# Stabilization of pupils in a zoom lens with two independent movements

TL;DR: A procedure for thin lens structural design of a new class of pupil stabilized zoom systems is presented, facilitated by an implementation of evolutionary programming that searches a multivariate hyperspace formed by design variables, namely, powers of individual components and intercomponent separations.

Abstract: A procedure for thin lens structural design of a new class of pupil stabilized zoom systems is presented. This is facilitated by an implementation of evolutionary programming that searches a multivariate hyperspace formed by design variables, namely, powers of individual components and intercomponent separations. Two coupled components in the lens system act as the variator for the zoom system, and another component in the system acts as the compensator. A fixed axial location of the image plane is achieved by moving the coupled variator and the compensator nonlinearly, while the entrance and the exit pupils are allowed small shifts in their axial locations over the zooming range. The latter relaxation opens up the possibility for effective two-conjugate zoom systems with only two independent component movements. Illustrative examples for thin lens structures of two-conjugate zoom systems are presented.

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TL;DR: This work performs a paraxial analysis of three-component zoom lens with a fixed position of image-space focal point and a distance between object and image points, which is composed of three tunable-focus elements.

Abstract: This work performs a paraxial analysis of three-component zoom lens with a fixed position of image-space focal point and a distance between object and image points, which is composed of three tunable-focus elements. Formulas for the calculation of paraxial parameters of such optical systems are derived and the calculation is presented on examples.

13 citations

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TL;DR: In this article, a method for the automatic design of a special mid-wavelength infrared zoom system in which the positions of both the pupil planes and the image plane are fixed during the zooming process is presented.

Abstract: This paper presents a method for the automatic design of a special mid-wavelength infrared zoom system in which the positions of both the pupil planes and the image plane are fixed during the zooming process. In this method, the formulas for the desired zoom system are derived to ensure the exact fulfillment of the conditions with three moving components based on Gaussian reduction. A mathematical model is established based on the particle swarm optimization to determine the first-order parameters of the paraxial design. Then, the model is optimized by iteratively updating a candidate solution with regard to a specific merit function that characterizes the zoom ratio, compactness, and aberration terms. In the optimization phase, the physical feasibility is considered as the constraint on the candidate solutions. Using two examples, this work demonstrates that the developed method is an efficient and practical tool for finding a realizable initial configuration of a dual-conjugate zoom system. Since this method is no longer reliant on the traditional trial-and-error technique, it is an important step toward the automatic design of complex optical systems using artificial intelligence.

11 citations

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TL;DR: General formulas are derived for the calculation of parameters of a three-component two-conjugate zoom lens system, which enable us to calculate the optical power of individual optical elements and their distances for a different range of magnification and imposed conditions.

Abstract: A method is described for the first-order analysis of a two-conjugate zoom lens composed of three movable elements. Such an optical system satisfies the requirement that the object, image, and pupil planes are fixed within the change of its magnification. General formulas are derived for the calculation of parameters of a three-component two-conjugate zoom lens system, which enable us to calculate the optical power of individual optical elements and their distances for a different range of magnification and imposed conditions. The application of derived formulas is presented on three examples of optical systems with different parameters.

8 citations

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TL;DR: Equations that enable to calculate mutual axial distances between individual elements of the three-element zoom optical system based on the axial position of the beam waist of the input Gaussian beam and the desired magnification of the system are derived.

Abstract: Our work is focused on the problem of theoretical analysis of paraxial properties of the three-element zoom optical system for laser beam expanders. Equations that enable to calculate mutual axial distances between individual elements of the system based on the axial position of the beam waist of the input Gaussian beam and the desired magnification of the system are derived. Finally, the derived equations are applied on an example of calculation of paraxial parameters of the three-element zoom system for the laser beam expander.

8 citations

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TL;DR: The Gaussian design of a two-conjugate zoom system, which does not require any mechanical compensation, is presented and the optical powers of the composing elements and the equivalent optical power as functions of the variable magnification are specified.

Abstract: We present the Gaussian design of a two-conjugate zoom system, which does not require any mechanical compensation. The device works in two stages. First, with fixed optical power, a lens images the pupil aperture, forming a pair of conjugate planes. Then, we invert the conjugate planes for setting the two-conjugate condition. At the second stage, two varifocal lenses generate a tunable magnified virtual image, at the fixed object plane. The varifocal lenses have fixed interlens separation, and they work with zero-throw. We specify the optical powers of the composing elements and the equivalent optical power as functions of the variable magnification.

7 citations

##### References

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01 Sep 1988

TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.

Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required

52,797 citations

01 Jan 1989

TL;DR: This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.

Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required.

33,034 citations

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TL;DR: In this paper, a general statement concerning conjugate points and a simple proof of the maximum number of crossing points of a zoom lens is given. And an algorithm for computing component focal lengths of a five-component symmetrical zoom lens has been proposed.

Abstract: Investigation of the thin lens theory of zoom lenses results in a general statement concerning conjugate points, a simple proof of the maximum number of crossing points, and an algorithm for computing component focal lengths of a five-component symmetrical zoom lens. The three-component optically compensated zoom lens is discussed in detail. Results of applying the algorithm are given. A prototype of the five-component zoom lens has been built and is briefly discussed.

43 citations

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TL;DR: Formulas are derived for the calculation of parameters of a three-component double conjugate zoom lens system with tunable focus lenses, which enable us to calculate the optical power of individual optical components with respect to the transverse magnification.

Abstract: A method for calculation of paraxial parameters of the double conjugate zoom lens is described. Such an optical system satisfies the requirement that the object, image, and pupil planes are fixed during the change of magnification. Formulas are derived for the calculation of parameters of a three-component double conjugate zoom lens system with tunable focus lenses, which enable us to calculate the optical power of individual optical components with respect to the transverse magnification. The main advantage of such an optical system is the possibility to achieve required zooming properties without any mechanical movement of individual components of the zoom lens.

24 citations

### "Stabilization of pupils in a zoom l..." refers methods in this paper

...Recently, Mikš and Novák [12] described a method for designing two-conjugate nonmoving zoom systems with tunable focus lenses....

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