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Laser powder bed fusion (LPBF) is a promising metal additive manufacturing technology for producing functional components. However, there are still a lot of obstacles to overcome before this technology is considered mature and trustworthy for wider industrial applications. One of the biggest obstacles is the difficulty in ensuring the repeatability of process and the reproducibility of products. To tackle this challenge, a prerequisite is to represent and communicate the data from the part realisation process in an unambiguous and rigorous manner. In this paper, a semantically enriched LPBF part data model is developed using a category theory-based modelling approach. Firstly, a set of objects and morphisms are created to construct categories for design, process planning, part build, post-processing, and qualification. Twenty functors are then established to communicate these categories. Finally, an application of the developed model is illustrated via the realisation of an LPBF truncheon.

As a member of the hexagonal boron nitride (h-BN) system, boron nitride nanoribbons (BNNRs) have a BN polar covalent bonding infrastructure, and there are small-scale effects with strong correlation with piezoelectric effects as well as edge-strengthening quantum effects. However, realizing the polarization effect on BNNRs through experiments remains challenging. Here, we verify the strain-induced polarization effect on BNNRs through computational simulations and experiments. Using the ten-point iterative method, a computational model that can be used for the discrete difference of the polarization charge density and energy density of BNNRs is developed, and the correctness of the model for the polarization effect of Gaussian strain-induced BNNRs is verified by the computational programming in Python language. The polarization effects of strain-induced zigzag-edge BNNRs (ZBNNRs) for sawtooth strain, parabolic strain and oblique sawtooth strain are also investigated separately. In addition, the results of the computational simulations are experimentally verified to be consistent with the theoretical calculations. And the piezoelectric constant of − 276.88 pm∙V−1 for strained ZBNNRs is found to be four times higher than that of unstrained ZBNNRs. This study provides a relevant reference for the study of realizing the high integration of nano-scale h-BN based piezoelectricity for piezoelectricity.

Fused silica is widely used as a material for optical lenses owing to its excellent optical properties and low thermal expansion coefficient. However, as a hard and brittle material, there is very limited option of processing technologies to machining fused silica with surface structures. In this paper, a picosecond laser based single crystal diamond tool fabrication technology is proposed to generate micro milling tools with different geometrical designs, and the tool cutting performance is experimentally tested through micro-milling of fused silica under different cutting conditions. An optimal picosecond laser processing path is proposed to inhibit the graphitization of diamond tool and improve the concentricity of tool blades, and a multi-edge milling tool with a minimum rotary diameter of 0.4 mm can be obtained. The effects of rake angle on cutting force and the degree of brittle damage on the subsurface of fused silica are studied by micro milling tests of fused silica using the laser-shaped tools. The results show that the fused silica machined by diamond milling tool with a rake angle of −30° has the best surface finish (Ra = 41.2 nm). Using this laser-machined milling tool, a plurality of micro Fresnel lenses with aperture of 1.6 mm were successfully machined on a fused silica sheet.

Boron nitride (BN) aerogels materials have low density characteristics and stable three-dimensional network structure, which can be used as high thermal conductivity ultralight materials or thermal conductive polymer additives. The hexagonal boron nitride nanoribbons (BNNRs) aerogels material not only has a three-dimensional network structure with high specific surface area, but also has a two-dimensional band structure. It has ultra-low thermal conductivity along the in-plane direction, and has ultra-high aspect ratio and electrical insulation energy. However, the research on the thermoelectric properties of BN Aerogels and its composites is still blank. Therefore, it is of great significance to carry out the research on BN Aerogels, its thermoelectric composites, thermoelectric properties and the design of thermoelectric devices. In this paper, BN Aerogels were prepared by the combination of freeze-drying and high temperature thermal annealing, and the effects of 2-methyl-2-propanol (TBA) modification on the yield and quality of BN Aerogels were investigated. The experimental results show that TBA greatly reduces the width and thickness of BNNRs in BN Aerogels, and increases the aspect ratio of BNNRs. The composite thermoelectric particles were prepared by hot pressing to combine BN Aerogels and Bi2Te3 and the influence of the doping concentration of BN Aerogels on the thermoelectric parameters such as Seebeck coefficient and power factor of the thermoelectric battery was studied. The experimental results reveal that when the concentration of BN Aerogels is 1.48 wt%, the ZT value of BN Aerogels/p-Bi2Te3 composite thermoelectric particles is 0.719, while when the doping concentration of BN Aerogels is 1.96 wt%, the ZT value of BN Aerogels/n-Bi2Te3 composite thermoelectric particles is 0.577. And the TBA modified BN Aerogels/Bi2Te3 composite thermoelectric particles show that when the TBA doping concentration is 19.35 wt%, the ZT value of the TBA modified BN Aerogels/p-Bi2Te3 composite thermoelectric particles can reach 0.87, which is higher than that of BN aerogels/p-Bi2Te3 thermoelectric particles, and also much higher than that of the intrinsic p-Bi2Te3 thermoelectric particles. When the TBA doping concentration is 28.57 wt%, the ZT value of the BN Aerogels/n-Bi2Te3composite thermoelectric particles modified by TBA can reach 0.623, which is also higher than that of the BN aerogels/n-Bi2Te3 thermoelectric particles, and also much higher than that of the intrinsic n-Bi2Te3 thermoelectric particles. And based on the self-prepared TBA modified BN Aerogels/Bi2Te3 composite thermoelectric particles, the TEG thermoelectric battery was designed and manufactured. The Seebeck coefficient of the TEG thermoelectric battery can be reached 886.08 μV/K, the conductivity can be reached 9.74 × 104 S/m, and the thermoelectric power factor and power density are 7.65 × 104 μW/mK2 and 14.49 μW/cm3, respectively. This system reduces the need for physical space by using a common framework, which is conducive to the application of thermoelectric power generation technology in micro and small fields.

The coded aperture correlation holography (COACH) is a powerful three-dimensional imaging technique. However, the conventional COACH method can only restore the three-dimensional images of the samples under test, but cannot specify the physical characteristics. We propose a full-dimensional measurement method based on the polarized coded aperture correlation holography. Specifically, the dynamic phase and geometric phase distributions can be separated from two holograms associated with the horizontal and vertical polarization components, then the Stokes parameters, surface topography and reflectivity can be calculated simultaneously. This method achieves the same spatial resolution for the two terms, which greatly improves the reliability and practicability with respect to conventional measurement methods.

The orbital angular momentum (OAM) holography has been developed and experimentally demonstrated the capability of holographic multiplexation and high-security encryption. However, the helical phase of an OAM mode can only be encoded into one hologram associated with a target image, and this severely limits the information capacity in practical applications. The modulated orbital angular momentum (MOAM) holography is proposed by imposing multiple modulation phase modes onto one OAM mode. Three essential properties, including the MOAM-preservation, MOAM-selectivity and MOAM-multiplexation are investigated. This method can significantly enhance the holographic information capacity and it has broad prospects for optical encryption and beam manipulations.

With the rapid development of aerospace, high-speed train, and automotive industries, the demand for the measurement of high-precision specular components is increasing. The acquisition of high-precision three-dimensional (3D) data is conducive to improving the performance of and extending the service life of these components. However, the existing 3D measurement methods of specular surfaces are affected by the inherent limitation of the depth of field (DOF) of camera lenses. Based on the principle of paraxial reflection imaging of a concave mirror, this paper introduces a concave mirror into a phase measuring deflectometry (PMD) system and proposes an aided imaging PMD (AIPMD) based on a concave focusing mirror. The proposed system realizes the clear imaging of the encoded patterns and the surface under test in the DOF of the camera lens, simultaneously. Meanwhile, the iterative coefficient specular reconstruction algorithm is studied based on this system. The feasibility and accuracy of the proposed method are verified by simulations and experiments.

This paper illustrates a systematical surface topography measurement and evaluation method based on a 3D optical system. Firstly, the point cloud data of the workpiece are extracted by the use of a 3D structured light measurement system, and the STEP file of the design model is converted into point cloud data. Secondly, the local measurement point cloud (LMPC) and digital model point cloud (DMPC) are registered by a multivariate local descriptor registration scheme proposed in this study. Thirdly, the surface shapes extracted from the STEP file are applied as a reference to segment the measuring point cloud. Finally, an error analysis scheme is conducted on specific functional surfaces. An experiment was conducted to analyse the flatness, cylindricity and roughness to demonstrate the effectiveness and advantage of the method. The comparison results show that the proposed method outperforms other 3D optical surface topography analysis methods.

In this paper, an automatic determination method of part build orientation for laser powder bed fusion is presented. This method includes two steps. First, an existing facet clustering-based approach is applied to automatically generate the alternative orientations of a laser powder bed fusion part. Second, support volume, volumetric error, surface roughness, build time and build cost are considered. Their values in each alternative orientation are estimated by certain estimation models. The weights of these factors are determined via pairwise comparison. The weighted sum model is used to calculate a summary value of the factors in each alternative orientation. According to the calculated summary values, an optimal orientation to build the part is generated. To demonstrate the method, a set of part orientation cases are tested, and effectiveness analysis and efficiency and characteristic comparisons are reported. The demonstration results suggest that the proposed method can work for both regular and freeform surface models, produce stable and reasonable results and provide desired efficiency.

In this paper, a novel facet clustering based method is proposed to generate alternative build orientations for laser powder bed fusion. This method consists of two steps. First, a hierarchical clustering algorithm is applied to divide facets of the design model in standard tessellation language format into different clusters, each of which shares a similar normal vector. Second, alternatives of each cluster are computed and the final set of alternative build orientations is generated by combining and refining the alternatives from all clusters. To illustrate and validate the method, a set of examples including both regular and freeform surface models are tested, and qualitative and quantitative comparisons between the method and the existing methods are reported. The results suggest that the proposed method is feasible and effective for both regular and freeform surface parts. It is evident that the proposed method can output stable results, provide satisfying efficiency, and work well with facet clusters of varying probability density.

Interferenceless coded aperture correlation holography (I-COACH) was recently introduced for recording incoherent holograms without two-wave interference. In I-COACH, the light radiated from an object is modulated by a pseudo-randomly-coded phase mask and recorded as a hologram by a digital camera without interfering with any other beams. The image reconstruction is conducted by correlating the object hologram with the point spread hologram. However, the image reconstructed by the conventional correlation algorithm suffers from serious background noise, which leads to poor imaging quality. In this work, via an effective combination of the speckle correlation and neural network, we propose a high-quality reconstruction strategy based on physics-informed deep learning. Specifically, this method takes the autocorrelation of the speckle image as the input of the network, and switches from establishing a direct mapping between the object and the image into a mapping between the autocorrelations of the two. This method improves the interpretability of neural networks through prior physics knowledge, thereby remedying the data dependence and computational cost. In addition, once a final model is obtained, the image reconstruction can be completed by one camera exposure. Experimental results demonstrate that the background noise can be effectively suppressed, and the resolution of the reconstructed images can be enhanced by three times.

This paper studies the cooperative control of multiple unmanned aerial vehicles (UAVs) with sensors and autonomous flight capabilities. In this paper, an architecture is proposed that takes a small quadrotor as a mission UAV and a large six-rotor as a platform UAV to provide an aerial take-off and landing platform and transport carrier for the mission UAV. The design of a tracking controller for an autonomous docking and landing trajectory system is the focus of this research. To examine the system’s overall design, a dual-machine trajectory-tracking control simulation platform is created via MATLAB/Simulink. Then, an autonomous docking and landing trajectory-tracking controller based on radial basis function proportional–integral–derivative control is designed, which fulfills the trajectory-tracking control requirements of the autonomous docking and landing process by efficiently suppressing the external airflow disturbance according to the simulation results. A YOLOv3-based vision pilot system is designed to calibrate the rate of the aerial docking and landing position to eight frames per second. The feasibility of the multi-rotor aerial autonomous docking and landing technology is verified using prototype flight tests during the day and at night. It lays a technical foundation for UAV transportation, autonomous take-off, landing in the air, and collaborative networking. In addition, compared with the existing technologies, our research completes the closed loop of the technical process through modeling, algorithm design and testing, virtual simulation verification, prototype manufacturing, and flight test, which have better realizability.

The fabrication process of vacuum ultraviolet (VUV) detectors based on traditional semiconductor materials is complex and costly. The new generation of wide-bandgap semiconductor materials greatly reduce the fabrication cost of the entire VUV detector. We use the chemical vapor deposition (CVD) method to grow boron nitride nanoribbons (BNNRs) for VUV detectors. Morphological and compositional characterization of the BNNRs was tested. VUV detector based on BNNRs exhibits strong response to VUV light with wavelengths as short as 185 nm. The photo–dark current ratio (PDCR) of this detector is 272.43, the responsivity is 0.47 nA/W, and the rise time and fall time are 0.3 s and 0.6 s. The response speed is faster than the same type of BN-based VUV detectors. This paper offers more opportunities for high-performance and low-cost VUV detectors made of wide-bandgap semiconductor materials in the future.

The orbital angular momentum (OAM) holography has been marked a path to achieving ultrahigh capacity holographic information systems. However, the practical applicability of the OAM holography is limited by the complicated optical setup and unadjustable image intensity and position. Here, a decoding method is proposed by using a binarized phase map derived from an autofocusing Airy beam. By adjusting the parameters of the phase map, the position and intensity distribution of the reconstructed image become flexibly adjustable. In addition, the cross-talk between different image channels can be effectively reduced thanks to the abruptly autofocusing capability of the Airy beams. As a result, the quality and practicability of the OAM holography can be greatly enhanced.

This paper presents a novel geometric parameters analysis to improve the measurement accuracy of stereo deflectometry. Stereo deflectometry can be used to obtain form information for freeform specular surfaces. A measurement system based on stereo deflectometry typically consists of a fringe-displaying screen, a main camera, and a reference camera. The arrangement of the components of a stereo deflectometry system is important for achieving high-accuracy measurements. In this paper, four geometric parameters of a stereo deflectometry system are analyzed and evaluated: the distance between the main camera and the measured object surface, the angle between the main camera ray and the surface normal, the distance between the fringe-displaying screen and the object, and the angle between the main camera and the reference camera. The influence of the geometric parameters on the measurement accuracy is evaluated. Experiments are performed using simulated and experimental data. The experimental results confirm the impact of these parameters on the measurement accuracy. A measurement system based on the proposed analysis has been set up to measure a stock concave mirror. Through a comparison of the given surface parameters of the concave mirror, a global measurement accuracy of 154.2 nm was achieved. Keywords: Optical metrology, Error analysis, Stereo deflectometry, Three-dimensional shape measurement, Performance evaluation, Simulation

Thermoelectric materials have attracted the attention of scientists because they directly convert waste heat of electric energy into valuable electrical energy. In recent years, the boron nitride structure has attracted much attention due to its thermoelectric properties and environmental friendliness. In this paper, the thermoelectric properties of boron nitride nanoribbons were simulated and analyzed, discovering that the figure-of-merit (ZT) value of armchair boron nitride nanoribbons is much better than that of zigzag boron nitride nanoribbons. Subsequently, we discuss the bandwidth effects and edge chirality on two important thermoelectric properties, Seebeck coefficient and ZT. Although edge passivation has been carried out, different edge chiralities still have a significant impact on carrier transport. The development of boron nitride-based materials will clarify their potential for developing high performance next generation thermoelectric devices.

In symmetric environment, as the tangential electric field is almost constant across the ultrathin film, the absorption rate of the film is up to 0.5 under single side illumination. In this letter, we propose a symmetrical single layer ultrathin metal grating structure where perfect absorption (up to 0.99) can be achieved with unilateral illumination. We consider that this phenomenon of extraordinary optical absorption is caused by the coupling of the localized surface plasmon resonance and the long range surface plasmon. In particular, the electromagnetic response of the metal grating we proposed greatly resembles the electromagnetic induced absorption (EIA) which shows a narrow absorption peak within a broad absorption profile.

With a view to develop a more realistic model for credit risk analysis in consumer loan, our paper addresses the problem of how to incorporate business cycles into a repayment behavior model of consumer loan in portfolio. A particular Triplet Markov Model (TMM) is presented and introduced to describe the dynamic repayment behavior of consumers. The particular TMM can simultaneously capture the phases of business cycles, transition of systematic credit risk of a loan portfolio, and Markov repayment behavior of consumers. The corresponding Markov chain Monte Carlo algorithms of the particular TMM are also developed for estimating the model parameters. We show how the transition of consumers’ repayment states and systematic credit risk of a loan portfolio are affected by the phases of business cycles through simulations.

Wavelength scanning interferometry is an interferometric technique for measuring surface topography without the well-known 2π phase ambiguity limitation. The measurement accuracy and resolution of this technique depends, among other factors, on the algorithm used to evaluate its sinusoidal interference pattern. The widely used fast Fourier transform analysis experiences problems such as waviness error across the measured surface due to spectral leakage. This paper introduces a new fringe analysis method based on the Carré phase shifting algorithm combined with a least squares fitting approach. Numerical simulation was carried out to assess the performance of the Carré algorithm in comparison to fast Fourier transform analysis, and the same was validated by presenting four experimental case study examples (a surface flat, a ceramic ball bearing, a flexible thin film, and a discontinuous step height sample). The analysis results show that the proposed Carré algorithm with least squares fitting can significantly eliminate the waviness error, especially when measuring steep surfaces.

A concurrent multiscale model coupling discrete dislocation dynamics to the finite element method is developed to investigate the plastic mechanism of materials at micron/submicron length scales. In this model, the plastic strain is computed in discrete dislocation dynamics (DDD) and transferred to the finite element method (FEM) to participate in the constitutive law calculation, while the FEM solves the complex boundary problem for DDD simulation. The implementation of the whole coupling scheme takes advantage of user subroutines in the software ABAQUS. The data structures used for information transferring are introduced in detail. Moreover, a FE mesh-based regularization method is proposed to localize the discrete plastic strain to continuum material points. Uniaxial compression tests of single crystal micropillars are performed to validate the developed model. The results indicate the apparent dependence of yield stress on sample size, and its underlying mechanisms are also analyzed.

In additive manufacturing (AM), especially for advanced powder fusion machines, it is of high importance to develop an in situ inspection system to monitor the printed surface and pre-print powder bed as the build cycle proceeds. Consequently, high resolution, high precision and fast detection measurement systems need to be investigated, as such optically based measurement systems can provide feedback for manufacturing process optimisation. Fringe projection technology has a great advantage in the measurement of topography in such environments. The implementation of a fringe projection system requires that the system is pre-calibrated in order to obtain high measurement resolution and repeatability. This paper presents a simple calibration method for an AM-based in situ fringe projection system using a phase-depth calibration model. If a calibration plate with certificated marks is used, however, the texture of the plate will affect the measured phase accuracy. A simple calibration method to reduce the calibration plate texture effect in the process of calibration is outlined. Experimental results show that the proposed method can eliminated these effects and improve measurement resolution and repeatability. The proposed in situ/in process inspection technique has been implemented within a commercial electron beam powder bed fusion additive manufacturing machine (EBAM), to demonstrate the capability for effective feedback during the manufacturing process.

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.

Abstract Misaligned edge-to-edge dimers are the common products during the preparation of Ag nanoprism dimers using self-assembly method. However, in the self-assembly method, Ag nanoprisms are easily truncated because they are easy to oxidize in an acidic environment. In this work, modeling a truncated Ag nanoprism on a misaligned edge-to-edge dimer provides a better understanding of the effects of the truncation and misalignment on localized surface plasmon resonance (LSPR) of the dimer. The resonant wavelength and intensity of the dimer are flexibly modulated by changing the misalignment length of the dimer. As the misalignment length increases, a stronger peak at the shorter wavelength and a weaker one at the longer wavelength are observed. The resonant wavelengths and intensities of the two peaks are also flexibly tuned by adjusting the truncated length of the Ag nanoprism in the dimer. The results are numerically demonstrated based on the finite element method (FEM) and show promising potential for nanoswitch, multi-channel tunable biosensor and other nanodevice applications.

Abstract We study the mode and dispersion properties of graphene-dielectric nonlinear plasmonic waveguide considering the dual nonlinearity of dielectric and graphene. For TM polarization, the mode distribution, the permittivity distribution, and dispersion relation were obtained by numerically solving the Maxwell equations. Compared with the case considering only the nonlinearity of dielectric, the initial field intensity to excite plasmon modes reduces obviously when introducing the dual nonlinearity. In addition, the influence of dual nonlinearity on dispersion relation is discussed, and we find that the graphene’s nonlinearity affects strongly the dispersion properties. The introduction of dual nonlinearity leads to the decrease of the initial field intensity, which has potential application in all-optical switches with low threshold.

Two critical tasks in multi-criteria group decision making (MCGDM) are to describe criterion values and to aggregate the described information to generate a ranking of alternatives. A flexible and superior tool for the first task is q-rung orthopair fuzzy number (qROFN) and an effective tool for the second task is aggregation operator. So far, nearly thirty different aggregation operators of qROFNs have been presented. Each operator has its distinctive characteristics and can work well for specific purpose. However, there is not yet an operator which can provide desirable generality and flexibility in aggregating criterion values, dealing with the heterogeneous interrelationships among criteria, and reducing the influence of extreme criterion values. To provide such an aggregation operator, Muirhead mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are concurrently introduced into q-rung orthopair fuzzy sets, and an Archimedean power partitioned Muirhead mean operator of qROFNs and its weighted form are presented and a MCGDM method based on the weighted operator is proposed in this paper. The generalised expressions of the two operators are firstly defined. Their properties are explored and proved and their specific expressions are constructed. On the basis of the specific expressions, a method for solving the MCGDM problems based on qROFNs is then designed. Finally, the feasibility and effectiveness of the method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons.

Freeform surfaces are featured with superior optical and physical properties and are widely adopted in advanced optical systems. Slow tool servo (STS) ultra-precision machining is an enabling manufacturing technology for fabrication of non-rotationally symmetric surfaces. This work presents a theoretical and experimental study of surface topography generation in STS machining of freeform surfaces. To achieve the nanometric surface topography, a systematic approach for tool path generation was investigated, including tool path planning, tool geometry selection, and tool radius compensation. The tool radius compensation is performed only in one direction to ensure no high frequency motion is imposed on the non-dynamic axis. The development of the surface generation simulation allows the prediction of the surface topography under various tool and machining variables. Furthermore, it provides an important means for better understanding the surface generation mechanism without the need for costly trial and error tests. Machining and measurement experiments of a sinusoidal grid and microlens array sample validated the proposed tool path generation and demonstrated the effectiveness of the STS machining process to fabricate freeform surfaces with nanometric topography. The measurement results also show a uniform topography distribution over the entire surface and agree well with the simulated results.

In order to enhance the measurement availability for manufacturing applications, on-machine surface measurement (OMSM) is integrated onto the machine tools, which avoids the errors caused by re-positioning workpieces and utilizes the machine axes to extend the measuring range as well. However, due to the fact that measurement probe actuation is performed using the machine tool axes, the inherent kinematics error will inevitably induce additional deviations onto the OMSM results. This paper presents a systematic methodology of kinematics error modelling, measurement, and compensation for OMSM on an ultra-precision turning lathe. According to the measurement task, a selective kinematics error model is established with four primary error components in the sensitive measurement direction, based on multi-body theory and a homogeneous transformation matrix (HTM). In order to separate the artefact error from the measurement results, the selected error components are measured using the reversal method. The measured error value agrees well with the machine tool’s specification and a kinematics error map is generated for further compensation. To verify the effectiveness of the proposed kinematics error modelling, measurement, and compensation, an OMSM experiment of an optically flat mirror is carried out. The result indicates the OMSM is the superposition of the sample surface form error and the machine tool kinematics error. With the implementation of compensation, the accuracy of the characterized flatness error from the OMSM improves by 67%.

The recently developed direct phase measuring deflectometry (DPMD) method can directly measure the three-dimensional (3D) shape of specular objects with discontinuous surfaces, but requires a calibrated distance between a reference plane and liquid crystal display screen. Because the plane and screen are different distances from the imaging device, they cannot be clearly captured given the limited depth of field (DOF) of the lens. Therefore, existing machine vision-based methods cannot be used to effectively calibrate a DPMD system. In this paper, a new distance calibration method that uses a mirror with a hollow ring matrix pattern and a mobile stage is presented. The direction of the mobile stage in the camera coordinate system is determined by the mirror’s pattern at several positions in the camera’s DOF so that the reference position outside of the DOF can be calculated. The screen’s position can also be calibrated by displaying patterns at a known scale. Therefore, the required distance is accurately obtained in the camera coordinate system. Evaluation results show that the maximum value of the absolute error is less than 0.031 mm. The experimental results on an artificial stepped mirror and a reflected diamond distribution surface demonstrate the accuracy and practicality of the proposed method.

The fast development in the fields of integrated circuits, photovoltaics, the automobile industry, advanced manufacturing, and astronomy have led to the importance and necessity of quickly and accurately obtaining three-dimensional (3D) shape data of specular surfaces for quality control and function evaluation. Owing to the advantages of a large dynamic range, non-contact operation, full-field and fast acquisition, high accuracy, and automatic data processing, phase-measuring deflectometry (PMD, also called fringe reflection profilometry) has been widely studied and applied in many fields. Phase information coded in the reflected fringe patterns relates to the local slope and height of the measured specular objects. The 3D shape is obtained by integrating the local gradient data or directly calculating the depth data from the phase information. We present a review of the relevant techniques regarding classical PMD. The improved PMD technique is then used to measure specular objects having discontinuous and/or isolated surfaces. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduced.