Precise Two-Dimensional Tilt Measurement Sensor with Double-Cylindrical Mirror Structure and Modified Mean-Shift Algorithm for a Confocal Microscopy System

Abstract

To improve the accuracy of three-dimensional (3D) surface contour measurements of freeform optics, a two-dimensional (2D) tilt measurement sensor for confocal microscopy (CM) systems is proposed based on a double-cylindrical mirror structure. First, the proposed system is accurately modeled. Second, we introduce a modified mean–shift-based peak-extraction algorithm with a novel kernel function (MSN) because the reflectivity of the measured object and fluctuation of the light source affect the measurement accuracy. Third, a partition fitting (PF) strategy is proposed to reduce the fitting error and improve the measurement accuracy. Simulations and experiments reveal that the robustness, speed, and angular prediction accuracy of the system effectively improved as a function of MSN and PF. The developed sensor can measure the 2D tilt, where each tilt is a composition of two separate dimensions, and the mean prediction errors in the 2D plane from −10°–+10° are 0.0134° (0.067% full scale (F.S)) and 0.0142° (0.071% F.S). The sensor enables the optical probe of a traditional CM to obtain accurate and simultaneous estimates of the 2D inclination angle and spatial position coordinates of the measured surface. The proposed sensor has potential in 3D topographic reconstruction and dynamic sampling rate optimization for 3D contour detection.

A Differential Confocal Sensor for Simultaneous Position and Slope Acquisitions Based on a Zero-Crossing Prediction Algorithm

“…From the above experiments, we proved the accuracy of the prediction of zero-crossing and the effectiveness of obtaining the tilt angle information of the SUT by using the single image of zero-crossing. Compared with the method of using a cylindrical mirror and linear CCD to obtain the distribution of light intensity on the focal plane of the microscope [ 15 ], the structure is simpler and the requirement for the precision of installation is lower. The proposed method can measure the tilt angle of the SUT by collecting images at the zero-crossing of the differential signal.…”

“…The FSC algorithm was used according to the training set to extract the peak position and establish the relationship between the peak position of the light spot and the tilt angle of the tested surface. Using the partition-fitting polynomial fitting method [ 15 ], surfaces determined by the relationship surfaces between the peak position and (a) tilt degree θ and (b) tilt direction φ were fitted, as shown in Figure 10 .…”

“…In a recent study, Wang [ 15 ] scanned a surface with an objective lens, used a data board card to establish the corresponding relationship between the real-time image information received by the two linear CCDs orthogonal in space and the axial position of the scan, and then transmitted it to the computer for storage. After the signal was calculated, the zero-crossing position was obtained, and the information related to the current measured point was extracted based on the established relationship.…”

“…Biharmonic spline interpolation based on surface interpolation can retain the details of the surface to a great extent [ 31 ]; however, the interpolation speed is low and cannot meet the system’s real-time prediction requirements. Therefore, in this study, a partition-fitting polynomial fitting method [ 15 ] was used to establish the relation surface between the peak position and ( θ , φ ).…”

“…These systems and measurement methods are associated with many problems, such as complex system structures and miscellaneous data processing, and their accuracy characteristics cannot meet practical application needs [ 15 , 16 , 17 , 18 ]. Wang et al [ 15 ] added a pair of spatially orthogonal, double-cylinder mirrors combined with a linear charged-coupled device (CCD) structure to the traditional DCM system, and successfully achieved dimensional reduction; this transformed the problem of two-dimensional (2D) peak search to a peak-extraction problem of one-dimensional data, and thus achieved high measurement accuracy. The mean prediction errors in the 2D plane tilt angle from −10° to +10° were 0.0134° (0.067% full-scale (F.S)) and 0.0142° (0.071% F.S).…”