Paraxial design of a four-component zoom lens with zero separation of principal planes and fixed position of an image focal point composed of members with constant focal length

Our paper presents a detailed theoretical analysis of a four-component zoom lens with coincident principal planes, fixed position of the image focal point, and an approximately corrected Petzval sum. New formulas enabling the calculation of paraxial parameters of such optical systems are derived, and the practical application of these formulas is shown in an example. The position of the optical center of these optical systems does not depend on the object distance (for a given value of focal length of the zoom), and the position of the image focal point (with respect to the last element of the system) is fixed during the operation of the zoom. Such optical systems could be used in various measuring systems in photogrammetry, computer vision, triangulation sensors, fringe projection techniques, surveying, machine vision, etc.