The concave grating dispersion principle is shown in Fig. 1. Similar to a plane grating, N is the normal of the concave grating, B is the angular bisector of incident light and diffraction light, i is incidence angle, θ is diffraction angle, 2δ is the included angle between incident light and diffraction light, and φ is the included angle between angular bisector B and normal N.
Where m is grating diffraction order, d is grating constant, and λ is system scanning wavelength; for the spectrometer system in this paper, m=1 and d=1/3 600 mm.
The following formula can be obtained from the geometrical relationship between the included angles in Fig. 1:
Substitute formula (2) into formula (1) and carry out simplification to obtain:
In formula (3), the grating constant d, the included angle 2δ between incident light and diffraction light and grating diffraction order all are a constant, so the linear relationship between control input and wavelength can be guaranteed as long as the relation of wavelength and sine of angle φ is linear. The schematic diagram of the sine mechanism used in wavelength scanning is shown in Fig. 2. The outer circle of the grating seat support bearing is fixed on the spectrometer cabinet wall, and the inner circle is fixed with the grating shaft and pendulum tail end, so that the pendulum rod can drive the grating to rotate. The other end of the pendulum rod keeps tight contact with the sliding block depending upon the spring tension. Driven by the stepper motor, the lead screw rotates, and the sliding block moves back and forth, so that the pendulum rod drives the grating to rotate and wavelength scanning is achieved.
本文光谱仪工作波段为170~380 nm，对应光栅转角为18.924 4°~46.464 8°，摆杆长度140 mm，丝杠有效行程75.27 mm。
The scanning band of the spectrometer in this paper is 170-380 nm, the corresponding grating rotation angle is 18.924 4°-46.464 8°, the pendulum rod length is 140 mm, and the effective travel of the lead screw is 75.27 mm.
For the well-adjusted spectrometer structure, the normal N of the grating rotates with grating rotation, and the position of the angular bisector is fixed. Therefore, if the pendulum rod is vertical to the lead screw initially in the sine mechanism design, the rotation angel α of the pendulum rod is always equal to the included angle φ between normal N and angular bisector B during grating rotation. The following formula can be obtained from the geometrical relationship:
Where x is the distance from the sliding block to the initial position, and l is the pendulum rod length. Substitute formula (4) into formula (3) to obtain:
According to formula (5), except the sliding block position variable x, all other parameters are a constant. The sliding block position is of linear relationship with the step number of the stepper motor, so the wavelength position also has linear relationship with the input step number of the stepper motor. The control relationship has been simplified via the sine mechanism, thus ensuring the improvement of the wavelength scanning accuracy and the reliability of the mechanism.
紫外双光栅光谱仪的基本结构如图 3所示，主要由入缝组件、光栅、中缝组件、反射镜、出缝组件和探测器等组成。遮光罩在系统的最前端，起到减少杂光的作用。光线依次经过遮光罩、石英窗口、漫透射板和入缝，在第一个光栅上进行色散，经反射镜折射通过中缝，再经第二块反射镜和光栅汇聚在出缝处，最后到达探测器进行数据的采集和处理。两个凹面光栅参数完全一致，安装在同一个光栅座内共轴转动，光谱仪工作时，波长扫描机构驱动光栅转动，在不同转角时探测器接收到不同波长光的能量，机构连续扫描从而完成170~380 nm波段范围内连续光谱测量。
The basic structure of the ultraviolet double grating spectrometer is shown in Fig. 3. The ultraviolet double grating spectrometer consists mainly of entrance slit component, gratings, intermediate slit component, reflectors, exit slit component, detector, etc. The light shield is at the foremost end of the system and plays a role in reducing stray light. Rays pass through the light shield, quartz window, diffuse transmission panel and entrance slit successively for dispersion on the first grating; refracted by the reflector, rays pass through the intermediate slit; after passing through the second reflector and grating, rays converge at the exit slit and finally reach the detector for data acquisition and processing. The parameters of the two concave gratings are completely identical and they are installed in the same grating seat to rotate co-axially. During spectrometer working, the wavelength scanning mechanism drives the grating to rotate; at different rotation angles, the detector receives the energy of lights with different wavelengths, and the mechanism performs continuous scanning so as to achieve continuous spectral measurement within the band range of 170-380 nm.
According to the operating principle of the ultraviolet double grating spectrometer, the wavelength scanning mechanism is the key mechanism of the spectrometer, and the reasonableness of the mechanism design has a decisive impact on wavelength repeatability accuracy. The lead screw mechanism has been improved on the basis of the traditional scanning mechanism based on lead screw pendulum rod in this paper. In order that the roller can tightly contact the sliding block in the whole scanning process, the fixed end of the pre-loaded spring is moved from the cabinet onto the sliding block, as shown in Fig. 4. In the scheme where the fixed end of the spring is fixed on the cabinet wall, the fixed end of the spring keeps still in the whole scanning process; as the travel of the sliding block increases, the spring length increases remarkably, and the needed driving torque of the stepper motor also increases accordingly. In the new scheme, the fixed end of the spring is fixed on the sliding block, the spring also plays a role in pre-tightening, and the spring size can be reduced remarkably. In the whole scanning process, the variation of the spring tension is very small, the friction between the roller and the sliding block is rolling friction, and the driving torque of the stepper motor almost remains unchanged. This scheme can effectively reduce the required motor torque and also has remarkable advantages in reducing spring amplitude during instrument vibration.
In order to improve the zero returning positioning accuracy of the wavelength scanning mechanism, the method of combining rough positioning with precise positioning is used in zero positioning, as shown in Fig. 5. The rough positioning sensor is installed on the sliding block to make linear motion and quickly search zero position; the precise positioning sensor is installed on the coupling and rotates with motor rotation. During zero position searching operation, the motor rotates reversely at quick speed and reaches the rough positioning sensor position; then the motor rotates positively at slow speed and finds the precise positioning sensor position. The motor always rotates positively in the whole scanning process, which can thus effectively reduce the lead screw backlash error and improve repeatability accuracy.
光谱仪整机结构如图 6所示，为保证光谱仪整机结构刚度，光谱仪壳体采用一体化加工方式，通过筋板对不同组件进行分仓，提高刚度的同时可以减少杂散光对系统的影响。三个狭缝组件通过对研的不锈钢片拼接而成，狭缝尺寸在50倍显微镜下进行调试，狭缝尺寸均为0.4 mm×1 mm。探测器采用光电倍增管，安装时与出缝组件紧密安装，避免杂光进入。
The structure of the whole spectrometer is shown in Fig. 6. In order to ensure the rigidity of the whole spectrometer structure, the housing of the spectrometer uses the integral machining mode, and different components are partitioned with rib plates, which can reduce the impact of stray lights on the system while increasing the rigidity. The three slit components are sliced from stainless steel sheets. The slit size is adjusted and tested under a 50-power microscope, and the size of all the three slits is 0.4 mm×1 mm. The detector uses photomultipliers and is tightly installed with the exit slit component to prevent stray lights from entering.
波长重复性精度高是光谱仪完成太阳光谱170~380 nm波段范围内精确扫描需要保证的基本要求，是后续波长线性标定和光谱测量的前提。光谱分辨率由入缝和出缝宽度决定，宽度越低，光谱分辨率越高，但是进入光谱仪系统的能量也会减少，降低系统的信噪比，所以需要综合考虑，满足信噪比指标的同时实现较高的光谱分辨率。本文所设计的紫外双光栅光谱仪设计指标为：光谱分辨率为1 nm，波长重复性为±0.02 nm。
High wavelength repeatability accuracy is the basic requirement satisfied to achieve accurate scanning within the solar spectral band range of 170-380 nm using the spectrometer and also the premise for subsequent linear calibration of wavelength and spectral measurement. Spectral resolution is decided by the width of the entrance slit and exit slit. The smaller the width, the higher the spectral resolution; but the energy entering the spectrometer system will also be reduce so as to reduce the system's SNR. Therefore, the width shall be considered comprehensively to achieve high spectral resolution while meeting the requirement of the SNR index. The design indexes of the ultraviolet double grating spectrometer in this paper:spectral resolution 1 nm, wavelength repeatability ±0.02 nm.
根据对波长扫描机构原理的分析，光谱仪中波长位置与结构参数的关系可以由公式(5)确定，同时公式(5)的推导依赖于公式(4)成立的假设，即在光栅零级时摆杆与丝杠垂直。由此可知，影响光谱仪波长重复性精度的误差源有[8, 11, 13, 15]：(1)光栅常数d；(2)光栅入射光线和衍射光线夹角2δ；(3)摆杆长度误差Δl；(4)滚轮在滑块上的跳动量Δe；(5)摆杆在弹簧作用下的变形量Δl′；(6)光栅轴轴系晃动误差Δβ；(7)丝杠机构回零位重复性误差ΔXj；(8)丝杠机构的重复定位误差Δx′。
According to the analysis of the principle of the wavelength scanning mechanism, the relation of the wavelength position in the spectrometer with the structure parameter can be determined from formula (5); in addition, formula (5) is derived depending on the assumption that formula (4) is workable; i.e. the pendulum rod is vertical to the lead screw at grating zero order. It can be seen from this that the error sources affecting the wavelength repeatability accuracy of the spectrometer include the following[8, 11, 13, 15]:(1)grating constant d; (2)included angle 2δ between incident ray and diffraction ray of grating; (3)pendulum rod length error Δl; (4)run-out of the roller on the sliding block Δe; (5)pendulum rod deformation under the action of the spring Δe; (6)waggling error of grating shaft system Δβ; (7)zero returning repeatability error of the lead screw mechanism ΔXj; (8)repeatability error of the lead screw mechanism Δx′.
在本光谱仪系统中，误差源(1)、(2)和(3)在光栅选定后就已经确定，若存在加工误差，也不随波长扫描过程发生变化，属于固有的系统误差，只影响波长与步进电机步数之间的当量，即波长线性，而不会影响波长重复性，波长线性可以进行测量来标定。由于本设计中，对弹簧拉紧方式进行了改进，选取较大刚度系数弹簧对滚轮进行预紧，滑块接触面进行精研，选用高精度的深沟球轴承作为滚轮，其径向跳动量也可以忽略不计[8, 14]。另外，由于弹簧不再对摆杆整体进行拉紧，因此，摆杆的变形量也可以忽略不计。光栅轴采用一对高精度背靠背安装的角接触球轴承进行支撑，经过精密装调后对光栅轴端部进行测量，其径向跳动量小于1 μm，对于本仪器是可以忽略的。
In our spectrometer system, error sources (1), (2) and (3) have been determined after selecting gratings; if there is a machining error, they will not change with the wavelength scanning process, are inherent system errors, and affect only the equivalent between wavelength and the step number of the stepper motor, i.e. wavelength linearity. Wavelength linearity can be calibrated through measurement. The spring tension mode has been improved in this design. Moreover, the spring with large rigidity coefficient is used to pre-tighten the roller, the sliding block contact surface is finely ground, and a high-precision deep groove ball bearing is used as the roller, so the radial run-out can be neglected[8, 14]. In addition, the spring doesn′t tension the pendulum rod integrally, so pendulum rod deformation can also be neglected. The grating shaft is supported by a pair of back-to-back mounted high-precision angular contact ball bearings. The measurement of the grating shaft end after precise adjustment shows that the radial run-out is less than 1 μm, which can be neglected for this instrument.
According to the actual test result, rough positioning method is adopted. As the induction distance between positioning magnet steel and Hall sensor is different, the positioning accuracy ΔXc ranges from 3 μm to 5 μm in general. The positioning accuracy of the precise positioning sensor installed on the rotating shaft can be deduced as follows:
其中，R为磁钢沿丝杠轴的回转半径，p为丝杠螺距。本丝杠机构中，R=10 mm，p=0.5 mm。将系统参数带入式(7)可得，精定位的重复定位精度约为0.04 μm。丝杠机构使用步进电机驱动，步进电机的步距角误差会对定位精度造成影响。本文使用的步进电机为德国进口步进电机，步距角1.8°，步距角误差优于3%。因此，受步进电机步距角精度限制，波长扫描机构的实际回零误差为1.8×0.03/360×0.5 mm=0.075 μm，该回零精度远高于丝杠的重复定位精度，在计算时可以忽略不计。
Where R is the turning radius of magnet steel along the lead screw axis, and p is lead screw pitch. For the lead screw mechanism, R=10 mm and p=0.5 mm. By substituting system parameters into formula (7), the obtained repeatability accuracy of the precise positioning sensor is about 0.04 μm. The lead screw mechanism is driven by a stepper motor. The step angle error of the stepper motor will have an impact on positioning accuracy. The stepper motor used in this paper is a stepper motor imported from Germany, its step angle is 1.8°, and its step angle error is better than 3%. Hence, limited by the step angle precision of the stepper motor, the actual zero returning error of the wavelength scanning mechanism is 1.8×0.03/360×0.55 mm=0.075 μm. The zero returning accuracy is far too higher than the repeatability accuracy of the lead screw and can be neglected in calculation.
The above analysis indicates that the repeatability error of the lead screw mechanism decides wavelength scanning repeatability accuracy. According to error independence, differentiate formula (5) by the lead screw travel x to obtain:
当波长重复性误差为Δλ=±0.002 nm时，丝杠的重复定位误差Δx应优于±5.3 μm。选用丝杠机构的重复定位精度标称值为±2 μm，在装配前进行实测，重复定位精度为±1.8 μm，满足波长重复性要求。
When the wavelength repeatability error is Δλ=±0.02 nm, the repeatability error Δx of the lead screw shall be better than ±5.3 μm. The nominal value of the repeatability accuracy of the used lead screw mechanism is ±2 μm. The measurement before assembling indicates that the repeatability accuracy is ±1.8 μm, which meets wavelength repeatability requirements.
使用汞灯253、296、313和365 nm等4个特征波长对光谱仪进行波长重复性验证, ，如图 7所示。测量时，汞灯放在入缝前，汞灯发出的光经漫透射板之后进入光谱仪，PC机发送控制指令驱动波长扫描机构回零，根据计算的全程扫描步数，从零点扫描到丝杠指定行程处，探测器对出射狭缝的光进行采集，可以得到在所扫描波段的能量分布情况。根据理论公式，将步进电机的步数转换为对应波长数，一个扫描周期的测量结果如图 8所示。根据波长间隔，确定4个特征波长的位置，对于其他不显著波长不进行处理。
4 characteristic wavelengths of a mercury lamp including 253 nm, 296 nm, 313 nm and 365 nm have been used to carry out wavelength repeatability verification of the spectrometer, as shown in Fig. 7. During measurement, the mercury lamp is placed before the entrance slit; the lights emitted by the mercury lamp enter the spectrometer after passing through the transmission panel; the PC sends out a control command to drive the wavelength scanning mechanism to return to zero. According to the calculated whole-process scanning steps, scanning is performed from zero to the designated lead screw travel. The detector acquires the lights out of the exit slit, and the energy distribution at the scanned band can be obtained. According to theoretical formulas, the step number of the stepper motor is converted into the corresponding wavelength number. The measurement result within one scanning period is shown in Fig. 8. The position of the 4 characteristic wavelengths is determined according to the wavelength interval, and other non-significant wavelengths are not processed.
表 1 4个典型波长重复性误差
Table 1. Repeatability error of 4 representative wavelength
波长/nm 重复性误差/nm 253.652 0.006 296.728 -0.005 313.184 0.007 365.016 0.004
Scanning is carried out for 5 times. Gaussian fitting of the data at 4 peak valve positions each time of scanning is performed to determine the actual central wavelength and full width at half maximum measured for each characteristic wavelength. The deviation between the central wavelength from 5 times of fitting for the same characteristic wavelength and the average value is taken as the repeatability error of the characteristic wavelength. The statistical results of the repeatability errors of the 4 characteristic wavelengths are shown in Tab. 1.
根据测量结果，在4个特征波长处的重复性在-0.005~+0.007 nm之间，光谱分辨率优于0.8 nm，满足紫外双光栅光谱仪波长重复性±0.02 nm和光谱分辨率1 nm的要求。该结果与光谱仪波长扫描机构理论分析结果相符，说明光机参数转换公式推导正确，机构设计合理，误差分析与实际机构设计吻合。
According to the measurement result, the repeatability errors of the 4 characteristic wavelengths are between -0.005 nm and +0.007 nm, and the spectral resolution is better than 0.8 nm, which meets the requirements of wavelength repeatability ±0.02 nm and spectral resolution 1 nm of ultraviolet double grating spectrometer. This result is consistent with the theoretical analysis result of the wavelength scanning mechanism of the spectrometer, indicating that the derived optical-mechanical parameter conversion formulas are correct and that the mechanism design is reasonable. The error analysis is in line with the actual mechanism design.
Operating principle and structure design of the spectrometer
Concave grating dispersion principle and sine mechanism principle
Spectrometer structure design
Wavelength repeatability error analysis