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Journals / Journal of Engineering Technology and Applied Sciences / 2026 / Cilt: 9 Sayı: 2

Modelling Real Valued Functions via Optical Lenses

Furkan Semih Dündar(AMASYA UNIVERSITY)0000-0001-5184-5749
Pages
63–70
Publication Date
2024-08-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we have calculated the lens surface for four functions numerically and have provided their plots respectively.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we modeled real valued functions using freeform lenses.
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Key Findings & Data:In our model, the bottom surface of the lens is flat whereas its top surface is determined by a function, f(x).
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Conclusion & Impact:Finally, we have calculated the lens surface for four functions numerically and have provided their plots respectively.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Freeform lens design · ray optics · mathematical modelling

Abstract

In this study, we modeled real valued functions using freeform lenses. In our model, the bottom surface of the lens is flat whereas its top surface is determined by a function, f(x). We consider vertically coming light rays with x-coordinate x. Our aim is to find f(x) such that x is mapped to F(x), the horizontal position where the light ray leaves the bottom surface. We have found the nonlinear differential equation for a generic lens to model a given function. Namely, given F(x), the solution of the differential equation gives us the lens surface f(x). Finally, we have calculated the lens surface for four functions numerically and have provided their plots respectively.

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Cite This Article

Dündar, F. S. (2024). Modelling Real Valued Functions via Optical Lenses. Journal of Engineering Technology and Applied Sciences, Cilt: 9 Sayı: 2, 63–70. https://doi.org/10.30931/jetas.1312369

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References (13)

  1. Doskolovich, L.L., Mingazov, A.A., Bykov, D.A., Bezus, E.A., “Formulation of the inverse problem of calculating the optical surface for an illuminating beam with a plane wavefront as the Monge Kantrovich problem”, Computer Optics 43(5) (2019): 705-713.
  2. Fang, F.Z., Zhang, X.D., Weckenmann, A., Zhang, G.X., Evans, C., “Manufacturing and measurement of freeform optics”, CIRP Annals 62(2) (2013): 823-846.
  3. Wolfram Research, Inc. Mathematica, Version 13.2. Champaign, IL. (2022)
  4. Kumar, S., Tong, Z., Jiang, X., “Advances in the design and manufacturing of novel freeform optics”, International Journal of Extreme Manufacturing 4(3) (2022): 032004.
  5. Valencia-Estrada, J.C., Garcia-Marquez, J., “Freeform geometrical optics i: principles”, Applied Optics 58(34) (2019): 9455-9464.
  6. van Roosmalen, A.H., Anthonissen, M.J.H., Ijzerman, W.L., ten Thije Boonkkamp, J.H.M., “Fresnel reflections in inverse double freeform lens design”, Journal of the Optical Society of America A 40(7) (2023): 1310-1318.
  7. Wu, R., Chang, S., Zheng, Z., Zhao, L., Liu, X., “Formulating the design of two freeform lens surfaces for point-like light sources.” Optics Letters 43(7) (2018): 1619-1622. [8] Yang, L., Liu, Y., Ding, Z., Zhang, J, Tao, X., Zheng, Z.R., Wu, R., “Design of freeform lenses for illuminating hard-to-reach areas through a light-guiding system”, Optics Express 28(25) (2020): 38155-38168.
  8. Doskolovich, L.L., Mingazov, A.A., Bykov, D.A., Bezus, E.A., “Formulation of the inverse problem of calculating the optical surface for an illuminating beam with a plane wavefront as the Monge Kantrovich problem”, Computer Optics 43(5) (2019): 705-713.
  9. Fang, F.Z., Zhang, X.D., Weckenmann, A., Zhang, G.X., Evans, C., “Manufacturing and measurement of freeform optics”, CIRP Annals 62(2) (2013): 823-846.
  10. Kumar, S., Tong, Z., Jiang, X., “Advances in the design and manufacturing of novel freeform optics”, International Journal of Extreme Manufacturing 4(3) (2022): 032004.
  11. Valencia-Estrada, J.C., Garcia-Marquez, J., “Freeform geometrical optics i: principles”, Applied Optics 58(34) (2019): 9455-9464.
  12. van Roosmalen, A.H., Anthonissen, M.J.H., Ijzerman, W.L., ten Thije Boonkkamp, J.H.M., “Fresnel reflections in inverse double freeform lens design”, Journal of the Optical Society of America A 40(7) (2023): 1310-1318.
  13. Wu, R., Chang, S., Zheng, Z., Zhao, L., Liu, X., “Formulating the design of two freeform lens surfaces for point-like light sources.” Optics Letters 43(7) (2018): 1619-1622. [8] Yang, L., Liu, Y., Ding, Z., Zhang, J, Tao, X., Zheng, Z.R., Wu, R., “Design of freeform lenses for illuminating hard-to-reach areas through a light-guiding system”, Optics Express 28(25) (2020): 38155-38168.