Paraxial determination of the general four-component zoom system with mechanical compensation

Abstract

ABSTRACT To determine paraxial properties of the general four-component zoom system with mechanical compensation we musthave the methods to obtain the optical power distribution and test and evaluate kinematics. There are two important ap-proaches to general conception of four-component zoom system. The first refers to the expansion of the method for threetypes of zoom systems. According to the location of an object and image in relation to a zoom system, we distinguish follow-ing zoom systems: variable focal lenses, projection or reproduction systems, and afocal aflachments. The second refers to theexpansion of kinematic possibilities of all zoom components and even an object plane. Research led to the conclusion thatknowing the marginal positions and extreme values of main useful parameters connected with them is quite sufficient to ob-tam the optical power distribution of the individual components. Changing the input data we may minimize the longitudinaldimension of the zoom system. Sort of a zoom system is determined by paraxial aperture co-ordinates at the edges of a zoomsystem. The first optical power is calculated from the equation being four degree of polynomial. We have four solutions ofthis equation and have four propositions of the optical power distributions in four-component zoom system. All remainingoptical powers in four-component zoom system are expressed by the first optical power. Calculation of optical powers in thisway means that the zoom system is good only in both marginal positions. Research led to the statement, that optical conjugateand fixed image location are determined from a quadratic equation. To verify kinematics of the zoom system it is necessary todetermine the variation of main useful parameter and, if required, variation of movements of the first and fourth component.After kinematic calculations we should first test, whether the travel from start to the final position is smooth. Later we evalu-ate kinematics and, if possible, correct it by mentioned changes or even by modification of marginal positions.Keywords: zoom systems, four-component zoom systems.1. INTRODUCTIONRelatively small account of publications issued to date deals with mechanically compensated zoom systems. Only few ofthem were dedicated to four-component zoom systems. Among mostly noted K.Yamaja's monograph published in Progress inOptics' should be mentioned. In Russia M.S.Stephansky and N.A.Gradoboyeva2 had published studies on four-componentsystems applied to wide-angle variable focal lenses and telescope zoom attachments. K.Tanaka's publications3'4 deals mainlywith kinematic paraxial analysis offour and five-component variable focal lenses. In available literature the importance of theproblem of determining the optical powers offour-component zoom system is still underestimated. Dominant is the simplifiedapproach proposed by K.Yamaya' consisting in pre-fixing the type of zoom system and magnification range of selected corn-ponents. Proper spacings between components are determined by trial method. Method of determining optical power distri-bution described in this paper tends in opposite direction -fromassigning the marginal positions of components to determin-ing the optical powers without pre-setting the type of the system and magnification range. Such problem was insolvable hith-erto due to mathematical difficulties.From designer's point of view the most important input data is component position along axis in both marginal locationsand main useful parameter values Pmin and Pmax connected with it. Both marginal positions are the result of anticipatedmovements of system components, pre-set safety margins for minimal spacings between thick components, margins foraligning, and also of natural designer's tendency to minimize the longitudinal dimension of the zoom system. In furtherstages of design all margins are usually specified regarding actual thick components and their alteration during optimization.Marginal positions of four-component zoom system are given by spacings between components in start ei and final E po-sition for i=O, 1,2,3 and 4. Spacings eo and E are distances to the object plane in start and final position respectively. Con-ventionally it is assumed that e0=E0=O, when the object is in infinity. Spacings e4 and B4 are distances to the image plane instart and final position respectively. Conventionally it is assumed that e4=B4=O when the image is in infinity. According toassumed formalism component indices i=O and i=5 relate to object and image plane respectively. Fig. 1 illustrates assumedspacing notation for both marginal positions.