Secondary spectrum correction in lens systems with large air spaces using the concept of equivalent lens

We present a theory for the correction of secondary chromatic aberration in systems of separated lenses with a primary goal of designing apochromatic lenses using inexpensive optical glasses. The method is to replace a group of widely spaced lenses with the imaginary equivalent lens so that the dioptric power and dispersion properties of this equivalent lens are the same as those for said group of lenses. This equivalent lens and the last lens of the optical system can be considered as a thin doublet lens. Thus, the complex problem of color correction of an arbitrary system of separated lenses is reduced to a simple problem of a system of two lenses in contact. The system of equations for thin lenses is solved to simultaneously correct three chromatic aberrations. The thin lens approximation yields good starting designs that can be easily optimized for well-corrected lens systems. The presented theory comprises algebraic equations for simultaneous correction of the primary and secondary longitudinal chromatic aberrations and lateral color for a system of three widely separated thin components. The process of lens design is based on solving algebraic equations, and it is quite straightforward. The results are illustrated by a numerical example of a thin-lens starting design and optimized apochromatic lens system with the use of inexpensive optical glasses. This approach is universal and can be extended to more complex optical systems using the methodology described in this work.