Abstract
When the number of lens groups is large, the zoom locus becomes complicated and thus cannot be determined by analytical means. By the conventional calculation method, it is possible to calculate the zoom locus only when a specific lens group is fixed or the number of lens groups is small. To solve this problem, we employed the Padé approximation to find the locus of each group of zoom lenses as an analytic form of a rational function consisting of the ratio of polynomials, programmed in MATLAB. The Padé approximation is obtained from the initial data of the locus of each lens group. Subsequently, we verify that the obtained locus of lens groups satisfies the effective focal length (EFL) and the back focal length (BFL). Afterwards, the Padé approximation was applied again to confirm that the error of BFL is within the depth of focus for all zoom positions. In this way, the zoom locus for each lens group of the optical system with many moving lens groups was obtained as an analytical rational function. The practicality of this method was verified by application to a complicated zoom lens system with five or more lens groups using preset patents.
Highlights
A zoom lens is an optical system, where the effective focal length (EFL) or magnification can change continuously, whereas the image distance remains fixed [1]
As a result of the calculation of the zoom locus, the error between the method mentioned in this paper and method by the conventional locus calculation is less than about 0.001 mm, and this error is within depth of (DOF), so it does not affect the resolution performances of the optical systems
In this process, the specific lens group can be corrected by moving back focal length (BFL) or EFL to the approximation
Summary
A zoom lens is an optical system, where the effective focal length (EFL) or magnification can change continuously, whereas the image distance remains fixed [1]. To commercialize this setup, when moving the lens group, the zoom locus must be calculated such that the EFL or magnification continuously changes to the desired value.
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