Zhang Zhipeng, Menq Chia-Hsiang
Precision Measurement and Control Laboratory, Department of Mechanical Engineering, The Ohio State University, 201 West Nineteenth Avenue, Columbus, Ohio 43210, USA.
Appl Opt. 2008 May 1;47(13):2361-70. doi: 10.1364/ao.47.002361.
A three-dimensional (3D) particle tracking algorithm based on microscope off-focus images is presented in this paper. Subnanometer resolution in all three axes at 400 Hz sampling rate is achieved using a complementary metal-oxide-semiconductor (CMOS) camera. At each sampling, the lateral position of the spherical particle is first estimated by the centroid method. The axial position is then estimated by comparing the radius vector, which is converted from the off-focus two-dimensional image of the particle with no information loss, with an object-specific model, calibrated automatically prior to each experiment. Estimation bias and variance of the 3D tracking algorithm are characterized through analytical analysis. It leads to an analytical model, enabling prediction of the measurement performance based on calibration data. Finally, experimental results are presented to illustrate the performance of the measurement method in terms of precision and range. The validity of the theoretical analysis is also experimentally confirmed.
本文提出了一种基于显微镜离焦图像的三维（3D）粒子跟踪算法。使用互补金属氧化物半导体（CMOS）相机以400 Hz采样率在所有三个轴上实现了亚纳米分辨率。在每次采样时，首先通过质心法估计球形粒子的横向位置。然后通过将从粒子的离焦二维图像转换而来且无信息损失的半径向量与在每次实验前自动校准的特定对象模型进行比较，来估计轴向位置。通过分析分析表征了3D跟踪算法的估计偏差和方差。由此得到一个分析模型，能够基于校准数据预测测量性能。最后，给出了实验结果，以说明该测量方法在精度和范围方面的性能。理论分析的有效性也通过实验得到了证实。
