Open AccessThe article focuses on the research of variable magnification optical systems of sophistic class - so-called double conjugation systems. When the magnification changes, they provide two pairs of fixed conjugate planes, namely object and image, as well as entrance and exit pupils. Similar systems are used in microscopy and complex schemes, where it is necessary to conform the pupils of contiguous removable optical components. Synthesis of double conjugation systems in Gauss region is not an easy task. To ensure complete immobility of the exit pupil in the system there should be three movable components or components with variable optical power.
Analysis of the literature shows that the design of double conjugation optical system in the paraxial region has been neglected, all methods are not completely universal and suitable for automation.
Based on the foregoing, the research and development of a universal method for automated synthesis of double conjugation systems in Gauss region formulated as an objective of the present work seem to be a challenge.
To achieve this goal a universal algorithm is used. It is based on the fact that the output coordinates of paraxial rays are multilinear functions of optical surfaces and of axial thicknesses between surfaces. It allows us to create and solve a system of multilinear equations in semi-automatic mode to achieve the chosen values of paraxial characteristics.
As a basic scheme for the synthesis a five-component system has been chosen with extreme fixed components and three mobile "internal" ones. The system was considered in two extreme states of moving parts. Initial values of axial thicknesses were taken from Hopkins' patent. Optical force five components were considered unknown. For calculation the system of five equations was created, which allowed us to obtain a certain back focal length, to provide the specified focal length and a fixed position of the exit pupil at a fixed entrance pupil.
The scheme of the algorithm is as follows. The initial thicknesses for two extreme states of the system are set, and their sum must be the same. Based on the given conditions a system of multilinear equations is generated in automatic mode. Using the numerical method all possible solutions are found. In case of failure, the air thicknesses are changed to a predetermined value, and the algorithm repeats. After finding the solutions a kinematics of three moving parts is calculated. To do this a new system of multilinear equations is automatically generated with the axial thicknesses to be as unknowns. The conditions are the following: constant back focal length and position of the exit pupil, immutable sum of axial thicknesses, providing a define focal length. Next, the resulting system focal length changes at a predetermined step, and the search for solutions of the system is carried out by methods of nonlinear programming. The solution results are the axial thicknesses corresponding to the specified focal length and determining the position of the moving components.
The proposed algorithm is universal and, a part from the other methods, in principle can be applied to design both the systems of double conjugation with mobile components and the systems based on liquid lenses. All methods revealed while analyzing the literature have been designed only for one of abovementioned cases.
The algorithm was tested using the Hopkins system of calculation as an example. As a result, two versions of double conjugation system with twentyfold magnification were calculated, optical forces and principles of motion components were determined. The developed algorithm allows us to facilitate a paraxial design of double conjugation systems with a high degree of automation. A designer, actually, has only to enter the required dimension and magnification. The main drawback of the proposed algorithm is the ambiguity in choice of the initial axial distances. The activities to eliminate it are underway.