Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal

Accurate and efficient peak extraction algorithm is essential in real-time chromatic confocal measurement. However, current state-of-art algorithms cannot simultaneously satisfy the requirement of high extraction accuracy and computational efficiency. In this paper, we propose a corrected fitting differential algorithm (CFDA) with good-accuracy and high computational efficiency. Firstly, the CFDA is conducted to extract the initial peak wavelength with the conventional linear fitting of the differential signal, which is derived from the spectral axial intensity signal. Secondly, the fitting error is characterized via a generalized differential equation. Finally, the error is estimated and corrected by solving this equation with a first-order approximation. Compared to the high-accuracy Gaussian fitting algorithm, our simulations and experiments demonstrate that the CFDA can achieve approximately a hundred times improvement in computing efficiency while maintaining a comparable peak extraction accuracy.