3D imaging of complex specular surfaces by fusing polarimetric and deflectometric information

446 Vol. 12, No. 4 / April 2025 / Optica Research Article 3D imaging of complex specular surfaces by fusing polarimetric and deflectometric information Jiazhang Wang,1,2,* Oliver Cossairt,2 AND Florian Willomitzer1,2 1Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA 2Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208, USA *jiazhangwang@arizona.edu Received 1 August 2024; revised 19 February 2025; accepted 22 February 2025; published 27 March 2025 Accurate and fast 3D imaging of specular surfaces still poses major challenges for state-of-the-art optical measurement principles. Frequently used methods, such as phase-measuring deflectometry (PMD) or shape-from-polarization (SfP), rely on strong assumptions about the measured objects, limiting their generalizability in broader application areas such as medical imaging, industrial inspection, virtual reality, or cultural heritage analysis. In this paper, we introduce a measurement principle that utilizes a technique to effectively encode and decode the information contained in a light field reflected off a specular surface. We combine polarization cues from SfP with geometric information obtained from PMD to resolve all arising ambiguities in the 3D measurement. Moreover, our approach avoids the unrealistic ortho- graphic imaging assumption for SfP, which significantly improves the respective results. We showcase our technique by demonstrating single-shot and multi-shot measurements on complex-shaped specular surfaces, displaying an evaluated accuracy of surface normals below 0.56◦. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement https://doi.org/10.1364/OPTICA.538331 1. INTRODUCTION Accurate, robust, and fast 3D reconstruction of specular surfaces plays a crucial role in industrial inspection [1–3], cultural heritage preservation and analysis [4,5], medical imaging [6], or potential implementations in novel viewpoint rendering approaches, which can be specifically tailored to specular objects [7]. However, state- of-the-art 3D imaging methods still face significant challenges in measuring specul