With the rapid development of modern manufacturing processes, ultra-precision structured freeform surfaces are being widely explored for components with special surface functioning. Measurement of the 3D surface form of structured specular objects remains a challenge because of the complexity of the surface form. Benefiting from a high dynamic range and large measuring area, phase measurement deflectometry (PMD) exhibits great potential in the inspection of the specular surfaces. However, the PMD is insensitive to object height, which leads to the PMD only being used for smooth specular surface measurement. Direct phase measurement deflectometry (DPMD) has been introduced to measure structured specular surfaces, but the surface form measurement resolution and accuracy are limited. This paper presents a method named stereo-DPMD for measuring structured specular objects by introducing a stereo deflectometor into DPMD, so that it combines the advantages of slope integration of the stereo deflectometry and discontinuous height measurement from DPMD. The measured object is separated into individual continuous regions, so the surface form of each region can be recovered precisely by slope integration. Then, the relative positions between different regions are evaluated by DPMD system to reconstruct the final 3D shape of the object. Experimental results show that the structured specular surfaces can be measured accurately by the proposed stereo-DPMD method.

Accurate and fast three-dimensional (3D) measurement for industrial products/components designed to possess 3D structured shapes is a key driver for improved productivity. However, challenges for current techniques are considerable to measure structured specular surfaces. A technique named segmentation phase measuring deflectometry (SPMD) is proposed in this paper, which enables structured specular surfaces to be measured with high accuracy in one setup. Concept of segmentation in topology is introduced into phase measuring deflectometry, which separates a surface with complex structures into continuous segments. Each segment can be reconstructed based on gradient information to achieve good form accuracy, and all reconstructed segments can be fused into a whole 3D strucutred form result based on their absolute spatial positioning data. Here, we propose and discuss the principle of SPMD, a segmentation technique to separate a strucured surface into segments, a spatial positioning technique to obtain absolute position of the segments, and a data fusion strategy to fuse all reconstructed segments. Experimental results show SPMD can achieve nanometer level accuracy for form measurement of continuous segments by comparing with stylus profilometer, which is significantly higher than the accuracy of direct phase measuring deflectometry. Meanwhile, SPMD has micron level spatial positioning accuracy for structures by measuring two specular steps and comparing with coordinate measuring machine, which differentiates this technique from gradient-based phase measuring deflectometry that extends measurement capability from continuous specular surfaces to complex structured specular surfaces. Compared with the existing measurement techniques, SPMD significantly improved the convenience and ability to measure freeform and structured specular surfaces with the advantages of high measurement accuracy, fast measurement, and potential application for embedded measurement.

Accurately measuring the form of structured composite surfaces in situ is critical for advanced manufacturing in various engineering fields. However, challenges persist in achieving precision, miniaturization, and calibration using current structured light techniques. In this work, a hybrid structured light with compact configuration is proposed for the in-situ and embedded form metrology of structured composite surfaces. The proposed technique contains three subsystems: phase-measuring deflectometry (PMD), fringe projection profilometry (FPP), and stereo vision. The PMD subsystem accurately reconstructs the form data of specular surfaces based on the principle of structured light reflection, and the FPP subsystem measures rough surfaces by projecting structured light onto them. Output data from these subsystems are then stitched to reconstruct a complete form of the measured composite surfaces. The compact configuration is explored to reduce the system volume to improve the technique’s portability and embedded measurement ability. With the stereo vision subsystem as an intermediary, a novel calibration method is applied for calculating the relations among the subsystems to improve the hybrid structured light system’s calibration and data stitching accuracy between PMD and FPP subsystems. Three calibration tools are designed and manufactured for the proposed calibration technique. A portable metrology prototype based on the proposed hybrid structured light technique’s principle and configuration is also developed and then calibrated using the novel calibration method. An embedded measurement experiment in a diamond turning machine demonstrates that the proposed techniques can achieve 400 nm form accuracy in specular surface measurement.

Form measurement of specular surfaces is critical for advanced manufacturing in various engineering fields. Near optical coaxial phase measuring deflectometry (NCPMD) has been proposed for in-situ form metrology with the advantages of good accuracy, small volume, lightweight, and minimal measurement errors caused by surface structure shadows. Accurate scanning of large freeform specular surfaces remains a challenge because there are no features on the surfaces that can be used for sub-surface stitching. In this paper, an accurate and automatic area scanning method is studied based on robotic near optical coaxial phase measuring stitching deflectometry (NCPMSD), which consists of an NCPMD system fixed on a robot arm. The NCPMSD scans the measured surface through robot arm control and reconstructs the form data of each sub-surface of the entire surface. Through the proposed robotic NCPMSD calibration method, the relationship between the NCPMD system and the robot arm is calibrated, and the coarse stitching is completed according to the coordinate transformation relationship and robot arm movement data. The stitching accuracy is then improved based on the gradient feature of the measured surfaces. The accuracy and effectiveness of the proposed method are verified through experiments by measuring a ring calibration mirror target and a freeform mirror. The method shows significant advancements in increasing the measurement field and flexibility of the in-situ metrology of the NCPMD system.

Propelled by the rapidly growing demand for function incorporation and performance improvement, various specular components with complex structured surfaces are broadly applied in numerous optical engineering arenas. Form accuracy of the structured surfaces directly impacts the functioning of the specular components. Because the scales of these structures and/or the importance of their functions are usually designed differently, the structures require different measurement demands in scale, lateral resolution, and accuracy. In this paper, a multiscale form measurement technique is proposed based on triple-sensor phase measuring deflectometry for measuring structured specular surfaces. The proposed technique contains two sub-phase measuring deflectometry(PMD)-systems. Each sub-system works as a single segmentation PMD (SPMD) system and is designed to have different measurement scales, lateral resolutions, and accuracies to meet the measurement demands of the targeted surfaces. Two imaging sensors in the proposed technique cover the measured full-scale surface. The specular surface is separated into several continuous segments through algorithms and the spatial relationship of the continuous segments is established based on absolute depth data calculated through the triangular relationship between the two imaging sensors. The third imaging sensor with a long working distance only captures the field of the small-scale structures and reconstructs the structures based on gradient data to improve the structures’ reconstruction resolution and accuracy. In order to make it suitable for portable and embedded measurement, a compact configuration is explored to reduce system volume. Data fusion techniques are also studied to combine the measurement data of the two sub-systems. Experimental results demonstrate the validity of a portable prototype developed based on the proposed technique by measuring a concave mirror with small-scale structures.