Abstract
Our paper presents a detailed theoretical analysis of the three-element optical system with zero separation of principal planes and approximately corrected Petzval sum, which has the required value of the axial position of its optical center for a given value of focal length and a given value of axial distance of the image focal point from the last element of the system. Formulas that make it possible to calculate paraxial parameters of such types of optical systems are derived, and the application of the derived formulas is presented in several examples. Such optical systems represent a subset of the new family of optical systems with the constant position of the optical center. The optical center of such an optical system is at a given required axial position, and this position does not change with the object distance, which could be advantageous for certain applications.
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