Iterative Computerized Method for Designing Achromatic Optical Systems with Shelled Ball Lens

Abstract

Many optical studies concentrate on designing achromatic lenses to limit the effects of chromatic and spherical aberration. Most of these studies concentrate on manipulating the profile of surfaces with complex aspheric surfaces. In this study another approach is producing, an optical concentric symmetry (spherical ball – spherical shell) system was optically designed and evaluated. The computational method in MATLAB, an iterative mathematical model, and Fermat's and symmetry principles were used to determine the optical design constructive parameters. The validity of the iterative computerized method to design an achromatic optical system was evaluated for three optical designs. These three designs were tested monochromatically and with Fraunhofer wavelengths for infinite conjugate. In addition, the ZEMAX was used to evaluate the optical designs for aberrations and spherochromatism in the optical systems. The spherochromatism analysis was done for three visible lines (Fraunhofer wavelengths) that fall inside the Airy disk and prove the diffracted limit by spot diagram analysis. This radially un-gradient index of symmetry concentric polymeric (three optical designs) was tested in a balanced focal ratio that appeared Sterhl ratio greater than 0.96.

Keywords

• Aberration
• Shell Thickness
• Iterative Model
• Symmetry System
• Ball Lens

References

1. [1] Gaafer, F. N., Al-Moudarris, F. A., and Hussein, O. A., “Investigation of the Optical Properties of the Achromatic Quadrupole Lens by Using the Rectangular Potential Distribution Model”, Baghdad Science Journal, 6(2): 386-393, (2009).
2. [2] Gonzalez-Acuna, R. G., “General equation of the achromatic stigmatic singlet”, JOSA A, 40(7): 1337-1342, (2023).
3. [3] Hanninen, A. M., and Potma, E. O., “Nonlinear optical microscopy with achromatic lenses extending from the visible to the mid-infrared”, APL Photonics, 4(8): 080801, (2019).
4. [4] Li, K., Guo, Y., Pu, M., Li, X., Ma, X., Zhao, Z., and Luo, X., "Dispersion controlling meta-lens at a visible frequency", Optics Express, 25(18): 21419-21427, (2017).
5. [5] Hecht, E. Optics Addison-Wesley Longman. Inc., New York, NY, (1998).
6. [6] Kasarova, S. N., Sultanova, N. G., Ivanov, C. D., and Nikolov, I. D., “Analysis of the dispersion of optical plastic materials”, Optical Materials, 29(11): 1481-1490, (2007).
7. [7] Othayoth, A. K., Srinivas, B., Murugan, K., and Muralidharan, K., “Poly (methyl methacrylate)/ polyphosphate blends with tunable refractive indices for optical applications”, Optical Materials, 104, 109841, (2020).
8. [8] Gonzalez-Acuna, R. G., and Gutiérrez-Vega, J. C., “Analytic design of a spherochromatic singlet”, JOSA A, 37(1): 149-153, (2020).

9. [9] Bagwell, J., Hebert, C., and Carlie, N., “An achromat singlet”, In Components and Packaging for Laser Systems VI, 11261: 150-157, (2020).
10. [10] Stephens, R. E., “Reduction of sphero-chromatic aberration in catadioptric systems”, JOSA, 38(8): 733-735, (1948).
11. [11] Smith, W. J. Modern optical engineering: the design of optical systems. McGraw-Hill Education, (2008).
12. [12] Berner, A., and Gross, H., “New surface contributions for higher order color aberrations and chromatic variations of Seidel aberrations”, In International Optical Design Conference, Washington, Proc., 1207807, (2021).
13. [13] Wei, X., Han, J., and Wan, X., “Aberration correction based on MTF testing for aspheric optical system”, Optik, 185: 1089-1095, (2019).
14. [14] Kingslake, R. Lens design fundamentals. Elsevier, (2012).
15. [15] Kim, M. S., Scharf, T., Muhlig, S., Fruhnert, M., Rockstuhl, C., Bitterli, R. and Herzig, H. P., “Refraction limit of miniaturized optical systems: a ball-lens example”, Optics express, 24(7): 6996-7005, (2016).
16. [16] Meena, A. K., Arad, O., and Zitrin, A., “An efficient method for simulating light curves of cosmological microlensing and caustic crossing events”, Monthly Notices of the Royal Astronomical Society, 514(2): 2545-2560, (2022).
17. [17] Kharitonov, S. I., Khonina, S. N., Volotovskiy, S. G., and Kazanskiy, N. L., “Caustics of the vortex beams generated by vortex lenses and vortex axicons” , JOSA A, 37(3): 476-482, (2020).
18. [18] Hadi, S. M., Abdella, M. M., and Mahdi, M. S. “A Monochromatic Optical Analytical Study of a Stepped Refractive Index Shell Spherical Polymeric Lens”, NeuroQuantology, 20(5): 251-259, (2022).
19. [19] Castro-Ramos, J., Chavez-Garcia, M. T., Vazquez-Montiel, S., and Cordero-Davila, A., “Thick lenses free from spherical aberration designed by using exact ray tracing”, In Current Developments in Lens Design and Optical Engineering VI , 5874: 270-280, (2005).
20. [20] Dereniak, E. L., and Dereniak, T. D., “Geometrical and trigonometric optics”, Geometrical and Trigonometric Optics, (2008).
21. [21] Fuchs, B., Lafond, O., Rondineau, S., and Himdi, M., “Design and characterization of half Maxwell fish-eye lens antennas in millimeter waves”, IEEE transactions on microwave theory and techniques, 54(6): 2292-2300, (2006).
22. [22] Zhao, C. H., “Analytic solution for an Eaton lens for rotating 90”, Current Optics and Photonics, 4(4): 326-329, (2020).
23. [23] Ullah, H., Zia, O., Kim, J. H., Han, K., and Lee, J. W., “Automatic 360 mono-stereo panorama generation using a cost-effective multi-camera system”, Sensors, 20(11): 3097, (2020).
24. [24] Ji, Z., Liu, Y., Zhao, C., Wang, Z. L., and Mai, W., “Perovskite Wide‐Angle Field‐Of‐View Camera”, Advanced Materials, 34(41): 2206957, (2022).
25. [25] Dragone, C., “Unique reflector arrangement with very wide field of view for multibeam antennas”, Electronics Letters, 19(25): 1061-1062, (1983).