基于阴影法的高精度大范围卡西米尔力测量

The Casimir effect is a multidisciplinary subject with important applications in the field of nanotechnology, MEMS, and so on. Highly sensitive precise Casimir force measurement is of great significance both in theory and engineering application. However, if we use the existing methods (such as torsion balance, atomic force microscope, etc.) to measure the Casimir force, the plates will move in the lateral direction, causing the surface roughness and the plate distance of the action points to change. The existence of lateral movement not only introduces greater measurement uncertainty, but also results in the inability to measure the Casimir force between asymmetric plates. This project proposes to measure Casimir force based on shadow method. In the process, the two plates do not move in the lateral direction, but only move vertically. Therefore, the shadow method can measure the Casimir force between the plates with different sizes and different shapes. This project is mainly based on the in-depth study of the physical essence of Casimir effect, using the shadow method to measure the Casimir force in the range of 50nm to 1μm with high accuracy and high stability. Within the distance range of 50nm to 200nm, the relative uncertainty is less than 5%. This will make an important contribution to MEMS instability analysis and the perfection of the mathematical model of Casimir force.

卡西米尔效应是一个涉及多学科的课题，在纳米技术、微机电等领域都有重要的应用。高精度测量卡西米尔力在理论和工程应用中都具有重要意义。但是，若采用现有的方法（如扭秤、原子力显微镜等）测量卡西米尔力，极板将发生横向偏移，而导致作用点的表面粗糙度变化以及极板间距变化。横向偏移的存在不仅引入较大的不确定度，而且导致无法测量非对称极板的卡西米尔力。本项目提出阴影法测量卡西米尔力，在测量过程中仅存在垂直移动，两极板不发生横向偏移。因此，阴影法能够高精确测量不同尺寸、不同形状极板间的卡西米尔力。本项目主要是在深入研究卡西米尔效应物理本质的基础上，基于阴影法高精度、高稳定地测量间距为50nm至1μm的卡西米尔力，在间距为50nm至200nm时相对不确定度小于5%。这对微机电系统失稳分析、卡西米尔力的数学模型的完善等具有重要意义。

针对现有微小力测量装置不确定度大、量程短且不能溯源至国际单位的缺点，探索基于阴影法的微小力测量装置。设计并搭建了基于阴影法的垂直式微纳力值测量系统，基于光线追迹软件Tracepro验证阴影的形成以及垂直压入深度与阴影直径的关系，通过设置光束与弯曲界面性质，对光线进行追迹。推导了基于阴影法的微纳力值测量模型。最终优化测量系统结构，如光源直径、胶体尺寸、镜头参数等。并采用标准砝码进行了系统标定实验，实验结果表明测量系统的灵敏度为2.15 μN/pixel。对阴影图像进行亚像素细分还可进一步改善传感器的分辨力，测量系统的测量范围为~0.981 mN。此外，由于胶体的粘弹性对环境噪声的过滤作用，系统阻尼比为0.22。对测量系统进行了抗噪性能实验，结果表明，与悬臂梁相比，扰动的影响降低了96.23%，该成果为测量卡西米尔力提供坚实的实验基础。

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