High-precision lateral distortion measurement and correction in coherence scanning interferometry using an arbitrary surface

Simulation-driven machine learning approach for high-speed correction of slope-dependent error in coherence scanning interferometry

Slope-dependent error often occurs in the coherence scanning interferometry (CSI) measurement of functional engineering surfaces with complex geometries. Previous studies have shown that these errors can be corrected through the characterization and phase inversion of the instrument's three-dimensional (3D) surface transfer function. However, since CSI instrument is usually not completely shift-invariant, the 3D surface transfer function characterization and correction must be repeated for different regions of the full field of view, resulting in a long computational process and a reduction of measurement efficiency. In this work, we introduce a machine learning approach based on a deep neural network that is trainable for slope-dependent error correction in CSI. Our method leverages a deep neural network to directly learn errors characteristics from simulated surface measurements provided by a previously validated physics-based virtual CSI method. The experimental results demonstrate that the trained network is capable of correcting the surface height map with 1024 × 1024 sampling points within 0.1 seconds, covering a 178 µm field of view. The accuracy is comparable to the previous phase inversion approach while the new method is two orders of magnitude faster under the same computational condition.

3D microscopy in industrial measurements

Quality control is essential to ensure the performance and yield of microdevices in industrial processing and manufacturing. In particular, 3D microscopy can be considered as a separate branch of microscopic instruments and plays a pivotal role in monitoring processing quality. For industrial measurements, 3D microscopy is mainly used for both the inspection of critical dimensions to ensure the design performance and detection of defects for improving the yield of microdevices. However, with the progress of advanced manufacturing technology and the increasing demand for high-performance microdevices, 3D microscopy has ushered in new challenges and development opportunities, such as breakthroughs in diffraction limit, 3D characterisation and calibrations of critical dimensions, high-precision detection and physical property determination of defects, and application of artificial intelligence. In this review, we provide a comprehensive survey about the state of the art and challenges in 3D microscopy for industrial measurements, and provide development ideas for future research. By describing techniques and methods with their advantages and limitations, we provide guidance to researchers and developers about the most suitable technique available for their intended industrial measurements.

Measurement and correction of lateral distortion in a Fizeau interferometer based on the self-calibration technique

The lateral distortion of a surface measuring Fizeau interferometer may cause distorted image features in the lateral direction, as well as the surface form error in the axial direction (which is a source of the retrace error). Traditional method for lateral distortion measurement requires a high-accuracy calibration plate featuring a grid pattern. Such a calibration plate is not always available, especially when the required accuracy of the grid pattern comes to the order of sub-micrometer or even nanometer level. To remove the dependence on the plate accuracy, we propose a self-calibration method for the measurement and correction of lateral distortion in Fizeau interferometer. The self-calibration technique may separate the lateral distortion and the geometric error of the calibration plate. This method is verified using a 108-mm-aperture Fizeau interferometer. The experiments show that the form measurement error of a surface tilted at approximately 5° and 16° can be reduced from 92 nm to 43 nm and from 251 nm to 144 nm (peak-to-valley value), respectively, after the distortion correction.

Learning-based self-calibration for correcting lateral and axial field distortions in 3D surface topography measurement

A learning-based self-calibration method is demonstrated to achieve simultaneous corrections for both lateral and axial field distortions in three-dimensional (3D) surface topography measurements. In this method, the back propagation neural network is introduced into the self-calibration technology to learn the mapping relationship between the distorted space and the undistorted space for realizing the separation of systematic errors and calibration sample topography. The rigid body feature of the artifact is used to construct the loss function to achieve the optimization of network parameters. This method not only retains the advantages of the self-calibration method but also characterizes a complex distortion model. Simulation results show that the accuracy of nanometers is achieved for the correction of lateral and axial field distortions. In the experiment, the root-mean-square (RMS) values of lateral correction residual errors are less than 30 nm, and the axial RMS values are less than 2 nm. Simulation and experimental results prove that this method can correct both lateral and axial field distortions to the level of nanometer by one calibration. It indicates that the learning-based self-calibration method might be the future development trend for lateral and axial field distortions corrections of measuring instruments in 3D surface topography measurement.

Digital Cultural Heritage Preservation in Art Painting: A Surface Roughness Approach to the Brush Strokes

There is a growing interest in cultural heritage preservation. The notion of HyperHeritage highlights the creation of new means of communication for the perception and data processing in cultural heritage. This article presents the Digital Surface HyperHeritage approach, an academic project to identify the topography of art painting surfaces at the scale at which the elementary information of sensorial rendering is contained. High-resolution roughness and imaging measurement tools are then required. The high-resolution digital model of painted surfaces provides a solid foundation for artwork-related information and is a source of many potential opportunities in the fields of identification, conservation, and restoration. It can facilitate the determination of the operations used by the artist in the creative process and allow art historians to define, for instance, the meaning, provenance, or authorship of a masterpiece. The Digital Surface HyperHeritage approach also includes the development of a database for archiving and sharing the topographic signature of a painting.

Noise Reduction in Coherence Scanning Interferometry for Surface Topography Measurement

Coherence scanning interferometry is one of the most accurate surface measuring technologies, and it is increasingly applied to challenging surface structures, such as additive manufactured parts and transparent films, directly in environments that resemble production areas more than metrology labs. Environmental disturbances may further compromise measurement accuracy. Data acquisition strategies to reduce measurement noise in coherence scanning interferometry include averaging a sequence of repeated topography measurements or increasing the sampling frequency of the fringe signal during a single data acquisition—sometimes referred to as oversampling. In this paper, we improve the understanding of the mechanisms of the two noise reduction methods and compare their effects on surface topography measurement in the presence of environment-induced vibration. The results provide guidance for good practice in the reduction of uncertainty in surface measurement for a wide range of applications.

Precision enhancement of three-dimensional displacement tracing for nano-fabrication based on low coherence interferometry

In the nano-fabrication field, high precision displacement tracing of the fabricating beam is extensively required. Due to the coherence noise and the sensitivity to environmental disturbances, the commonly used measuring methods base on the laser interferometry are unstable. In this paper, a high-precision measuring method for the three-dimensional displacements is developed based on the low coherence interferometry. The interferogram at a particular location is unique and distinctive, which can be applied as a benchmark for the absolute measurement of positions. Consequently, interferograms are continuously acquired during the movement of the nano-stage, then the quantitative relationship between the stage position/tilt and the interferograms is established by analytic calculation. Besides, the influence of random errors can be suppressed by the averaging effect of the least squares fitting, thereby enhancing the precision by more than an order of magnitude compared with traditional methods. The measuring uncertainty is derived and the impacts of the main influencing factors are investigated. Experiments demonstrate that the measuring repeatability can achieve 1.16 nm. As a result, the proposed method can reliably obtain the absolute position and three dimensional trajectory of the nano-stage, and it is of significance to improve the reliability of nano-measurement and fabrication.

Resolution enhancement for topography measurement of high-dynamic-range surfaces via image fusion

In this paper, we introduce a method and algorithm for resolution enhancement of low-resolution surface topography data by fusing them with corresponding high-resolution intensity images. This fusion is achieved by linking the three-dimensional topographical map to its intensity image via an intrinsic image-based shape-from-shading algorithm. Through computational simulation and physical experiments, the proposed method's effectiveness and repeatability have been evaluated, and the computational cost has been shown to be less than other state-of-the-art algorithms. This proposed method can be easily integrated with high-speed in-line measurements of high-dynamic-range surfaces.