小型掠入射式近邊X射線吸收譜儀的設(shè)計

陳晨曦陽，金春水，王　君，謝　耀

(1.中國科學(xué)院 長春光學(xué)精密機械與物理研究所 應(yīng)用光學(xué)國家重點實驗室，吉林 長春 130033；2.中國科學(xué)院大學(xué)， 北京 100049)

1　引　言

Introduction

近邊X射線吸收精細結(jié)構(gòu)(Near Edge X-ray Absorption Fine Structure，NEXAFS)光譜是由吸收原子的內(nèi)層電子吸收光子躍遷到外層的空軌道產(chǎn)生的[1]，反映了吸收原子與周圍原子間的相互作用，因此通過分析近邊結(jié)構(gòu)可以獲得吸收原子的電子結(jié)構(gòu)和近鄰幾何結(jié)構(gòu)信息。與電子能量損失譜(EELS)和X射線拉曼散射(XRS)等方法相比[2]，NEXAFS技術(shù)不易造成輻射損傷，對樣品的物理狀態(tài)沒有要求，適用范圍廣泛。起初，這項技術(shù)僅僅用于研究小分子，隨著理論和實驗技術(shù)的發(fā)展，如今，它已經(jīng)廣泛應(yīng)用于各種復(fù)雜大分子的研究，例如有機高分子材料[3-4]，土壤、大氣中的天然有機物[5-6]，甚至是水環(huán)境中的生物分子[7]。

Near Edge X-ray Absorption Fine Structure(NEXAFS) spectrum is produced due to transition of the inner electrons of absorbing atoms to the outer unoccupied molecular orbital by absorbing photons[1]and reflects the interaction of absorbing atoms with ambient atoms, so the information on the electron structure and adjacent geometric structure of absorbing atoms can be obtained through analyzing the near edge structure. In comparison with the methods such as electron energy loss spectroscopy(EELS), X-ray Raman Scattering(XRS),etc.[2], the NEXAFS technology doesn′t result in radiation damage easily and has no requirements for the physical state of samples, so it has a wide range of application. At first, this technology was only used to study small molecules. With the development of theories and experimental technologies, it has now been extensively applied in the study of various complex macromolecules,e.g. organic polymer materials[3-4], natural organic substances in soils and atmosphere[5-6], and even biomolecules in water environment[7].

目前，國內(nèi)外大多數(shù)NEXAFS實驗都是在同步輻射線上進行的，然而同步輻射裝置機時非常有限，且建造運營成本極高，短期內(nèi)難以滿足大量NEXAFS科研需求。因此，研究基于小型X射線源的實驗裝置具有重要研究意義和實用價值。近年來，國內(nèi)外的研究人員已經(jīng)基于激光等離子體光源開展了許多相關(guān)工作。Osamu Yoda等人[8]利用超環(huán)面鏡收集X射線、平場光柵和彎晶分別對低能和高能光子分光，微通道檢波器二極管陣列系統(tǒng)作為探測器，設(shè)計了一套工作在100～3 000 eV的吸收譜儀；Hidetoshi Nakano等人[9]使用了兩個凹面鏡將X射線聚焦到樣品上，用平場光柵分光，再由微通道檢波器和CCD接收，在12 nm處分辨率(λ/Δλ)250；U Vogt等人[10]利用透射光柵和CCD搭建了一臺用于水窗波段的實驗裝置，成功獲得了β胡蘿卜素的近邊吸收譜，但是這套裝置在4.4 nm處的分辨率只有300，不足以區(qū)分有機物吸收譜的所有典型峰，后來他們用離軸反射波帶片取代了透射光柵[11]，分辨率提高了一倍，獲得的聚酰亞胺和PET(poly ethylene terephthalate)薄膜的近邊吸收譜均與同步輻射上的實驗結(jié)果相當(dāng)；Christian Peth等人[12]研制的吸收譜儀以消像差的平場光柵作為分光器，背照射式CCD作為探測器，在2.87 nm處分辨率200，他們使用這套設(shè)備研究了高分子材料、生物樣品以及土壤提取物的NEXAFS譜[12,7,13]。

At present, most domestic and foreign NEXAFS experiments are conducted on synchrotron radiation lines, but the machine-hour of synchrotron radiation facilities is very limited. Their construction and operation cost is extremely high, and they are difficult to meet the needs of plentiful NEXAFS scientific studies in short term. Hence, the research on the experimental equipment based small X-ray sources has vital research significance and practical value. In recent years, domestic and foreign researchers have carried out a lot of relevant work based on a laser plasma source. Osamu Yodaetal.[8]designed a set of absorption spectroscopy apparatus working at 100-3 000 eV using toroidal mirrors to collect X-rays, using flat-field gratings and bent crystals to carry out light splitting of low energy and high energy photons respectively and using a micro-channel detector diode array system as a detector. Hidetoshi Nakanoetal.[9]used two concave mirrors to focus X-rays onto samples, flat-field gratings to carry out light splitting, and used micro-channel detectors and CCD to receive information, with the resolution at 12 nm being(λ/Δλ)250. U Vogtetal.[10]erected a set of experimental equipment in the water window using transmission gratings and CCD; with the equipment, they successfully obtained the near edge absorption spectrum of β carotene, but the resolution of the equipment was only 300 at 4.4 nm and it was not enough to differentiate all typical peaks of the absorption spectrum of organic substances. Afterwards, they replaced transmission gratings with off-axis reflection zone plates[11], the resolution of the equipment was increased by 100%, and the obtained near edge absorption spectrum of both polyimide and poly ethylene terephthalate(PET) film was equivalent with the experimental result from synchrotron radiation. Christian Pethetal.[12]developed an absorption spectrometer using an aberration-reduced flat-field grating as the light splitter and back-illuminated CCD as the detector. The resolution of the spectrometer is 200 at 2.87 nm; they studied the NEXAFS spectrum[12,7,13]of high polymer materials, biological samples and soil extracts using the spectrometer.

現(xiàn)有的小型NEXAFS光譜儀的研究主要采用透射式光路，這種結(jié)構(gòu)只能得到體相信息，為了獲得高信噪比的譜線，被測樣品一般為無支撐的薄膜結(jié)構(gòu)，且厚度需嚴格控制，通常為100～200 nm，制備困難。而另一種掠入射式光路則對樣品厚度沒有要求，因為只有表面很薄的分子層產(chǎn)生吸收，反射光較強，信噪比高，能適應(yīng)較弱光源；同時還具有很強的表面敏感性，可以用于表面分子變化的研究。近年來，具有特殊光電性質(zhì)的有機材料[14-16]的研究越來越多，本文基于掠入射光路，利用小型的氣體激光等離子體X射線光源，設(shè)計了一臺用于研究有機材料碳1s NEXAFS譜的近邊X射線吸收譜儀，并對譜儀的分辨率等指標(biāo)以及元件的裝配公差進行了分析。

A transmissive light path is mainly used in the study of the existing compact NEXAFS spectrometers, but with this structure, only bulk phase information can be obtained. In order to obtain high SNR spectral lines, the tested sample is generally an unsupported membrane structure, and its thickness needs to be strictly controlled and tends to be 100-200 nm, so its preparation is difficult. Another grazing incidence light path has no requirement for sample thickness. This is because only the very thin surface molecular layer has an absorption. The reflected lights is strong with high SNR, and the grazing incidence light path is suitable for weak light sources. In addition, it also has a very strong surface sensitivity and can be used in the study of surface molecule variation. In recent years, there are more and more studies of organic materials[14-16]with special photoelectric properties. A design of a compact near edge X-ray absorption spectrometer under grazing incidence conditions to study the NEXAFS spectrum of organic material carbon(1s) is presented, based on a grazing incidence light path, using a small laser-produced plasma source. In addition, the resolution of the spectrometer and the fitting allowance of components have been analyzed.

2　X射線吸收譜儀設(shè)計

Design of the X-ray absorption spectrometer

碳的近邊吸收精細結(jié)構(gòu)在280～320 eV的能量范圍內(nèi)，對應(yīng)波長范圍為3.8～4.4 nm，為了研究碳的譜線，要求譜儀在3～5 nm波段工作。碳的內(nèi)層電子從1s軌道躍遷到外層的未占分子軌道引起的吸收峰的典型能量寬度為0.5 eV[11]，為了能準(zhǔn)確反映碳的1s NEXAFS譜的特征，譜儀在4.4 nm處的分辨率須在600以上。本文據(jù)此要求展開設(shè)計。

The corresponding wavelength range of the near edge absorption fine structure of carbon is 3.8-4.4 nm within the energy range of 280-320 eV. In order to study the spectrum of carbon, the spectrometer is required to work at 3-5 nm. The typical energy width of the absorption peak caused by the transition of the inner electrons of carbon from 1s orbital to the outer unoccupied molecular orbital is 0.5 eV[11]. In order to accurately reflect the features of the NEXAFS spectrum of carbon(1s), the resolution of the spectrometer shall be over 600 at 4.4 nm. In this paper, the spectrometer has been designed based on above requirements.

2.1　譜儀結(jié)構(gòu)設(shè)計

Spectrometerstructuredesign

本文采用攝譜法設(shè)計近邊X射線吸收譜儀，光源產(chǎn)生的“白光”先經(jīng)過樣品再分光，然后利用一維或二維探測器測定通過樣品前后的所有波長光的強度，從而獲得吸收譜，它能同時獲得所有波長光的強度，無需掃描，還可以做瞬態(tài)光譜分析。

The near edge X-ray absorption spectrometer has been designed using the spectrography in this paper. The “white lights” generated by the light source pass through the sample and then are split. Later on, the intensity of lights with all wavelengths before and after passing through the sample is measured with a 1D or 2D detector so as to obtain the absorption spectrum. With the spectrometer, the intensity of lights with all wavelengths can be obtained simultaneously without scanning, and a transient spectrum analysis can also be made.

設(shè)計的掠入射式近邊X射線吸收譜儀結(jié)構(gòu)示意圖如圖1所示，系統(tǒng)由氣體激光等離子體光源、樣品、狹縫、光柵和CCD組成。光源以氪氣作為靶材，經(jīng)過濾光產(chǎn)生波長2～6 nm的連續(xù)譜軟X射線，掠入射到樣品表面，反射光經(jīng)光柵分光，再由CCD測定各波長射線的強度，結(jié)合光源的譜線即可得到包含了吸收信息的反射譜。

The sketch of the structure of the designed near edge X-ray absorption spectrometer under grazing incidence conditions is shown in Fig.1. The system consists of gas laser plasma source, sample, slit, grating and CCD(camera). Krypton is used as the target light source. 2-6 nm continuous spectral soft X-rays are generated through filtering and they are of grazing incidence to the sample surface. The reflected lights are split by the grating, and then the intensity of rays with various wavelengths is measured using the CCD(camera). The reflectance spectrum containing absorption information can be obtained according to the spectral line of the light source.

圖1　掠入射式X射線吸收譜儀示意圖 Fig.1　Sketch of the designed X-ray absorption spectrometer under grazing incidence conditions

菲涅耳公式給出了反射率與折射率間的關(guān)系，由于存在吸收，物質(zhì)對X射線的折射率不再是實數(shù)，而是與吸收有關(guān)的復(fù)數(shù)形式n=1-δ-iβ，其中1-δ表示色散，β表示吸收，由β可以直接得到線吸收系數(shù)μ=4πβ/λ，因此反射率同樣包含吸收信息。將復(fù)折射率代入菲涅耳公式，可分別得到掠入射時p偏振和s偏振的X射線反射率，圖2為δ=0.001時不同吸收下反射率隨入射角的變化曲線，比較不同偏振光的反射率可知，無論吸收強弱，兩種偏振光反射率近似相等，因此，總反射率可以用s偏振光的反射率近似表示:

Fresnel formula gives the relationship between reflectivity and refractive index. Due to existence of absorption, the refractive index of substances to X-ray is not a real number but a complex number related to absorption,i.e.n=1-δ-iβ, where 1-δdenotes dispersion andβdenotes absorption. The linear absorption coefficient can be directly obtained fromβ,i.e.μ=4πβ/λ. Therefore, reflectivity also contains absorption information. Substitute complex refractive index into Fresnel formula to obtain p-polarized X-ray reflectivity and s-polarized X-ray reflectivity under grazing incidence conditions respectively. Fig.2 is the curve of variation of reflectivity with incidence angle at different absorption intensity in case ofδ=0.001. According to the comparison of reflectivity of different polarized lights, in spite of absorption intensity, the reflectivity of two polarized lights is approximately equal, so the total reflectivity can be expressed approximately in the reflectivity of s-polarized light.

(1)

式中，φ是掠入射角，可以看出，反射率R(E)是δ(E)和β(E)的函數(shù)，E為光子能量，利用公式(1)結(jié)合數(shù)據(jù)庫CXRO[17]中得到的δ(E)可以從測得的反射率譜線中提取出NEXAFS譜。

Whereφis grazing incidence angle. It can be seen that reflectivityR(E) is the function ofδ(E) andβ(E), where E is photon energy. NEXAFS spectrum can be extracted from the measured reflectivity spectral line using formula (1) in combination withδ(E) obtained from the database CXRO[17].

從圖2可以看出，反射率總是隨掠入射角的增大而減小，當(dāng)掠入射角增大到臨界角φc，低吸收的反射率迅速下降，這個角即為全反射臨界角。為了使反射率譜線能清晰反映吸收的變化，譜儀的掠入射角需小于樣品的全反射臨界角，考慮到有機物在碳的吸收邊4.4 nm附近的全反射臨界角約為3°，因此本文設(shè)計的譜儀取2°掠入射。

As shown in Fig.2, reflectivity always decreases as grazing incidence angle increases. When grazing incidence angle increases to the critical angleφc, the reflectivity at low absorption intensity decreases rapidly. This angle is a critical angle of total reflection. In order that the reflectivity spectral line can clearly reflect absorption variation, the grazing incidence angle of the spectrometer would be less than the sample′s critical angle of total reflection. In view of the fact that the critical angle of total reflection of organic substances is about 3° near the carbon's absorption edge of 4.4 nm, the grazing incidence angle of the spectrometer designed in this paper is taken as 2°.

圖2　反射率隨掠入射角的變化 Fig.2　Reflectivity as a function of grazing incidence angle

2.2　光柵選型

Gratingselection

分光元件對譜儀的性能具有決定性作用。普通的平面光柵分辨能力較差，無法滿足X射線波段的高分辨率要求，如果增加聚焦鏡，會降低系統(tǒng)的光能利用率。常規(guī)的凹面等間距光柵具有分光和聚焦作用，但為使像差最小必須采用羅蘭圓結(jié)構(gòu)，不能用平面探測器采集。因此，本文使用矯正像差的全息變柵距凹球面光柵，既能同時實現(xiàn)分光和聚焦，又具有平場特性，便于使用面陣型CCD接收。變柵距凹面光柵的原理示意圖如圖3所示，其中x軸為光柵中心法線方向，y軸為光柵中心切線方向，α為入射角，β為衍射角，r為入射臂長，r′為出射臂長。

The light splitting element plays a decisive role in the performance of the spectrometer. The resolution capability of an ordinary plane grating is poor and cannot meet the high resolution requirements of X-ray wavelengths. In case of adding focusing mirrors, the system′s efficiency of light energy utilization will be reduced. The conventional concave evenly-spaced grating has functions such as light splitting and focusing, but to minimize aberration, Rowland circle structure must be adopted, and a plane detector cannot be used in acquisition. Therefore, the aberration-corrected holographic varied line-space concave spherical grating is used in this paper, which can achieve both light splitting and focusing and also has flat field characteristics, for convenience of using the area array type CCD to receive

information. The schematic diagram of the aberration corrected flat-field grating is shown in Fig.3, wherexaxis is the central normal direction of the grating,yaxis is the central tangent direction of the grating,αis incidence angle,βis diffraction angle,ris incidence arm length, andr′ is emergence arm length.

圖3　變柵距凹面光柵原理圖 Fig.3　Schematic diagram of the aberration corrected flat-field grating

利用費馬原理[18]可以得到光柵色散方程和色散方向的聚焦方程分別為:

Based on Fermat principle[18], the obtained grating′s dispersion equation and focusing equation in dispersion direction are respectively as follows:

d0(sinα+sinβ)=mλ,

(2)

(3)

式中，d0為光柵中心的刻線寬度，也稱為公稱線寬，R為光柵基底的曲率半徑，b2為光柵線密度參數(shù)，選擇合適的值可以使光柵聚焦面近似為一平面。

Whered0is the scale line width of grating center, also called nominal line width;Ris the radius of curvature of grating substrate;b2is the linear density parameter of grating. By selecting appropriate values, the focusing surface of the grating can be approximately a plane.

本文選取Shimadzu的30-001型光柵，該光柵公稱線密度n02 400線/mm，工作波長范圍1～6 nm，入射臂長237 mm，入射角88.65°。 圖4給出了該光柵不同入射角對應(yīng)的聚焦曲線，坐標(biāo)系定義與圖3中一致，光柵參數(shù)來自于文獻[19]。 可以看出，入射角88.65°時，光柵中心到探測面距離D0為235 mm。不同入射角的聚焦曲線不同，但是都可以擬合成直線，因此可以根據(jù)需要改變光柵的使用結(jié)構(gòu)參數(shù)。

Shimadzu 30-001 grating is selected. The parameters of the grating are the following: nominal linear densityn0is 2 400 lines/mm; wavelength range is 1-6 nm; incidence arm length is 237 nm, and incidence angle is 88.65°. Fig.4 shows the focusing curves at different incidence angles, where the coordinate system definition is in line with that in Fig.3, and grating parameters come from the reference [19]. As shown in Fig.4, when the incidence angle is 88.65°, the distanceD0from the grating center to the detection surface is 235 mm. Focusing curves at different incidence angles are different, but all of them can be fitted into straight lines, so the structure parameters of the grating can be changed as needed.

圖4　不同入射角對應(yīng)的聚焦曲線，紅線表示聚焦曲線，黑色虛線表示其擬合直線，綠線表示不同波長 Fig.4　Focusing curves and fitting straight lines at different incidence angles. The red lines represent the focus curves, the black dashed lines are straight fitting lines and the green lines are different wavelengths

2.3　裝配方案優(yōu)化

Assemblyschemeoptimization

光柵常規(guī)的裝配方案是CCD平面與光柵中心的切平面垂直，如圖5(a)所示，這樣的方案在實際使用中存在很大的困難，一方面，入射角的精度要求太高，需要借助高精度的調(diào)整機構(gòu)和測量裝置反復(fù)調(diào)試來保證；另一方面，CCD與光柵聯(lián)系緊密，調(diào)整光柵姿態(tài)時，CCD也必須相應(yīng)調(diào)整，提高了調(diào)整的難度。

The conventional grating assembly scheme is that the CCD plane is vertical to the tangent plane of the grating center, as shown in Fig.5. Such scheme is very difficult in an actual application. On one hand, there are too high requirements for the incidence angle precision, and it can be guaranteed with the aid of a high precision adjusting mechanism and measuring device. On the other hand, CCD is closely linked with the grating. When the grating attitude is adjusted, CCD must be adjusted accordingly, thereby increasing the adjustment difficulty.

圖5　光柵的不同使用結(jié)構(gòu) Fig.5　Structures of the grating (a)the conventional scheme, (b)the optimized scheme

為了可以分開獨立調(diào)整光柵和CCD，我們以CCD平面與入射光線方向垂直作為目標(biāo)對裝配結(jié)構(gòu)進行優(yōu)化，如圖5(b)所示，這樣得到的方案下，CCD的傾角不再依賴光柵，從而可以先安裝調(diào)整好CCD再調(diào)節(jié)光柵，在真空中只需要轉(zhuǎn)動光柵，使特定波長的譜線的像最窄，就可以獲得較高的安裝精度。入射角α取88.6°進行設(shè)計，利用公式(2)和公式(3)，以聚焦曲線的擬合直線與入射光線方向垂直為目標(biāo)，獲得了對應(yīng)的最佳入射臂長r和光柵中心到CCD探測面的距離D，結(jié)果見表1。這樣在安裝時就只有光柵需要在真空中調(diào)整，同時也降低了入射角的調(diào)整難度。

In order that the grating and CCD can be adjusted separately, the assembly structure has been optimized by aiming at making the CCD plane be vertical to the incident ray direction, as shown in Fig.5(b). In such scheme obtained, the dip angle of the CCD doesn't rely on the grating any longer, so that the CCD can be firstly installed and adjusted well and then the grating is adjusted. High installation precision can be obtained by only turning the grating in vacuum to make the image of the spectral line of the specific wavelength be the narrowest. The incidence angleαis taken as 88.6° in the design. Using formulas (2) and (3) and aiming at making the fitting straight line of the focusing curve vertical to the incident ray direction, the corresponding optimum incidence arm lengthrand distance D from the grating center to the CCD detection surface have been obtained. The result is shown in Tab.1. Thus, only the grating needs to be adjusted in vacuum during installation, which also reduces the difficulty in incidence angle adjustment.

表1　優(yōu)化的裝配方案參數(shù)

3　分辨率

Resolution

分辨率是光譜類儀器的重要指標(biāo)。本文設(shè)計的譜儀的分辨率主要受入射狹縫的寬度S1、光柵的衍射極限和像差、CCD像元尺寸S2等多項因素的影響，狹縫寬度和光柵性能決定了單色波長譜線的半高寬，像元尺寸則限制了譜儀的極限分辨率。

Resolution is an important index of an optical spectrum instrument. The resolution of the spectrometer designed in this paper is affected mainly by multiple factors such as entrance slit widthS1, grating′s diffraction limit and aberration, CCD pixel sizeS2,etc. Slit width and grating performance decide the FWHM of monochromatic wavelength spectral line, and pixel size limits the limiting resolution of the spectrometer.

由光柵方程結(jié)合幾何關(guān)系可得，光柵在探測面上的線色散為:

According to the grating equation coupled with the geometrical relationship, the linear dispersion of the grating on the detection surface can be obtained as follows:

(4)

若已知某波長的光譜像的半高寬FWHM，則可以得到該波長的線寬為:

If the FWHM of the spectral image at a wavelength is known, the line width of this wavelength can be obtained as follows:

(5)

利用光線追跡[20]可以獲取特定波長的譜線在探測面上的光譜像，從而綜合分析入射狹縫寬度和光柵性能的影響。狹縫寬度設(shè)為100 μm，入射臂長為270 mm，入射角為88.6°，光譜探測面放置在D=234 mm處，令光線在入射范圍內(nèi)隨機生成，可以模擬獲得探測面上的點列圖。通過統(tǒng)計寬度方向上各個像素內(nèi)的光線數(shù)量，得到光強統(tǒng)計分布圖，對光強分布進行高斯擬合，求出半高寬，即可利用公式(5)計算線寬。圖6為4.4 nm波長的譜線光線追跡獲得的點列圖、統(tǒng)計直方圖以及高斯擬合曲線，半高寬FWHM即像的寬度為13.8 μm，對應(yīng)線寬為0.003 5 nm。圖中橫坐標(biāo)表示譜線的像到入射光線的距離，對應(yīng)于圖5(b)中的長度l。

The spectral image of the spectral line at a specific wavelength on the detection surface can be obtained using the ray tracing method[20], thus comprehensively analyzing the influence of entrance slit and grating performance. The spot diagram on the detection surface can be obtained on the assumption that the slit width is 100 μm, the incidence arm length is 270 nm, the incidence angle is 88.6°, the spectral detection surface is placed atD=234 mm and rays are generated randomly within the incidence range. The statistical distribution chart of light intensity is obtained from the statistical analysis of rays of each pixel in the width direction. The FWHM is calculated through Gaussian fitting of the light intensity distribution, and then the line width can be calculated using formula (5). Fig.6 shows the spot diagram, histogram and Gauss fitting curve obtained using ray tracing at 4.4 nm. The FWHM i.e. image width is 13.8 μm, and the corresponding line width is 0.003 5 nm. In the figure, the abscissa denotes the distance from the spectral line image to the incident ray, which is corresponding with the lengthlin Fig.5(b).

圖6　4.4 nm波長的光線追跡結(jié)果 Fig.6　The result of ray tracing at 4.4 nm (a)Spot diagram, (b)Histogram, (c)Gauss fitting curve

受探測器像元尺寸的限制，光譜儀的分辨率往往不能直接由譜線線寬決定。根據(jù)奈奎斯特抽樣定理，為了能真實反映信號特征，采樣頻率應(yīng)大于信號頻率的兩倍，由公式(4)可以得到單個像元對應(yīng)的譜線線寬ΔλS2，則譜儀極限分辨率為Remax=λ/2ΔλS2。像元寬度為13 μm，4.4 nm的半高寬小于像元尺寸的兩倍，因此設(shè)計的譜儀可以實現(xiàn)極限分辨率，4.4 nm處分辨率為666，對應(yīng)線寬0.006 6 nm。使用像元數(shù)1 024的CCD，譜儀工作范圍超過3 nm，滿足設(shè)計要求。

Limited by the pixel size of the detector, the resolution of the spectrometer cannot be determined directly by the spectral line width in general. According to Nyquist sampling theorem, the sampling frequency would be larger than twice of the signal frequency in order to truly reflect signal features. According to formula (4), the spectral line width corresponding with a single pixel can be obtained, and then the limiting resolution of the spectrometer isRemax=λ/2ΔλS2. The pixel width is 13 μm, and the FWHM of 4.4 nm is less than twice of the pixel size, so the designed spectrometer can achieve the limiting resolution, its resolution is 666 at 4.4 nm, and the corresponding line width is 0.006 6 nm. The CCD with 1 024 pixels is used and the wavelength range of the spectrometer is over 3 nm, which meets the requirements of the design.

基于以上分析，本文設(shè)計的掠入射式近邊X射線吸收譜儀的參數(shù)如表2所示。

表2　掠入射式近邊X射線吸收譜儀設(shè)計參數(shù)

According to the above analysis, the parameters of the near-edge X-ray absorption spectrometer under grazing incidence conditions designed in this paper are shown in Tab.2.

4　公差分析及裝調(diào)方案設(shè)計

Tolerance analysis and assembly scheme design

根據(jù)前文的分析，為了使譜儀實現(xiàn)極限分辨率，譜線的半高寬應(yīng)小于兩個像元的尺寸，即26 μm，而半高寬主要取決于入射狹縫、光柵和CCD之間的相對位置。圖7給出了各參數(shù)的偏差對4.4 nm波長的半高寬的影響，可以看出，入射臂長r的誤差δr對半高寬的影響幾乎可以忽略，D、θ和α的偏差主要表現(xiàn)為向系統(tǒng)引入離焦像差，而半高寬對入射角α的變化最為敏感。綜合考慮各參數(shù)的作用，結(jié)合機械結(jié)構(gòu)的調(diào)整能力，確定r、D、θ、α的公差分別為±1 mm、±0.1 mm、±0.5°、±0.04°，譜線在極限誤差下的半高寬為24.8 μm，滿足設(shè)計要求。

圖7　各參數(shù)(r、D、θ、α)的誤差對4.4 nm單色譜線的半高寬的影響 Fig.7　Influence of the error of each parameter on the FWHM at 4.4 nm (a)r, (b)D, (c)θ, (d)α

According to the previous analysis, in order to achieve the limiting resolution of the spectrometer, the FWHM of spectra line would be less than the size of two pixels,i.e. 26 μm. The FWHM depends mainly on the relative position among the entrance slit, grating and CCD. Fig.7 shows the influence of the error of each parameter on the FWHM at 4.4 nm. As shown in the figure, the influence of the errorδrof the incidence arm lengthron the FWHM can be neglected, the error ofD,θandαis manifested mainly as the defocus aberration introduced to the system, and the FWHM is the most sensitive to the variation of the incidence angleα. Comprehensively considering the role of each parameter in combination with the adjusting capacity of the mechanical structure, the tolerance ofr,D,θandαis determined to be ±1 mm, ±0.1 mm, ±0.5° and ±0.04° respectively, and the FWHM of spectral line at the limiting error is 24.8 μm, which meets the requirements of the design.

公差分析結(jié)果表明，在本文優(yōu)化的方案下，r、D和θ可以在大氣環(huán)境中使用常規(guī)方法測量并調(diào)整到位，在真空環(huán)境中利用高精度電動轉(zhuǎn)臺連續(xù)改變α，使氮氣等離子體發(fā)出的2.878 7 nm譜線的半高寬最小，從而可以滿足入射角的高精度要求。

According to the tolerance analysis result, using the optimized scheme in this paper,r,Dandθcan be measured in atmospheric environment with a conventional method and well adjusted. In addition,αis changed continuously in vacuum environment using a high precision electric rotary table so as to minimize the FWHM of the 2.878 7 nm spectral line emitted by nitrogen plasma, which can thus meet the high precision requirements of incidence angle.

5　分辨率測試與波長標(biāo)定

Resolution test and wavelength calibration

圖8展示了搭建完成的小型掠入射式近邊X射線吸收譜儀。光譜儀工作在10-4Pa真空環(huán)境下。沿著光路方向(在圖中標(biāo)注光源、各個腔體)，3個真空腔體分別為光源室、樣品室和光柵室，激光聚焦到噴出的氣體團上形成等離子體，產(chǎn)生X射線輻射輸出，經(jīng)Ti膜后照射到樣品表面，Ti膜用于過濾帶外光。為了結(jié)構(gòu)緊湊，入射狹縫安置在樣品室中，CCD通過波紋管與光柵室相連，以便通過調(diào)整機構(gòu)微調(diào)CCD位置。

Fig.8 shows the well-erected compact near edge X-ray absorption spectrometer under grazing incidence conditions. The spectrometer works in 10-4Pa vacuum environment. Along the light path direction(light source and each chamber marked in the figure), the three vacuum chambers are light source chamber, sample chamber and grating chamber respectively. Laser is focused onto the ejected gas clumps to form plasma and generate X-ray radiation output. After passing through the Ti membrane, rays shine on the sample surface. The Ti membrane is used to filter out-of-band lights. In order to achieve a compact structure, the entrance slit is placed in the sample chamber, and the CCD is connected with the grating chamber via the corrugated pipe, for convenience of micro-adjusting the CCD position through the adjusting mechanism.

圖8　光譜儀實物圖 Fig.8　Picture of the spectrometer

氮氣作為激光等離子體光源靶材對光譜儀分辨率進行測試，圖9為實驗測得的光譜圖。可以看出，氮氣在2～5 nm波段的譜線均清晰可見，波長2.478 nm和2.49 nm兩條譜線也能明顯區(qū)分。對這兩個光譜峰進行高斯擬合得到曲線C1和C2，曲線C1的半高寬FWHM為1.9，不足兩個像元，表明搭建的光譜儀可實現(xiàn)極限分辨，滿足設(shè)計指標(biāo)。

圖9　氮氣等離子體譜線 Fig.9　Spectrum of N2 plasma

The resolution of the spectrometer has been tested using nitrogen as the laser plasma source target. Fig.9 shows the spectrogram obtained from the test. It can be seen that the spectral lines of nitrogen at 2-5 nm are clearly visible and the two spectral lines at 2.478 nm and 2.49 nm can also be identified obviously. The curves C1 and C2 are obtained from Gauss fitting of the two spectral peaks. The HWHM of curve C1 is 1.9 that is less than two pixels, indicating that the erected spectrometer can achieve the limiting resolution and the design index.

采用參數(shù)擬合法[19]進行波長標(biāo)定，模型如式(6)所示:

Wavelength calibration is performed using the parameter fitting method[19]. The model is shown in formula (6).

(6)

式中，各參數(shù)的定義參考圖5(b)，N為CCD像素的位置，上邊緣對應(yīng)N為0的位置，n0表示光柵的公稱線密度。表3給出了像素位置對應(yīng)的實際波長和標(biāo)定波長，結(jié)果顯示波長標(biāo)定的誤差小于0.001 nm，光譜儀實際工作波長范圍2～5 nm。

Refer to Fig.5(b) for the definition of each parameter in the above formula. N is the position of CCD pixel, the upper edge is the position atN=0, andn0denotes the nominal linear density of the grating. Tab.3 shows the actual wavelength and calibration wavelength at pixel positions. The results show that the wavelength calibration error is less than 0.001 nm and the actual wavelength range of the spectrometer is 2-5 nm.

表3　波長標(biāo)定結(jié)果

利用參數(shù)擬合法標(biāo)定波長可以反求出系統(tǒng)各參數(shù)的實際值，并與理論設(shè)計值進行比較，結(jié)果如表4所示，可見各參數(shù)的實際值與設(shè)計值基本吻合，偏差均滿足公差分配要求。

The actual value of each parameter of the system can be calculated through wavelength calibration with the parameter fitting method. The actual value is compared with the theoretical design value. The result is shown in Tab.4. As shown in the table, the actual value of each parameter is basically consistent with the design value, and all deviations meet the tolerance distribution requirements.

表4　光學(xué)系統(tǒng)參數(shù)設(shè)計值與實際值比較

6　結(jié)　論

Conclusion

采用激光等離子體光源、球面變柵距光柵和面型CCD設(shè)計了一臺用于研究有機物的碳1s NEXAFS譜掠入射式近邊X射線吸收譜儀，掠入射角取2°。為了方便調(diào)節(jié)光學(xué)元件的相對位置和姿態(tài)，以探測面與入射光線垂直為目標(biāo)對安裝參數(shù)進行了優(yōu)化，得到了光柵入射角88.6°時的安裝方案，入射臂長270 mm，光柵中心到CCD探測面垂直距離234.0 mm。利用光線追跡的方法模擬了譜儀的光譜，縫寬100 μm時光譜儀在4.4 nm處的分辨率達到666，可以滿足研究碳1s NEXAFS譜的要求。分析了各裝配參數(shù)的誤差對4.4 nm處分辨率的影響，確定了r、D、θ、α的公差分別為±1 mm、±0.1 mm、±0.5°、±0.04°，據(jù)此設(shè)計了譜儀的裝調(diào)方案。最后通過測量氮氣等離子體光譜，對光譜儀性能進行了測試，結(jié)果顯示，譜儀各項性能滿足設(shè)計要求。

In order to study the NEXAFS spectrum of the organic material carbon(1s), we design a near edge X-ray absorption spectrometer under grazing incidence conditions using a laser-produced plasma source, an aberration corrected flat-field grating and a planar CCD. The grazing incidence angle of the spectrometer is taken as 2°. In order to conveniently adjust the relative position and attitude of optical elements, the installation parameters have been optimized aiming at making the detection surface vertical to the incident ray direction. The optimized installation scheme where the incidence angle of the grating is 88.6° has been obtained. The incidence arm length is 270 mm, and the vertical distance from the grating center to the CCD detection surface is 234.0 mm. Using the ray tracing method, the spectrum of the spectrometer has been simulated. When the slit width is 100 μm, the resolution of the spectrometer reaches 666 at 4.4 nm, which can meet the requirements of research on the NEXAFS spectrum of carbon(1s). The influence of the error of each assembly parameter on the resolution at 4.4 nm has been analyzed, and the tolerance ofr,D,θandαhas been determined to be ±1 mm, ±0.1 mm, ±0.5° and ±0.04°, respectively. Based on above parametors, the assembly scheme of the spectrometer has been designed. Finally the performance of the spectrometer has been tested by measuring nitrogen plasma spectrum. The results show that all performance indexes of the spectrometer meet the design requirements.

參考文獻：

[1]馬禮敦.X射線吸收光譜及發(fā)展[J].上海計量測試,2007,34(6):2-11.

MA L D. X-ray absorption Spectroscopy and its developments[J].ShanghaiMeasurement&Testing,2007,34(6):2-11.(in Chinese)

[2]GROOT D. XANES spectra of transition metal compounds[J].JournalofPhysics:ConferenceSeries,2009,190(1):111-116.

[3]WEISS K,WOELL C,JOHANNSAMANN D. Near-surface molecular orientation in polymeric alignment layers:a NEXAFS investigation[J].ProceedingsofSPIE,1999,3800:104-111.

[4]潘宵.聚合物光電器件中金屬/聚合物界面結(jié)構(gòu)與性質(zhì)的研究[D].合肥:中國科學(xué)技術(shù)大學(xué),2015.

PAN X. The structures and properties of metal/polymer interfaces in polymer-based photoelectronic devices[D]. Hefei:University of Science and Technology of China,2015.(in Chinese)

[5]李輝,高強,王帥,等.同步輻射軟X射線近邊吸收譜方法研究長期施肥對黑土有機氮官能團的影響[J].光譜學(xué)與光譜分析,2015(7):2038-2042.

LI H,GAO Q,WANG SH,etal.. Effect of long-term fertilization on organic nitrogen functional groups on black soil as revealed by synchrotron-based X-ray absorption near-edge structure spectroscopy[J].SpectroscopyandSpectralAnalysis,2015(7):2038-2042.(in Chinese)

[6]BRAUN A. Carbon speciation in airborne particulate matter with C(1s) NEXAFS spectroscopy[J].JournalofEnvironmentalMonitoringJem,2005,7(11):1059-65.

[7]NOV KOV E,MITREA G,PETH C,etal.. Solid supported multicomponent lipid membranes studied by x-ray spectromicroscopy[J].Biointerphases,2008,3(2):FB44-FB54.

[8]YODA O,MIYASHITA A,MURAKAMI K,etal.. Time-resolved X-ray absorption spectroscopy apparatus using laser plasma as an X-ray source[J].ProceedingsofSPIE,1991,1503:463-466.

[9]NAKANO H,GOTO Y,LU P,etal.. Time-resolved soft X-ray absorption spectroscopy of silicon using femtosecond laser plasma X-rays[J].AppliedPhysicsLetters,1999,75(16):2350-2352.

[10]BECK M,VOGT U,WILL I,etal.. A pulse-train laser driven XUV source for picosecond pump probe experiments in the water window[J].OpticsCommunications,2001,190(1-6):317-326.

[11]VOGT U,WILHEIN T,STIEL H,etal.. High resolution X-ray absorption spectroscopy using a laser plasma radiation source[J].ReviewofScientificInstruments,2004,75(11):4606-4609.

[12]PETH C,BARKUSKY F,SEDLMAIR J,etal.. Near-edge X-ray absorption fine structure measurements using a laser plasma XUV source[J].JournalofPhysics:ConferenceSeries,2009,186(1):012032.

[13]SEDLMAIR J,GEBER S,PETH C,etal.. NEXAFS spectroscopy with a laser plasma X-ray source on soil samples[J].JournalofPhysics:ConferenceSeries,2009,186(1):012034.

[14]薛守慶,薛兆民.二次摻雜聚吡咯/聚噻吩膜的制備及其光電性能[J].發(fā)光學(xué)報,2016,37(9):1124-1129.

XUE SH Q,XUE Z M. Preparation and anti-corrosive performance of Ppy/PTh composites redoped with zinc phosphate[J].ChineseJournalofLuminescence,2016,37(9):1124-1129.

[15]鄒鳳君,范思大,謝強,等.摻雜石墨烯量子點對P3HT:PCBM太陽能電池性能的影響[J].發(fā)光學(xué)報,2016,37(9):1082-1089.

ZOU F J,FAN S D,XIE Q,etal.. Effect of doping graphene quantum dots on the performance of P3HT:PCBM Solar Cells[J].ChineseJournalofLuminescence,2016,37(9):1082-1089.

[16]彭博,曹亞鵬,胡煜峰,等.P3HT/PMMA雙層聚合物電雙穩(wěn)器件的研究[J].發(fā)光學(xué)報,2016,37(9):1090-1096.

PENG B,CAO Y P,HU Y F,etal.. Polymer bistable devices based on poly(3-hexylthiophene)/ poly(methylmethacrylate) bilayer films[J].ChineseJournalofLuminescence,2016,37(9):1090-1096.

[17]ANDERSON C. Center for X-Ray Optics:http://www-cxro.lbl.gov/.

[18]HARADA T,KITA T. Mechanically ruled aberration-corrected concave gratings[J].AppliedOptics,1980,19(23):3987-3993.

[19]杜學(xué)維.凹面變線距光柵的二維線密度分布測試及軟X射線平場光譜儀的研制[D].合肥:中國科學(xué)技術(shù)大學(xué),2013.

DU X W. Measurement of groove density 2D distribution of concave VLS grating and construction of a soft X-ray flat field spectrograph[D]. Hefei:University of Science and Technology of China,2013.(in Chinese)

[20]LAI B,CERRINA F. SHADOW:a synchrotron radiation ray tracing program[J].NuclearInstruments&MethodsinPhysicsResearch,1986,246(1-3):337-341.