Open AccessCorrected parabolic fitting for height extraction in confocal microscopy
Author(s) -
Chen Cheng,
Jian Wang,
Richard Leach,
Wenlong Lu,
Xiaojun Liu,
Xiangqian Jiang
Publication year - 2019
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.27.003682
Subject(s) - a priori and a posteriori , monte carlo method , nonlinear system , compensation (psychology) , optics , curve fitting , parabolic partial differential equation , gaussian , algorithm , mathematics , physics , partial differential equation , mathematical analysis , statistics , psychology , philosophy , epistemology , quantum mechanics , psychoanalysis
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 2 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.