I.R. Kabirov1, V.G. Bondarev2, D.V. Lopatkin3, S.V. Ippolitov4

1–4 MESC of Air Forces N.Е. Zhukоvsky and Yu.А. Gаgаrin Air Force Academy (Vоrоnеzh, Russia)

1 ilsur@inbox@gmail.com; 2 bondarevstis@mail.ru; 3 dimkaao@yandex.ru; 4 s_ippolitoff@mail.ru

The relevance of the problem of distortion compensation of cameras with variofocal lenses is aimed at improving the quality of images in vision systems (and is caused by the need to use optoelectronic systems as a measure of navigation parameters. The quality of the image obtained by means of a digital camera determines the accuracy of coordinate measurement. At the same time, known algorithmic methods of distortion compensation do not provide the necessary level of elimination of this error, which does not allow using digital cameras as a precision meter. In addition, due to the variability of conditions of application of vision systems on unmanned aerial vehicles there is a need to use variofocal motorized lenses, distortion compensation of which is even less studied and solved problem.

The aim of article is to development a mathematical model of distortion for variofocal lenses for the purpose of algorithmic compensation through its application over the entire range of focal length variation.

The study of discretization errors of vision systems by means of the developed hardware-software complex for camera calibration has shown a smooth character of change in the values of coefficients in the decompositions of distortion components from the value of focal length. These studies led to the development of a mathematical model of distortion, in which these coefficients are represented as functions of the focal length value and are represented by third degree polynomials of the steppe series. In addition, the presented hardware-software complex and the method of distortion compensation provide precision calculation of the focal length by the indirect method. The obtained results of the distortion study allow algorithmic distortion compensation for the selected configuration of vision systems with variofocal lenses in the whole range of focal length in the navigation task requiring precision measurements. The optoelectronic system can be used as an onboard autonomous global navigation system in low-altitude flight, resistant to radio-technical influences.

Kabirov I.R., Bondarev V.G., Lopatkin D.V., Ippolitov S.V. Mathematical model of distortion of cameras with varifocal lenses. Information-measuring and Control Systems. 2025. V. 23. № 3. P. 15−26. DOI: https://doi.org/10.18127/j20700814-202503-02 (in Russian)

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