinear and matrix transformations we develop exact corrections on-axis aberrations and field aberrations such as distortion, astigmatism, and curvatures (including sagittal and tangential). The theory with an accuracy of 10^-8 mm (except for tangential and sagittal coma) allows precise radius and thickness calculation of components and systems for aberration corrections, sets exact coordinates of free-form surfaces, and enables the study of the surface and component capacities for aberration correction. The theory has supported the design of more than 10 different patented optical systems.

Key words: aberration theory, optical system design, free-form lens design, optical components, lens system design, nonspherical lens design, medical optics, microscopy, telescopes

^*E-mail address: bhristov@abv.bg