CN114488519A - Diffraction optical lens with continuously adjustable large-angle incident focal length and design method thereof - Google Patents
Diffraction optical lens with continuously adjustable large-angle incident focal length and design method thereof Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及衍射透镜的技术领域。The present invention relates to the technical field of diffractive lenses.
背景技术Background technique
目前广泛使用的变焦技术有光学变焦和数码变焦。光学变焦的实现途径是在光学系统中加入可机械移动的透镜组。因此,要使系统有很好的变焦能力,就必须有足够大的移动空间,这也使得传统的光学变焦系统存在体积大、结构复杂、制造成本高昂等缺点,很难适应目前光学系统小型化,集成化的需求;数码变焦则是使用影响处理器或者图像处理软件将感光元件中某一区域所获得的图像进行单独的放大,从而给人以变焦的感觉,这种单纯的局部放大没有真正意义上的聚焦变化,而且由于使用的感光元件的区域变小,所以图像质量要比正常情况下差。Currently, the widely used zoom technologies include optical zoom and digital zoom. The way to realize optical zoom is to add a mechanically movable lens group to the optical system. Therefore, in order to make the system have good zooming ability, it must have a large enough moving space, which also makes the traditional optical zoom system have disadvantages such as large volume, complex structure, high manufacturing cost, etc., and it is difficult to adapt to the miniaturization of the current optical system. , the need for integration; digital zoom is to use the influence processor or image processing software to separately enlarge the image obtained by a certain area in the photosensitive element, so as to give people the feeling of zoom, this simple partial enlargement does not really The focus changes in the sense, and because the area of the photosensitive element used becomes smaller, the image quality is worse than normal.
近些年来,随着衍射光学器件的发展,带来了光学系统设计的新思路。衍射光学结构是一种以亚波长特征尺寸的介质材料天线为光波前调制器的超薄结构。经过近年来的深入研究,衍射光学结构已经被用来解决很多的传统光学器件中的问题,如色差、单色像差和焦距可调节等。但是这些结构和设计都有结构复杂、设计加工难度高等缺点,并且功能较为单一。In recent years, with the development of diffractive optical devices, new ideas for optical system design have been brought. Diffractive optical structure is an ultra-thin structure using a dielectric material antenna with sub-wavelength characteristic size as a light wavefront modulator. After intensive research in recent years, diffractive optical structures have been used to solve many problems in traditional optical devices, such as chromatic aberration, monochromatic aberration, and adjustable focal length. However, these structures and designs have the disadvantages of complex structure, high difficulty in design and processing, and relatively single function.
如由美国罗彻斯特大学的陈飞、裘亮宇等人提出的反射镜,其采用柔性材料聚二甲基硅氧烷(polydimethylsiloxane,PDMS)作为基底,在其上通过电子束刻蚀和沉积法生长出银-二氧化硅-银的单元结构,最后再以PDMS封装,形成最终的反射镜。该反射镜可以通过拉伸PDMS基底改变单元结构所处位置,从而改变衍射光学元件的位相分布,以实现焦距的变化。但其需要三层结构,且结构十分复杂,加工难度很高,基底必须为透明柔性材料,对波长和材料要求苛刻,同时柔性材料拉伸程度十分有限,焦距变化范围十分有限;并且该反射镜的有效使用需要正入射光,无法实现大角度聚焦。For example, the mirror proposed by Chen Fei, Qiu Liangyu and others from the University of Rochester in the United States uses a flexible material polydimethylsiloxane (PDMS) as a substrate, on which electron beam etching and deposition methods are used. A unit structure of silver-silicon dioxide-silver is grown, and finally encapsulated with PDMS to form the final mirror. The mirror can change the position of the unit structure by stretching the PDMS substrate, thereby changing the phase distribution of the diffractive optical element, so as to realize the change of the focal length. However, it requires a three-layer structure, and the structure is very complex and the processing is very difficult. The substrate must be a transparent and flexible material, which requires strict wavelength and material requirements. At the same time, the stretching degree of the flexible material is very limited, and the focal length variation range is very limited; and the mirror Effective use requires normal incident light and cannot achieve large-angle focusing.
又如湖南大学的唐栋梁和重庆大学的张小虎等人提出的大视场角的消色差透镜,其通过光学设计的方法在一定角度范围内设计出对473nm、532nm、633nm三个波长(即红绿蓝)消色差透镜的位相,再在玻璃基底的两侧生长二氧化钛纳米柱,引入设计好的位相,从而实现对应波长大视场角消色差的功能。虽然该结构只有一片基底,但其两侧都需要生长单元结构,加工操作十分困难,加工完成后由于单元结构暴露在外容易使透镜受损从而影响效果;同时该透镜的焦距是固定的,必须等于光学设计的消色差透镜的焦距,无法适应需要变焦镜头的工作环境。Another example is the achromatic lens with a large field of view proposed by Tang Dongliang of Hunan University and Zhang Xiaohu of Chongqing University, etc., which is designed by the method of optical design within a certain angle range. The phase of the red, green and blue) achromatic lens, and then grow titanium dioxide nano-columns on both sides of the glass substrate, and introduce the designed phase, so as to realize the function of achromatic achromatic with a large angle of view corresponding to the wavelength. Although the structure has only one substrate, the cell structure needs to be grown on both sides of the structure, and the processing operation is very difficult. After the processing is completed, the lens is easily damaged due to the exposure of the cell structure, which affects the effect. At the same time, the focal length of the lens is fixed and must be equal to The focal length of the optically designed achromatic lens cannot adapt to the working environment that requires a zoom lens.
如上所述,尽管随着现代光学的发展,高度集成化和小型化是现代光学器件发展的一大趋势,尤其在AR、VR等医用、民用领域,轻便小巧更是对光学系统的一大要求。伴随着这一趋势,以小而薄作为突出优势的衍射光学结构就有了很广阔的用武之地。但现有技术中仍缺少结构简单、加工难度低,具有较大视场角并能连续变焦的小尺寸衍射光学结构的成像系统以及设计方法。As mentioned above, although with the development of modern optics, high integration and miniaturization are a major trend in the development of modern optical devices, especially in medical and civil fields such as AR and VR, lightness and compactness are a major requirement for optical systems. . Along with this trend, diffractive optical structures with small and thin as their outstanding advantages have a wide range of uses. However, the prior art still lacks an imaging system and a design method of a small-sized diffractive optical structure with a simple structure, low processing difficulty, a large angle of view and continuous zooming.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种能够同时实现连续焦距调节和扩大系统视场角功能的衍射光学透镜的设计方法。The purpose of the present invention is to provide a design method of a diffractive optical lens that can simultaneously realize the functions of continuous focal length adjustment and expansion of the viewing angle of the system.
本发明的目的还在于提供上述设计方法得到的一些具体衍射光学透镜。The present invention also aims to provide some specific diffractive optical lenses obtained by the above-mentioned design method.
本发明首先提供了如下的技术方案:The present invention first provides the following technical solutions:
大角度入射焦距连续可调的衍射光学透镜的设计方法,其包括:A design method of a diffractive optical lens with continuously adjustable focal length of large angle incident, comprising:
以线性偏振入射光在入射角±30°内均可通过所述衍射光学透镜聚焦至焦平面为优化目标,获得优化后的透镜参数;Taking the linearly polarized incident light to be focused to the focal plane through the diffractive optical lens within the incident angle ±30° as the optimization goal, the optimized lens parameters are obtained;
根据所述优化后的透镜参数,通过透镜设计模型获得所述衍射光学透镜,其中,所述透镜设计模型包括:According to the optimized lens parameters, the diffractive optical lens is obtained through a lens design model, wherein the lens design model includes:
目标透镜包括两个相对放置的、中心轴重合且以中心轴为轴的相互旋转角为β的、表面具有衍射光学结构的衍射光学单元,其中,0<β<2π;The target lens includes two diffractive optical units with the central axes coinciding and the mutual rotation angle β taking the central axis as the axis and having diffractive optical structures on the surface, wherein 0<β<2π;
目标透镜的整体出射相位满足:The overall exit phase of the objective lens Satisfy:
其中,λ表示入射光波长,n0表示空气折射率,H表示所述衍射光学透镜的整体厚度,n1表示所述衍射光学透镜的材料折射率,表示第一衍射光学单元的出射相位,表示第二衍射光学单元的出射相位,hl(r)表示通过下式获得的所述衍射光学透镜的的透镜曲面厚度:Among them, λ represents the wavelength of incident light, n 0 represents the refractive index of air, H represents the overall thickness of the diffractive optical lens, n 1 represents the refractive index of the material of the diffractive optical lens, represents the exit phase of the first diffractive optical unit, represents the exit phase of the second diffractive optical unit, and h l (r) represents the lens surface thickness of the diffractive optical lens obtained by the following formula:
其中,c表示所述衍射光学透镜的表面曲率半径,k和am表示所述衍射光学透镜的非球面系数,m表示所述衍射光学透镜的偶次非球面的阶数,r表示在极坐标系下、所述衍射光学透镜中任一点与z轴的距离,其中,所述极坐标系以两个衍射光学单元的中心轴为z轴,以第一衍射光学单元的圆心为原点建立;Among them, c represents the surface curvature radius of the diffractive optical lens, k and a m represent the aspheric coefficient of the diffractive optical lens, m represents the order of the even-order aspheric surface of the diffractive optical lens, and r represents the polar coordinate Under the system, the distance between any point in the diffractive optical lens and the z-axis, wherein, the polar coordinate system is established with the center axis of the two diffractive optical units as the z-axis and the center of the first diffractive optical unit as the origin;
在平行光入射后,目标透镜的所述两个衍射光学单元分别的出射相位满足:After the parallel light is incident, the respective outgoing phases of the two diffractive optical units of the target lens satisfy:
且 and
其中,α表示极坐标系下,衍射光学单元上任一点到中心的连线与极轴的夹角。Among them, α represents the angle between the line connecting any point on the diffractive optical unit to the center and the polar axis in the polar coordinate system.
以上过程中,所述优化可通过光学设计软件如Zemax Optic Studio等实现。In the above process, the optimization can be realized by optical design software such as Zemax Optic Studio.
根据本发明的一些优选实施方式,所述优化过程包括:According to some preferred embodiments of the present invention, the optimization process includes:
S1设定入射光波长及其在±30°内的多个入射角,设定所述衍射光学透镜材料及其前后表面面型;S1 sets the incident light wavelength and multiple incident angles within ±30°, and sets the diffractive optical lens material and its front and rear surface profiles;
S2设置所述衍射光学透镜的初始结构参数,包括其初始焦距、前表面的初始曲率半径、后表面的初始曲率半径、前后表面之间的初始距离、前后表面的初始非球面系数和其2阶、4阶、6阶、8阶、10阶初始参数;S2 sets the initial structural parameters of the diffractive optical lens, including its initial focal length, the initial radius of curvature of the front surface, the initial radius of curvature of the back surface, the initial distance between the front and rear surfaces, the initial aspheric coefficient of the front and rear surfaces, and its 2nd order , 4th order, 6th order, 8th order, 10th order initial parameters;
S3基于所述初始结构参数,并以其对应得到的边缘光线高度解作为后表面与像面之间的距离,根据优化函数进行优化,至满足聚焦要求后,得到优化后的透镜参数。S3 is based on the initial structural parameters, and uses the corresponding obtained edge light height solution as the distance between the back surface and the image surface, and optimizes according to the optimization function, and obtains the optimized lens parameters after the focusing requirements are met.
根据本发明的一些优选实施方式,所述2阶、4阶、6阶、8阶、10阶初始参数设置为0。According to some preferred embodiments of the present invention, the initial parameters of the 2nd order, 4th order, 6th order, 8th order and 10th order are set to 0.
根据本发明的一些优选实施方式,所述多个入射角分别设定为0°、5°、10°、15°、20°、25°、30°。According to some preferred embodiments of the present invention, the plurality of incident angles are respectively set to 0°, 5°, 10°, 15°, 20°, 25°, and 30°.
根据本发明的一些优选实施方式,所述透镜材料设定为ZnSe。According to some preferred embodiments of the present invention, the lens material is set to be ZnSe.
根据本发明的一些优选实施方式,所述透镜的前后表面面型设定为偶次非球面。According to some preferred embodiments of the present invention, the front and rear surfaces of the lens are set as even-order aspheric surfaces.
根据本发明的一些优选实施方式,所述优化函数为均方根波前差函数。According to some preferred embodiments of the present invention, the optimization function is a root mean square wavefront difference function.
根据本发明的一些优选实施方式,所述透镜设计模型还包括:所述衍射光学单元具有阶梯型衍射结构或超颖表面结构中的一种或多种。According to some preferred embodiments of the present invention, the lens design model further comprises: the diffractive optical unit has one or more of a stepped diffractive structure or a metasurface structure.
根据本发明的一些优选实施方式,所述透镜设计模型还包括:所述衍射光学单元具有柱状阵列的超颖表面结构。According to some preferred embodiments of the present invention, the lens design model further includes: the diffractive optical unit has a metasurface structure of a columnar array.
本发明进一步提供了根据上述设计方法设计得到的衍射光学透镜,其具有大角度入射焦距连续可调的特性,其焦距优选为15.2μm-9.9μm。The present invention further provides a diffractive optical lens designed according to the above-mentioned design method, which has the characteristics of continuously adjustable focal length of large-angle incident, and its focal length is preferably 15.2 μm-9.9 μm.
根据本发明的一些优选实施方式,所述衍射光学透镜包括相对平行放置的第1一.衍射光学单元和第二衍射光学单元,所述第一衍射光学单元和第二衍射光学单元均包括一个圆形平板基底和在所述基底相对侧生长的、垂直于所述基底的一系列纳米柱,所述基底的半径均为14μm、相互间的距离为100nm、厚度均为1μm,所述纳米柱的高度均为600nm,所述一系列纳米柱以所述基底的圆心为原点按极坐标周向排列、且其整体分布涵盖的极长范围为0~基底半径,极角范围为0~2π,且自所述原点向外,相邻周向的纳米柱具有不同的半径大小、间隔周向的纳米柱具有相等的半径大小。According to some preferred embodiments of the present invention, the diffractive optical lens includes a first diffractive optical unit and a second diffractive optical unit that are placed relatively in parallel, and both the first diffractive optical unit and the second diffractive optical unit include a circle A flat plate substrate and a series of nanopillars grown on opposite sides of the substrate and perpendicular to the substrate, the substrates have a radius of 14 μm, a mutual distance of 100 nm, and a thickness of 1 μm. The heights are all 600 nm, the series of nano-pillars are arranged in the circumferential direction of polar coordinates with the center of the base as the origin, and the overall distribution covers a very long range of 0 to the base radius, a polar angle range of 0 to 2π, and From the origin to the outside, the adjacent circumferential nano-columns have different radii, and the spaced circumferential nano-columns have equal radii.
根据本发明的一些优选实施方式,所述衍射光学透镜包括相对平行放置的第一衍射光学单元和第二衍射光学单元,所述第一衍射光学单元和第二衍射光学单元均为外表面为圆形平面、内表面均呈螺旋型阶梯起伏的结构,每个所述阶梯的高度分布如下:According to some preferred embodiments of the present invention, the diffractive optical lens includes a first diffractive optical unit and a second diffractive optical unit that are relatively parallel to each other, and both the first diffractive optical unit and the second diffractive optical unit have a circular outer surface The shape plane and the inner surface are all spiral staircase undulating structure, and the height distribution of each step is as follows:
其中,d表示所述阶梯的高度,表示透镜的出射相位,其中r表示该阶梯距离所述圆形平面的圆心的距离,λ表示入射光波长。where d represents the height of the ladder, represents the outgoing phase of the lens, where r represents the distance of the step from the center of the circular plane, and λ represents the wavelength of the incident light.
本发明具备以下有益效果:The present invention has the following beneficial effects:
根据本发明的设计方法可得到在大角度范围内实现连续焦距变化的光学衍射透镜,在具体应用中,将所得透镜的衍射光学单元以其中心轴为轴进行相对旋转,如沿着中心轴,一个衍射光学单元保持不变,另一个衍射光学单元沿逆时针或者顺时针方向旋转,即可使大角度入射的入射光出射后聚焦在不同的焦平面上。According to the design method of the present invention, an optical diffractive lens that realizes continuous focal length change in a large angle range can be obtained. In a specific application, the diffractive optical unit of the obtained lens is relatively rotated with its central axis as the axis, such as One diffractive optical unit remains unchanged, and the other diffractive optical unit rotates in the counterclockwise or clockwise direction, so that the incident light incident at a large angle can be focused on different focal planes after exiting.
根据本发明的设计方法得到的衍射光学透镜可极大地消除单色像差,同时当入射光的入射角最大达到±30°时,所有的入射光都能很好的聚焦在对应的焦平面上。The diffractive optical lens obtained by the design method of the present invention can greatly eliminate the monochromatic aberration, and at the same time, when the incident angle of the incident light reaches ±30° at the maximum, all the incident light can be well focused on the corresponding focal plane .
根据本发明的设计方法实际得到的衍射光学透镜应用高效快捷,结构简单、加工难度低。The diffractive optical lens actually obtained according to the design method of the present invention is efficient and fast in application, simple in structure and low in processing difficulty.
附图说明Description of drawings
图1为本发明实施例1的衍射光学透镜整体结构示意图。FIG. 1 is a schematic diagram of the overall structure of the diffractive optical lens according to
图2为本发明实施例1的衍射光学单元的表面结构示意图。FIG. 2 is a schematic diagram of the surface structure of the diffractive optical unit according to
图3为本发明实施例1中不同入射角下的相位分布效果图。FIG. 3 is an effect diagram of phase distribution under different incident angles in
图4为本发明实施例1中β=1rad时两个衍射光学单元的出射相位及加和相位分布示意图。FIG. 4 is a schematic diagram of the outgoing phase and the summed phase distribution of the two diffractive optical units when β=1rad in
图5为本发明实施例1中透镜在β=1rad时的透射远场的电场分布情况。FIG. 5 is the electric field distribution of the transmitted far field of the lens in
图6为本发明实施例1中透镜在β=1.2rad时的透射远场的电场分布情况。FIG. 6 is the electric field distribution of the transmitted far field of the lens in
图7为本发明实施例1中透镜在β=1.4rad时的透射远场的电场分布情况。FIG. 7 is the electric field distribution of the transmitted far field of the lens in
图8为本发明实施例2的衍射光学透镜整体结构示意图。FIG. 8 is a schematic diagram of the overall structure of the diffractive optical lens according to
图9为本发明实施例2中透镜在β=1rad时的透射远场的电场分布情况。FIG. 9 is the electric field distribution of the transmitted far field of the lens in
图10为本发明实施例2中透镜在β=1.2rad时的透射远场的电场分布情况。FIG. 10 is the electric field distribution of the transmitted far field of the lens in
图11为本发明实施例2中透镜在β=1.4rad时的透射远场的电场分布情况。FIG. 11 is the electric field distribution of the transmitted far field of the lens in Example 2 of the present invention when β=1.4rad.
具体实施方式Detailed ways
以下结合实施例和附图对本发明进行详细描述,但需要理解的是,所述实施例和附图仅用于对本发明进行示例性的描述,而并不能对本发明的保护范围构成任何限制。所有包含在本发明的发明宗旨范围内的合理的变换和组合均落入本发明的保护范围。The present invention will be described in detail below with reference to the embodiments and drawings, but it should be understood that the embodiments and drawings are only used to describe the present invention by way of example, but do not limit the protection scope of the present invention. All reasonable transformations and combinations included within the scope of the inventive concept of the present invention fall into the protection scope of the present invention.
实施例1Example 1
根据本发明的技术方案,通过以下过程获得一种具体的衍射光学透镜结构:According to the technical solution of the present invention, a specific diffractive optical lens structure is obtained through the following process:
通过光学设计软件Zemax Optic Studio进行透镜的优化设计以获得其具体的相位,优化过程包括:The optical design software Zemax Optic Studio is used to optimize the design of the lens to obtain its specific phase. The optimization process includes:
S1入射光波长设为810nm,入射角分别为0°、5°、10°、15°、20°、25°、30°,透镜材料选择ZnSe(对波长高透),透镜前后表面的面型均采用偶次非球面,距离前表面15μm处设置一个直径10μm的孔径光阑;The wavelength of the S1 incident light is set to 810nm, the incident angles are 0°, 5°, 10°, 15°, 20°, 25°, and 30°, respectively. All adopt even-order aspheric surfaces, and an aperture diaphragm with a diameter of 10 μm is set at a distance of 15 μm from the front surface;
S2设置初始参数如下,前表面的曲率半径50μm,后表面的曲率半径-50μm,前后表面中间的距离(即透镜厚度H)为10μm,后表面到像面之间的距离(即实际焦距f)为15μm,前后表面的非球面系数和2阶、4阶、6阶、8阶、10阶参数均设为0;S2 sets the initial parameters as follows: the radius of curvature of the front surface is 50μm, the radius of curvature of the rear surface is -50μm, the distance between the front and rear surfaces (ie the lens thickness H) is 10μm, and the distance between the rear surface and the image surface (ie the actual focal length f) is 15μm, and the aspheric coefficients and the 2nd, 4th, 6th, 8th, and 10th order parameters of the front and rear surfaces are set to 0;
S3设置变量的求解条件如下,后表面到像面之间距离设为边缘光线高度解,前后表面的曲率半径、前后表面间距、非球面系数和4阶、6阶、8阶、10阶参数均设为变量;The solution conditions for the variables set by S3 are as follows. The distance between the rear surface and the image surface is set as the edge ray height solution. The curvature radius of the front and rear surfaces, the distance between the front and rear surfaces, the aspheric coefficient, and the 4th, 6th, 8th, and 10th order parameters are all set to variable;
S4设置优化函数如下,默认评价函数采用均方根波前3环6臂,球差、彗差、像散均设为0,有效焦距设为15μm;S4 sets the optimization function as follows. The default evaluation function adopts the RMS wavefront with 3 rings and 6 arms. The spherical aberration, coma and astigmatism are all set to 0, and the effective focal length is set to 15μm;
S5点击“工具”-“优化”对上述设为变量的参数进行优化,打开“散点图”观察像面的聚焦情况,反复优化使得散点尽可能小,得到最终优化结果。S5 Click "Tools" - "Optimize" to optimize the parameters set as variables above, open "Scatter Graph" to observe the focusing of the image surface, and repeat the optimization to make the scatter points as small as possible to obtain the final optimization result.
所得优化后的参数包括:优化后的焦距为15.21μm,第一个面的曲率半径c=1/0.042063(mm-1),非球面参数k=-1.046556,非球面系数a2=-9694.283695,非球面系数a3=-1.883979×108,非球面系数a4=6.180475×1011,非球面系数a5=-2.282475×1013;第二个面:曲率半径c=-1/0.05356(mm-1),非球面参数k=-3.90567,非球面系数a2=-9480.947625,非球面系数a3=-1.883979×107,非球面系数a4=-8.44613×1010,非球面系数a5=-9.964269×1014;透镜厚度H=9.7μm。The obtained optimized parameters include: the optimized focal length is 15.21 μm, the curvature radius of the first surface c=1/0.042063 (mm -1 ), the aspherical surface parameter k=-1.046556, the aspherical surface coefficient a2=-9694.283695, the non-spherical surface Spherical coefficient a3=-1.883979×10 8 , aspheric coefficient a4=6.180475×10 11 , aspheric coefficient a5=-2.282475×10 13 ; the second surface: curvature radius c=-1/0.05356(mm -1 ), Aspheric parameter k=-3.90567, aspheric coefficient a2=-9480.947625, aspheric coefficient a3=-1.883979×10 7 , aspheric coefficient a4=-8.44613×10 10 , aspheric coefficient a5=-9.964269×10 14 ; lens Thickness H=9.7 μm.
在上述优化参数下,获得其对应的出射相位及透镜曲面厚度hl(r),代入设计模型,具体得到的一种由具有超颖表面结构的光学单元组成的衍射光学透镜,如附图1所示,该衍射光学透镜包括均由一个圆形平板基底和在基底一侧生长的垂直于基底的一系列纳米柱组成的第一衍射光学单元1和第二衍射光学单元2,且第一衍射光学单元1和第二衍射光学单元2的两片基底平行放置,纳米柱在两片基底相对面之间,第一衍射光学单元1和第二衍射光学单元2的半径r均为14μm,相互间的距离d=100nm,其基底厚度均为1μm,纳米柱高度均为600nm,纳米柱分布如附图2所示,其以基底中心为原点按极坐标周向排列、且整体分布涵盖的极长范围为0~基底半径,极角范围为0~2π,纳米柱的位相范围覆盖0~2π。Under the above optimized parameters, the corresponding outgoing phase is obtained And the lens surface thickness h l (r), substitute into the design model, a kind of diffractive optical lens that is made up of the optical unit with the metasurface structure specifically obtained, as shown in accompanying drawing 1, this diffractive optical lens includes all by a circle The first diffractive
在全矢量仿真软件FDTD(Lumerical Solution)里对上述衍射光学透镜进行仿真测试,其中,两片衍射光学单元的基底选用SiO2(Glass)-Palik作为材料,半径设置为14μm,厚度设置为1μm,两片衍射光学单元上的纳米柱选用a-Si作为材料,半径根据光学设计得到的位相以及通过扫描得到的柱子半径与引入位相对应关系插值得到,纳米柱高度均为600nm、分布如附图2所示,设置FDTD仿真区,选择纳米柱所在范围设置mesh,精度为40nm,入射光设置为波长810nm的不同入射角θ的线偏振光,并在整个结构后100nm处设置一面监视器,选择入射光为波长810nm的线偏振光,两层衍射光学单元以自身纵向中心轴线为旋转轴进行旋转角为β的旋转,可得到如附图3所示的不同入射角θ下的该透镜出射相位分布效果图,及如附图4所示的不同旋转角β下出射相位分布效果图,进一步的,通过基尔霍夫衍射积分公式获得在不同入射角及旋转角情况下的在x-z平面和x-y平面上的远场电场分布情况,如附图5-7所示,其旋转角依次为β=1rad、β=1.2rad和β=1.4rad。The above-mentioned diffractive optical lens was simulated and tested in the full vector simulation software FDTD (Lumerical Solution). The substrates of the two diffractive optical units were made of SiO 2 (Glass)-Palik, the radius was set to 14 μm, and the thickness was set to 1 μm. The nano-pillars on the two diffractive optical units use a-Si as the material. The radius is obtained by interpolation according to the phase obtained by optical design and the corresponding relationship between the column radius and the introduction position obtained by scanning. The height of the nano-pillars is 600nm, and the distribution is as shown in Figure 2. As shown, set the FDTD simulation area, select the range where the nano-columns are located, set the mesh, the precision is 40nm, the incident light is set to linearly polarized light with different incident angles θ with a wavelength of 810nm, and a monitor is set at 100nm behind the entire structure, and the incident light is set to 100nm. The light is linearly polarized light with a wavelength of 810 nm, and the two-layer diffractive optical unit takes its own longitudinal central axis as the rotation axis to rotate at a rotation angle of β, and the lens output phase distribution under different incident angles θ as shown in Figure 3 can be obtained. The effect diagram, and the effect diagram of the outgoing phase distribution under different rotation angles β as shown in accompanying drawing 4, further, obtained by the Kirchhoff diffraction integral formula The distribution of the far-field electric field on the xz plane and the xy plane under different incident angles and rotation angles, as shown in Figure 5-7, the rotation angles are β=1rad, β=1.2rad and β=1.4 rad.
上述结果显示,在入射角θ分别为0°、10°、20°和30°时,入射光都能在距离出射面15.21μm的焦平面处很好的聚焦。The above results show that when the incident angle θ is 0°, 10°, 20° and 30°, the incident light can be well focused at the focal plane 15.21 μm away from the exit surface.
当旋转角β为0°时,整个透镜的出射相位为此时没有聚焦效果,当其中一个衍射光学单元,如第二衍射光学单元2具有一定旋转角时,即β>0时,此时有聚焦效果,当β的值不同时,焦距不同,说明其可实现连续焦距调节效果。When the rotation angle β is 0°, the exit phase of the entire lens is At this time, there is no focusing effect. When one of the diffractive optical units, such as the second diffractive
随着β的值从1rad变化到1.2rad,进而变化到1.4rad,透镜系统的焦距分别为15.21μm、11.55μm和9.896μm,呈逐渐变小的趋势,证明该透镜的焦距连续变化的特性。与此同时,从仿真结果中也可看出当β值固定,而入射角θ在±30°的范围内变化时,焦平面上没有出现单色像差,仍能很好地聚焦,证明该透镜在焦距连续变化的同时,能很好的对单色像差进行校正。As the value of β changes from 1rad to 1.2rad, and then to 1.4rad, the focal lengths of the lens system are 15.21 μm, 11.55 μm and 9.896 μm, respectively, showing a decreasing trend, which proves the continuous change of the focal length of the lens. At the same time, it can be seen from the simulation results that when the β value is fixed and the incident angle θ varies within the range of ±30°, there is no monochromatic aberration on the focal plane, and the focus is still very good, which proves that the The lens can correct the monochromatic aberration very well while the focal length changes continuously.
实施例2Example 2
通过与实施例1相同的方式获得优化后的透镜参数,并调整初始参数为前表面的曲率半径为5mm,后表面的曲率半径为-5mm,前后表面中间的距离(即透镜厚度H)为1mm,后表面到像面之间的距离(即实际焦距f)为15mm,其余参数不变,优化函数与之对应,改变有效焦距为15mm,得到优化后的参数为:曲率半径c=1/44.514(mm-1),非球面参数k=2.688699,非球面系数a2=-8.526631×10-5,非球面系数a3=6.33103×10-4,非球面系数a4=-2.332903×10-5,非球面系数a5=--2.038745×10-4;第二个面:曲率半径c=-1/50.12889(mm-1),非球面参数k=-61.490765,非球面系数a2=-8.942814×10-4,非球面系数a3=6.875003×10-4,非球面系数a4=-1.76955×10-6,非球面系数a5=--1.135695×10-4;透镜厚度H=14.48465mm。The optimized lens parameters are obtained in the same way as in Example 1, and the initial parameters are adjusted as the radius of curvature of the front surface is 5mm, the radius of curvature of the rear surface is -5mm, and the distance between the front and rear surfaces (ie the lens thickness H) is 1mm , the distance between the rear surface and the image surface (that is, the actual focal length f) is 15mm, and the other parameters remain unchanged. The optimization function corresponds to it, changing the effective focal length to 15mm, and the optimized parameters are: curvature radius c=1/44.514 (mm-1), aspherical parameter k=2.688699, aspherical coefficient a2=-8.526631× 10-5 , aspherical coefficient a3=6.33103× 10-4 , aspherical coefficient a4=-2.332903× 10-5 , aspherical The coefficient a5=--2.038745×10 -4 ; the second surface: the radius of curvature c=-1/50.12889(mm -1 ), the aspheric surface parameter k=-61.490765, the aspheric surface coefficient a2=-8.942814×10 -4 , Aspheric coefficient a3=6.875003×10 -4 , aspheric coefficient a4=-1.76955×10 -6 , aspheric coefficient a5=--1.135695×10 -4 ; lens thickness H=14.48465mm.
根据以上参数,本实施例具体得到的一种由具有阶梯型衍射结构的光学单元组成的衍射光学透镜,如附图8所示,该衍射光学透镜包括外表面均为圆形平面、内表面均呈螺旋型阶梯起伏的、相对放置的第一衍射光学单元1和第二衍射光学单元2,每个所述阶梯的高度分布如下:According to the above parameters, a diffractive optical lens composed of optical units with a stepped diffractive structure specifically obtained in this embodiment, as shown in FIG. 8 , the diffractive optical lens includes a circular plane on the outer surface and a The first diffractive
其后通过与实施例1类似的过程对该衍射光学透镜进行仿真测试,包括先创建两个代表两层阶梯型衍射光学元件位相的矩阵,再根据位相提取公式计算出矩阵中每个位置处的数值并填入(此处可以通过变换坐标实现角度的更改),将二者叠加可以得到一个合位相(即为出射面位相),最后编写一个基于惠更斯原理的衍射算法,带入所得位相进行计算获得在不同入射角及旋转角情况下在x-z平面和x-y平面上的远场电场分布情况,如附图9-11所示,其旋转角依次为β=1rad、β=1.2rad和β=1.4rad。Afterwards, the diffractive optical lens is simulated and tested through a process similar to that of Example 1, including first creating two matrices representing the phases of the two-layer stepped diffractive optical element, and then calculating the phase at each position in the matrix according to the phase extraction formula. Value and fill in (here, the angle can be changed by transforming the coordinates), superimpose the two to get a combined phase (that is, the phase of the exit plane), and finally write a diffraction algorithm based on Huygens' principle to bring in the obtained phase Perform calculations to obtain the far-field electric field distributions on the x-z plane and x-y plane under different incident angles and rotation angles, as shown in Figure 9-11, the rotation angles are β=1rad, β=1.2rad and β =1.4rad.
结果显示,随着β的值从1rad变化到1.2rad,进而变化到1.4rad,透镜系统的焦距分别为14.15mm、10.9mm和9.2mm,也呈逐渐减小的趋势,证明阶梯型衍射光学元件同样可以实现连续可调的功能且单元尺寸的范围能从微米量级拓展到毫米量级。The results show that as the value of β changes from 1rad to 1.2rad, and then to 1.4rad, the focal lengths of the lens system are 14.15mm, 10.9mm and 9.2mm, respectively, which also show a decreasing trend, which proves that the stepped diffractive optical element Continuously tunable functions can also be achieved and the range of cell sizes can be extended from micrometers to millimeters.
以上实施例仅是本发明的优选实施方式,本发明的保护范围并不仅局限于上述实施例。凡属于本发明思路下的技术方案均属于本发明的保护范围。应该指出,对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下的改进和润饰,这些改进和润饰也应视为本发明的保护范围。The above embodiments are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All the technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, improvements and modifications without departing from the principles of the present invention should also be regarded as the protection scope of the present invention.
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