As for chromatic confocal sensor system with limited computational capacity, a fast peak extraction algorithm with considerate accuracy is in urgent demand. However, current peak extraction algorithms such as the centroid algorithm (CA) and nonlinear fitting algorithms can not balance the accuracy and computational efficiency. Thus, we propose an accurate peak extraction algorithm with good computational efficiency called corrected differential fitting algorithm (CDFA). At first, the differential signal derived from the original axial response signal is linearly fitted for initial peak extraction. Then corresponding systematic error of this linear fitting operation is analyzed using a first-order linear nonhomogeneous differential equation. At last, error compensation, that is, the solution to this equation is implemented with an introduction of "sum differences of sampling intensity". The performance of CDFA is compared with two conventional peak extraction algorithms including the CA and Gaussian fitting algorithm (GFA) using Monte Carlo simulations. CDFA is found to have a comparable accuracy performance with GFA while have a much higher computational efficiency.
Based on vector diffraction theory and inverse Faraday effect, we report on the generation of optical needle and magnetization needle with tunable longitudinal depth by focusing a narrow annulus of azimuthally polarized beams using optmagnetic materials and an elliptical mirror. In this paper, we present the expression of the approximate result between the angular thickness Δθ and the longitudinal depth when the annulus is assumed to be sufficiently narrow (Δθ<<π/2). We theoretically demonstrate that the induced magnetization needle has the same longitudinal depth as optical needle, but with different distributions. The results are applied to the specific cases of the elliptical mirror and the parabolic mirror, then we further theoretically demonstrate that the longitudinal depth is equally long in the elliptical mirror focusing system and the parabolic mirror focusing system.
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