The polarized energy dispersive X-ray fluorescence analysis method can effectively reduce detection limits by improving the signal-to-noise ratio. However, the lack of high-power density and small analysis area of the polarized X-ray beam has hindered more accurate analysis of samples in conventional laboratory. A polycapillary X-ray lens can be applied to micro-area analysis. Therefore, a micro-area polarized energy dispersive X-ray fluorescence spectrometer based on a bent highly oriented pyrolytic graphite and a polycapillary X-ray lens is proposed. The polarization degree of the polarized X-ray beam is 99.76% and its focal spot size is 338.8 μm × 404.5 μm. The new spectrometer feasibility was proved by effective production of high-resolution element distribution maps of a holly (Ilex chinensis Sims) leaf sample.

A simulation model is established to simulate the X-ray transmission performance through a polycapillary focusing X-ray lens whose configuration curve was described by a piecewise function. The shape of the lens is segmented, and each segment uses different function curve. The ray tracing principle is used to simulate the transmission performance of X-rays through the polycapillary focusing X-ray lens. And the simulation results were compared with the experimental results.

Curve approximation is a challenging issue to precisely depict exquisite shapes of natural phenomena, in which the piecewise Bézier curve is one of the most widely utilized tools due to its beneficial properties. It is essential to determine the quantity and location of control points through the process of generating the mathematical representation of desired objects. This paper presents a new algorithm called adaptive extension fitting scheme (AEFS) to determine a piecewise Bézier curve that best fits a given sequence of data points as well as locate the coordinates of the connecting points between the pieces adaptively. Taking full advantage of the scalability of the Bézier curve segment, AEFS is effective in sequential knot searching within an impressively small computational consumption. The capability of the proposed stepwise extension strategy is deduced from rigorous theoretical proof, resulting in proper connecting points together with well-fitted Bézier curves. The proposed algorithm is evaluated by some popular benchmarks for curve fitting, and compared with several state-of-the-art approaches. Experimental results indicate that AEFS outperforms other models involved in terms of execution time, fitting accuracy, number of segments, and the authenticity of shape contours.