Aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces for designing astigmatic spectacle lenses with axis orientation

• Autorzy: Xiang Huazhong , Wang Peng , Zheng Zexi , Zheng Gang , Chen Jiabi , Wang Cheng , Zhang Dawei , Zhuang Songlin

Identyfikatory

DOI

10.37190/oa230304

• Języki publikacji: EN

Abstrakty

EN

In this paper, formulas for aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces with astigmatic axes are derived. Based on this, four types of curved surfaces were designed to correct astigmatism with axis, and, subsequently, the lenses were simulated, fabricated, and measured. A total of ten spectacle lenses in two groups were designed. Those in the first group used identical optical parameters. The spherical and cylindrical powers and maximum and minimum edge thicknesses of aspherical, sphero-cylindrical, and ellipsoidal surfaces were compared. The results indicated that the power of the lens constructed using the toroidal surface was more accurate than those of the other three lenses. Moreover, the minimum edge thickness of the toroidal surface was 1.2%, 4.98%, and 4.87% lower than those of the aspherical, sphero-cylindrical, and ellipsoidal surfaces, respectively. The powers and edge thicknesses of toroidal surfaces with different diopters were compared in the second group. The minimum and maximum edge thicknesses were observed to be reduced by 8.97% and 6.05%, respectively, corresponding to the conic constants obtained via ray tracing. The conclusion will be significant for clinical ophthalmology and optical design for the patients with astigmatism.

Słowa kluczowe

EN

toric; astigmatism; spherocylinder; aspheric; ellipsoidal surface

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Optica Applicata
• Rocznik: 2023
• Tom: Vol. 53, nr 3
• Strony: 377--391
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Xiang Huazhong

• School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Wang Peng

• School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Zheng Zexi

• School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Zheng Gang

• School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
• School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Chen Jiabi

• School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Wang Cheng

• School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Zhang Dawei

• School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
• Engineering Research Center of Optic Instrument and System, Shanghai Engineering University of Shanghai for Science and Technology, Shanghai 200093, China

autor

Zhuang Songlin

• School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
• Engineering Research Center of Optic Instrument and System, Shanghai Engineering University of Shanghai for Science and Technology, Shanghai 200093, China

Bibliografia

• [1] READ S.A., VINCENT S.J., COLLINS M.J., The visual and functional impacts of astigmatism and its clinical management, Ophthalmic and Physiological Optics 34(3), 2014: 267-294. https://doi.org/10.1111/opo.12128
• [2] YAMAMOTO T., HIRAOKA T., BEHEREGARAY S., OSHIKA T., Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses, Japanese Journal of Ophthalmology 58(5), 2014: 409-414. https://doi.org/10.1007/s10384-014-0337-1
• [3] READ S.A., COLLINS M.J., CARNEY L.G., A review of astigmatism and its possible genesis, Clinical and Experimental Optometry 90(1), 2007: 5-19. https://doi.org/10.1111/j.1444-0938.2007.00112.x
• [4] HASHEMI H., FOTOUHI A., YEKTA A., PAKZAD R., OSTADIMOGHADDAM H., KHABAZKHOOB M., Global and regional estimates of prevalence of refractive errors: Systematic review and meta-analysis, Journal of Current Ophthalmology 30(1), 2018: 3-22. https://doi.org/10.1016/j.joco.2017.08.009
• [5] FOZAILOFF A., TARCZY-HORNOCH K., COTTER S., WEN G., LIN J., BORCHERT M., AZEN S., VARMA R., Prevalence of astigmatism in 6- to 72-month-old African American and Hispanic children: The multiethnic pediatric eye disease study, Ophthalmology 118(2), 2011: 284-293. https://doi.org/10.1016/j.ophtha.2010.06.038
• [6] JALIE M., Modern spectacle lens design, Clinical and Experimental Optometry 103(1), 2020: 3-10. https://doi.org/10.1111/cxo.12930
• [7] BAUDE D., CHAVEL P., JOYEUX D., TABOURY J., Optical lens for correcting astigmatism, U.S. Patent, 5,016,977 (1991).
• [8] JALIE M., The Principles of Ophthalmic Lenses, 4th Ed., Association of Dispensing Opticians, London, 1984.
• [9] MURRAY A.E., A toric skew ray trace, Journal of the Optical Society of America 44(9), 1954: 672-676. https://doi.org/10.1364/JOSA.44.000672
• [10] FOWLER C.W., Assessment of toroidal surfaces by the measurement of curvature in three fixed meridians, Ophthalmic and Physiological Optics 9(1), 1989: 79-80. https://doi.org/10.1111/j.1475-1313.1989.tb00812.x
• [11] LANDGRAVE J.E.A., VILLALOBOS A., GONZÁLEZ C., Simple mathematical representation of toroidal surfaces, Proceedings of the SPIE, Vol. 6046, Fifth Symposium Optics in Industry, 2006: 604601. https://doi.org/10.1117/12.674372
• [12] XIANG H., LI N., GAO J., ZHENG G., CHEN J., WANG C., ZHUANG S., Comparison and applications of spherocylindrical, toroidal, and ellipsoidal surfaces for the correction of astigmatism in spectacle lenses, Optics Express 28(2), 2020: 1745-1757. https://doi.org/10.1364/OE.380700
• [13] REMON L., TORNEL M., FURLAN W.D., Visual acuity in simple myopic astigmatism: Influence of cylinder axis, Optometry and Vision Science 83(5), 2006: 311-315. https://doi.org/10.1097/01.opx.0000216099.29968.36
• [14] KOBASHI H., KAMIYA K., SHIMIZU K., KAWAMORITA T., UOZATO H., Effect of axis orientation on visual performance in astigmatic eyes, Journal of Cataract & Refractive Surgery 38(8), 2012: 1352-1359. https://doi.org/10.1016/j.jcrs.2012.03.032
• [15] ATCHISON D.A., MATHUR A., Visual acuity with astigmatic blur, Optometry and Vision Science 88(7), 2011: E798-E805. https://doi.org/10.1097/OPX.0b013e3182186bc4
• [16] MATHUR A., SUHEIMAT M., ATCHISON D.A., Pilot study: Effect of age on visual acuity with defocus and astigmatism, Optometry and Vision Science 92(3), 2015: 267-271. https://doi.org/10.1097/OPX.0000000000000459
• [17] MIMOUNI M., NEMET A., POKROY R., SELA T., MUNZER G., KAISERMAN I., The effect of astigmatism axis on visual acuity, European Journal of Ophthalmology 27(3), 2017: 308-311. https://doi.org/10.5301/ejo.5000890
• [18] PUJOL J., ARJONA M., ARASA J., BADIA V., Influence of amount and changes in axis of astigmatism on retinal image quality, Journal of the Optical Society of America A 15(9), 1998: 2514-2521. https://doi.org/10.1364/JOSAA.15.002514
• [19] MILLER A.D., KRIS M.J., GRIFFITHS A.C., Effect of small focal errors on vision, Optometry and Vision Science 74(7), 1997: 521-526.
• [20] MALACARA Z., MALACARA-DOBLADO D., MALACARA-HERNANDEZ D., LANDGRAVE J., Astigmatic optical surfaces, characteristics, testing, and differences between them, Optical Engineering 46(12), 2007: 123001. https://doi.org/10.1117/1.2818211