紫外雙光柵光譜儀結(jié)構(gòu)設(shè)計與波長精度分析

曹佃生，林冠宇，楊小虎，張子輝，聞寶朋

(1.中國科學(xué)院 長春光學(xué)精密機(jī)械與物理研究所，吉林 長春 130033；2.一汽轎車股份有限公司，吉林 長春 130000)

1　引　言

Introduction

太陽輻射持續(xù)為地球提供外部能量，其能量波動對地球氣候變化、天氣和環(huán)境異常等具有顯著的影響，研制專門的儀器對太陽輻照度進(jìn)行長期精確監(jiān)測，對于地球科學(xué)具有重要的研究價值[1-7]。太陽光譜輻射的精確測量對提高痕量氣體的反演精度等其他學(xué)科領(lǐng)域也具有積極的作用[3,8]。

Solar radiation continuously provides the Earth with an external source of energy, and solar energy fluctuation has a remarkable impact on Earth′s climate change, weather, environmental anomaly,etc. Therefore, the development of specialized instruments for long-term accurate monitoring of solar irradiance has important research value for geoscience[1-7]. Accurate measurement of solar spectral radiation also plays an active role in other disciplines involving the improvement trace gas inversion accuracy,etc[3,8].

太陽輻射能量具有波長依賴性，可見光和近紅外波段集中了太陽輻射的大部分能量，但是在太陽周期內(nèi)的變化較為平穩(wěn)，紫外波段雖然能量占比不多，但是在太陽周內(nèi)變化較大，并且這部分變化可能會對地球大氣成分和氣候造成顯著影響[7]。本文設(shè)計的紫外雙光柵光譜儀就是為了對紫外170～380 nm波段太陽輻射進(jìn)行精確監(jiān)測的儀器。為了滿足波長增量和控制輸入的線性關(guān)系，此類光譜儀一般采用正弦機(jī)構(gòu)作為波長掃描機(jī)構(gòu)[8-10,12-15]，即擺桿轉(zhuǎn)角的正弦值與波長值為線性關(guān)系。與采用平面光柵和CCD組合形式的光譜儀相比，掃描型光柵光譜儀具有更高的光譜分辨率，且結(jié)構(gòu)簡單緊湊，更容易實現(xiàn)小型化。掃描型光譜儀的波長重復(fù)性精度取決于波長掃描機(jī)構(gòu)的精度。目前，常用的波長掃描機(jī)構(gòu)有凸輪和絲杠等形式[8,10-13]，基于凸輪的波長掃描機(jī)構(gòu)由于凸輪自身廓線精度和體積等因素不能滿足本文設(shè)計光譜儀的需要，因此，選用絲杠擺桿機(jī)構(gòu)作為雙光柵光譜儀的波長掃描機(jī)構(gòu)。

Solar radiation energy has wavelength dependence, and the majority of solar radiation energy is concentrated at visible light and near-infrared bands, but the variation of solar radiation energy is stable within solar cycles. The proportion of energy at ultraviolet band is not high, but the energy changes greatly within solar cycles and its variation may have a remarkable impact on the Earth′s atmosphere composition and climate[7]. The ultraviolet double grating spectrometer designed in this paper is an instrument intended for accurate monitoring of solar radiation at ultraviolet 170-380 nm band. In order to reach the linear relationship between wavelength increment and control input, such spectrometer generally uses a sine mechanism as the wavelength scanning mechanism[8-10,12-15];i.e. the sine of the pendulum rod′s rotation angle has linear relationship with the wavelength. In comparison with the spectrometer using plane grating and CCD, the scanning type grating spectrometer has higher spectral resolution and simple and compact structure and achieves miniaturization more easily. The wavelength repeatability accuracy of the scanning type spectrometer depends on the accuracy of the wavelength scanning mechanism. At present, typical wavelength scanning mechanisms include the forms such as cam, lead screw,etc[8,10-13]. The cam-based wavelength scanning mechanism cannot meet the requirements of the spectrometer designed in this paper due to the factors such as cam′s profile accuracy and volumeetc. Thus，a lead screw pendulum rod mechanism is used as the wavelength scanning mechanism of the double grating spectrometer in is paper.

本文根據(jù)凹面光柵色散原理和光譜儀結(jié)構(gòu)特點(diǎn)，推導(dǎo)了光學(xué)指標(biāo)到結(jié)構(gòu)設(shè)計輸入?yún)?shù)的轉(zhuǎn)換公式，在傳統(tǒng)的基于絲杠擺桿的波長掃描機(jī)構(gòu)的基礎(chǔ)上，改進(jìn)了設(shè)計，改進(jìn)后掃描機(jī)構(gòu)的零點(diǎn)定位精度獲得提高，在整個掃描過程中，驅(qū)動力變化更加均勻。對影響波長重復(fù)性精度的誤差源進(jìn)行了分析，以汞燈為光源對光譜儀的波長重復(fù)性指標(biāo)進(jìn)行測量，以驗證理論分析的正確性和指標(biāo)的可實現(xiàn)性。

According to the concave grating dispersion principle and spectrometer structure features, conversion formulas from optical indexes to spectrometer structure parameters have been derived in this paper. In addition, the scanning mechanism design has been improved on the basis of the traditional wavelength scanning mechanism based on lead screw pendulum rod. The zero positioning accuracy of the improved scanning mechanism has been improved, and the driving force variation is more uniform in the whole scanning process. Error sources affecting wavelength repeatability accuracy have been analyzed, and the wavelength repeatability of the spectrometer has been measured using a mercury lamp as the light source so as to verify the correctness of theoretical analysis and the realizability of the index.

2　光譜儀工作原理與結(jié)構(gòu)設(shè)計

Operating principle and structure design of the spectrometer

2.1　凹面光柵色散和正弦機(jī)構(gòu)原理

Concavegratingdispersionprincipleandsinemechanismprinciple

凹面光柵色散原理如圖1所示。與平面光柵相似，N為凹面光柵法線，B為入射光線和衍射光線的角平分線，i為入射角，θ為衍射角，2δ為入射光線和衍射光線的夾角，φ為角平分線B和法線N的夾角。

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,iis incidence angle,θis diffraction angle, 2δis the included angle between incident light and diffraction light, andφis the included angle between angular bisector B and normal N.

圖1　光柵色散原理 Fig.1　Grating dispersion principle

根據(jù)衍射型光柵的色散公式[10-13]，有：

The following formula is obtained from the diffraction grating dispersion formula[10-13]:

(1)

其中，m為光柵衍射級次，d為光柵常數(shù)，λ為系統(tǒng)掃描波長，對于本文光譜儀系統(tǒng)，m=1，d=1/3600 mm。

Wheremis grating diffraction order,dis grating constant, andλis system scanning wavelength; for the spectrometer system in this paper,m=1 andd=1/3 600 mm.

由圖1中的夾角幾何關(guān)系可得：

The following formula can be obtained from the geometrical relationship between the included angles in Fig.1:

(2)

將公式(2)帶入公式(1)并進(jìn)行簡化，可得：

Substitute formula (2) into formula (1) and carry out simplification to obtain:

(3)

在式(3)中，光柵常數(shù)d，入射光線和衍射光線夾角2δ和光柵衍射級次都是常數(shù)，因此只需要保證波長與角度值φ的正弦為線性關(guān)系，就能保證控制輸入和波長的線性關(guān)系。波長掃描所采用的正弦機(jī)構(gòu)原理圖如圖2所示。光柵座支撐軸承的外圈固定在光譜儀箱體壁上，內(nèi)圈與光柵軸以及擺桿末端固定，使擺桿能夠帶動光柵轉(zhuǎn)動。擺桿的另一端通過彈簧的拉力與滑塊保持緊密接觸，在步進(jìn)電機(jī)的驅(qū)動下絲杠旋轉(zhuǎn)，滑塊前后移動，從而驅(qū)動擺桿帶動光柵轉(zhuǎn)動，完成波長掃描。

In formula (3), the grating constantd, the included angle 2δbetween 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 angleφis 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.

圖2　波長掃描機(jī)構(gòu) Fig.2　Wavelength scanning mechanism

本文光譜儀工作波段為170～380 nm，對應(yīng)光柵轉(zhuǎn)角為18.924 4°～46.464 8°，擺桿長度140 mm，絲杠有效行程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.

對于已經(jīng)裝調(diào)完的光譜儀結(jié)構(gòu)，光柵法線N隨光柵的轉(zhuǎn)動而轉(zhuǎn)動，角平分線B的位置是固定的。因此，在設(shè)計正弦機(jī)構(gòu)時，若初始位置將擺桿與絲杠置于垂直位置，那么光柵轉(zhuǎn)動時擺桿的轉(zhuǎn)角α與法線N和角平分線B的夾角φ始終相等。根據(jù)幾何關(guān)系，可得：

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 angelαof the pendulum rod is always equal to the included angleφbetween normal N and angular bisector B during grating rotation. The following formula can be obtained from the geometrical relationship:

(4)

式中，x為滑塊距離初始位置的距離，l為擺桿長度。將式(4)帶入式(3)可得：

Wherexis the distance from the sliding block to the initial position, andlis the pendulum rod length. Substitute formula (4) into formula (3) to obtain:

(5)

根據(jù)式(5)，除滑塊位置變量x之外，所有參數(shù)均為常量，滑塊的位置與步進(jìn)電機(jī)的步數(shù)之間為線性關(guān)系，因此，波長位置與步進(jìn)電機(jī)的輸入步數(shù)之間也為線性關(guān)系。通過正弦機(jī)構(gòu)，簡化了控制關(guān)系，為提高波長掃描精度和機(jī)構(gòu)可靠性提供了保證。

According to formula (5), except the sliding block position variablex, 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.

2.2　光譜儀結(jié)構(gòu)設(shè)計

Spectrometerstructuredesign

紫外雙光柵光譜儀的基本結(jié)構(gòu)如圖3所示，主要由入縫組件、光柵、中縫組件、反射鏡、出縫組件和探測器等組成。遮光罩在系統(tǒng)的最前端，起到減少雜光的作用。光線依次經(jīng)過遮光罩、石英窗口、漫透射板和入縫，在第一個光柵上進(jìn)行色散，經(jīng)反射鏡折射通過中縫，再經(jīng)第二塊反射鏡和光柵匯聚在出縫處，最后到達(dá)探測器進(jìn)行數(shù)據(jù)的采集和處理。兩個凹面光柵參數(shù)完全一致，安裝在同一個光柵座內(nèi)共軸轉(zhuǎn)動，光譜儀工作時，波長掃描機(jī)構(gòu)驅(qū)動光柵轉(zhuǎn)動，在不同轉(zhuǎn)角時探測器接收到不同波長光的能量，機(jī)構(gòu)連續(xù)掃描從而完成170～380 nm波段范圍內(nèi)連續(xù)光譜測量。

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.

圖3　紫外雙光柵光譜儀結(jié)構(gòu)簡圖. Fig.3　Schematic view of ultraviolet double grating spectrometer

由紫外雙光柵光譜儀的工作原理可知，波長掃描機(jī)構(gòu)是光譜儀的關(guān)鍵機(jī)構(gòu)，其設(shè)計是否合理對光譜儀的波長重復(fù)性精度具有決定性影響。本文在傳統(tǒng)基于絲杠擺桿的掃描機(jī)構(gòu)基礎(chǔ)上，對絲杠機(jī)構(gòu)進(jìn)行了改進(jìn)。為了保持在整個掃描過程中滾輪能與滑塊緊密接觸，將預(yù)緊彈簧的固定端由箱體移動到滑塊上，如圖4所示。彈簧固定端在箱體壁上的方案中，彈簧固定端在整個掃描過程保持不動，隨著滑塊行程的增加，彈簧長度增加顯著，需要步進(jìn)電機(jī)的驅(qū)動力矩也隨之增大。新方案中，彈簧固定端安裝在滑塊上，同樣可以起到預(yù)緊的作用，彈簧尺寸可以顯著減少。在整個掃描過程中，彈簧拉力變化量很小，且滾輪與滑塊之間為滾動摩擦，步進(jìn)電機(jī)的驅(qū)動力矩幾乎保持不變。該方案可以有效減少對電機(jī)力矩的要求，對降低儀器在振動時彈簧的振幅也具有顯著優(yōu)勢。

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.

圖4　彈簧設(shè)計改進(jìn) Fig.4　Diagram of improvemental spring design

為了提高波長掃描機(jī)構(gòu)的回零定位精度，采用精定位和粗定位結(jié)合的方式進(jìn)行零點(diǎn)定位，如圖5所示。粗定位傳感器安裝在滑塊上做直線運(yùn)動，用于快速尋找零位，精定位傳感器安裝在聯(lián)軸器上，隨著電機(jī)的旋轉(zhuǎn)而旋轉(zhuǎn)。尋零位操作時，電機(jī)快速反轉(zhuǎn)達(dá)到粗定位傳感器位置，然后慢速正向旋轉(zhuǎn)，找到精定位傳感器位置，整個掃描過程中，電機(jī)始終正向轉(zhuǎn)動，可以有效減小絲杠回程間隙誤差，提高重復(fù)定位精度。

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.

圖5　粗、精定位方式 Fig.5　Rough and precise positioning method

光譜儀整機(jī)結(jié)構(gòu)如圖6所示，為保證光譜儀整機(jī)結(jié)構(gòu)剛度，光譜儀殼體采用一體化加工方式，通過筋板對不同組件進(jìn)行分倉，提高剛度的同時可以減少雜散光對系統(tǒng)的影響。三個狹縫組件通過對研的不銹鋼片拼接而成，狹縫尺寸在50倍顯微鏡下進(jìn)行調(diào)試，狹縫尺寸均為0.4 mm×1 mm。探測器采用光電倍增管，安裝時與出縫組件緊密安裝，避免雜光進(jìn)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.

圖6　光譜儀整機(jī)結(jié)構(gòu)圖 Fig.6　Structure diagram of spectrometer model

3　波長重復(fù)性誤差分析

Wavelength repeatability error analysis

波長重復(fù)性精度高是光譜儀完成太陽光譜170～380 nm波段范圍內(nèi)精確掃描需要保證的基本要求，是后續(xù)波長線性標(biāo)定和光譜測量的前提。光譜分辨率由入縫和出縫寬度決定，寬度越低，光譜分辨率越高，但是進(jìn)入光譜儀系統(tǒng)的能量也會減少，降低系統(tǒng)的信噪比，所以需要綜合考慮，滿足信噪比指標(biāo)的同時實現(xiàn)較高的光譜分辨率。本文所設(shè)計的紫外雙光柵光譜儀設(shè)計指標(biāo)為：光譜分辨率為1 nm，波長重復(fù)性為±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.

根據(jù)對波長掃描機(jī)構(gòu)原理的分析，光譜儀中波長位置與結(jié)構(gòu)參數(shù)的關(guān)系可以由公式(5)確定，同時公式(5)的推導(dǎo)依賴于公式(4)成立的假設(shè)，即在光柵零級時擺桿與絲杠垂直。由此可知，影響光譜儀波長重復(fù)性精度的誤差源有[8,11,13,15]：(1)光柵常數(shù)d；(2)光柵入射光線和衍射光線夾角2δ；(3)擺桿長度誤差Δl；(4)滾輪在滑塊上的跳動量Δe；(5)擺桿在彈簧作用下的變形量Δl′；(6)光柵軸軸系晃動誤差Δβ；(7)絲杠機(jī)構(gòu)回零位重復(fù)性誤差ΔXj；(8)絲杠機(jī)構(gòu)的重復(fù)定位誤差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 constantd; (2)included angle 2δbetween 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′.

在本光譜儀系統(tǒng)中，誤差源(1)、(2)和(3)在光柵選定后就已經(jīng)確定，若存在加工誤差，也不隨波長掃描過程發(fā)生變化，屬于固有的系統(tǒng)誤差，只影響波長與步進(jìn)電機(jī)步數(shù)之間的當(dāng)量，即波長線性，而不會影響波長重復(fù)性，波長線性可以進(jìn)行測量來標(biāo)定。由于本設(shè)計中，對彈簧拉緊方式進(jìn)行了改進(jìn)，選取較大剛度系數(shù)彈簧對滾輪進(jìn)行預(yù)緊，滑塊接觸面進(jìn)行精研，選用高精度的深溝球軸承作為滾輪，其徑向跳動量也可以忽略不計[8,14]。另外，由于彈簧不再對擺桿整體進(jìn)行拉緊，因此，擺桿的變形量也可以忽略不計。光柵軸采用一對高精度背靠背安裝的角接觸球軸承進(jìn)行支撐，經(jīng)過精密裝調(diào)后對光柵軸端部進(jìn)行測量，其徑向跳動量小于1 μm，對于本儀器是可以忽略的。

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.

根據(jù)實際測試結(jié)果，采用粗定位的方式，隨著定位磁鋼和霍爾傳感器之間的感應(yīng)距離不同，其定位精度ΔXc一般在3～5 μm，可以推導(dǎo)安裝在旋轉(zhuǎn)軸上精定位的定位精度為：

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 ΔXcranges 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:

(7)

其中，R為磁鋼沿絲杠軸的回轉(zhuǎn)半徑，p為絲杠螺距。本絲杠機(jī)構(gòu)中，R=10 mm，p=0.5 mm。將系統(tǒng)參數(shù)帶入式(7)可得，精定位的重復(fù)定位精度約為0.04 μm。絲杠機(jī)構(gòu)使用步進(jìn)電機(jī)驅(qū)動，步進(jìn)電機(jī)的步距角誤差會對定位精度造成影響。本文使用的步進(jìn)電機(jī)為德國進(jìn)口步進(jìn)電機(jī)，步距角1.8°，步距角誤差優(yōu)于3%。因此，受步進(jìn)電機(jī)步距角精度限制，波長掃描機(jī)構(gòu)的實際回零誤差為1.8×0.03/360×0.5 mm=0.075 μm，該回零精度遠(yuǎn)高于絲杠的重復(fù)定位精度，在計算時可以忽略不計。

WhereRis the turning radius of magnet steel along the lead screw axis, andpis lead screw pitch. For the lead screw mechanism,R=10 mm andp=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.

根據(jù)以上分析，絲杠機(jī)構(gòu)的重復(fù)定位誤差決定了波長掃描的重復(fù)性精度。根據(jù)誤差的獨(dú)立性，將式(5)對絲杠行程x取微分可得：

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 travelxto obtain:

(8)

當(dāng)波長重復(fù)性誤差為Δλ=±0.002 nm時，絲杠的重復(fù)定位誤差Δx應(yīng)優(yōu)于±5.3 μm。選用絲杠機(jī)構(gòu)的重復(fù)定位精度標(biāo)稱值為±2 μm，在裝配前進(jìn)行實測，重復(fù)定位精度為±1.8 μm，滿足波長重復(fù)性要求。

When the wavelength repeatability error is Δλ=±0.02 nm, the repeatability error Δxof 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.

4　實驗驗證

Experimental verification

使用汞燈253、296、313和365 nm等4個特征波長對光譜儀進(jìn)行波長重復(fù)性驗證,，如圖7所示。測量時，汞燈放在入縫前，汞燈發(fā)出的光經(jīng)漫透射板之后進(jìn)入光譜儀，PC機(jī)發(fā)送控制指令驅(qū)動波長掃描機(jī)構(gòu)回零，根據(jù)計算的全程掃描步數(shù)，從零點(diǎn)掃描到絲杠指定行程處，探測器對出射狹縫的光進(jìn)行采集，可以得到在所掃描波段的能量分布情況。根據(jù)理論公式，將步進(jìn)電機(jī)的步數(shù)轉(zhuǎn)換為對應(yīng)波長數(shù)，一個掃描周期的測量結(jié)果如圖8所示。根據(jù)波長間隔，確定4個特征波長的位置，對于其他不顯著波長不進(jìn)行處理。

圖7　測量裝置及測量原理圖 Fig.7　Measurement equipment view and its measurement schematic diagram

圖8　一個掃描周期測量結(jié)果 Fig.8　Measurement result within one scanning period

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.

重復(fù)掃描5次，對每次掃描的4個峰值處數(shù)據(jù)進(jìn)行高斯擬合，確定各個特征波長測量的實際中心波長和半高寬。取同一特征波長處5次擬合中心波長與其平均值的偏差作為該特征波長處的波長重復(fù)性誤差，4個特征波長的重復(fù)性誤差統(tǒng)計結(jié)果如表1所示。

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.

表1　4個典型波長重復(fù)性誤差

根據(jù)測量結(jié)果，在4個特征波長處的重復(fù)性在-0.005～+0.007 nm之間，光譜分辨率優(yōu)于0.8 nm，滿足紫外雙光柵光譜儀波長重復(fù)性±0.02 nm和光譜分辨率1 nm的要求。該結(jié)果與光譜儀波長掃描機(jī)構(gòu)理論分析結(jié)果相符，說明光機(jī)參數(shù)轉(zhuǎn)換公式推導(dǎo)正確，機(jī)構(gòu)設(shè)計合理，誤差分析與實際機(jī)構(gòu)設(shè)計吻合。

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.

5　結(jié)　論

Conclusion

本文根據(jù)凹面光柵色散原理，對紫外雙光柵光譜儀的波長掃描機(jī)構(gòu)進(jìn)行了理論計算，針對結(jié)構(gòu)設(shè)計中對波長重復(fù)性精度有影響的誤差源進(jìn)行了分析，確定了絲杠重復(fù)定位誤差是影響波長重復(fù)性的主要誤差源，根據(jù)理論計算結(jié)果選擇高精度的絲杠機(jī)構(gòu)，并對波長掃描機(jī)構(gòu)進(jìn)行了改進(jìn)，完成了整機(jī)結(jié)構(gòu)設(shè)計。以汞燈為光源，選用其4個特征波長對波長重復(fù)性精度進(jìn)行了驗證，實驗結(jié)果表明，波長重復(fù)性滿足±0.02 nm的指標(biāo)要求，為后續(xù)波長線性標(biāo)定等工作提供了基礎(chǔ)。本文的波長掃描機(jī)構(gòu)設(shè)計和誤差分析方法對同類型光譜儀的設(shè)計具有參考價值。

In this paper, the wavelength scanning mechanism of the ultraviolet double grating spectrometer has been theoretically calculated according to the concave grating dispersion principle, the error sources affecting wavelength repeatability accuracy in the structure design have been analyzed, and the repeatability error of the lead screw has been determined to be the main error source. According to the theoretical calculation result, a high accuracy lead screw mechanism has been selected, the wavelength scanning mechanism has been improved, and the design of the whole spectrometer structure has been completed. Using a mercury lamp as the light source, the wavelength repeatability accuracy has been verified with 4 characteristic wavelengths of mercury lamp. The experiment result indicates that the wavelength repeatability meets the requirements of ±0.02 nm index, thereby providing a foundation for subsequent linear calibration of wavelength,etc. The wavelength scanning mechanism design and the error analysis method in this paper have a reference value for the design of like spectrometers.

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曹佃生(1987—)，男，山東日照人，博士，助理研究員，2007年于吉林大學(xué)獲得學(xué)士學(xué)位，2012年于中國科學(xué)院長春光學(xué)精密機(jī)械與物理研究所獲得博士學(xué)位，主要從事空間光學(xué)遙感儀器光機(jī)結(jié)構(gòu)設(shè)計方面的研究。E-mail:caodiansheng1987@163.comCAO Dian-sheng(1987—), male, born in Rizhao, Shandong, doctor, research assistant. He was received a B.S. degree from Jilin University in 2007 and a doctor′s degree from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, and is engaged mainly in the research on the optical-mechanical structure design of space optics remote sensing instruments. E-mail:caodiansheng1987@163.com

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—EI核心期刊(物理學(xué)類；無線電電子學(xué)、電信技術(shù)類)

《發(fā)光學(xué)報》是中國物理學(xué)會發(fā)光分會與中國科學(xué)院長春光學(xué)精密機(jī)械與物理研究所共同主辦的中國物理學(xué)會發(fā)光分會的學(xué)術(shù)會刊。 該刊是以發(fā)光學(xué)、 凝聚態(tài)物質(zhì)中的激發(fā)過程為專業(yè)方向的綜合性學(xué)術(shù)刊物。

《發(fā)光學(xué)報》于1980年創(chuàng)刊， 曾于1992年， 1996年， 2000年和2004年連續(xù)四次被《中文核心期刊要目總覽》評為“物理學(xué)類核心期刊”， 并于2000年同時被評為“無線電電子學(xué)、 電信技術(shù)類核心期刊”。2000年獲中國科學(xué)院優(yōu)秀期刊二等獎。 現(xiàn)已被《中國學(xué)術(shù)期刊(光盤版)》、 《中國期刊網(wǎng)》和“萬方數(shù)據(jù)資源系統(tǒng)”等列為源期刊。 英國《科學(xué)文摘》(SA)自1999年； 美國《化學(xué)文摘》(CA)和俄羅斯《文摘雜志》(AJ)自2000年； 美國《劍橋科學(xué)文摘社網(wǎng)站》自2002年； 日本《科技文獻(xiàn)速報》(CBST， JICST)自2003年已定期收錄檢索該刊論文； 2008年被荷蘭“Elsevier Bibliographic Databases”確定為源期刊; 2010年被美國“EI”確定為源期刊。2001年在國家科技部組織的“中國期刊方陣”的評定中， 《發(fā)光學(xué)報》被評為“雙效期刊”。2002年獲中國科學(xué)院2001～2002年度科學(xué)出版基金“擇重”資助。2004年被選入《中國知識資源總庫·中國科技精品庫》。本刊內(nèi)容豐富、 信息量大，主要反映本學(xué)科專業(yè)領(lǐng)域的科研和技術(shù)成就， 及時報道國內(nèi)外的學(xué)術(shù)動態(tài)， 開展學(xué)術(shù)討論和交流， 為提高我國該學(xué)科的學(xué)術(shù)水平服務(wù)。

《發(fā)光學(xué)報》自2011年改為月刊， A4開本， 144頁， 國內(nèi)外公開發(fā)行。 國內(nèi)定價： 40元， 全年480元， 全國各地郵局均可訂閱。 《發(fā)光學(xué)報》歡迎廣大作者、 讀者廣為利用， 踴躍投稿。

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