A Method for Eliminating Mixed Errors in Confocal Images by Integrating System Error Matrices with Low-Rank Approximation

In view of the difficulty in simultaneously eliminating multiple systematic errors and random errors in parallel bilateral chromatic dispersion differential confocal images, this paper proposes a hybrid error simultaneous removal method that integrates its prior systematic error matrix and low-rank approximation of random errors. Firstly, the causes of multiplicative systematic errors such as uneven illumination, different reflectivity, and stage tilt in the parallel bilateral chromatic dispersion differential confocal microscopy (PBCDDCM) measurement system are analyzed, and the systematic error matrix is experimentally measured. Then, the causes of random errors such as dead pixels and Gaussian noise in confocal images are analyzed, and the prior knowledge of the low-rank matrix recovery model is utilized to simultaneously eliminate multiple types of random noise. By integrating the systematic error matrix into the low-rank matrix recovery model, designing a low-rank approximation function, and solving the low-rank matrix recovery model using the alternating direction method of multipliers, a confocal image with eliminated systematic and random errors is obtained. This method is applied to eliminate mixed errors in confocal images of standard step samples and industrial sample gold fingers, and their surface topography is measured and Poisson surface modeling is performed. Experiments show that for a standard step sample with a height of 15 μm, the average height value of the measured step surface before correction is 15.14 μm, with a relative error of 1.06%. After correction, the average height value of the measured step surface is 14.99 μm, with a relative error of 0.07%. The surface topography of the gold finger is restored, and its imaging quality is significantly improved. The average height value of the steps obtained from multiple measurements of the gold finger is 19.54 μm, which has a relative deviation of 2.51% compared to the height measurement result of 19.06 μm obtained at the same position on an Olympus laser microscope. Therefore, this method enriches the field of confocal image surface measurement and topography restoration with noise elimination in both theory and practice.