Chongfan Technology
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2025
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04
Optica | Mirror 3D Imaging Fusing Polarization and Deflection Information
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Introduction
High-precision and fast 3D reconstruction of specular objectsIt is of great significance in industrial inspection, cultural heritage protection, medical imaging, and virtual reality. However, current advanced 3D imaging methods still face significant challenges when dealing with specular objects with complex shapes.
Recently,AmericanProfessor Florian Willomitzer's research group at the Optical Sciences Center, University of Arizonaproposed a 3D reconstruction method that integrates phase measurement deflectometry with polarization imaging. This method combines the angle of incidence provided by polarization information with the geometric correspondence obtained by deflectometry to achieve simultaneous reconstruction of surface normal vectors and depth information of specular objects. This new scheme not only compensates for the limitations of phase deflectometry and polarization imaging in their respective applications but also opens up more possibilities and new research directions for 3D reconstruction of specular objects.
The results were published inOpticaentitled3D Imaging of Complex Specular Surfaces by Fusing Polarization and Deflection InformationThe first author and corresponding author are both from the Optical Sciences Center (Wyant College of Optical Sciences), University of ArizonaDr. Jiazhang WangNorthwest UniversityProfessor Oliver Cossairtand the University of ArizonaProfessor Florian Willomitzerprovided important guidance and support for this research.
Specular 3D reconstruction in optical metrology and computer vision
The problem of specular 3D reconstruction has received widespread attention in both optical metrology and computer vision fields. Optical metrology methods have excellent measurement accuracy but usually rely on strict experimental conditions, such as high-precision joint calibration between multiple devices. Therefore, their applications are mainly concentrated in optical component measurement and high-end industrial inspection scenarios. In contrast, computer vision methods have stronger versatility and adaptability, suitable for various environments and target types, but these methods usually focus more on the visual effect reconstruction, while compromising on accuracy.
Phase measurement deflectometry (PMD) is one of the widely used methods in the field of optical metrology, known for its ability to achieve sub-micron depth resolution using low-cost standard components (such as displays and cameras). Its basic principle is to project a known pattern on the display screen and observe the deformation of the pattern reflected by the specular surface through a camera, thereby calculating the surface normal and finally recovering the 3D shape. However, PMD has a "normal-depth ambiguity" problem [seeFigure 1(a)]: Because the precise path of the incident light cannot be determined solely by its emission pixel on the display screen, it usually requires strong prior assumptions about the spatial position or approximate shape of the object. To overcome this ambiguity, methods have been introduced that use a second camera or a second display screen, but this significantly increases the system complexity and geometric calibration difficulty.
Polarization stereoscopic imaging (SfP) is a 3D reconstruction method that has received considerable attention in the field of computer vision in recent years, and has recently been combined with deep learning and event camera technology. SfP usually uses a non-polarized light source to illuminate the object surface. According to the Fresnel equation, the reflected or scattered light will be in a partially polarized state and collected by a polarization camera. By analyzing the polarization state, the surface normal vector map of the measured surface can be resolved. However, this method also has significant limitations: firstly, it assumes an orthographic projection model, which is difficult to satisfy in practice and can cause normal errors as high as 5° to 25°; secondly, polarization information has multiple solution ambiguities under specular reflection conditions (two possible elevation angles and two possible azimuth angles, combining into four possible normals) [see Figure 1(b)], usually requiring additional information (such as prior shape or a second sensor) to eliminate it.
Figure 1: (a) & (b) PMD and SfP principle diagrams and their limitations (c) A new 3D reconstruction method integrating PMD and SfP
Optics × Vision: The Next Generation of 3D Sensing Technology
This study proposes a 3D imaging method that integrates polarization information and deflection information. By jointly overcoming the respective limitations of PMD and SfP, it achieves simultaneous reconstruction of absolute surface normals and 3D shapes.
AsFigure 1(c)shows, the system consists of a non-polarized display screen and a polarization camera. This polarization camera can simultaneously acquire images at four different polarization angles in a single exposure. After image acquisition, we extract the pixel-level correspondence between the display screen and the camera from one of the images using the PMD method, establishing a mapping between the display screen pixel D and the corresponding point C in the camera image.
Subsequently, combined with the polarization information provided by the four-channel images, we extract the reflection angle θ for each object surface point. It should be emphasized that we did not simplify θ to the zenith angle of the normal to avoid introducing the assumption of the orthographic projection model, which may cause significant errors in practical applications. The traditional PMD method cannot directly solve the object surface information because the surface point position S and the reflection angle θ are both unknown quantities, forming the so-called "normal-depth ambiguity." The key innovation of this method is that SfP can directly estimate θ through the degree of polarization (DoP), thus enabling complementary fusion of PMD and SfP. Through the measured θ and pixel correspondence (C, D), we can unambiguously and synchronously recover the surface normal map and 3D shape. In addition, this method does not rely on the orthographic projection assumption and is suitable for common perspective camera systems. Compared with existing perspective model methods of SfP, this scheme significantly improves accuracy without relying on multi-view geometry and does not require prior information about the surface shape, making it more adaptable and practical.
The experimental results are shown inFigure 2To verify the accuracy of the proposed method, the research team first measured a reflective metal steel ball with knownFigure 2(a)-(d)The experiment used a single-frame projection method and successfully reconstructed the surface normal and three-dimensional shape. The average normal error was 0.56°, and the radius error was 70μm, indicating that the method has sub-millimeter-level 3D reconstruction accuracy. Subsequently, the study further evaluated the applicability of this method to complex freeform specular objectsFigure 2(e)-(l)using multi-frame phase-shifting projection for measurement. The reconstruction results show good surface structure restoration capabilities and can accurately capture local geometric details. Due to the lack of available true value references for such objects, only qualitative analysis was performed. In contrast, traditional PMD and SfP methods are difficult to achieve effective reconstruction of the above specular objects under the experimental conditions of this study, often relying on strong prior assumptions or additional hardware support. The method proposed in this paper can still achieve high-quality reconstruction without prior information and additional equipment, demonstrating its good flexibility and application potential.
Figure 2: Experimental Results
Summary and Outlook
This study proposes a novel 3D imaging method that integrates polarization information and deflection geometry, achieving simultaneous reconstruction of surface normals and shapes of complex specular surfaces without prior information and in a single frame. Compared with traditional PMD and SfP methods, it ensures accuracy while avoiding common geometric ambiguities and modeling assumptions. This research provides new ideas for the integration of optical metrology and computer vision and has broad application potential in medicine, AR/VR, robotics, and other fields.
Paper Information
Jiazhang Wang, Oliver Cossairt, and Florian Willomitzer, “3D Imaging of Complex Specular Surfaces by Fusing Polarization and Deflection Information”, Optica 12, 446-450 (2025).
https://doi.org/10.1364/OPTICA.538331
Research Group Introduction
Professor Florian Willomitzer's Computational 3D Imaging and Measurement (3DIM) Lab is dedicated to solving a series of broad and challenging key problems in the field of computational imaging. The research integrates multidisciplinary theories such as physical optics, image and signal processing, computer vision, and information theory, aiming to design, develop, and build a new generation of 2D/3D computational imaging and display systems to break through the limitations of traditional imaging technologies in resolution, dynamic range, and imaging speed, realizing the research vision of “making the invisible visible”. The core technologies developed by the laboratory have been widely used in medicine, virtual/augmented/mixed reality (VR/AR/MR), robotics, industrial inspection, remote sensing, automotive perception, precision metrology, and cultural heritage protection. Current research directions include: innovative methods for high-resolution holographic displays, high-precision eye-tracking schemes for virtual reality, and the technical implementation of integrating high-precision metrology technology into low-cost portable devices. In addition, the laboratory is also developing a new time-of-flight (ToF) and structured light imaging system with a depth resolution of hundreds of micrometers, providing advanced solutions for high-precision 3D sensing.
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