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在杜瓦组件中多余物主要是一些机械加工碎屑、毛刺、焊渣以及涂层脱落物等,为了简化分析,假设多余物为直径d的球形颗粒。图1展示了球形多余物颗粒在探测器组件光路中与焦平面以及冷屏的位置关系。
在图1中,入射光为平行光,入射波长为λ(单位: μm),b为冷屏开口(单位:mm),d为多余物颗粒直径(单位:mm),R是多余物到冷屏开口的距离(单位:mm),L为多余物与光敏面的距离(单位:mm),冷屏高H=L+R。根据菲涅尔衍射理论,光束经过多余物呈现衍射斑需要满足光束到达多余物时的光斑半径
$\Delta x$ 大于多余物颗粒的直径d[6]。由于光束通过冷屏圆形开口后形成的艾里光斑的半发散角$\Delta \theta $ 为[7-8]:$$\Delta \theta {\rm{ = }}\dfrac{{1.22\lambda }}{b}$$ (公式Ⅰ) 则对应到达多余物时艾里光斑的半径
$\Delta x$ 为:$$\Delta x{\rm{ = }}\dfrac{{1.22\lambda R}}{b}$$ (公式Ⅱ) 当
$\Delta x$ 大于多余物颗粒直径时,无法挡住光斑的大部分光强,多余物便可以得到充分照明,从而能再次通过多余物颗粒产生衍射效应,使得焦平面上呈现衍射斑。衍射斑可分为两种,多余物颗粒呈圆形时,颗粒边缘的衍射光到达颗粒正下方对应圆心位置处的相位相同,可得到中心有亮斑的黑斑,即“泊松亮斑”。若多余物颗粒边缘不光滑,形状偏离圆形,那么颗粒边缘衍射的光到达颗粒下方投影中心的相位不同,也就无法得到中心亮斑(或中心亮斑非常弱),此时呈现出中心没有亮斑的黑斑[7-10]。
故结合理论分析,光束通过冷屏开口后,经直径为d的多余物颗粒在焦平面上形成衍射斑的条件为:
$$d < \frac{{1.22\lambda R}}{b}$$ (公式Ⅲ) 而根据菲涅尔衍射理论,同样也可估算出其对应在焦平面上形成的衍射斑直径D为[6-7]:
$$D{\rm{ = }}\frac{{2.44\lambda L}}{d}$$ (公式Ⅳ) 要产生明显的衍射现象,D值当小于焦平面的对角线长度C(单位:mm)[3-4],即:
$${D_{\max }}{\rm{ = }}\frac{{2.44\lambda L}}{{{d_{\min }}}} < C,{d_{\min }} > \frac{{2.44\lambda L}}{C}$$ (公式Ⅴ) 其中公式(3)右侧项计算值为颗粒满足衍射条件的最大直径dmax,多余物颗粒直径d比dmax小时会产生衍射效应。因此,当波长λ、冷屏开口b及多余物位置R不变时,多余物越小就越容易形成衍射斑;而其他因素不变,冷屏开口b越大,dmax越小,符合公式(3)能产生衍射的d值区间也就越小,则越难形成衍射斑;同理,入射波长λ越长,多余物产生衍射越容易。结合公式(3)和公式(5)可以估算出探测器杜瓦内多余物颗粒可发生明显衍射现象的尺寸范围。
由于在杜瓦冷屏设计中,冷屏高度H和冷屏开口b尺寸需满足红外光学系统F数限制,同时兼顾杜瓦结构的安装尺寸,所以产品设计中往往针对不同的冷屏高度H会匹配相应的冷屏开口尺寸b,即H与b相联系。不同的杜瓦结构H和b不同,典型的几种红外探测器冷屏,其H和b取值分别为20 mm和25 mm、30 mm和10 mm、12 mm和18 mm。文中针对这几种杜瓦冷屏的光路,进行了多余物衍射尺寸的计算,其中入射波长均取10 μm,具体如图2所示。
图 2 不同杜瓦冷屏结构下满足衍射条件的多余物颗粒直径dmax与其距焦平面距离L的关系曲线,斜虚线2.44λL/C为颗粒明显衍射的尺寸下限dmin,阴影区内可发生明显衍射现象,焦平面对角线长度C值取15 mm
Figure 2. Distance L between remainders and the focal plane-remainders diameter dmax satisfying diffraction curves for different Dewar cold-shielding structures, slant dashed line 2.44λL/C denotes diameter lower limit value for diffraction, shadow region indicates obvious diffraction. Focal plane diagonal length C=15 mm
图2中的实曲线展示了形成衍射斑所要求的最大多余物尺寸dmax随其距离焦平面距离L的变化情况。颗粒离焦平面越近,L越小,dmax就越大。不同的实曲线分别代表不同冷屏结构下的dmax计算结果,结果表明L较小时,冷屏高度H与开口b的比值越大,各位置处对应的dmax越大,即多余物可产生衍射的d值区间越大,越容易发生衍射现象。
由于要产生明显的衍射斑,需要衍射斑直径Dmax=(2.44λL/dmin)<C,此处C为常见的探测器焦平面对角线长15 mm,将C=15 mm代入公式(5)的右侧,可在图2中画出dmin=2.44λL/15的斜虚线,此虚线上方满足公式(5),能产生明显的衍射斑。结合公式(3),实曲线dmax以下的颗粒直径才能满足发生衍射的条件,这样,由斜虚线与实曲线所交成的阴影区域,即为能发生明显衍射现象的多余物颗粒尺寸范围。斜虚线2.44λL/C与实曲线1.22λ(H-L)/b的交点(LC, dc)处LC值为:
$$\begin{split} \\ L_C = HC/\left( {2b + C} \right) \end{split}$$ (公式Ⅵ) 如图2所示,C取15 mm,三种冷屏结构中最大的LC值为9.6 mm,对应H/b值最高的结构,也是明显衍射区(图2阴影区)范围最大的结构。
综上所述,为了减少衍射斑的出现,应设计H/b较小的冷屏结构,多余物筛查时更应当注意距离焦平面较近的位置,即L<LC的区域。比如针对这几种杜瓦而言,应分别重点筛查L<8.6 mm、L<8.8 mm、L<9.6 mm的区域(图2),并且在对应的0<L<Lc区间内,需要尽量控制直径位于图2所示阴影区域内的颗粒出现。
Diffraction analysis and control of remainders in infrared detector Dewar packaging
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摘要: 红外探测器组件中一定尺寸大小多余物的存在,容易造成探测器服役状态下其光路中产生衍射现象,并改变焦平面局部光场分布,导致像面上形成“黑斑”或“泊松亮斑”。为了减少此类异常图像的出现,根据菲涅耳衍射原理,计算了几种典型探测器组件内不同位置处的多余物颗粒满足衍射斑形成条件时的尺寸范围,并分析了多余物尺寸、杜瓦结构、波长以及衍射斑之间的关系,结果表明,波长越长、多余物距离焦平面越近,越容易发生衍射;对于不同的探测器杜瓦组件,容易产生衍射的位置为距离焦平面距离L<LC的区域。此外结合生产实践提出了控制多余物的相应措施,研究结果对于红外探测器组件的设计和工程应用具有一定指导意义。Abstract: Remainders with a certain size in the infrared detector assembly easily cause the diffraction phenomenon in the optical path of infrared detector in service, which would change the local luminous flux distribution on the focal plane, resulting in 'black spot' and 'Poisson bright spot ' on the image. In order to reduce the occurrence of such abnormal images, according to Fresnel diffraction theory, the remainder particles diameter satisfying the diffraction spot formation for several typical detector Dewar assemblies was calculated, and the relationship among the remainders dimension, Dewar structure, wavelength and diffraction spot was also analyzed. The results show that diffraction is more likely to happen for longer wavelength and smaller distance between remainders and focal plane; for different detector Dewar assembly, the position inclined to diffraction is the region where the distance denoted by "L" between remainders and focal plane satisfies the equation "L<LC". Besides, combined with the production practice, some corresponding measures to control the remainders were offered. These conclusions in the article provide a reference for the infrared detector production design and engineering application.
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Key words:
- infrared detector /
- Dewar /
- remainders control /
- diffraction /
- black spot
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图 2 不同杜瓦冷屏结构下满足衍射条件的多余物颗粒直径dmax与其距焦平面距离L的关系曲线,斜虚线2.44λL/C为颗粒明显衍射的尺寸下限dmin,阴影区内可发生明显衍射现象,焦平面对角线长度C值取15 mm
Figure 2. Distance L between remainders and the focal plane-remainders diameter dmax satisfying diffraction curves for different Dewar cold-shielding structures, slant dashed line 2.44λL/C denotes diameter lower limit value for diffraction, shadow region indicates obvious diffraction. Focal plane diagonal length C=15 mm
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