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.

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.

One of the key issues in photometric stereo is the extension of its application in real world objects which shows non-Lambertian reflectance. This letter proposes a multi-scale weighted convolutional fusion network with deep learning architecture to realize high-precision perception of non-Lambertian surfaces under arbitrary illumination conditions. A multi-scale convolutional fusion module is designed to strengthen the photometric physics and the utilization of the neighborhood features at the same time so as to overcome shadows and distinguish multiple materials. In order to further deal with the problem of arbitrary illumination conditions, a multi-resolution polar coordinate division method is proposed to integrate the input image information and fully utilizes the multi-scale convolution. Both syntheses and real-world experiments verifies the performance of the proposed method in recovery accuracy and computational efficiency.

Current non-Lambertian photometric stereo methods generally require a large number of images to ensure accurate surface normal estimation. To achieve accurate surface normal recovery under a sparse set of lights, this paper proposes a non-Lambertian photometric stereo network based on a derived inverse reflectance model with collocated light. The model is deduced using monotonicity of isotropic reflectance and the univariate property of collocated light to decouple the surface normal from the reflectance function. Thus, the surface normal can be estimated by three steps, i.e., model fitting, shadow rejection, and normal estimation. We leverage a supervised deep learning technique to enhance the shadow rejection ability and the flexibility of the inverse reflectance model. Shadows are handled through max-pooling. Information from a neighborhood image patch is utilized to improve the flexibility to various reflectances. Experiments using both synthetic and real images demonstrate that the proposed method achieves state-of-the-art accuracy in surface normal estimation.