A Novel Analytical Interpolation Approach for Determining the Locus of a Zoom Lens Optical System

Abstract

In an optical system with multiple lens groups and increased zoom magnification levels, achieving a smooth zoom locus is increasingly difficult. Traditional methods for calculating zoom loci often involve complex and time-consuming formulas. Consequently, we utilized the Padé approximation in optical design software to compute the zoom locus analytically, irrespective of the number of zoom positions (nodes). The initial data were used to assign orders to rational function polynomials, facilitating Padé approximation. If the image surface extended beyond the depth of focus (DOF), a node was added, with adjustments made until it fell within the DOF range. Furthermore, Padé approximation was performed to prevent singularities. The loci of all lens groups in the optical system can be expressed in a rational function format. Specifically, the numerator and denominator polynomial degrees were 20° and 1°, respectively, with their sum being the total number of nodes. In addition, we calculated the zoom locus by increasing the numerator sequence to minimize the occurrence of the singularity and added the node automatically to enable zoom locus calculation in all optical systems. Accordingly, we could make fast calculations, unlike conventional methods, using complex and time-consuming simultaneous equations. Therefore, we could express the locus of the compensated group in the form of a smooth function, as presently shown.