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摘要:
当前市面上的视觉训练产品大多采用电子屏幕显示远近大小交替变化的物体，通过观看屏幕刺激睫状肌，进行视功能训练，但该方法存在蓝光辐射，对人眼构成潜在危害。针对此问题，设计了一种基于Varifocal变焦结构的视光学系统，该系统通过控制两组垂直于光轴镜片的横向移动实现光焦度连续变倍，模拟物体远近的变化，刺激睫状肌调节训练。本文首先推导可变焦距透镜的面型限制，加入可变焦距球面效应方程优化Alvarez透镜基础面型，并采用Zemax软件进行设计。所设计的透镜面型由三阶XY多项式自由曲面表征，其中两组透镜最大相对垂轴偏移量为5.6 mm，实现屈光度在+4D—−8D的连续变倍。设计结果表明，全视场调制传递函数在奈奎斯特频率30 lp/mm处均大于0.3，均方根（RMS）半径值接近于艾里斑半径值，畸变均小于2%，该光学系统成像质量较好。
Abstract:Most of the current visual training products available on the market use electronic screens to display objects of varying dimensions and distances, thereby stimulating the ciliary muscle through looking at the screen for visual function training. However, this method involves blue light radiation, which poses a potential hazard to the human eye. To address this issue, a visual optical system based on a Varifocal zoom structure has been designed. The system achieves continuous magnification of optical power by manipulating the lateral movement of two sets of lenses perpendicular to the optical axis. This simulates changes in object distance and stimulating ciliary muscle regulation training. This paper first derives the surface shape limits of variable focal length lenses, incorporates the variable focal length spherical effect equation to optimize the basic surface shape of Alvarez lenses, and uses Zemax software for design. The designed lens surface is characterized by a third-order XY polynomial free-form surface, with a maximum relative vertical axis offset of 5.6 mm between the two groups of lenses, achieving continuous magnification of refractive power between +4D and −8D. The design results indicate that the full-field modulation transfer function exceeds 0.3 at a Nyquist frequency of 30lp/mm, with root mean square (RMS) radius values approaching the Airy spot radius value and distortion below 2%. The imaging quality of this optical system is satisfactory.
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Key words:
- progressive multifocal /
- optical power /
- Varifocal /
- Alvarez lens /
- free-form surface
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图 2 Alvarez透镜变焦原理 （a）平行玻璃板 （b）凸透镜 （c）凹透镜
Figure 2. Alvarez lens zoom principle (a) parallel glass plate (b) convex lens (c) concave lens
表 1 连续变焦光学系统参数指标
Table 1. Parameters and indicators of continuous zoom optical system
Parameter Value Wavelength/nm 486-656 Full field of view /(°) 15° Entrance pupil diameter/mm 4 Focal power variation/D +4D—−8D Distortion/% <2% MTF 30line pairs >0.3 
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表 2 连续变焦光学系统基本参数
Table 2. Basic parameters of continuous zoom optical system
Type A Radius Thickness Material Standrad - 无限 3 APL5014CL XY polynomial − 0.0006 −3.940E-09 1 XY polynomial − 0.0006 −3.940E-09 3 APL5014CL Standrad - 无限 12 Standrad
（角膜）- 6.896 0.6 Nd:1.377
Vd:55Standrad
(液状体）- 3.365 3 Nd:1.335
Vd:55Standrad（stop）
（瞳孔）- 10.100 0 Standrad
（晶状体）- 10.485 4 Nd:1.405
Vd:55Even Aspheric
（玻璃体）- −5.673 17.25 Nd:1.335
Vd:55Standrad
（视网膜）−12.5 0
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表 3 XY多项式自由曲面系数
Table 3. polynomial free-form surface coefficients
Coefficient Value X3 2.11×10−4 XY2 6.31×10−4 X2 2.01×10−5 Y2 1.38×10−6 X 3.48×10−5
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表 4 系统公差设置
Table 4. System tolerance settings
Type Operator Item Target Index tolerances TIND Index 0.0005 TABB Abbe 0.3 Surface tolerances TIRR Irregularity 0.5 TFRN Radius/fringe 3 TTHI Thickness/mm 0.002 TSDX(Y) Decenter/mm 0.02 TSTX(Y) Tilt/° 0.0167 Element tolerances TEDX(Y) Decenter/mm 0.015 TETX(Y) Tilt/° 0.0167
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