Absolute testing is a key technique for achieving nanoscale measurements in Fizeau interferometry. Traditional methods use Zernike polynomials to fit the test surface form and indirectly infer the reference surface form, which can lead to error accumulation. In this article, we propose a neural absolute testing method that uses an advanced neural radiance field to directly model the reference surface form, thereby reducing error accumulation. The proposed framework includes an invariant surface branch and a variant surface branch; the sum of these two branches is expected to closely approximate the measured data under varying rotations and shifts. Consequently, a self-supervised training strategy has been developed to optimize the model parameters, eliminating the need for extensive training datasets with ground truth labels. Synthetic experiments demonstrate that the proposed method achieves superior absolute calibration accuracy compared to the traditional Zernike polynomial approach. Furthermore, real-world experiments performed using a Fizeau interferometer confirm that the proposed method produces a more robust reference surface form than the classical Zernike polynomial technique.

The achievable performance with repetitive control is limited due to its inherent sensitivity to the frequency shift away from the intended periodic frequencies and the undesired gain amplification of the aperiodic disturbances. To address these limitations, the paper proposed a general parametric repetitive control (GPRC) method based on the IIR filter with the features of low-order and excellent magnitude responses to result in better tracking performance in diverse applications. By analyzing its sensitivity function, it is found that the design of GPRC can be converted to the explicit parametric design of an IIR high pass filter. The controller design process and the stability analysis are presented in detail. To show the effectiveness of GPRC, comparative experiments are conducted via tracking sinusoids, triangular trajectories and other complex trajectories with multi-frequency components. The experimental results show that, in contrast with the conventional repetitive control (CRC) and a modified repetitive control (MRC), the GPRC exhibits excellent robustness against the frequency shift and advanced performance at the aperiodic frequencies. The tracking results of the sinusoids show that the maximum tracking error obtained with GPRC for a frequency shift of 3 Hz decreases from$0.0259~\mu m$(CRC) and$0.2207~\mu m$(MRC) to$0.0101~\mu m$at the nominal frequency of 1000 Hz, demonstrating the merits of the proposed GPRC. Note to Practitioners—To enable automation systems, one of the crucial requirements is to track repetitive references with high precision. Although the normal repetitive control (RC) based schemes are successfully applied to improve the tracking accuracy of periodic trajectories, the existing RC schemes suffer from the problems of lower robustness against frequency shift and the unwanted gain amplification at the aperiodic frequencies due to Bode’s sensitivity integral. To overcome this problem, this paper proposes a novel general parametric repetitive control (GPRC) method via characterizing the loop properties quantitatively based on the IIR high pass filter design. Focusing on specific issues, the detailed variations to handle the errors at only the odd- and even-harmonics are also demonstrated. This framework leads to a flexible solution in practical implementations. The experimental validation on a piezo-actuated nanopositioning stage is comparatively presented in terms of tracking accuracy and rejection ability of the gain amplification at the aperiodic frequencies. With its flexibility and effectiveness, the proposed GPRC can be easily implemented in diverse applications.

Surface texture measurement helps control the quality of large workpieces produced by machine systems. Current optical measurement methods, e.g., fringe projection profilometry and coherent scanning interferometry, are difficult to perform full-field measurements of microtextures on large-sized surfaces. Photometric stereo could potentially address this challenge; however, machined metal surfaces exhibit highly reflective non-Lambertian reflectance that dramatically decreases its effectiveness. To solve this problem, a task-specific near-field photometric stereo approach is proposed to dramatically enhance the accuracy of the surface normal estimation on machined metal surfaces. First, a near-field photometric stereo network is designed for efficient industrial applications, which fully employs the pixelwise information under a small number of lights to achieve surface normal estimation. Then, a task-specific training strategy is proposed to train the proposed network, where a task-specific real dataset is established for each specific combination of material and machine processing to optimize the network parameters initially trained by a synthetic dataset. Experiments on synthetic sinusoidal surfaces and real machined surfaces validated the superiority of the proposed method for metal reflectance compared with the state-of-the-art photometric stereo methods and the sub/micrometer-level sensitivity to surface height variations. Two case studies on tool marks on a large freeform surface and defects on a stamping surface are presented, demonstrating their potential for industrial applications.

The highlight reflectance on machined metal surfaces dramatically influences the performance of optical measurement sensors, such as fringe projector profilometers. Previous research addressed such an issue through fusion of images under different camera exposure times or modulation of the lighting intensity of the projector. Differently, this article provides a new research perspective that resorts to the modeling of complicated anisotropic reflectance on machined metal surfaces, which essentially causes the decrease in the quality of fringe images. In this article, an anisotropic neural reflectance model is proposed for the effective description of machined metal reflectance. Then, a facility with one camera, one projector, and several lighting emittance didoes is designed for the application of the proposed model in the measurement of curved machined metal surfaces. A complete and accurate point cloud is finally obtained through fitting of the real reflectance using the proposed model in a self-supervision way. Synthetic experiments illustrate that the capability of the proposed model to describe the machined metal reflectance is considerably enhanced compared with the traditional parameterized reflectance model and isotropic neural reflectance model. Real experiments prove that the proposed method can achieve measurement accuracy of 23 μm on machined metal surfaces with repeated accuracy of 0.15 μm, where the ground truth is given by the coordinate measuring machine.

To ensure the machining quality of micro/nano scale structural units for meter scale workpieces, relay turning with multiple single-point diamond tools has been broadly required. However, the existing tool setting methods have the problems of long tool setting time and low tool setting accuracy. To address the above issues, a novel normalized variational auto-encoder model with an adaptive activation function (NVAE-AAF) is proposed in this article. The batch normalization and the adaptive activation function are introduced into the variational auto-encoder model to learn robust features of force signals at the tool idle move state. Then, the reconstruction error threshold is constructed according to the kernel density estimation method to realize the nanoscale tool setting. In the ultraprecision tool setting experiments based on piezoelectric ceramic force sensing, the reconstruction error of the force signals at the tool idle move state is less than 0.07%, and the contact detection accuracy reached 92%. Compared to the traditional trial cutting for tool setting method, the proposed method significantly improves tool setting accuracy by 75%–85%, reaching a level of 75 nm.

In this article, an intelligent feedforward prediction and compensation scheme to combine with a dual-loop high-bandwidth controller is proposed for high-speed and high-precision tracking controls of a nanopositioning stage. First, the dual-loop controller consisting of an inner loop damping and an outer loop tracking controller is developed with all the parameters optimized simultaneously, which could provide a control bandwidth over the first resonant frequency of the stage. Next, the Gaussian process machine learning model is employed to capture the dynamic characteristics of the tracking error of the dual-loop controlled plant. Then, a feedforward compensator is constructed to add a compensation term to the initial reference trajectory. Experimental investigations on a self-made piezoelectric-actuated stage validate the effectiveness of the intelligent tracking error prediction method and the excellent performance of the control strategy for high-precision tracking of high-frequency reference trajectories.