Second-order supporting quadric method for designing freeform refracting surfaces generating prescribed irradiance distributions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908865990230016 |
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| author | Mingazov, Albert A. Bykov, Dmitry A. Bezus, Evgeni A. Doskolovich, Leonid L. |
| author_facet | Mingazov, Albert A. Bykov, Dmitry A. Bezus, Evgeni A. Doskolovich, Leonid L. |
| contents | We consider the inverse problem of calculating a refracting surface that generates a prescribed irradiance distribution in the far field for a collimated incident beam. This problem can be formulated as a mass transportation problem (MTP) with a quadratic cost function. To solve this problem, we propose a version of the supporting quadric method (SQM), in which the calculation of the quadric parameters is reduced to the problem of minimizing a convex function. We obtain simple analytical expressions for the second derivatives of this function, making it possible to calculate the quadric parameters using second-order optimization methods. This allows us to refer to the proposed method as the second-order SQM. We demonstrate high efficiency of this approach by designing several optical surfaces that generate complex irradiance distributions. We also consider the application of the second-order SQM to nonimaging optics problems described by MTPs with a non-quadratic cost function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Second-order supporting quadric method for designing freeform refracting surfaces generating prescribed irradiance distributions Mingazov, Albert A. Bykov, Dmitry A. Bezus, Evgeni A. Doskolovich, Leonid L. Optics We consider the inverse problem of calculating a refracting surface that generates a prescribed irradiance distribution in the far field for a collimated incident beam. This problem can be formulated as a mass transportation problem (MTP) with a quadratic cost function. To solve this problem, we propose a version of the supporting quadric method (SQM), in which the calculation of the quadric parameters is reduced to the problem of minimizing a convex function. We obtain simple analytical expressions for the second derivatives of this function, making it possible to calculate the quadric parameters using second-order optimization methods. This allows us to refer to the proposed method as the second-order SQM. We demonstrate high efficiency of this approach by designing several optical surfaces that generate complex irradiance distributions. We also consider the application of the second-order SQM to nonimaging optics problems described by MTPs with a non-quadratic cost function. |
| title | Second-order supporting quadric method for designing freeform refracting surfaces generating prescribed irradiance distributions |
| topic | Optics |
| url | https://arxiv.org/abs/2603.04036 |