Chen Cheng, Wang Jian, Leach Richard, Lu Wenlong, Liu Xiaojun, Jiang Xiangqian Jane
Opt Express. 2019 Feb 4;27(3):3682-3697. doi: 10.1364/OE.27.003682.
Accurate and reliable peak extraction of axial response signals plays a critical role in confocal microscopy. For axial response signal processing, nonlinear fitting algorithms, such as parabolic, Gaussian or sinc fitting may cause significant systematic peak extraction errors. Also, existing error compensation methods require a priori knowledge of the full-width-at-half-maximum of the axial response signal, which can be difficult to obtain in practice. In this paper, we propose a generalised error compensation method for peak extraction from axial response signals. This full-width-at-half-maximum-independent method is based on a corrected parabolic fitting algorithm. With the corrected parabolic fitting algorithm, the systematic error of a parabolic fitting is characterised using a differential equation, following which, the error is estimated and compensated by solving this equation with a first-order approximation. We demonstrate, by Monte Carlo simulations and experiments with various axial response signals with symmetrical and asymmetrical forms, that the corrected parabolic fitting algorithm has significant improvements over existing algorithms in terms of peak extraction accuracy and precision.
轴向响应信号的准确可靠峰值提取在共聚焦显微镜中起着关键作用。对于轴向响应信号处理，诸如抛物线、高斯或正弦拟合等非线性拟合算法可能会导致显著的系统峰值提取误差。此外，现有的误差补偿方法需要轴向响应信号半高宽的先验知识，而这在实际中可能难以获得。在本文中，我们提出了一种用于从轴向响应信号中提取峰值的广义误差补偿方法。这种与半高宽无关的方法基于一种修正的抛物线拟合算法。利用修正的抛物线拟合算法，通过一个微分方程来表征抛物线拟合的系统误差，随后，通过用一阶近似求解该方程来估计和补偿误差。我们通过蒙特卡罗模拟以及对各种对称和非对称形式的轴向响应信号进行实验证明，修正的抛物线拟合算法在峰值提取精度和精密度方面比现有算法有显著改进。
