{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T11:10:48Z","timestamp":1789125048215,"version":"build-2803163510"},"reference-count":23,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:00:00Z","timestamp":1789084800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Self-developed Program of Optoelectronic Technology department","award":["GDJSB202404"],"award-info":[{"award-number":["GDJSB202404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a novel outpainting technique for quadri-wave lateral shearing interferograms which employs Quadri-Wave Generative Adversarial Networks (QW-GANs). QW-GAN is adversarially trained to capture the high-order statistics of real interferograms. It thereby avoids the Gibbs-ringing artifacts and spectral leakage caused by deterministic interpolation or single-frame extrapolation. The recovered fringes remain physically consistent with preserved Fourier support, enabling more accurate wavefront phase retrieval. Numerical simulations and comparisons with aberrations (defocus, astigmatism, coma, spherical, and random), along with real experimental results, demonstrate the enhanced reconstruction precision of our method, providing an efficient solution for wavefront reconstruction in optical applications.<\/jats:p>","DOI":"10.3390\/s26185771","type":"journal-article","created":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T10:51:37Z","timestamp":1789123897000},"page":"5771","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quadri-Wave Lateral Shearing Interferogram Outpainting Using QW-GAN for Accurate Wavefront Reconstruction"],"prefix":"10.3390","volume":"26","author":[{"given":"Yao","family":"Fan","sequence":"first","affiliation":[{"name":"Advanced Optical Instrument Laboratory, Xi\u2019an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"School of Information and Communications Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"University of Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"Xi\u2019an Key Laboratory of High Power Laser Measurement Technology and Instrument, Xi\u2019an 710119, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"given":"Yaxuan","family":"Duan","sequence":"additional","affiliation":[{"name":"Advanced Optical Instrument Laboratory, Xi\u2019an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"Xi\u2019an Key Laboratory of High Power Laser Measurement Technology and Instrument, Xi\u2019an 710119, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"}]},{"given":"Yiwen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Drilling & Production Technology Research Institute, Chuanqing Drilling Engineering Company Limited, Guanghan 618300, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"}]},{"given":"Zhengshang","family":"Da","sequence":"additional","affiliation":[{"name":"Advanced Optical Instrument Laboratory, Xi\u2019an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Xi\u2019an 710119, China"},{"name":"Xi\u2019an Key Laboratory of High Power Laser Measurement Technology and Instrument, Xi\u2019an 710119, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Yang","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Information and Communications Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5715","DOI":"10.1364\/AO.39.005715","article-title":"Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard","volume":"39","author":"Primot","year":"2000","journal-title":"Appl. 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Opt. Soc. Am. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"18192","DOI":"10.1364\/OE.423336","article-title":"Fringe analysis: Single-shot or two-frames? Quantitative phase imaging answers","volume":"29","author":"Trusiak","year":"2021","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"073501","DOI":"10.1063\/5.0197071","article-title":"A frequency-response-optimized Shack\u2013Hartmann zonal wavefront reconstructor based on Fan\u2019s model","volume":"95","author":"Fan","year":"2024","journal-title":"Rev. Sci. Instrum."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00340-024-08353-3","article-title":"Wavefront reconstruction based on multi-directional orthogonal lateral shearing interferometry","volume":"130","author":"Zhu","year":"2024","journal-title":"Appl. Phys. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3138","DOI":"10.1364\/OE.510692","article-title":"High-resolution iterative reconstruction at extremely low sampling rate for Fourier single-pixel imaging via diffusion model","volume":"32","author":"Song","year":"2024","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1364\/OL.44.001964","article-title":"Diffusion-based single-shot diffraction tomography","volume":"44","author":"Horisaki","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8811","DOI":"10.1109\/TMM.2024.3382484","article-title":"MMGInpainting: Multi-Modality Guided Image Inpainting Based on Diffusion Models","volume":"26","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Multimed."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"024107","DOI":"10.1117\/1.OE.62.2.024107","article-title":"Fast exemplar-based fringe extrapolation technology","volume":"62","author":"Zhan","year":"2023","journal-title":"Opt. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1364\/OE.538515","article-title":"Adaptive patch-based ring artifacts removal for photon-counting CT","volume":"33","author":"Liu","year":"2025","journal-title":"Opt. Express"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"390","DOI":"10.3807\/JOSK.2015.19.4.390","article-title":"Neighboring Elemental Image Exemplar Based Inpainting for Computational Integral Imaging Reconstruction with Partial Occlusion","volume":"19","author":"Ko","year":"2015","journal-title":"J. Opt. Soc. 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