Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 μm, which is significantly better than RANSAC’s value of 25.41 μm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters.

Spectral confocal displacement sensors are non-contact optoelectronic sensors widely utilized for their high accuracy, speed, and ability to measure diverse surfaces. However, challenges including vibration, angular deflection, and surface quality variations can reduce sensor stability and accuracy when performing measurements such as lithium battery wafer thickness, wafer warpage, and optical component surface topography. This study proposes a line-spot-based measurement method using a binary diffractive lens and cylindrical lens with a 20× objective, and then the overall structure is simulated and optimized by using ZEMAX, which realizes a confocal measurement system with a measurement range of 800 μm, line spot length of 3.8 mm, and width of 0.2 mm. The system, calibrated with a nanometer displacement stage, achieved 30 nm resolution and significantly improved dynamic stability (standard deviation (SD) of 0.013 μm) compared to a point spectral confocal sensor (SD of 0.064 μm). The results indicate the proposed sensor exhibits improved stability during scanning measurements.

To improve the accuracy of in situ measurement of the standard volumes of pipe provers and to shorten the traceability chain, a new method of in situ pipe prover volume measurement was developed alongside a supporting measurement device. This method is based on the geometric dimension approach, which measures the inner diameter and length of a pipe prover to calculate its volume. For inner diameter measurement, a three-probe inner-diameter algorithm model was established. This model was calibrated using a standard ring gauge of Φ313 mm, with the parameters calculated through fitting. Another standard ring gauge of Φ320 mm was used to verify the inner diameters determined by the algorithmic model. A laser interferometer was employed for the segmented measurement of the pipe prover length. The comprehensive measurement system was then used for in situ measurement of the standard pipe prover. The newly developed system achieved an expanded uncertainty of 0.012% (k = 2) in volume measurement, with the deviation between the measured and nominal pipe prover volumes being merely 0.007%. These results demonstrate that the proposed in situ measurement method offers ultra-high-precision measurement capabilities.