Compound refractive lens (CRL) is an indispensable component for focusing high-energy X-rays in the new generation of light source scientific apparatus. CRL achieves focusing by stacking multiple unit lenses, which can easily lead to the accumulation of error defects. Various problems often arise during their fabrication, such as surface deviations, relative transverse offsets, and mutual tilt angles of the front and back surfaces, which can affect the intensity and focal position of the focused beam. It is very important to measure these parameters without damaging the sample to adjust process parameters and optimize lens application. For two-dimensional focusing lenses, microscopy can only detect the single-sided surface profile, and wavefront metrology methods such as X-ray speckle can only qualitatively judge the alignment by restoring figure errors. X-ray computed tomography (CT) can meet the need for overall characterization of the three-dimensional structure of the lens, but there is a problem of missing subsequent data processing. To solve the issue of three-dimensional profile characterization of hyperbolic refractive lenses, we propose a measurement method based on point cloud processing. By fitting and calculating the surface point cloud model obtained from X-ray CT, typical double-sided processing quality parameters, including relative transverse offset, mutual tilt angle, and single-sided curvature radius, can be accurately measured, which provide accurate and detailed data support for fabrication optimization.

This method is mainly divided into three steps: first, X-ray CT scanning is used for three-dimensional reconstruction; then, the surface boundary point cloud data is extracted through threshold segmentation; finally, the point cloud model is segmented, fitted, and calculated. In the first step, the sample is scanned using synchrotron radiation X-ray CT to obtain several projection images, which are reconstructed into a three-dimensional slice image with varying grayscale values. Due to the presence of noise in the image, the air and diamond matrix cannot be completely separated using a single threshold segmentation method. Therefore, based on the global threshold, watershed segmentation is applied to re-mark and define overlapping pixels to complete the clear surface boundary segmentation. The surface mesh is then generated to extract its point cloud data. The point clouds on both sides are divided at equal distances, and the centroid points of each layer are found. Straight lines are fitted based on the coordinates of the centroid points. The angle between the two straight lines represents the mutual inclination angle of the two sides. The relative transverse offset is calculated by finding the distance between the overall centroid points of the point clouds on both sides. For the curvature radius of a single-sided surface, after cutting off the point cloud data from the top flat part of the surface, a polynomial equation is fitted to achieve its numerical calculation.

Taking six samples of double parabolic refractive lenses made of diamond material through femtosecond laser processing as examples, we carry out the verification experiment at the beamline BL13HB at the Shanghai Synchrotron Radiation Facility (SSRF). Samples are placed on a rotating table, as shown in Fig. 3(c), and 1080 projection images are taken, as shown in Fig. 4(a). The ideal segmentation boundary, obtained by combining global threshold segmentation and watershed segmentation through Avizo software, is shown in right of Fig. 4(b). Fig. 4(c) shows the three-dimensional visualization of the lens sample. In the equidistant segmentation of the point cloud model, the number of layers is key to the numerical calculation. The relationship between the calculated value of the mutual tilt angle and the number of layers is analyzed. Among the extracted centroid coordinates, some centroid points are far away from the center position. When the number of layers is too small, these deviation points will affect the straight-line fitting results. Figure 8 shows the angle calculation values θ of the six lens samples as the number of layers changes. The calculation results tend to stabilize after 200 layers, so 250 layers are an appropriate choice. Table 2 gives the calculated values of the relative transverse offsets and mutual tilt angles for the six samples. The calculation of the single-surface curvature radius is compared with the measurement results of the confocal laser scanning microscope. As shown in Table 3, the two results are in good agreement, with the maximum error being 1.58% and the minimum error being as low as 0.09%.

To address the contour characterization problem of hyperbolic refractive lenses, we propose a point cloud processing method. With the aid of synchrotron X-ray CT technique, a method combining global threshold segmentation and watershed segmentation is used to extract surface boundaries and point cloud models. No filtering or denoising is required. The million-coordinate data contained in the model can fully restore the contour morphology of the lens sample and can accurately characterize cases of excessive inner wall inclination. The accuracy of this method is further verified through comparison tests with laser scanning confocal microscopy. The proposed method can enable the quantitative calculation of relative transverse offset and mutual inclination angle in three-dimensional space and has significant application value in improving and optimizing fabrication technology.