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大视场光学系统的渐晕会影响像面照度均匀性,轴外视场的像面照度遵循余弦四次方的规律进行衰减[10-11],视场角越大,像面照度越低,导致像面照度不均匀。
图1所示为一个同心反射式手机镜头全视场的能量分布图,由于轴外视场实际入瞳孔径为轴上视场垂轴方向的入瞳孔径在轴外视场垂轴方向上的投影,呈视场角余弦乘积的关系,因此大量轴外光线被阻拦,使轴上到达像面的光束宽度大于轴外视场,产生渐晕现象,导致整个像面照度分布不均匀[12-13],影响光学系统的成像性能。
在同心透镜的两片透镜之间注入某种胶合剂,其折射率低于两边透镜的折射率,并在中心透镜处设置挡板避免杂散光。如图2所示,轴上视场的上边缘光线1由第一片透镜入射至胶层时,即从光密介质入射到光疏介质,如果入射角I满足临界条件,将发生全内反射[14],光线全部返回,无法到达像面,下边缘光线2也是如此。同理,对于轴外视场也存在这种情况,这样,所有入射角大于临界角的光线都会被遮拦,相当于在两片透镜之间形成了一个“虚拟”的孔径光阑对光束进行控制,称之为 “虚拟光阑”。
如图3所示,视场角为
$ \theta $ 的平行光束,入射光束宽度为D,同心透镜内的k个表面同心,任何角度入射的主光线都可以看作光轴,则上下边缘光线1、2关于光轴对称。在△
$ O{A_1}{B_1} $ 中:$$ \sin {i_1} = \frac{{{A_1}{B_1}}}{{{R_1}}} $$ (1) 在点
$ {A_1} $ 处,根据折射定律有:$$ \sin i_1' = \frac{{{n_1}{A_1}{B_1}}}{{{n_2}{R_1}}} $$ (2) 在△
$ O{A_1}{A_2} $ 中,根据正弦定理有:$$ \sin {i_2} = \frac{{{n_1}{A_1}{B_1}}}{{{n_2}{R_2}}} $$ (3) 以此类推:
$$ \sin {i_k} = \frac{{{n_1}{A_1}{B_1}}}{{{n_k}{R_2}}} $$ (4) 当光束的边缘光线1在第k个面处达到临界角的条件时将发生全反射,根据全反射临界角公式有:
$$ \sin {i_k} = \frac{{{n_{TIR}}}}{{{n_k}}} $$ (5) 可得:
$$ {A_1}{B_1} = \frac{{{n_{TIR}}{R_k}}}{{{n_1}}} $$ (6) 同理:
$$ {B_1}{C_1} = \frac{{{n_{TIR}}{R_k}}}{{{n_1}}} $$ (7) 若透镜在空气中,可得到光束宽度:
$$ D = 2{n_{TIR}}{R_k} $$ (8) 可知,使用虚拟光阑的同心透镜,入射光束宽度D只与内球的半径和胶层折射率有关,而与视场角无关,可以消除系统渐晕。
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根据市场上手机镜头总长和工作距的要求[15],参考笔者课题组设计的反射式同心透镜与虚拟光阑的建立条件,确定手机镜头的参数如表1所示。
表 1 光学设计参数
Table 1. Optical design parameters
Parameter Value Waveband/nm 486-656 (F, d, C) Relative aperture 1/1.8 Full field of view/(°) 100 Focal length/mm 2.7 Total length/mm $ \leqslant $2.7 Back focal length/mm $ \geqslant $0.5 如图4所示,两片透镜中间设置了低折射率胶层,过同心透镜中心点
$ O $ 且垂直于反射面的直线作为光轴,引出一条投射高度为$ {h_1} $ 的平行于光轴的光线,经过四次折射和一次反射,交于光轴上的点为焦点$ {F'} $ ,光学系统焦距为$ {f'} $ ,角度、半径和折射率的定义如图4所示。表面Ⅰ与光轴交点为
$ {H_1} $ ,高度为$ {h_1} $ 的光线与表面Ⅰ的交点为$ {Q_1} $ ,入射角为$ {\;\beta _1} $ ,出射角为$ \;\beta _1' $ ,入射光孔径角为$ {u_1} $ ,过点$ {Q_1} $ 做光轴的垂线交光轴于$ {P_1} $ 点,出射光的延长线与光轴交于点$ Q_1' $ 。入射光经过表面Ⅰ折射后交表面Ⅱ于点$ {Q_2} $ ,入射角为$ {\;\beta _2} $ 。经反射面Ⅲ反射,再经两次折射与光轴交于点$ {F'} $ ,即像方焦点。在$ \Delta O{P_1}{Q_1} $ 中:$$ \sin {\;\beta _1} = \angle {Q_1}O{P_1} = \frac{{{Q_1}{P_1}}}{{O{Q_1}}} $$ (9) 在
$ {P_1} $ 处,根据折射定律有:$$ \sin \;\beta _1' = \frac{{{h_1}}}{{{n_1}{R_1}}} $$ (10) 表面Ⅰ的像方孔径角
$ u_1' $ 与$ {\;\beta _1} $ 、$ \;\beta _1' $ 的关系为:$$ u_1' = {\;\beta _1} - \;\beta _1' $$ (11) 设
$ {H_1}Q_1' = L_1' $ ,即光线经表面Ⅰ折射后的像距:$$ L_1' = {R_1}\left( {1 + \frac{{\sin \;\beta _1'}}{{\sin u_1'}}} \right) $$ (12) 根据过渡公式,在实际光路计算中有:
$$ \sin {\;\beta _1} = \frac{{\left( {{L_1} - {R_1}} \right)\sin {u_1}}}{{{R_1}}} $$ (13) 中间胶层选用美国Norland生产的胶合剂NOA1315,设其折射率为
$ {n_{TIR}} $ ,当光线在胶合层发生全反射时,根据全反射条件有:$$ \sin {\;\beta _2} = \frac{{{n_{TIR}}}}{{{n_1}}} $$ (14) 联立公式(10)~公式(14),可以得到:
$$ {R_2} = \frac{{{n_1}\left( {L_1' - {R_1}} \right)\sin u_1'}}{{{n_{TIR}}}} $$ (15) 同心透镜像面也与各表面同心,所以像面半径
$ R $ 即为同心透镜焦距$ {f'} $ 。根据以上条件计算,表面Ⅰ的半径$ {R_1} $ 为1.9 mm,表面Ⅱ的半径$ {R_2} $ 为0.57 mm,初始结构经过优化后得到$ F $ 数为1.8、焦距为2.7 mm、总长为2.7 mm的同心反射式手机镜头,结果如图5(a)所示。由于同心反射式透镜的结构特点,轴上部分视场不可见,该设计的视场范围为10°~50°,系统的点列图结果如图5(b)所示,四个视场的弥散斑RMS半径最大值为0.761 μm,接近衍射极限。
Relative illuminance improvement method of monocentric reflective mobile phone lens
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摘要: 为了提高同心透镜的轴外视场照度,通过在同心透镜内部设置一个基于全内反射的虚拟光阑,可使系统的能量分布更加均匀,进而改善同心透镜的成像性能。结合虚拟光阑的建立条件以及手机镜头要求,计算了一个基于反射式同心透镜手机镜头的初始结构,优化后的系统焦距2.7 mm,最大视场角±50°,系统F数1.8,总长2.7 mm。照度分析结果表明,利用传统孔径光阑的手机镜头相对照度随视场增大逐渐下降,最大视场仅为0.64;采用虚拟光阑的手机镜头在0°~28°视场的相对照度保持不变,全视场的相对照度在0.85以上。可见,采用虚拟光阑的手机镜头全视场照度的均匀性得到了明显改善,可有效提高系统的成像性能。Abstract:
Objective Enlarging the field of view of an optical system while maintaining good imaging quality is a difficult problem in modern optical design. The large field of view and high resolution of optical lenses are mutually restricted, and it is generally difficult to realize them at the same time. It requires complex structure design, expensive manufacturing, and large volume. Each surface of the monocentric lens is monocentric, and the curved imaging plane is also monocentric with each surface. The special structure enables it to achieve a large field of view and high resolution. It also has the advantages of simple structure, small size, and light weight. It is widely used in aerial remote sensing, security monitoring, photography, videography and so on, and may be first applied in miniaturized mobile phone lenses in the future. However, because the monocentric lens sets a conventional stop in the center to block the light beam of the off-axis field of view, when the field of view is larger, more light will be blocked, which causes greater vignetting, reduces the uniformity of illumination of the imaging plane, and affects the imaging quality. In order to improve the relative illuminance of the monocentric lens, a monocentric reflective mobile phone lens that uses a total reflection surface to control the light beam is designed. Methods A monocentric reflective mobile phone lens structure is designed in this paper. The initial structure is obtained by calculating the optical path of two reflective monocentric lenses (Fig.4). The optimized structure consists of a meniscus lens and a hemispherical lens, which are glued together using a low-refractive-index cement (Fig.5(a)). The spot for different fields of view of monocentric reflective lenses using conventional stop and virtual stop are simulated (Fig.6, Fig.8). Under different stop conditions, the relative illuminance curves of monocentric reflective lens are drawn (Fig.9). Results and Discussions The designed monocentric reflective mobile phone lens has a focal length of 2.7 mm, a maximum field of view of ±50°, a system F number of 1.8, a total length of 2.7 mm, and a maximum RMS radius of no more than 0.8 μm (Fig.5(b)). Under the conditions of conventional stop and virtual stop, the spot illuminance simulation of monocentric reflective lens is carried out. From the illumination diagrams of different fields of view, it can be seen that under the condition of conventional stop, the shape of the spot becomes ellipse when the field of view is 30°, and the minor axis of the ellipse is smaller when the field of view is 50° (Fig.6). Under the condition of virtual stop, the spot is circular in the 30° field of view, and the spot in the 50° field of view is rounder than the spot with the conventional stop. The relative illuminance curves of the mobile phone lens under the two kinds of stops are drawn, and the results show that the relative illuminance of the monocentric lens using the virtual stop is above 0.85, and the relative illuminance of the monocentric lens using the conventional stop is above 0.64 (Fig.9). Conclusions A monocentric reflective mobile phone lens is designed with a total reflection surface to restrict the light. Based on the establishment conditions of the virtual stop and the requirements of the mobile phone lens, an initial structure of the mobile phone lens based on the monocentric reflective lens is calculated. The focal length of the optimized system is 2.7 mm, the maximum field of view is ±50°, the system F# is 1.8, and the total length is 2.7 mm. The illuminance analysis results show that the relative illuminance of the mobile phone lens using the conventional stop gradually decreases with the increase of the field of view, and it is only 0.64 in the 50° field of view. However, the relative illuminance of a mobile phone lens with a virtual stop remains constant at 0° to 28° and is above 0.85 in the 50° field of view. The illuminance uniformity of the full field of view of the monocentric reflective lens using the virtual stop has been significantly improved, which can effectively improve the imaging performance of the system. -
Key words:
- optical design /
- virtual stop /
- relative illuminance /
- monocentric lens /
- reflective type /
- vignetting
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表 1 光学设计参数
Table 1. Optical design parameters
Parameter Value Waveband/nm 486-656 (F, d, C) Relative aperture 1/1.8 Full field of view/(°) 100 Focal length/mm 2.7 Total length/mm $ \leqslant $ 2.7Back focal length/mm $ \geqslant $ 0.5 -
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