High-precision measurement of low reflectivity specular object based on phase measuring deflectometry

Fringe projection profilometry (FPP) and phase measuring deflectometry (PMD) are the currently popular technologies for measuring diffuse and specular reflective surfaces respectively. Both methodologies demonstrate superior performance for single-type reflective surfaces. However, with the rapid development of advanced manufacturing and intelligent manufacturing technologies, products have seen significant improvements in complexity, diversity, and personalization, often exhibiting composite reflective characteristics on their surfaces. The aforementioned single technology cannot meet the measurement requirements for composite reflective surfaces. To address this challenge, this paper presents a composite reflective surfaces measurement method combining FPP with PMD techniques, and an optimized system calibration method based on binocular stereo vision is proposed to enhance the system's measurement accuracy. To improve the measurement efficiency, a strategy in which the LCD screen and projector project different colorful fringe patterns simultaneously is adopted. To mitigate stray light interference from the projector on specular surface profilometry, a partition projection method is presented. Instead of establishing the pixel mapping relationship between the projector and diffused surface aeras, the coordinate mapping relationship between the specular reflective region and the projector pixel is established according to the phase-height relationship to realize the accurate projection of the projector to the diffused surface. Experiments have been performed to validate the proposed method, and the results demonstrate that it can reconstruct the composite surfaces with higher accuracy. In particular, the reconstruction accuracy of specular surface can reach several tens of nanometres.

This paper presents a short review for phase measuring deflectometry (PMD). PMD is a phase calculation based technique for three-dimensional (3D) measurement of specular surfaces. PMD can achieve nano-scale form measurement accuracy with the advantages of high dynamic range, non-contact, full field measurement which makes it a competitive method for specular surface measurement. With the development of computer science, display and imaging technology, there has been an advancement in speed for PMD in recent years. This paper discusses PMD focusing on the difference on its system configuration. Measurement principles, progress, advantages and problems are discussed for each category. The challenges and future development of PMD are also discussed.

Phase measuring deflectometry (PMD) is a well-established method for determining the topography of specular freeform surfaces. A disadvantage of the classical PMD method, however, is the sequential measurement process - it requires at least six camera images of phase-shifted sinusoidal fringe patterns for one measurement. Therefore, for moving objects in industrial production, as well as for non-fixable objects such as the human cornea, the classical PMD evaluation is not suitable anymore. To overcome this problem, single-shot methods using single-side-band demodulation have been presented, which allow for a deflectometric measurement based on just one single image capture. However, this kind of evaluation does not work for complex surface geometries that result in broadband fringe patterns, since the phase is only considered globally in the Fourier space. A new single-shot evaluation method for the phase determination using the Continuous Wavelet Transform (CWT) is presented. The advantage of the wavelet transform is that the signal can be evaluated locally in both spatial and frequency space, making it possible to measure even complex reflective surfaces in motion. First measurement results are shown and compared to the classic phase-shifting evaluation for a non-moving object. Furthermore, limits and possible enhancements of this new method are discussed. Phase measuring deflectometry (PMD) is a well-established method for determining the topography of specular freeform surfaces. A disadvantage of the classical PMD method, however, is the sequential measurement process - it requires at least six camera images of phase-shifted sinusoidal fringe patterns for one measurement. Therefore, for moving objects in industrial production, as well as for non-fixable objects such as the human cornea, the classical PMD evaluation is not suitable anymore. To overcome this problem, single-shot methods using single-side-band demodulation have been presented, which allow for a deflectometric measurement based on just one single image capture. However, this kind of evaluation does not work for complex surface geometries that result in broadband fringe patterns, since the phase is only considered globally in the Fourier space. A new single-shot evaluation method for the phase determination using the Continuous Wavelet Transform (CWT) is presented. The advantage of the wavelet transform is that the signal can be evaluated locally in both spatial and frequency space, making it possible to measure even complex reflective surfaces in motion. First measurement results are shown and compared to the classic phase-shifting evaluation for a non-moving object. Furthermore, limits and possible enhancements of this new method are discussed.

This paper proposes a new shearing approach to eliminate the systematic errors in phase measuring deflectometry (PMD). Besides a normal measurement using PMD, another three measurements are taken when the test surfaces are translated and rotated with an amount of known magnitude in our proposed method. The four measurements give three sheared wavefronts, and then the difference Zernike polynomial fitting and a least squares algorithm are proposed to reconstruct the true test surface figure. The proposed method is demonstrated and verified through computer simulation and experimental results. The error propagation when the sheared wavefronts include random noise and the introduced errors due to the incorrect shearing values are both analyzed.

Phase measuring deflectometry (PMD) is a competitive method for specular surface measurement that offers the advantages of a high dynamic range, non-contact process, and full field measurement; furthermore, it can also achieve high accuracy. Camera calibration is a crucial step for PMD. As a result, a method based on the calibration of the entrance pupil center is introduced in this paper. Then, our proposed approach is compared with the most popular photogrammetric method based on Zhang’s technique (PM) and Huang’s modal phase measuring deflectometry (MPMD). The calibration procedures of these three methods are described, and the measurement errors introduced by the perturbations of degrees of freedom in the PMD system are analyzed using a ray tracing technique. In the experiment, a planar window glass and an optical planar element are separately measured, and the measurement results of the use of the three methods are compared. The experimental results for the optical planar element (removing the first 6 terms of the Zernike polynomial) show that our method’s measurement accuracy reached 13.71 nm RMS and 80.50 nm PV, which is comparable to accuracy values for the interferometer.

Phase Measuring Deflectometry (PMD) and Structured-Light Modulation Analysis Technique (SMAT) perform effectively in shape and defect measurements of specular objects, but the difficulty of giving consideration to accuracy and speed has also restricted the further development and application of them. Inspired by recent successes of deep learning techniques for computational imaging, we demonstrate for the first time that deep learning techniques can be used to recover high-precision modulation distributions of specular surfaces from a single-frame fringe pattern under SMAT, enabling fast and high-quality defect detection of specular surfaces. This method can also be applied to recover higher-precision phase distributions of specular surfaces from a single-frame fringe pattern under PMD, so as to realize the 3D shape measurement. In this paper, we combine depthwise separable convolution, residual structure and U-Net to build an improved U-Net network. The experimental results prove that the method has excellent performance in the phase and modulation retrieval of specular surfaces, which almost reach the accuracy of the results obtained by ten-step phase-shifting method.

In phase measuring deflectometry (PMD), the fringe pattern deformed according to slope deviation of a specular surface is digitized employing a phase-shift technique. Without height-angle ambiguity, carrier-removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. This paper investigates nonlinear carrier components introduced by the generalized imaging process in PMD and the nonlinear carrier removal methods. To remove the nonlinear carrier components in PMD, the reference subtraction technique, series-expansion technique and Zernike polynomials which are normally used in fringe projection profilometry are analyzed on accuracy, processing time and experimental simplicity. What’s more, a new nonlinear carrier removal technique is proposed according to the analytical expression of carrier phase. The theoretical analysis and the experiment results show that the new technique is accurate, simple and time-saving.

Line-art illustrations are effective tools for conveying shapes and shading of complex objects. We present a set of new algorithms to render line-art illustrations of dynamic and specular (reflective and refractive) surfaces. We first introduce a real-time principal direction estimation algorithm to determine the line stroke directions on dynamic opaque objects using neighboring normal ray triplets. To render reflections or refractions in a line-art style, we develop a stroke direction propagation algorithm by using multi-perspective projections to propagate the stroke directions from the nearby opaque objects onto specular surfaces. Finally, we present an image-space stroke mapping method to draw line strokes using the computed or propagated stroke directions. We implement these algorithms using a GPU and demonstrate real-time illustrations of scenes with dynamic and specular 3D models in line-art styles.

In modern fields including reverse engineering, virtual reality, and machine vision, three-dimensional (3D) measurement of specular surfaces has consistently been a key, challenging, and hot research topic. However, the reflective characteristics of specular surfaces render many conventional 3D reconstruction methods (e.g., phase-shifting method, phase unwrapping, or stereo vision scanning) incapable of achieving high-precision 3D reconstruction of objects. This paper utilizes a five-line laser projector to generate stripe patterns and adopts a novel laser rectification and optimization method to obtain analytical solutions for laser equidistant points on specular surfaces, thereby enabling high-precision 3D reconstruction. Experimental results verify the effectiveness of the proposed method. Since the method requires only a single-shot laser pattern, it can serve as an effective approach for reconstructing highly dynamic and irregular specular surfaces. The proposed analytical solution acquisition for specular surfaces proves critical in effectively measuring such dynamic and irregular specular surfaces.

Phase-measuring deflectometry is a full-field gradient technique that lends itself very well to testing reflective optical surfaces. In the past, the industry’s interest has been focussed mainly on the detection of defects and ripples, since it is easy to achieve sensitivity in the nm range. On the other hand, attempts to reconstruct the absolute surface shape from the gradient map have been plagued by systematic errors that accumulate to unacceptable uncertainties during data integration. Recently, thanks to improved measurement and evaluation techniques, the state of the art in absolute surface measurement has reached a level of maturity that allows its practical usage in precision optical manufacturing and qualification systems. We demonstrate the techniques, and the progress, by way of results from mirrors for telescopes, solar concentrators, and precision laboratory assemblies.

Measuring specular surfaces is of importance in both scientific and industrial applications. In this paper, we present a structured light method to measure the shapes of specular surfaces with one-shot projection. This method projects a pattern of laser rays onto the specular surface. By intercepting the reflection of a projected laser pattern twice, two points of each reflected ray are obtained. Then each reflected ray is determined with an analytical solution. Further, the interception points of the projected pattern on the specular surface are obtained with the analytical solutions of the intersections between the incident rays and the reflected rays. Due to the smoothness of the specular surface, the finer surface with higher resolution can thus be reconstructed by polynomial interpolation based on these reconstructed points. To increase the measurement accuracy, we propose a pattern registration method to eliminate the noise and radial lens distortion by decreasing the degree of freedom of the projected rays to one during system calibration. Experimental results showed that this structured light method with pattern registration could achieve the femtometre measurement accuracy.

Space observatory missions requires the development of low-reflectivity surfaces for space-borne instruments, such as seeker telescopes, optical sensors, etc., to minimize stray and reflected light across the visible and infrared wavebands for facilitating the direct exoplanet detection and characterization. For example, in order to improve the sensitivity of missile-defense sensors and seekers, baffles are used within optical telescopes to reduce stray light. Some materials (e.g., aluminum, beryllium, etc.) are too reflective to use as absorptive baffles without surface processing, although they have lightweight and good thermo-structural properties, and survive harsh environments. Black surface coating treatments have been demonstrated as effective approaches to obtain low reflective surfaces. The surface features and intrinsic properties of the coating materials play an important role for scattering, absorbing, or trapping light. The excellent optical absorption performance and light weight of carbon nanotubes (CNTs) make them as ideal coating materials for obtaining low reflectivity surfaces. In this presentation, we will discuss the feasibility of a low-cost, efficient and scalable manufacturing process for the deposition of durable, low reflectivity carbon nanotube black coatings based on the use of pulse and pulse reverse electrophoretic deposition technology. The low-reflectivity CNT coatings have been successfully deposited on various surfaces, including flat, bent, and sharp substrates. The CNT coatings show the reflectance of 0.4% ~ 0.8% across visible to near infrared (NIR) wavebands.Within this context, Faraday Technology Inc. demonstrated the feasibility of a low-cost, efficient and scalable manufacturing process for the deposition of durable, low reflectivity carbon nanotube black coatings based on the use of pulse and pulse reverse electrophoretic deposition. As shown in Figure 1, the uniform CNT coatings are formed on an aluminum (Figure 1, Inset (Right)), and the diffuse reflectance of the CNT coatings is ~ 0.5% over the visible range. We also demonstrated the potential to apply CNT coating on the internal diameter of cylinders at room temperature (Figure 1, Inset (Lef)t). Faraday are currently working on developing CNT coatings on the surface of absorptive baffle materials, such as beryllium and aluminum. The developed economic and scalable technology for producing CNT black coatings on desired substrates can not only be used for minimizing stray and reflected light for space-borne instruments, but also offer potential applications in other optical related devices which request low reflective surfaces, such as solar cells. Acknowledgements: The financial support of NASA SBIR/STTR program through contracts No. 80NNSC18P2062 & 80NSSC19C0177 is acknowledged. Figure 1

We present a novel range sensing method that is capable of constructing accurate 3D models of specular objects. Our method utilizes a new range imaging concept called multipeak range imaging, which accounts for the effects of mutual reflections. False measurements generated by mutual reflections are then eliminated by applying a series of constraint tests based on local smoothness, global coordinate consistency and visibility consistency. We show the usefulness of our method by applying the method to three real objects with specular surfaces. The ground truth data for those three objects were also acquired in order to evaluate the elimination of false measurements and to justify the selection of the parameters in the constraint tests. Experimental results indicate that our method significantly improves upon the traditional methods for constructing reliable 3D models of specular objects with complex shapes.

Phase measurement deflectometry (PMD) is an excellent method for high-precision optical surface measurement; through the simple system structure, accuracy comparable to that of interference methods can be realized. The key of PMD is to solve the ambiguity between the surface shape and normal vector. Considering all kinds of methods, the binocular PMD method is undoubtedly a method with a very simple system structure and can be easily applied to complex surfaces, such as free-form surfaces. However, this method relies on a large screen with high accuracy, which not only increases the weight of the system, but also reduces the flexibility of the system, and manufacturing errors in the large-size screen can easily become error sources. In this Letter, we have made some improvements based on the traditional binocular PMD. At first, we try to replace the large screen with two small screens to increase the flexibility and accuracy of the system. Further, we replace one small screen with a single point to simplify the system structure. Experiments show that the proposed methods not only improve the system flexibility and reduce the complexity, but can also achieve high measurement accuracy.

Deflectometry has been widely used in topography measurement of the specular surface due to the merits of full-field data acquisition, automatic data processing, high accuracy, and large dynamic range. Existing deflectometry-based methods, such as model phase measuring deflectometry, direct phase measuring deflectometry, and stereo deflectometry, employ a plane screen, so they have a small field view. The characteristics of curved screens can effectively expand the range of the gradient and height field of the measured specular surface. This paper presents a novel deflectometric technique by using a curved screen to measure large-curvature specular surface. In order to obtain a model of the curved screen, a stereo vision method has been proposed to capture fringes displayed on the curved screen. After phase correction along epipolar lines and homologous points matching, the point cloud containing location and phase is obtained. A virtual plane fixed on the screen is assumed to gain posture and position of the screen. The model of the curved screen is transferred to the deflectometric system through the virtual plane. After calibrating the deflectometric system, height of specular objects can be obtained. Simulated and actual experiments on measuring specular objects have been carried out and the results show high accuracy and large field view for large-curvature specular surface of the proposed technique.