关 键 词：光栅；浸入式；折射率；谱线漂移
中图分类号：TN214，P412 文献标识码：A

In aerospace applications，especially those tasks for monitoring the Earth＇s atmospheric composition，the use of instruments with ultrahigh spectral resolution is often necessary to measure the scattering and transmission spectra of the Earth＇s atmosphere ${}^{[1-3]}$${}^{[1-3]}$^([1-3]){ }^{[1-3]} ．The grating spec－ trometers，such as SCIAMACHY and TROPOMI，are ex－ tensively applied due to its high resolution and wide range of spectral bands ${}^{[4-5]}$${}^{[4-5]}$^([4-5]){ }^{[4-5]} ．The immersion gratings can substantially increase angular dispersion in comparison with normal gratings ${}^{[6]}$${}^{[6]}$^([6]){ }^{[6]} ，thus significantly reducing the size of grating and equipment，or significantly increasing spectral resolution under the premise of maintaining the existing volume of grating．
在航空航天应用中，特别是那些监测地球大气成分的任务中，通常需要使用具有超高光谱分辨率的仪器来测量地球大气层 ${}^{[1-3]}$${}^{[1-3]}$^([1-3]){ }^{[1-3]} 的散射和透射光谱。SCIAMACHY 和 TROPOMI 等光栅光谱仪因其高分辨率和宽光谱带 ${}^{[4-5]}$${}^{[4-5]}$^([4-5]){ }^{[4-5]} 范围而得到广泛应用。与普通光栅 ${}^{[6]}$${}^{[6]}$^([6]){ }^{[6]} 相比，浸入式光栅可以大大增加角色散，从而显著减小光栅和设备的尺寸，或在保持现有光栅体积的前提下显著提高光谱分辨率。

Fig． 1 Structure chart of immersion gratings
图 1 浸没式格栅的结构图
图1 浸入式光栅结构图

The structure chart of immersion gratings is shown in Fig．1．The main difference between immersion grat－ ings and normal gratings（ $n=1,n$$n=1,n$n=1,nn=1, n is the refractive in－ dex of the medium）is that the refractive indexes of the media．As an example，for common materials of infrared spectral bands，such as silicon and germanium，the re－ fractive indexes of them are 3.4 and 4.1 ，respectively． If the same spectral resolution is reached，the volume of immersion gratings is only $1/n^3$$1/n^3$1//n^(3)1 / n^{3} of normal gratings．Con－ versely，the spectral resolution of immersion gratings is $n$$n$nn times of normal gratings．The effect of shrinkage in size or improvement in resolution is significant．Thus，the immersion gratings are mainly used in infrared spectral bands．
浸没式光栅与普通光栅 $n=1,n$$n=1,n$n=1,nn=1, n 的主要区别在于 media.As 的折射率为例，对于红外光谱波段的常见材料，如硅、锗等，它们的折射率分别为3.4和4.1。如果达到相同的光谱分辨率，则浸没式光栅的体积仅为 $1/n^3$$1/n^3$1//n^(3)1 / n^{3} 普通光栅的体积，反之，浸没式光栅的光谱分辨率是 $n$$n$nn 普通光栅的倍数，尺寸缩小或分辨率提高的影响显著，因此，浸没式光栅主要用于红外光谱波段。

Numerous countries have invested a considerable a－ mount of manpower，material，and financial resources to study immersion gratings for their distinct advanta－ ges ${}^{[7-8]}$${}^{[7-8]}$^([7-8]){ }^{[7-8]} ．Consensus has been reached on the basic princi－ ples of immersion gratings，and application researches have been extensively conducted globally ${}^{[9]}$${}^{[9]}$^([9]){ }^{[9]} ．Due to their
许多国家投入了大量的人力、物力和财力来研究浸入式格栅，以获得其独特的优势 ${}^{[7-8]}$${}^{[7-8]}$^([7-8]){ }^{[7-8]} ，对浸入式格栅的基本原则已经达成共识，应用研究已在全球范围内 ${}^{[9]}$${}^{[9]}$^([9]){ }^{[9]} 广泛进行。
unique working modes，however，immersion gratings still encounter a range of new problems that must be re－ searched promptly，such as the influence of medium ab－ sorption on light intensity distribution ${}^{[10]}$${}^{[10]}$^([10]){ }^{[10]} ．Currently，the characteristics of the spectral lines of immersion gratings have not been encountered in related researches．Such problem is critical to the design and application of im－ mersion grating spectrometers．This research carried out analysis and discussion on this problem．
然而，独特的工作模式，浸没式光栅仍遇到了一系列需要及时重新审视的新问题，如介质吸收对光强分布 ${}^{[10]}$${}^{[10]}$^([10]){ }^{[10]} 的影响，目前，浸没式光栅光谱线的特性在相关研究中尚未遇到，这些问题对浸没式光栅光谱仪的设计与应用至关重要。

As no dispersion occurs in the air＇s refractive index （ $n\equiv 1$$n\equiv 1$n-=1n \equiv 1 ），symmetrically distributed trapezoids for diffrac－ tion spectral lines at various orders are imaged on the CCD focal plane when normal reflection gratings are used （ see Fig．2）．
由于空气的折射率 （ $n\equiv 1$$n\equiv 1$n-=1n \equiv 1 ） 不会发生色散，因此当使用法向反射光栅时，不同阶次衍射光谱线的对称分布梯形会在 CCD 焦平面上成像（见图 2）。

Fig． 2 Spot diagram of the wavelength selected in the working spectral band ${}^{[11]}$${}^{[11]}$^([11]){ }^{[11]}
图 2 在工作光谱带 ${}^{[11]}$${}^{[11]}$^([11]){ }^{[11]} 中选择的波长的点图
图2 工作谱段中所选波长的点列图 ${}^{[11]}$${}^{[11]}$^([11]){ }^{[11]}

The relations between the lengths of long and short waves of normal gratings working in the air are mathemat－ ically derived，as follows．
在空气中工作的正常光栅的长波和短波长度之间的关系在数学上推导出来，如下所示。

For the same equipment，the wave number intervals of long－and－short waves are identical，with the working spectral band of ${\lambda }_{\text{short}}\sim {\lambda }_{\text{long}}(\mathrm{nm})$${\lambda }_{\text{short }}\sim {\lambda }_{\text{long }}(\mathrm{nm})$lambda_("short ")∼lambda_("long ")(nm)\lambda_{\text {short }} \sim \lambda_{\text {long }}(\mathrm{nm}) ．The wave number in－ terval of the instrument is assumed to be $N\left({\mathrm{cm}}^{-1}\right)$$N\left({\mathrm{cm}}^{-1}\right)$N(cm^(-1))N\left(\mathrm{~cm}^{-1}\right) ，and the sampling interval of spectra is assumed to be $a(\mathrm{nm})$$a(\mathrm{nm})$a(nm)a(\mathrm{~nm}) ．
对于相同的设备，长短波的波数间隔是相同的，工作光谱波段为 ${\lambda }_{\text{short}}\sim {\lambda }_{\text{long}}(\mathrm{nm})$${\lambda }_{\text{short }}\sim {\lambda }_{\text{long }}(\mathrm{nm})$lambda_("short ")∼lambda_("long ")(nm)\lambda_{\text {short }} \sim \lambda_{\text {long }}(\mathrm{nm}) ，假设仪器的波数为 $N\left({\mathrm{cm}}^{-1}\right)$$N\left({\mathrm{cm}}^{-1}\right)$N(cm^(-1))N\left(\mathrm{~cm}^{-1}\right) ，光谱的采样间隔为 $a(\mathrm{nm})$$a(\mathrm{nm})$a(nm)a(\mathrm{~nm}) 。
i）Pixel number when ${\lambda }_{\text{shor}}$${\lambda }_{\text{shor }}$lambda_("shor ")\lambda_{\text {shor }} is classified
i） 分类时的 ${\lambda }_{\text{shor}}$${\lambda }_{\text{shor }}$lambda_("shor ")\lambda_{\text {shor }} 像素数
The corresponding wave number of ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} is $\frac{{10}^7}{{\lambda }_{\text{short}}(\mathrm{nm})}$$\frac{{10}^7}{{\lambda }_{\text{short }}(\mathrm{nm})}$(10^(7))/(lambda_("short ")(nm))\frac{10^{7}}{\lambda_{\text {short }}(\mathrm{nm})} ，and the corresponding wave number of ${\lambda }_{\text{shori}}$${\lambda }_{\text{shori }}$lambda_("shori ")\lambda_{\text {shori }}
对应的波数 ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} 为 $\frac{{10}^7}{{\lambda }_{\text{short}}(\mathrm{nm})}$$\frac{{10}^7}{{\lambda }_{\text{short }}(\mathrm{nm})}$(10^(7))/(lambda_("short ")(nm))\frac{10^{7}}{\lambda_{\text {short }}(\mathrm{nm})} ，对应的波数为 ${\lambda }_{\text{shori}}$${\lambda }_{\text{shori }}$lambda_("shori ")\lambda_{\text {shori }}
$+\mathrm{\Delta }{\lambda }_{\text{short}}$$+\mathrm{\Delta }{\lambda }_{\text{short }}$+Deltalambda_("short ")+\Delta \lambda_{\text {short }} is $\frac{{10}^7}{{\lambda }_{\text{short}}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$$\frac{{10}^7}{{\lambda }_{\text{short }}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$(10^(7))/(lambda_("short ")(nm))-N(cm^(-1))\frac{10^{7}}{\lambda_{\text {short }}(\mathrm{nm})}-N\left(\mathrm{~cm}^{-1}\right) ．Therefore，
$+\mathrm{\Delta }{\lambda }_{\text{short}}$$+\mathrm{\Delta }{\lambda }_{\text{short }}$+Deltalambda_("short ")+\Delta \lambda_{\text {short }} 是 $\frac{{10}^7}{{\lambda }_{\text{short}}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$$\frac{{10}^7}{{\lambda }_{\text{short }}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$(10^(7))/(lambda_("short ")(nm))-N(cm^(-1))\frac{10^{7}}{\lambda_{\text {short }}(\mathrm{nm})}-N\left(\mathrm{~cm}^{-1}\right) .因此，

The pixel number of ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} is：
的 ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} 像素数为：
$M_1=\frac{\mathrm{\Delta }{\lambda }_{\text{short}}(\mathrm{nm})}{a}$$M_1=\frac{\mathrm{\Delta }{\lambda }_{\text{short }}(\mathrm{nm})}{a}$M_(1)=(Deltalambda_("short ")(nm))/(a)M_{1}=\frac{\Delta \lambda_{\text {short }}(\mathrm{nm})}{a}

ii）Pixel number when ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} is classified
ii） 分类时的 ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} 像素编号
The corresponding wave number of ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} is $\frac{{10}^7}{{\lambda }_{\text{long}}(\mathrm{nm})}$$\frac{{10}^7}{{\lambda }_{\text{long }}(\mathrm{nm})}$(10^(7))/(lambda_("long ")(nm))\frac{10^{7}}{\lambda_{\text {long }}(\mathrm{nm})} ，and the corresponding wave number of ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} $+\mathrm{\Delta }{\lambda }_{\text{long}}$$+\mathrm{\Delta }{\lambda }_{\text{long }}$+Deltalambda_("long ")+\Delta \lambda_{\text {long }} is $\frac{{10}^7}{{\lambda }_{\text{long}}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$$\frac{{10}^7}{{\lambda }_{\text{long }}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$(10^(7))/(lambda_("long ")(nm))-N(cm^(-1))\frac{10^{7}}{\lambda_{\text {long }}(\mathrm{nm})}-N\left(\mathrm{~cm}^{-1}\right) ．Therefore，
对应的波数 ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} 为 $\frac{{10}^7}{{\lambda }_{\text{long}}(\mathrm{nm})}$$\frac{{10}^7}{{\lambda }_{\text{long }}(\mathrm{nm})}$(10^(7))/(lambda_("long ")(nm))\frac{10^{7}}{\lambda_{\text {long }}(\mathrm{nm})} ，对应的波数 ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} $+\mathrm{\Delta }{\lambda }_{\text{long}}$$+\mathrm{\Delta }{\lambda }_{\text{long }}$+Deltalambda_("long ")+\Delta \lambda_{\text {long }} 为 $\frac{{10}^7}{{\lambda }_{\text{long}}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$$\frac{{10}^7}{{\lambda }_{\text{long }}(\mathrm{nm})}-N\left({\mathrm{cm}}^{-1}\right)$(10^(7))/(lambda_("long ")(nm))-N(cm^(-1))\frac{10^{7}}{\lambda_{\text {long }}(\mathrm{nm})}-N\left(\mathrm{~cm}^{-1}\right) ，因此，

The pixel number of is：
的像素数为：

The lengths ratio of spectral lines of ${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} and ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} is the ratio of CCD pixel numbers，each accounting for：
${\lambda }_{\text{long}}$${\lambda }_{\text{long }}$lambda_("long ")\lambda_{\text {long }} 的光谱线长度比为 和 ${\lambda }_{\text{short}}$${\lambda }_{\text{short }}$lambda_("short ")\lambda_{\text {short }} 的 CCD 像素数的比值，每个像素数占：

Considering that ${10}^7\gg {\lambda }_{\text{long}}(\mathrm{nm}),{10}^7\gg {\lambda }_{\text{short}}$${10}^7\gg {\lambda }_{\text{long }}(\mathrm{nm}),{10}^7\gg {\lambda }_{\text{short }}$10^(7)≫lambda_("long ")(nm),10^(7)≫lambda_("short ")10^{7} \gg \lambda_{\text {long }}(\mathrm{nm}), 10^{7} \gg \lambda_{\text {short }} （ nm ），so
考虑到 ${10}^7\gg {\lambda }_{\text{long}}(\mathrm{nm}),{10}^7\gg {\lambda }_{\text{short}}$${10}^7\gg {\lambda }_{\text{long }}(\mathrm{nm}),{10}^7\gg {\lambda }_{\text{short }}$10^(7)≫lambda_("long ")(nm),10^(7)≫lambda_("short ")10^{7} \gg \lambda_{\text {long }}(\mathrm{nm}), 10^{7} \gg \lambda_{\text {short }} （ nm ），所以

Note that the computational analysis in this case is based on derivation under ideal conditions．In practical engineering applications，the relations of spectral line
请注意，在这种情况下的计算分析是基于理想 conditions.In 实际工程应用下的推导，即谱线的关系
lengths obtained on the CCD focal plane do not strictly comply with the ratio of ${\lambda }_{\text{long}}^2/{\lambda }_{\text{short}}^2$${\lambda }_{\text{long }}^2/{\lambda }_{\text{short }}^2$lambda_("long ")^(2)//lambda_("short ")^(2)\lambda_{\text {long }}^{2} / \lambda_{\text {short }}^{2} due to the nonlineari－ ties of grating dispersion and other reasons．This problem will be studied and presented in a subsequent work．
由于光栅色散的非线性和其他原因，在 CCD 焦平面上获得的长度并不严格符合比率 ${\lambda }_{\text{long}}^2/{\lambda }_{\text{short}}^2$${\lambda }_{\text{long }}^2/{\lambda }_{\text{short }}^2$lambda_("long ")^(2)//lambda_("short ")^(2)\lambda_{\text {long }}^{2} / \lambda_{\text {short }}^{2} 。

The design of the spectrometer based on the techni－ cal index presented in Table 1 is taken as an example to analyze the variation in the distribution of immersion grat－ ings in relation to normal gratings working in the air．
以表 1 中所示的技术指数为基础的光谱仪设计以分析与在空气中工作的正常光栅相关的浸入式格栅分布的变化。

Figure 3 presents the spectral line distribution on CCD when normal gratings are adopted under the spectral band of $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} and working series of the ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} or－ $\mathrm{der}(1.5\mu \mathrm{m})$$\mathrm{der}(1.5\mu \mathrm{m})$der(1.5 mum)\operatorname{der}(1.5 \mu \mathrm{~m}) to the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order（ $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ）．Clearly， the diffraction angles for the central wavelengths under all orders are all ${63.5}^{\circ }$${63.5}^{\circ }$63.5^(@)63.5^{\circ} ．The diffraction angle at the long－ wave end gradually decreases as the order increases（the wavelength decreases）．The diffraction angle at the short－wave end gradually increases as the order increases （and the wavelength rises）．Theoretically，the ratio of the spectral line length of the long－wave $AB$$AB$ABA B（i．e．， 2.5 $\mu \mathrm{m}$$\mu \mathrm{m}$mum\mu \mathrm{m} ，the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order）and the spectral line length of the short wave CD（i．e．， $1.5\mu \mathrm{m}$$1.5\mu \mathrm{m}$1.5 mum1.5 \mu \mathrm{~m} ，the ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} order）meets the proportional relation derived in Eq． 4.
图 3 显示了在 ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} or- $\mathrm{der}(1.5\mu \mathrm{m})$$\mathrm{der}(1.5\mu \mathrm{m})$der(1.5 mum)\operatorname{der}(1.5 \mu \mathrm{~m}) ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 到 （ $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ） 的光谱带 $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} 和工作系列下采用普通光栅时 CCD 上的光谱线分布，显然，所有阶次下中心波长的衍射角都是 ${63.5}^{\circ }$${63.5}^{\circ }$63.5^(@)63.5^{\circ} .长波端的衍射角随着阶数的增加而逐渐减小（短波端的衍射角随着阶数的增加（波长的增加）逐渐增大。理论上，长波 $AB$$AB$ABA B 的光谱线长度（即 2.5 $\mu \mathrm{m}$$\mu \mathrm{m}$mum\mu \mathrm{m} ， ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶数）与短波 CD 的光谱线长（即 $1.5\mu \mathrm{m}$$1.5\mu \mathrm{m}$1.5 mum1.5 \mu \mathrm{~m} ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} ，阶数）的比值满足方程 4 中得出的比例关系。

Fig． 3 Distribution of the spectral lines of normal gratings
图 3 普通光栅光谱线分布
图3 普通光栅谱线在 CCD 上的分布

When the light is dispersed by immersion gratings， dispersion occurs inside the immersion medium．The Cauchy dispersion formula reveals that the refractive in－ dex is a function of the wavelength，where $a,b$$a,b$a,ba, b ，and $c$$c$cc are the values which differ according to the substance ex－ amined．
当光被浸没光栅分散时，分散发生在浸没介质内部。柯西色散公式表明，折射阻抗是波长的函数，其中 $a,b$$a,b$a,ba, b ，和 $c$$c$cc 是根据所检测物质的不同而不同的值。

This study takes Si as grating material for which the refractive index distribution curve of $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} spec－ tral bands at normal temperature is shown in Fig． 4.
本研究以 Si 为光栅材料，常温下光谱带的 $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} 折射率分布曲线如图 4 所示。

Table 1 Technical index of Spectrometer
表 1 光谱仪技术指标
表1 光谱仪技术参数

Fig． 4 Refractive index of $\mathrm{Si}(1.5\sim 2.5\mu \mathrm{m})$$\mathrm{Si}(1.5\sim 2.5\mu \mathrm{m})$Si(1.5∼2.5 mum)\mathrm{Si}(1.5 \sim 2.5 \mu \mathrm{~m})
图 4 折射率 $\mathrm{Si}(1.5\sim 2.5\mu \mathrm{m})$$\mathrm{Si}(1.5\sim 2.5\mu \mathrm{m})$Si(1.5∼2.5 mum)\mathrm{Si}(1.5 \sim 2.5 \mu \mathrm{~m})
图4 硅的折射率（ $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} ）
图4 硅的折射率（ $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} ）
The case presented in Fig． 5 differs from that in Fig． 3 ，as shape of the spectral line on the CCD focal plane twists．When the Littrow condition is registered by the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order（ $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ），as shown in Fig．5，the green spot of each order represents the diffraction angle of the short－wave end，the red spot represents the diffraction angle of the central wavelength，and the blue spot repre－ sents the diffraction angle of the long－wave end．Lines connecting the spots of different colors indicate the dif－ fraction angle distribution of the short－wave end wave－ length，central wavelength，and long－wave end wave－ length of each order from the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order to the ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} order．
图 5 中的情况与图 3 中的情况不同，因为 CCD 焦平面上的光谱线形状是扭曲的，当 Littrow 条件以 ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶数（ ）记录时 $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ，如图 5 所示，每个阶次的绿点代表短波端的衍射角，红点代表中心波长的衍射角，蓝色点代表长波端的衍射角，连接不同颜色的光斑的线条表示每个阶次的短波端波长、中心波长和长波端波长从 ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶到 ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} 阶的差异分数角分布。

Fig． 5 Spectral line distribution of immersion gratings
图 5 浸没式光栅的光谱线分布
图5 浸人式光栅谱线在 CCD 上的分布

Figure 5 shows the spectral line distribution of im－ mersion gratings．EF is the spectral line length of the long wave（i．e．， $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ，the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order）and GH is the spectral line length of the short wave（i．e．， 1.5 $\mu \mathrm{m}$$\mu \mathrm{m}$mum\mu \mathrm{m} ，the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order）．Moreover，the＂trapezoid＂of the spectral line tilts．
图 5 显示了浸没光栅的光谱线分布，EF 是长波的谱线长度（即 $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ， ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶数），GH 是短波的谱线长度（即 1.5 $\mu \mathrm{m}$$\mu \mathrm{m}$mum\mu \mathrm{m} ， ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶数），此外，谱线的“梯形”倾斜。

The following conclusions can be drawn based on the figures presented in this study．
根据本研究中提供的数字，可以得出以下结论。
（1）Considering the changes in the refractive index with the wavelength，when Littrow conditions are regis－ tered by the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order $(2.5\mu \mathrm{m})$$(2.5\mu \mathrm{m})$(2.5 mum)(2.5 \mu \mathrm{~m}) ，the spectral lines of each order gradually drift toward the short－wave end． Similarly，when Littrow conditions are registered by the ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} order $(1.5\mu \mathrm{m})$$(1.5\mu \mathrm{m})$(1.5 mum)(1.5 \mu \mathrm{~m}) ，the spectral lines of each order gradually drift toward the long－wave end．
（1）考虑折射率随波长的变化，当利特罗条件按 ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶 $(2.5\mu \mathrm{m})$$(2.5\mu \mathrm{m})$(2.5 mum)(2.5 \mu \mathrm{~m}) 数记录时，各阶数的光谱线逐渐向短波端漂移。同样，当利特罗条件按 ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} 阶 $(1.5\mu \mathrm{m})$$(1.5\mu \mathrm{m})$(1.5 mum)(1.5 \mu \mathrm{~m}) 数记录时，各阶数的光谱线逐渐向长波端漂移。
（2）When the central wavelength of the ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} order meets Littrow conditions，the central wavelength of each
（2）当 ${108}^{\text{th}}$${108}^{\text{th }}$108^("th ")108^{\text {th }} 阶次的中心波长满足利特罗条件时，每个
order progressively deviates from such conditions．Fur－ thermore，the wavelength that meets Littrow conditions gradually increases．At the ${135}^{\text{th}}$${135}^{\text{th }}$135^("th ")135^{\text {th }} order，the wavelength that meets Littrow conditions is the wavelength of the long－wave end．For a higher order，all wavelengths in the spectral bands of such order deviate from Littrow con－ ditions．At this point，the diffraction efficiency is low－ ered．
此外，满足 Littrow 条件的波长逐渐 increases.At ${135}^{\text{th}}$${135}^{\text{th }}$135^("th ")135^{\text {th }} 阶，满足 Littrow 条件的波长是长波端的波长。对于更高的阶数，该阶数的光谱带中的所有波长都偏离 Littrow ditions.At 这一点，衍射效率较低。
（3）The spectral line length of the order for the shortest wavelength（i．e．， $1.5\mu \mathrm{m}$$1.5\mu \mathrm{m}$1.5 mum1.5 \mu \mathrm{~m} ，the ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} order in this study）increases，and no longer complies with the condition of ${\left[{\lambda }_{\text{long}}/{\lambda }_{\text{short}}\right]}^2$${\left[{\lambda }_{\text{long }}/{\lambda }_{\text{short }}\right]}^2$[lambda_("long ")//lambda_("short ")]^(2)\left[\lambda_{\text {long }} / \lambda_{\text {short }}\right]^{2} ，and turns into EF／GH $=$$=$== ${1.7}^{\times }$${1.7}^{\times }$1.7^(xx)1.7^{\times}due to changes in the refractive index．This propor－ tion is associated with the characteristics of the refractive indexes of the selected materials．
（3）最短波长的 阶数（即 $1.5\mu \mathrm{m}$$1.5\mu \mathrm{m}$1.5 mum1.5 \mu \mathrm{~m} 本研究中的 ${180}^{\text{th}}$${180}^{\text{th }}$180^("th ")180^{\text {th }} 阶数 ）的光谱线长度增加，不再符合 ${\left[{\lambda }_{\text{long}}/{\lambda }_{\text{short}}\right]}^2$${\left[{\lambda }_{\text{long }}/{\lambda }_{\text{short }}\right]}^2$[lambda_("long ")//lambda_("short ")]^(2)\left[\lambda_{\text {long }} / \lambda_{\text {short }}\right]^{2} 的条件，由于折射率的变化而变成 EF/GH $=$$=$== ${1.7}^{\times }$${1.7}^{\times }$1.7^(xx)1.7^{\times} 。
（4）Considering the aforementioned condition of spectral line drift，the number of spectral dimensional pixel must increase，and some blank pixels should be re－ served when the CCD is selected．
（4）考虑到上述光谱线漂移的条件，光谱维数像素的数量必须增加，在选择CCD时应保留一些空白像素。

Fig． 6 Refractive index of $\mathrm{Si}(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$$\mathrm{Si}(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$Si(1.2∼14 mum)^([12])\mathrm{Si}(1.2 \sim 14 \mu \mathrm{~m})^{[12]}
图 6 折射率 $\mathrm{Si}(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$$\mathrm{Si}(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$Si(1.2∼14 mum)^([12])\mathrm{Si}(1.2 \sim 14 \mu \mathrm{~m})^{[12]}
图 6 硅的折射率 $(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$$(1.2\sim 14\mu \mathrm{m}{)}^{[12]}$(1.2∼14 mum)^([12])(1.2 \sim 14 \mu \mathrm{~m})^{[12]}
Figure 6 presents the refractive index curve of Si in infrared spectral bands．In the spectral band of $1.2\sim$$1.2\sim$1.2∼1.2 \sim $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ，significant changes are observed in the refrac－ tive index．For the spectral band of $2.5\sim 5\mu \mathrm{m}$$2.5\sim 5\mu \mathrm{m}$2.5∼5mum2.5 \sim 5 \mu \mathrm{~m} ，the changes in the refractive index tend to flatten，and only slight changes occur in the refractive index for the spec－ tral band of $7.5\sim 14\mu \mathrm{m}$$7.5\sim 14\mu \mathrm{m}$7.5∼14 mum7.5 \sim 14 \mu \mathrm{~m} ．The above analysis indicates that variations in the shape of the spectral line of the de－ tector result from changes in the refractive index．In the region where changes in the refractive index are ob－ served，e．g．，in the wave band of $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} ，as shown in Fig 5，the＂inclination＂degree of the spectral line is larger．Therefore，immersion gratings are applied in the thermal infrared spectral band for which minimal variation occurs in the refractive index，such as the spec－ tral band of $8\sim 14\mu \mathrm{m}$$8\sim 14\mu \mathrm{m}$8∼14 mum8 \sim 14 \mu \mathrm{~m} ．The＂inclination＂degree of such spectral line will be significantly improved，similar to the situation of normal gratings．
图 6 显示了 Si 在红外光谱 bands.In 光谱带 $1.2\sim$$1.2\sim$1.2∼1.2 \sim 的折射率曲线 $2.5\mu \mathrm{m}$$2.5\mu \mathrm{m}$2.5 mum2.5 \mu \mathrm{~m} ，观察到折射率发生了显著变化。对于光谱带 $2.5\sim 5\mu \mathrm{m}$$2.5\sim 5\mu \mathrm{m}$2.5∼5mum2.5 \sim 5 \mu \mathrm{~m} ，折射率的变化趋于平坦，光谱带的折射率仅发生轻微变化 $7.5\sim 14\mu \mathrm{m}$$7.5\sim 14\mu \mathrm{m}$7.5∼14 mum7.5 \sim 14 \mu \mathrm{~m} 。上述分析表明，探测器光谱线形状的变化是由于反射的变化引起的。裂 index.In 观察到折射率变化的区域，例如，在波段 $1.5\sim 2.5\mu \mathrm{m}$$1.5\sim 2.5\mu \mathrm{m}$1.5∼2.5 mum1.5 \sim 2.5 \mu \mathrm{~m} 中，如图 5 所示，谱线的“倾角”度较大，因此，浸没式光栅应用于折射率变化最小的热红外光谱带，例如这种光谱线的光谱带 $8\sim 14\mu \mathrm{m}$$8\sim 14\mu \mathrm{m}$8∼14 mum8 \sim 14 \mu \mathrm{~m} 的“倾角”度将得到显着提高，类似于普通光栅的情况。