WO2022095237A1 - 波数线性色散光学系统的设计方法及成像光谱仪 - Google Patents

波数线性色散光学系统的设计方法及成像光谱仪 Download PDF

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WO2022095237A1
WO2022095237A1 PCT/CN2020/137811 CN2020137811W WO2022095237A1 WO 2022095237 A1 WO2022095237 A1 WO 2022095237A1 CN 2020137811 W CN2020137811 W CN 2020137811W WO 2022095237 A1 WO2022095237 A1 WO 2022095237A1
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prism
wavenumber
optical system
objective lens
lens
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包建
沈秋阳
陈新华
沈为民
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Suzhou University
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/12—Generating the spectrum; Monochromators
    • G01J3/14—Generating the spectrum; Monochromators using refracting elements, e.g. prisms
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/12—Generating the spectrum; Monochromators
    • G01J3/18—Generating the spectrum; Monochromators using diffraction elements, e.g. grating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/28—Investigating the spectrum
    • G01J3/2823—Imaging spectrometer
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/12—Generating the spectrum; Monochromators
    • G01J2003/1208—Prism and grating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/02—Details
    • G01J3/0297—Constructional arrangements for removing other types of optical noise or for performing calibration

Definitions

  • the invention relates to the technical field of spectrometers, in particular to a design method of a wavenumber linear dispersion optical system and an imaging spectrometer.
  • the linear distribution of the wavenumber of the spectrometer system can not only significantly reduce the interpolation error of the image and improve the image quality, but also improve the imaging speed and sensitivity of the system.
  • Traub used the prismatic structure for the first time to obtain a near-linear distribution of wavenumbers, but its linearity was not high.
  • Hu achieved a higher linear distribution of wavenumbers by separating gratings and prisms, and introduced them into the spectral domain optical coherence tomography system.
  • the first one is obtained by the combination of grating and prism, which is realized by optimizing the groove density of the grating, the angle between the grating and the prism, the apex angle of the prism, and the prism material.
  • Linear distribution of wave number however, only using the combination of grating and prism to achieve linear distribution of wave number has the disadvantage that to obtain a high linear distribution, the grating and prism must form a certain angle, which will increase the volume of the system and the difficulty of installation;
  • the second method is to achieve the linear distribution of wavenumbers by optimizing the groove density of the grating and the angle between the gratings through the combined light splitting of the double gratings.
  • the combined light splitting of the double gratings will lead to low energy utilization; It is based on the combination of prism gratings to introduce free-form surfaces to achieve a higher linear distribution of wavenumbers. However, the introduction of free-form surfaces will lead to high cost.
  • the technical problem to be solved by the present invention is that the existing optical system for realizing high wavenumber linearity has complex structure, large volume, low energy utilization rate and high cost.
  • the present invention provides a method for designing a wavenumber linear dispersion optical system, comprising the following steps:
  • the optical system includes a grating, a prism and an objective lens arranged in sequence, and the grating is attached to the prism; wherein, after the collimated light is split by the grating and the prism, light with different wave numbers is obtained, and the light with different wave numbers is Enter the objective lens from different angles and image on the image plane;
  • the linearity evaluation coefficient RMS is the root mean square error of the position interval of the equal difference wavenumber of the working band on the image plane
  • S4 and S5 designing an objective lens capable of introducing negative distortion and vertical chromatic aberration.
  • the objective lens includes a first positive lens, a first negative lens, a second positive lens and a third positive lens arranged in sequence; by increasing the incident height and incident angle of the chief ray of the off-axis field of view on the third positive lens to generate negative spherical aberration to introduce negative distortion.
  • a side of the third positive lens away from the second positive lens is further provided with a second negative lens to correct field curvature.
  • the first positive lens, the first negative lens, the second positive lens, the third positive lens and the second negative lens are made of the same material to introduce vertical-axis chromatic aberration.
  • the refractive index range of the first positive lens, the first negative lens, the second positive lens, the third positive lens and the second negative lens is 1.5-2.3.
  • the step S5 includes: optimizing the optical system by changing the curvature of the objective lens, the interval between adjacent lenses, the thickness of the lens and the material of the lens.
  • the S2 specifically includes:
  • d is the grating constant
  • ⁇ ⁇ 1 - ⁇ d
  • ⁇ 3 ⁇ - ⁇ 2 ;
  • the focal length of the objective is given by the paraxial relationship
  • Y is the length of the image plane; is the field angle of the light with wave number k n entering the objective lens; is the field angle of the light with wave number k 1 entering the objective lens;
  • the compensation amount of the distortion of the objective lens is the compensation amount of the distortion of the objective lens
  • the invention also discloses an imaging spectrometer obtained by the above-mentioned design method of the wavenumber linear dispersion optical system.
  • the design idea of the objective aberration compensation wavenumber linearity proposed by the present invention can further improve the wavenumber linearity of the spectrometer by designing the objective lens.
  • the compensation of the objective image aberration can achieve higher wavenumber linearity than when the grating and prism are separated, and at the same time reduce the volume of the light splitting structure.
  • the energy utilization rate of the optical system is high, the scope of application is wide, and the cost is low.
  • Fig. 1 is the schematic diagram of the optical path of the objective lens
  • Figure 2 is a schematic diagram of the wavenumber linear design
  • Fig. 3 is the curve of R MS value changing with ⁇ and ⁇ when the prism material is ZnS;
  • FIG. 4 is a schematic diagram of the position interval between adjacent wavenumbers before aberration compensation
  • Fig. 5 is a graph showing the variation of image height with wavenumber before aberration compensation
  • FIG. 6 is a schematic cross-sectional view of a wavenumber linear optical system
  • Figure 7 is a schematic diagram of objective lens distortion
  • Figure 8 is the vertical axis chromatic aberration curve of wavelength 750nm (left) and 950nm (right);
  • FIG. 9 is a schematic diagram of the position interval between adjacent wavenumbers after aberration compensation.
  • Figure 10 is the curve of image height changing with wavenumber after aberration compensation
  • Figure 11 is a dot plot at different wavelengths, wherein (a) is a dot plot at 750 nm, (b) is a dot plot at 840 nm, and (c) is a dot plot at 950 nm;
  • Figure 12 is a schematic diagram of the encircled energy percentage of the pixel, where (a) is the encircled energy percentage of the pixel with a wavelength of 750 nm, (b) is the encircled energy percentage of the pixel with a wavelength of 840 nm, and (c) is the pixel with a wavelength of 950 nm. Circle the energy percentage.
  • grating 11, protective glass before grating; 12, protective glass after grating; 20, prism; 30, objective lens; 31, first positive lens; 32, first negative lens; 33, second positive lens lens; 34, the third positive lens; 35, the second negative lens; 40, the image plane; 50, the collimating lens.
  • the present invention utilizes the objective image aberration to compensate the wavenumber linearity to achieve higher wavenumber linearity without separating the grating and the prism, and the basic principle is as follows: After beam splitting, light rays with different wave numbers enter the objective lens at different angles. As shown in Figure 1, it is the optical path diagram of the objective lens phase difference compensation wave number. The direction of the center wave number light is the optical axis direction. If the minimum wave number and the maximum wave number light are incident at the angles of ⁇ and - ⁇ , respectively, the Gaussian image planes are in A and B.
  • Negative distortion means that the height of the intersection of the chief ray and the Gaussian image plane is smaller than the ideal image height with the increase of the field of view.
  • Positive distortion is the height of the intersection of the chief ray and the Gaussian image plane. It is larger than the ideal image height as the field of view increases.
  • the present invention discloses a method for designing a wavenumber linear dispersion optical system, comprising the following steps:
  • Step 1 Build an optical system.
  • the optical system includes a grating 10 , a prism 20 and an objective lens 30 arranged in sequence.
  • the grating 10 is attached to the prism 20 , that is, the angle ⁇ between the grating and the prism is zero.
  • the collimated light is split by the grating 10 and the prism 20 to obtain light with different wave numbers, and the light with different wave numbers enters the objective lens 30 at different angles and is imaged on the image plane 40 .
  • Step 2 Define the linearity evaluation coefficient RMS, where the linearity evaluation coefficient RMS is the root mean square error of the position interval of the equal difference wavenumber of the working band on the image plane, and specifically includes:
  • d is the grating constant
  • ⁇ ⁇ 1 - ⁇ d
  • ⁇ 3 ⁇ - ⁇ 2 ;
  • the focal length of the objective is given by the paraxial relationship
  • Y is the length of the image plane; is the field angle of the light with wave number k n entering the objective lens; is the field angle of the light with wave number k 1 entering the objective lens;
  • Step 3 Let the image plane length Y be a fixed value, and adjust the prism apex angle ⁇ to obtain the minimum value of the linearity evaluation coefficient RMS; when the linearity evaluation coefficient RMS is the smallest, the prism apex angle is ⁇ 1 .
  • Step 4 Obtain the compensation amount of the distortion of the objective lens and the vertical axis chromatic aberration according to the position interval of the aberration wave number on the image plane when the prism apex angle is ⁇ 1 , which specifically includes:
  • the structure of the objective lens can be designed to introduce negative distortion and vertical axis chromatic aberration, and the objective lens can include a combination of multiple lenses.
  • the objective lens 30 includes a first positive lens 31, a first negative lens 32, a second positive lens 33 and a third positive lens 34 which are arranged in sequence.
  • a second negative lens 35 is also provided on the side of the third positive lens away from the second positive lens 33 to correct field curvature.
  • the same material is used for the first positive lens 31 , the first negative lens 32 , the second positive lens 33 , the third positive lens 34 and the second negative lens 35 to introduce vertical-axis chromatic aberration.
  • the refractive indices of the first positive lens 34, the first negative lens 32, the second positive lens 33, the third positive lens 34 and the second negative lens 35 are in the range of 1.5-2.3.
  • Step 5 Optimize the objective lens according to the compensation amount of the distortion of the objective lens and the vertical chromatic aberration to obtain the optimized optical system, including:
  • the least squares method is used to obtain the values of these variables, and the optical system is optimized.
  • the working waveband of the wavenumber linear spectrometer is 750nm-950nm
  • the protective glass on both sides of the transmission grating 10 is BK7
  • the line logarithm of the grating is 1200/mm
  • the prism material is ZnS
  • the size of the line detector is 20.4mm
  • the size of the pixel is 20.4mm.
  • the arithmetic wavenumber sampling is shown in Table 1.
  • FIG. 3 in order to draw the variation curve of R MS with ⁇ and ⁇ according to the above scheme. It can be seen from the figure that RMS achieves the minimum value of 0.0094 when ⁇ and ⁇ are 26.9° and 37.7°, respectively. When ⁇ is 0, that is, when the grating and the prism are attached, the RMS reaches the minimum value of 0.0539 when ⁇ is 32.0°.
  • FIG. 4 it is a schematic diagram of the position interval between adjacent wave numbers before aberration compensation.
  • FIG. 5 it is a curve of image height changing with wave number before aberration compensation. The wavenumber linearity of this optical system is nearly 6 times lower than when the grating and the lens are separated.
  • the grating and the prism with the apex angle of 32.0° are attached as the initial structure of the beam splitting element. It is estimated that the distortion of the objective lens and the compensation amount of the vertical axis chromatic aberration of the maximum field of view are respectively
  • the corresponding objective lens is designed according to the estimated aberration value, and the system structure of the obtained wavenumber linear spectrometer is optimized.
  • FIG. 6 a schematic diagram of the structure of the wavenumber linear optical system obtained for optimization.
  • the collimated light emitted by the collimating lens 50 is sequentially injected into the objective lens through the protective glass 11 in front of the grating, the protective glass 10 after the grating, and the protective glass 12 after the grating, where the objective lens includes a first positive lens 31 and a first negative lens arranged in sequence 32 .
  • the second positive lens 33 , the third positive lens 34 and the second negative lens 35 are examples of the objective lens 35 .
  • FIG. 7 it is a schematic diagram of the distortion of the objective lens
  • FIG. 8 it is a graph of the vertical axis chromatic aberration.
  • the maximum distortion value is -3.74%
  • the vertical axis chromatic aberration that can be generated at the maximum field of view is 113 ⁇ m.
  • Figure 9 it is a schematic diagram of the position interval between adjacent wave numbers after aberration compensation.
  • Figure 10 shows the curve of image height versus wave number after aberration compensation. Better linearity than grating prism separation.
  • each dot plot is within the Airy disk, which indicates that the system has Diffraction-theoretical limit of focusing characteristics; the surrounding energy of each pixel is greater than 80%.

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Abstract

一种波数线性色散光学系统的设计方法及成像光谱仪，包括构建光学系统，光学系统包括依次设置的光栅（10）、棱镜（20）和物镜（30），光栅（10）与棱镜（20）贴合；定义线性度评价系数R MS；通过调整棱镜（20）顶角以使得线性度评价系数R MS取得最小值；当线性度评价系数R MS最小时，棱镜（20）顶角为α 1；由棱镜（20）顶角为α 1时等差波数在像面（40）的位置间隔，获取物镜（30）的畸变和垂轴色差的补偿量；根据物镜（30）的畸变和垂轴色差的补偿量优化物镜（30），获得优化后的光学系统。其利用物镜（30）像差补偿波数线性，实现在不分离光栅（10）和棱镜（20）的情况下获得更高的波数线性，能量利用率高，适用范围广，成本低。

Description

波数线性色散光学系统的设计方法及成像光谱仪 技术领域
本发明涉及光谱仪技术领域，具体涉及一种波数线性色散光学系统的设计方法及成像光谱仪。
背景技术
在谱域光学相干层析系统中，光谱仪系统实现波数的线性分布不仅可以显著降低图像的插值误差提高图像质量，而且可以提高系统的成像速度和灵敏度。在1990年Traub首次使用棱栅结构得到波数的近线性分布，但其线性度并不高。2007年Hu通过分离光栅和棱镜实现波数更高的线性分布，并将其引入谱域光学相干层析系统中。
目前，实现高的波数线性的光学方法，主要有三种：第一种是通过光栅棱镜组合的方式获得，其以光栅的槽密度、光栅与棱镜夹角、棱镜顶角、棱镜材料为变量优化实现波数的线性分布，然而，仅仅利用光栅与棱镜的组合分光实现波数线性分布，其缺点是获得高的线性分布必须使光栅与棱镜成一定夹角，这会增大系统的体积和装调难度；第二种方法是通过双光栅的组合分光，以光栅的槽密度、光栅间的夹角为变量优化实现波数的线性分布，然而，双光栅的组合分光会导致能量利用率过低；第三种方法是在棱镜光栅组合的基础上引入自由曲面实现波数更高的线性分布，然而，引入自由曲面将导致成本过高。
发明内容
本发明要解决的技术问题是现有的实现高的波数线性的光学系统，结构复杂，体积大，能量利用率低，成本高。
为了解决上述技术问题，本发明提供了一种波数线性色散光学系统的设计方法，包括以下步骤：
S1、构建光学系统，所述光学系统包括依次设置的光栅、棱镜和物镜，所述光栅与棱镜贴合；其中，准直光经光栅和棱镜分光后获得不同波数的光线，不同波数的光线以不同角度进入物镜并在像面上成像；
S2、定义线性度评价系数RMS，其中，所述线性度评价系数RMS为工作波段等差波数在像面的位置间隔的均方根误差；
S3、令像面长度Y为定值，通过调整棱镜顶角α以使得线性度评价系数RMS取得最小值；当所述线性度评价系数RMS最小时，所述棱镜顶角为α 1；
S4、由棱镜顶角为α 1时等差波数在像面的位置间隔，获取物镜的畸变和垂轴色差的补偿量；
S5、根据物镜的畸变和垂轴色差的补偿量优化物镜，获得优化后的光学系统。
作为优选的，所述S4和S5之间还包括：设计能够引入负畸变和垂轴色差的物镜。
作为优选的，所述物镜包括依次设置的第一正透镜、第一负透镜、第二正透镜和第三正透镜；通过提高轴外视场主光线在第三正透镜的入射高度和入射角度以产生负球差以引入负畸变。
作为优选的，所述第三正透镜远离所述第二正透镜的一侧还设置有第二负透镜以校正场曲。
作为优选的，所述第一正透镜、第一负透镜、第二正透镜、第三正透镜和第二负透镜采用同种材料以引入垂轴色差。
作为优选的，所述第一正透镜、第一负透镜、第二正透镜、第三正透镜和第二负透镜的折射率范围为1.5-2.3。
作为优选的，所述S5包括：通过改变物镜的曲率、相邻透镜间的间隔、透镜厚度和透镜材料，优化光学系统。
作为优选的，所述S2具体包括：
S21、根据工作波段选取n个等差波数；
S22、设准直的光线到光栅的入射角为θ in，衍射角为θ d，光栅与棱镜的夹角为β，棱镜的顶角为α，光线入射到棱镜前后表面的入射角分别为θ 1、θ 3及相应的岀射角分别为θ 2、θ，棱镜的折射率为n(λ)，令中心波数
Figure PCTCN2020137811-appb-000001
在棱镜后表面的出射角为
Figure PCTCN2020137811-appb-000002
其岀射方向作为物镜的光轴方向，由几何关系、光栅方程和折射定律得到：
Figure PCTCN2020137811-appb-000003
sinθ＝n(λ)sinθ 3，             (2)
其中，d为光栅常数，λ＝2π/k为光波长，β＝θ 1-θ d，θ 3＝α-θ 2；
S23、联立(1)(2)式，得到光线在棱镜后表面岀射角为
Figure PCTCN2020137811-appb-000004
物镜的焦距由近轴关系得到
Figure PCTCN2020137811-appb-000005
其中，Y为像面长度；
Figure PCTCN2020137811-appb-000006
为波数k n光线进入物镜的视场角；
Figure PCTCN2020137811-appb-000007
为波数k 1光线进入物镜的视场角；
S24、定义线性度评价系数R MS：
Figure PCTCN2020137811-appb-000008
其中，
Figure PCTCN2020137811-appb-000009
为相邻波数像面间隔，
Figure PCTCN2020137811-appb-000010
为第i个波数在像面的y坐标，
Figure PCTCN2020137811-appb-000011
为等差波数在像面的平均间隔。
作为优选的，所述S4中，物镜的畸变的补偿量
Figure PCTCN2020137811-appb-000012
物镜的垂轴色差的补偿量
Figure PCTCN2020137811-appb-000013
本发明还公开了一种成像光谱仪，通过上述的波数线性色散光学系统的设计方法获得。
本发明的有益效果：
1、本发明提出的物镜像差补偿波数线性的设计思想，通过对物镜的设计可以进一步提高光谱仪的波数线性。
2、本发明在不分离光栅与棱镜的情况下，利用物镜像差的补偿可实现较光栅棱镜分离时的更高的波数线性，同时减小了分光结构的体积。
3、本发明中，光学系统的能量利用率高，适用范围广，成本低。
附图说明
图1为物镜光路示意图；
图2为波数线性设计示意图；
图3为棱镜材料为ZnS时R MS值随β和α变化曲线；
图4为像差补偿前相邻波数位置间隔示意图；
图5为像差补偿前像高随波数变化曲线图；
图6为波数线性光学系统剖面示意图；
图7为物镜畸变示意图；
图8为波长750nm(左)与950nm(右)垂轴色差曲线；
图9为像差补偿后相邻波数位置间隔示意图；
图10为像差补偿后像高随波数变化曲线；
图11为不同波长下的点列图，其中，(a)为750nm的点列图，(b)为840nm的点列图，(c)为950nm的点列图；
图12为像元圈入能量百分数示意图，其中，(a)为波长750nm的像元圈入能量百分数，(b)为波长840nm的像元圈入能量百分数，(c)为波长950nm的像元圈入能量百分数。
图中标号说明：10、光栅；11、光栅前保护玻璃；12、光栅后保护玻璃；20、棱镜；30、物镜；31、第一正透镜；32、第一负透镜；33、第二正透镜；34、第三正透镜；35、第二负透镜；40、像面；50、准直镜。
具体实施方式
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人 员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。
为实现波数线性光谱仪的小型化和提高波数线性，本发明利用物镜像差补偿波数线性，实现在不分离光栅和棱镜的情况下获得更高的波数线性，基本原理如下：准直光经分光元件分光后，不同波数的光线以不同角度入射进入物镜。如图1所示，为物镜相差补偿波数的光路图，以中心波数光线方向为光轴方向，若最小波数与最大波数光线分别以ω，-ω角度入射，则交高斯像面于A、B两点，由于物镜材料对不同波数折射率不同，且波数越大折射率越大，故A点距光轴的距离大于B点距光轴的距离。所以在设置总像面长度为定值时，调整光谱仪中物镜的焦距并使物镜产生垂轴色差可使大波数像点靠近光轴，小波数像点远离光轴。光学系统中畸变可分为负畸变和正畸变，负畸变即主光线和高斯像面交点的高度随视场增大而小于理想像高，正畸变即主光线和高斯像面交点的高度随视场增大而大于理想像高。在设置像面长度为定值时，调整光谱仪中物镜的焦距并使物镜产生负(正)畸变，可使像面中心的波数像点远离(靠近)光轴，像面边缘的波数像点靠近(远离)光轴。故物镜产生的像差可以改善波数在像面的分布。
参照图2所示，本发明公开了一种波数线性色散光学系统的设计方法，包括以下步骤：
步骤一、构建光学系统，光学系统包括依次设置的光栅10、棱镜20和物镜30，光栅10与棱镜20贴合，即光栅与棱镜的夹角β为0。准直光经光栅10和棱镜20分光后获得不同波数的光线，不同波数的光线以不同角度进入物镜30并在像面40上成像。
步骤二、定义线性度评价系数RMS，其中，线性度评价系数RMS为工作波段等差波数在像面的位置间隔的均方根误差，具体包括：
S21、根据工作波段选取n个等差波数；
S22、设准直的光线到光栅的入射角为θ in，衍射角为θ d，光栅与棱镜的夹角为β，棱镜的顶角为α，光线入射到棱镜前后表面的入射角分别为θ 1、θ 3及相应的岀射角分别为θ 2、θ，棱镜的折射率为n(λ)，令中心波数
Figure PCTCN2020137811-appb-000014
在棱镜后表面的出射角为
Figure PCTCN2020137811-appb-000015
其岀射方向作为物镜的光轴方向，由几何关系、光栅方程和折射定律得到：
Figure PCTCN2020137811-appb-000016
sinθ＝n(λ)sinθ 3，              (2)
其中，d为光栅常数，λ＝2π/k为光波长，β＝θ 1-θ d，θ 3＝α-θ 2；
S23、联立(1)(2)式，得到光线在棱镜后表面岀射角为
Figure PCTCN2020137811-appb-000017
物镜的焦距由近轴关系得到
Figure PCTCN2020137811-appb-000018
其中，Y为像面长度；
Figure PCTCN2020137811-appb-000019
为波数k n光线进入物镜的视场角；
Figure PCTCN2020137811-appb-000020
为波数k 1光线进入物镜的视场角；
S24、定义线性度评价系数R MS：
Figure PCTCN2020137811-appb-000021
其中，
Figure PCTCN2020137811-appb-000022
为相邻波数像面间隔，
Figure PCTCN2020137811-appb-000023
为第i个波数在像面的y坐标，
Figure PCTCN2020137811-appb-000024
为等差波数在像面的平均间隔，如此，得到R MS随β、α变化曲线，当β为0时，光栅与棱镜贴合。
步骤三、令像面长度Y为定值，通过调整棱镜顶角α以使得线性度评价系数RMS取得最小值；当线性度评价系数RMS最小时，棱镜顶角为α 1。
步骤四、由棱镜顶角为α 1时等差波数在像面的位置间隔，获取物镜的畸变和垂轴色差的补偿量，具体包括：
物镜的畸变的补偿量
Figure PCTCN2020137811-appb-000025
物镜的垂轴色差的补偿量
Figure PCTCN2020137811-appb-000026
本发明中，可设计物镜的结构，引入负畸变和垂轴色差，物镜可包括多个透镜的组合。
参照图6所示，为波数线性光学系统剖面示意图，其物镜由多个透镜组成。其中，物镜30包括依次设置的第一正透镜31、第一负透镜32、第二正透镜33和第三正透镜34.通过提高轴外视场主光线在第三正透镜34的入射高度和入射角度以产生负球差以引入负畸变。34第三正透镜远离第二正透镜33的一侧还设置有第二负透镜35以校正场曲。第一正透镜31、第一负透镜32、第二正透镜33、第三正透镜34和第二负透镜35采用同种材料以引入垂轴色差。第一正 透镜34、第一负透镜32、第二正透镜33、第三正透镜34和第二负透镜35的折射率范围为1.5-2.3。
步骤五、根据物镜的畸变和垂轴色差的补偿量优化物镜，获得优化后的光学系统，包括：
通过改变物镜的曲率、相邻透镜间的间隔、透镜厚度和透镜材料，利用最小二乘法来获得这些变量的取值，优化光学系统。
以下，通过具体的实施例对本发明的技术方案做进一步说明。
本实施例中，波数线性光谱仪工作波段为750nm-950nm，透射光栅10两边的保护玻璃为BK7，光栅线对数为1200/mm，棱镜材料为ZnS，线探测器尺寸为20.4mm，像元尺寸为10μm×20μm，光谱分辨率为0.1nm。等差波数取样如表1所示。
表1
Figure PCTCN2020137811-appb-000027
表1(续)
Figure PCTCN2020137811-appb-000028
如图3所示，为按照上述方案绘出R MS随β、α变化曲线。从图中可知，R MS在β、α分别为26.9°、37.7°取得最小值0.0094。当β为0即光栅与棱镜贴合时，R MS在α为32.0°时取得最小值0.0539。如图4所示，为像差补偿前相邻波数位置间隔示意图，如图5所示，为像差补偿前像高随波数变化曲线。此光学系统的波数的线性度较光栅与透镜分离时下降近6倍。
将光栅与顶角为32.0°的棱镜贴合作为分光元件的初始结构。估计所需的物镜的畸变与最大视场的垂轴色差的补偿量分别为
Figure PCTCN2020137811-appb-000029
Figure PCTCN2020137811-appb-000030
根据像差估计值设计相应的物镜，优化得到的波数线性光谱仪系统结构。如图6所示，为优化得到的波数线性光学系统的结构示意图。其中，经准直镜50出射的准直光依次经光栅前保护玻璃11、光栅10和光栅后保护玻璃12射入物镜中，此处物镜包括依次设置的第一正透镜31、第一负透镜32、第二正透镜33、第三正透镜34和第二负透镜35。
如图7所示，为物镜畸变示意图，如图8所示，为垂轴色差曲线图。其中，最大畸变量-3.74％，在最大视场处所能产生的垂轴色差为113μm。
如图9所示，为像差补偿后相邻波数位置间隔示意图，如图10为像差补偿后像高随波数变化曲线，R MS值为0.0056，线性度提高到原来的近10倍，且优于光栅棱镜分离时的线性度。
如图11所示，为不同波长下的点列图，如图12所示，为像元圈入能量百分数示意图，由图可知各点列图均在艾里斑以内，这就表明该系统具有衍射理论极限的聚焦特性；像元包围能量均大于80％。
以上所述实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。

Claims (10)

  1. 一种波数线性色散光学系统的设计方法，其特征在于，包括以下步骤：
    S1、构建光学系统，所述光学系统包括依次设置的光栅、棱镜和物镜，所述光栅与棱镜贴合；其中，准直光经光栅和棱镜分光后获得不同波数的光线，不同波数的光线以不同角度进入物镜并在像面上成像；
    S2、定义线性度评价系数RMS，其中，所述线性度评价系数RMS为工作波段等差波数在像面的位置间隔的均方根误差；
    S3、令像面长度Y为定值，通过调整棱镜顶角α以使得线性度评价系数RMS取得最小值；当所述线性度评价系数RMS最小时，所述棱镜顶角为α 1；
    S4、由棱镜顶角为α 1时等差波数在像面的位置间隔，获取物镜的畸变和垂轴色差的补偿量；
    S5、根据物镜的畸变和垂轴色差的补偿量优化物镜，获得优化后的光学系统。
  2. 如权利要求1所述的波数线性色散光学系统的设计方法，其特征在于，所述S4和S5之间还包括：
    设计能够引入负畸变和垂轴色差的物镜。
  3. 如权利要求2所述的波数线性色散光学系统的设计方法，其特征在于，
    所述物镜包括依次设置的第一正透镜、第一负透镜、第二正透镜和第三正透镜；通过提高轴外视场主光线在第三正透镜的入射高度和入射角度以产生负球差以引入负畸变。
  4. 如权利要求3所述的波数线性色散光学系统的设计方法，其特征在于， 所述第三正透镜远离所述第二正透镜的一侧还设置有第二负透镜以校正场曲。
  5. 如权利要求4所述的波数线性色散光学系统的设计方法，其特征在于，所述第一正透镜、第一负透镜、第二正透镜、第三正透镜和第二负透镜采用同种材料以引入垂轴色差。
  6. 如权利要求5所述的波数线性色散光学系统的设计方法，其特征在于，所述第一正透镜、第一负透镜、第二正透镜、第三正透镜和第二负透镜的折射率范围为1.5-2.3。
  7. 如权利要求5所述的波数线性色散光学系统的设计方法，其特征在于，所述S5包括：
    通过改变物镜的曲率、相邻透镜间的间隔、透镜厚度和透镜材料，优化光学系统。
  8. 如权利要求1所述的波数线性色散光学系统的设计方法，其特征在于，所述S2具体包括：
    S21、根据工作波段选取n个等差波数；
    S22、设准直的光线到光栅的入射角为θ in，衍射角为θ d，光栅与棱镜的夹角为β，棱镜的顶角为α，光线入射到棱镜前后表面的入射角分别为θ 1、θ 3及相应的岀射角分别为θ 2、θ，棱镜的折射率为n(λ)，令中心波数
    Figure PCTCN2020137811-appb-100001
    在棱镜后表面的出射角为
    Figure PCTCN2020137811-appb-100002
    其岀射方向作为物镜的光轴方向，由几何关系、光栅方程和折射定律得到：
    Figure PCTCN2020137811-appb-100003
    sinθ＝n(λ)sinθ 3，     (2)
    其中，d为光栅常数，λ＝2π/k为光波长，β＝θ 1-θ d，θ 3＝α-θ 2；
    S23、联立(1)(2)式，得到光线在棱镜后表面岀射角为
    Figure PCTCN2020137811-appb-100004
    物镜的焦距由近轴关系得到
    Figure PCTCN2020137811-appb-100005
    其中，Y为像面长度；
    Figure PCTCN2020137811-appb-100006
    为波数k n光线进入物镜的视场角；
    Figure PCTCN2020137811-appb-100007
    为波数k 1光线进入物镜的视场角；
    S24、定义线性度评价系数R MS：
    Figure PCTCN2020137811-appb-100008
    其中，
    Figure PCTCN2020137811-appb-100009
    为相邻波数像面间隔，
    Figure PCTCN2020137811-appb-100010
    为第i个波数在像面的y坐标，
    Figure PCTCN2020137811-appb-100011
    为等差波数在像面的平均间隔。
  9. 如权利要求8所述的波数线性色散光学系统的设计方法，其特征在于，所述S4中，物镜的畸变的补偿量
    Figure PCTCN2020137811-appb-100012
    物镜的垂轴色差的补偿量
    Figure PCTCN2020137811-appb-100013
  10. 一种成像光谱仪，其特征在于，通过权利要求1-9任一项所述的波数线性色散光学系统的设计方法获得。
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