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ISSN: 1023-5086


ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

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DOI: 10.17586/1023-5086-2022-89-03-13-19

УДК: 535.317

Systems of generalized harmonic lenses for image formation

For Russian citation (Opticheskii Zhurnal):

Скиданов Р.В., Ганчевская С.В., Васильев В.С., Бланк В.А. Системы обобщенных гармонических линз для формирования изображений // Оптический журнал. 2022. Т. 89. № 3. С. 13–19.


Skidanov R.V., Ganchevskaya S.V., Vasil’ev V.C., Blank V.A. Systems of generalized harmonic lenses for image formation [in Russian] // Opticheskii Zhurnal. 2022. V. 89. № 3. P. 13–19. 10.17586/1023-5086-2022-89-03-13-19

For citation (Journal of Optical Technology):

R. V. Skidanov, S. V. Ganchevskaya, V. S. Vasil’ev, and V. A. Blank, "Systems of generalized harmonic lenses for image formation," Journal of Optical Technology. 89(3), 132-136 (2022).


Subject of study. The simplest scheme comprising two harmonic lenses is considered, which allows the formation of an image with higher quality than that obtained using each of these lenses individually owing to the accurate selection of the heights of their microreliefs. Method. Two harmonic lenses with coupled microrelief heights are fabricated using the direct laser writing method on the photoresist. An experiment is conducted on the formation of images by the system comprising two harmonic lenses and an individual harmonic lens. Main results. A “HarmLens” software for modeling of the systems comprising harmonic and diffractive lenses is designed. Modeling is performed within the geometric optic approximation using the ray tracing method. The possibility of obtaining a significant reduction in the displacement of the primary focal plane in comparison with the individual harmonic lens case is demonstrated by the specific selection of the microrelief height in this system. The system of two harmonic lenses is demonstrated to form an image with an average contrast exceeding the average contrast of the image formed by the individual harmonic lens by 1.4 times. The point spread function of the system comprising two harmonic lenses is experimentally demonstrated to be 1.6 times narrower than that of the individual harmonic lens with an equivalent focal length. Practical significance. The system of two harmonic lenses proposed in this work allows a sharper image than the image formed by an individual harmonic lens to be obtained. The system of two harmonic lenses can be adopted in machine vision systems where the compact arrangement of the objective’s elements is more important than the high quality of the formed image.


harmonic lens, objective, system of harmonic lenses, microrelief, point spread function


The research was supported by the grant of RSF No. 20-69-47110 as related to the performance of the experiment and by the  Ministry of Science and Higher Education of RF within the state assignment of the Federal Scientific Research Centre "Crystallography and Photonics" of RAS as related to calculation and manufacturing of harmonic lenses.

OCIS codes: 050.1970, 040.1880, 050.1965, 120.4820, 110.0110


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