A new sensor type is proposed to accurately detect the surface profiles of three-dimensional (3D) free-form surfaces. This sensor is based on the single-exposure, zero-crossing method and is used to measure position and angle simultaneously. First, the field intensity distribution in the posterior focal plane of the confocal microscope’s objective was modeled accurately. Second, because the camera needs to trigger acquisition when the surface (to be measured) reaches the focal position of the sensor, a zero-crossing prediction method based on a sliding window was proposed. Third, a fast, spatially convergent, peak-extraction algorithm was proposed to improve the accuracy and efficiency of peak extraction. This scheme reduces system installation and adjustment difficulties, and the single-exposure, zero-crossing method achieves high-speed, real-time image acquisitions. The experimental results indicate that the average error of the zero-crossing prediction system was 17.63 nm, the average error of the tilt degree measurement was 0.011° in the range of 0–8°, and the prediction error of the tilt direction measurement was 0.089° in the range of 0–360°. The sensor can measure the slope and can be potentially used for 3D surface precision detection.

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.

Quantifying free-form surfaces using differential confocal microscopy can be challenging, as it requires balancing accuracy and efficiency. When the axial scanning mechanism involves sloshing and the measured surface has a finite slope, traditional linear fitting can introduce significant errors. This study introduces a compensation strategy based on Pearson’s correlation coefficient to effectively reduce measurement errors. Additionally, a fast-matching algorithm based on peak clustering was proposed to meet real-time requirements for non-contact probes. To validate the effectiveness of the compensation strategy and matching algorithm, detailed simulations and physical experiments were conducted. The results showed that for a numerical aperture of 0.4 and a depth of slope < 12°, the measurement error was <10 nm, improving the speed of the traditional algorithm system by 83.37%. Furthermore, repeatability and anti-disturbance experiments demonstrated that the proposed compensation strategy is simple, efficient, and robust. Overall, the proposed method has significant potential for application in the realization of high-speed measurements of free-form surfaces.

To address the difficulty in simultaneously improving the lateral resolution and axial response sensitivity in differential confocal microscopy, this study proposes a differential confocal measurement method based on the collaborative optimization of the heterogeneous pupil filters in the illumination and detection paths. An analytical model of the heterogeneous pupil differential confocal system is established, achieving the coordinated enhancement of the lateral resolution and axial response sensitivity. A fast evaluation mechanism is introduced to improve the computational efficiency by 65%. Based on the optimized parameters, the heterogeneous pupil filters are fabricated. Experimental results demonstrate that the lateral full width at half maximum of the focal spot is reduced by approximately 14%, and the slope of the axial differential response within the linear region is increased by approximately 13%, consistent with the simulation results. The proposed method achieves the simultaneous enhancement of the lateral resolution and axial response sensitivity while maintaining a compact system structure, providing an effective optical enhancement strategy for high-precision three-dimensional surface profile measurement.

Distortion is a key parameter affecting the imaging performance of lenses. In this study, we propose a testing method based on detector Nyquist sampling of image data to achieve high-precision measurements of the distortion distribution of lenses. The distribution patterns of distortions in horizontal and vertical directions can be obtained by analyzing the distribution patterns of Moiré fringes in images under Nyquist sampling conditions and using phase-shift algorithms. The distortion-distribution characteristics of the lens are then calculated using distortion formulas. This method is characterized by high testing accuracy and sampling resolution. The image-plane distortion distribution exhibited a consistent linear trend when the object-plane position varied within a limited spatial range. Furthermore, the proposed method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm³. This method enables a high-precision distortion evaluation of conventional industrial imaging lenses.