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共焦成像是一种采用点对点照明及空间针孔调制,从而消减样品在非焦平面散射光的光学成像方法,此方法具有很高的光谱分辨率[19]。
布里渊散射光谱是通过散射光的光谱偏移来研究样品中入射光和声学声子之间的相互作用,从而提供关于材料的声学,热力学和粘弹性特性的信息。在单一材料中,声学声速和布里渊光谱频移的关系为:
$$\Delta \nu {\rm{ = }} \pm \dfrac{{{{2n}}V}}{{{\lambda _{}}}}\sin \dfrac{\theta }{2}$$ (1) 式中:
$\Delta \nu $ 为布里渊光谱的频移量;$\lambda $ 为入射波长;$V$ 为声学声速;${{n}}$ 为折射率;$\theta $ 为散射角。若是后向散射模式,则
$\theta $ =180°,由公式(1)可得:$$\Delta \nu {\rm{ = }} \pm \dfrac{{{{2n}}V}}{\lambda }$$ (2) 由参考文献[8]可知,单一材料的纵向弹性模量M为:
$$M{\rm{ = }}\rho {V^{{2}}}$$ (3) 式中:
$\rho $ 为材料的密度。因此,通过公式(2)~(3),布里渊光谱在后向散射的情况下,通过测量材料的布里渊频移
$\Delta \nu $ ,并结合该材料的密度$\rho $ ,就可得到该材料的纵向弹性模量M。 -
虚像相位阵列(Virtual Image Phase Array, VIPA)实质上是一个表面粗糙度小于0.01的平行平板,它的基本原理如图1所示。入射面和出射面都被镀上高反膜,一般分别为100%和95%。入射光以小角度进入玻璃板并聚焦到出射面上,其中一小部分会穿过出射面,通过光束腰后发散,大部分的光被反射到入射面后会再次反射到出射面,然后再有一小部分光从出射面射出。如此反复,直到所有光泄露出VIPA。所有的出射光之间会产生相互干涉,被分成无数间隔固定的光束,而每一个光束都可以假设成是由一个虚像产生的。一般情况下,VIPA的光谱分辨率为[20]:
$$ f = \dfrac{{\lambda _0^2}}{{2\pi nd\cos {\theta _1}}}\dfrac{{1 - {R_1}{R_2}}}{{\sqrt {{R_1}{R_2}} }} $$ (4) 式中:
${\theta _1}$ 为VIPA的倾角;$d$ 为VIPA 的厚度;${\lambda _0}$ 为激光中心波长;${{n}}$ 为空气折射率;${{{R}}_1}$ 、${R_2}$ 分别为VIPA前后表面膜的反射率。出射光束中的光由于波长不同,折射出的光角度各不相同,形成色散效应[21]。根据VIPA的色散效应,可以获得不同入射光的光谱特征。此外,由于VIPA是标准具,受到自由光谱范围(Free Spectral Range, FSR)的限制,会出现级次重叠现象,如图2所示,VIPA标准具无法区分550.00 nm与550.06 nm波长的光。因此,VIPA常与其他角度色散光学元件级联使用,不仅提高了采集速率和分辨率,而且能够改善级次重叠的现象,从而获得二维光谱图像。该系统中使用的VIPA是LightMachinery Inc.的OP-6721-2000-2Rev.F VIPA500~600 nm, 厚度为2 mm ,光谱分辨率为1 pm,同步测量范围为4 nm。
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图3为共焦布里渊光谱成像系统,由光谱激发、白光照明、光谱采集、三维空间运动四个模块组成。首先,使用白光照明模块和三维空间运动实现被测样品的定焦与目标区域的确定;然后,利用光谱激发模块产生布里渊散射光,并收集后向散射光进入光谱采集模块,利用VIPA光谱仪采集被测目标的布里渊光谱信息,每个模块的具体组成和作用见3.1~3.4小节。
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光谱激发模块如图3中红色实线部分所示,它的作用是激发布里渊散射光。包含激光、会聚物镜、准直器扩散器、分束棱镜、显微物镜和共焦针孔等。激光器使用的是Verdi G-2W 532 nm单纵模、连续、大功率、光抽运半导体激光器,由相干公司生产。激光输出通过光束扩散器扩展光束,微元区域汇聚到焦平面上,实现“点光源”。焦平面处的微元物质和激光激发出的光子相互作用,从而激发出布里渊散射光,显微物镜将收集的背向散射光汇聚进入物镜A、直径为100 μm的共焦针孔及物镜B中,为了将针孔置于物镜A的物侧焦点处,实现“点检测”,需要反复调整针孔的位置。
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图3中的白光照明模块设计用于确定被测样品的固定焦点和靶区,主要组件有CCD、分光棱镜、显微物镜和白光光源。CCD获得样品的靶区和样品的轴向聚焦,显微物镜进行显微成像。显微物镜使用的是Olympus生产的PLAN系列、数值孔径是0.25的10倍显微镜,其作用是白光聚焦成像。在进行样品光谱测量之前,使用白光照明模块。
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图3所示的三维空间运动模块用于样品观测、靶区选择和布里渊光谱成像。平台分为横向(垂直于光轴) XY平面及轴向(光轴)。其中横向XY平面运动平台有两种调节方式,分别为粗调、精调,粗调二维平台使用的是BioPrecision2系列电动平移平台,分辨率为50 nm,行程为100 mm×100 mm。精控部分采使用P-542.2CD二维运动平台,行程为200 μm×200 μm,闭环分辨率与线性度为2 nm及0.03%,重复性小于5 nm。轴向运动部件使用的是SGSP80-20ZF型升降平台,用于样品定位过程中的轴向位置的调节。
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布里渊弹性散射的频移大致在1~50 GHz范围内,所以光谱仪的分辨率必须满足R> 106的要求。现在已有的光谱检测方法有多通道扫描FP干涉仪法[22]、光栅单色仪法[23]等。然而,上述扫描方法不仅分辨率低而且采集速度慢,缓慢的采集时间将布里渊光谱限制为点采样或静态测量。针对上述问题,该系统使用基于虚像相位阵列(Virtual Image Phase Array,VIPA)的光谱仪作为布里渊光谱采集模块。图4为VIPA光谱仪的示意图,红色实线部分为激光和背向散色光抑制模块,红色虚线部分为二维光谱成像模块。
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为了提高布里渊光谱的采集速度和光谱分辨率,该系统将VIPA与衍射光栅级联。图5为VIPA和衍射光栅联合的二维光谱原理图。垂直方向上,VIPA提供高分辨率;水平方向上,衍射光栅将重叠的标准具级次分开,以扩展整个高分辨率光谱。所有波长可以同时采集,大大缩短了光谱的采集时间。此外,将VIPA与衍射光栅结合,输出光束会根据不同的波长在二维平面展开,从而使得波长和成像面空间中的坐标一一对应,从而测量出物体的二维光谱图像信息。
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布里渊散射在自发状态下是相对较弱的过程,并且光频移很小,大约为10 GHz。在大多数情况下,由瑞利散射或光学反射引起的弹性散射光比布里渊信号强几个数量级,因此弹性散射信号很容易淹没布里渊信号。为了改善这一情况,该方案采用超窄线宽滤波器来抑制激光在光谱仪内部的反射,其滤波原理与F-P标准具相似。F-P标准具透射率最大的条件为:
$$2d\cos \alpha = m\lambda $$ (5) 图6为超窄线宽滤波器原理图,根据不同波长
$\lambda $ ,通过调节可移动平板来改变间距${{d}}$ ,即可达到滤波的目的。 -
为了检验该装置的光谱检测特性及成像功能,进行了单个点的光谱探测和二维光谱成像两个实验。
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对聚甲基丙烯酸甲酯(PMMA)、聚乙烯和二氧化硅玻璃样品分别进行了单点的布里渊光谱测试。图7分别为PMMA、聚乙烯和二氧化硅玻璃样品的典型光谱仪输出图。
使用洛伦兹峰值拟合方法,获得了PMMA、聚乙烯和二氧化硅玻璃的布里渊光谱频移,分别为15.4 GHz、16 GHz和33.8 GHz,如图8所示,然后根据公式(2)及公式(3)计算得出上述各材料的纵向弹性模量M,如表1所示,实验结果与参考文献[12]测试结果一致。
Sample Density/
g·cm−3Refractive
indexFrequency
shift/GHzElastic
modulus/GPaPMMA 1.18 1.49 15.4 8.92 Polyethylene 0.19 1.51 16 7.23 Silica glass 2.23 1.47 33.8 83.4 该系统布里渊光谱的分辨率计算式为[24]:
$$\Delta {{f}} = \dfrac{{c\Delta \lambda }}{{N\lambda _0^2}}$$ (6) 式中:
$\Delta {{f}}$ 为光谱分辨率;$c$ 为光速(3×108 m/s);$N$ 为通道数(4096);$\Delta \lambda $ 是同步测量范围(4 nm);${\lambda _0}$ 为激光中心波长(532 nm)。代入测量参数,可以得到该实验装置的光谱分辨率为0.25 GHz。 -
由于容易获得PMMA的布里渊信号,因此在该实验中选择了PMMA来验证成像性能。图9是PMMA的二维布里渊光谱图像。图9(a)是在没有激光和反向散射光抑制模块的情况下测得的PMMA的布里渊光谱图像。图9(b)是添加了激光和反向散射光抑制模块后测得的PMMA的布里渊光谱图像,图中两个白色亮点即为PMMA的布里渊光谱图像。通过实验可知,加入激光和背向散色光抑制模块,可以更清楚更有效地获得物质的布里渊光谱图像信息。
Elastic modulus measurement based on virtual image phase array confocal Brillouin spectroscopy technology
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摘要: 生物组织和材料的弹性模量是决定其力学性能的关键因素,对生物医学和材料监测等领域至关重要。提出了一种基于虚像相位阵列的弹性模量测量方法,虚像相位阵列与共聚焦显微系统相结合,能够快速获得生物组织和材料的布里渊光谱频移,从而计算得到其弹性模量。首先,理论上分析了材料的弹性模量和布里渊光谱频移之间的关系;然后,介绍了虚像相位阵列的原理及系统的各组成部分;最后,对样品材料进行光谱测试,分别测得了聚乙烯、二氧化硅玻璃和聚甲基丙烯酸甲酯(PMMA)的光谱,求得纵向弹性模量M分别为7.23 GPa、83.4 GPa和8.92 GPa,并且测得了PMMA的布里渊光谱图像。结果表明:虚像相位阵列与衍射光栅级联使用,能够改善标准具的级次重叠现象,提高布里渊光谱的分辨率和采集速率,该系统设计的激光和背向散色光抑制模块,显著提高了布里渊信号的对比度,在材料特性、结构监测和生物医学等方面具有重要意义。Abstract: The elastic modulus of biological tissues and materials is the key factor to determine their mechanical properties, which is very important for biomedicine and material monitoring. A method for measuring elastic modulus based on virtual image phase array was proposed. Combining virtual image phase array with confocal microscopy system, the Brillouin spectrum frequency shift of biological tissues and materials could be obtained quickly, and then the elastic modulus could be calculated. Firstly, the relationship between the elastic modulus and Brillouin spectrum frequency shift was analyzed theoretically; Then, the principle of the virtual image phase array and the components of the system were introduced; Finally, the spectrum test of the sample material was performed, and the spectra of polyethylene, silica glass, and polymethyl methacrylate (PMMA) were measured, the longitudinal elastic modulus M was calculated to be 7.23 GPa, 83.4 GPa and 8.92 GPa, respectively, and the Brillouin spectral image of PMMA was measured. The results show that the cascade use of the virtual image phase array and the diffraction grating can improve the order overlap phenomenon of the etalon, and increase the resolution and acquisition rate of the Brillouin spectrum. The laser and backscattering light suppression module designed by this system can significantly improve the contrast of the Brillouin signal which is of great significance in material properties, structure monitoring and biomedicine.
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