{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T16:26:24Z","timestamp":1774974384171,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T00:00:00Z","timestamp":1703808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2020YFE024600"],"award-info":[{"award-number":["2020YFE024600"]}]},{"name":"National Key R&amp;D Program of China","award":["61975112"],"award-info":[{"award-number":["61975112"]}]},{"name":"National Natural Science Foundation of China","award":["2020YFE024600"],"award-info":[{"award-number":["2020YFE024600"]}]},{"name":"National Natural Science Foundation of China","award":["61975112"],"award-info":[{"award-number":["61975112"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Digital"],"abstract":"<jats:p>In this paper, based on Gaussian 1\u03c3-criterion and histogram segmentation, a weighted least-squares algorithm is applied and validated on digital holographic speckle pattern interferometric data to perform phase separation on the complex interference fields. The direct structural diagnosis tool is used to investigate defects and their impact on a complex antique wall painting of Giotto. The interferometry data is acquired with a portable off-axis interferometer set-up with a phase-shifted reference beam coupled with the object beam in front of the digital photosensitive medium. A digital holographic speckle pattern interferometry (DHSPI) system is used to register digital recordings of interferogram sequences over time. The surface is monitored for as long as it deforms prior to returning to its initial reference equilibrium state prior to excitation. The attempt to separate the whole vs. local defect complex amplitudes from the interferometric data is presented. The main aim is to achieve isolation and visualization of each defect\u2019s impact amplitude in order to obtain detailed documentation of each defect and its structural impact on the surface for structural diagnosis purposes.<\/jats:p>","DOI":"10.3390\/digital4010004","type":"journal-article","created":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T09:15:11Z","timestamp":1703841311000},"page":"104-113","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Defect Isolation from Whole to Local Field Separation in Complex Interferometry Fringe Patterns through Development of Weighted Least-Squares Algorithm"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6372-2148","authenticated-orcid":false,"given":"Zhenkai","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjing","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingjie","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7198-9504","authenticated-orcid":false,"given":"Vivi","family":"Tornari","sequence":"additional","affiliation":[{"name":"Institute of Electronic Structure and Laser, Foundation for Research and Technology, Hellas, 71110 Heraklion, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8693-7392","authenticated-orcid":false,"given":"Gilberto","family":"Artioli","sequence":"additional","affiliation":[{"name":"Centro CIRCe e Dipartimento di Geoscienze, Universit\u00e0 di Padova, 35131 Padova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Anaf, W., Cabal, A., Robbe, M., and Schalm, O. (2020). Real-Time Wood Behaviour: The Use of Strain Gauges for Preventive Conservation Applications. Sensors, 20.","DOI":"10.3390\/s20010305"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1186\/s40494-021-00552-x","article-title":"Evolution of the Viscoelastic Properties of Painting Stratigraphies: A Moisture Weathering and Nanoindentation Approach","volume":"9","author":"Tiennot","year":"2021","journal-title":"Herit. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jacquot, P., and Fournier, J.-M. (2000). Interferometry in Speckle Light, Springer.","DOI":"10.1007\/978-3-642-57323-1"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e12269","DOI":"10.1111\/str.12269","article-title":"Combination of FEM Simulations and Shearography for Defect Detection on Artwork","volume":"54","author":"Buchta","year":"2018","journal-title":"Strain"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhao, Q., Dan, X., Sun, F., Wang, Y., Wu, S., and Yang, L. (2018). Digital Shearography for NDT: Phase Measurement Technique and Recent Developments. Appl. Sci., 8.","DOI":"10.3390\/app8122662"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.culher.2014.01.006","article-title":"Obtaining Noninvasive Stratigraphic Details of Panel Paintings Using Terahertz Time Domain Spectroscopy Imaging System","volume":"16","author":"Picollo","year":"2015","journal-title":"J. Cult. Herit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/j.ndteint.2009.04.002","article-title":"2D and 3D Non-Destructive Evaluation of a Wooden Panel Painting Using Shearography and Terahertz Imaging","volume":"42","author":"Groves","year":"2009","journal-title":"NDT E Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MSP.2015.2407091","article-title":"Automatic Thread-Level Canvas Analysis: A Machine-Learning Approach to Analyzing the Canvas of Paintings","volume":"32","author":"Erdmann","year":"2015","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1038\/nphoton.2012.222","article-title":"Quasi-Reflectography","volume":"6","author":"Baxter","year":"2012","journal-title":"Nat. Photon"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1017\/S1431927611000201","article-title":"Portable Apparatus for In Situ X-Ray Diffraction and Fluorescence Analyses of Artworks","volume":"17","author":"Eveno","year":"2011","journal-title":"Microsc. Microanal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1002\/jrs.2693","article-title":"A Joint Use of Raman and Infrared Spectroscopies for the Identification of Natural Organic Media Used in Ancient Varnishes: Spectroscopic Identification of Natural Organic Media Used in Ancient Varnishes","volume":"41","author":"Daher","year":"2010","journal-title":"J. Raman Spectrosc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1007\/s003400100582","article-title":"Compact and Portable Holographic Camera Using Photorefractive Crystals. Application in Various Metrological Problems","volume":"72","author":"Georges","year":"2001","journal-title":"Appl. Phys. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1109\/JDT.2015.2405972","article-title":"Automatic Frames Extraction and Visualization From Noisy Fringe Sequences for Data Recovering in a Portable Digital Speckle Pattern Interferometer for NDI","volume":"11","author":"Memmolo","year":"2015","journal-title":"J. Disp. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0030-3992(02)00160-3","article-title":"Measurement of Shock Waves Using Phase Shifting Pulsed Holographic Interferometer","volume":"35","author":"Kang","year":"2003","journal-title":"Opt. Laser Technol."},{"key":"ref_15","unstructured":"Pryputniewicz, R.J., Brown, G.M., and Jueptner, W.P.O. (1994). Knowledge-Assisted Evaluation of Fringe Patterns for Automatic Fault Detection, Springer."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"108758","DOI":"10.1016\/j.optlastec.2022.108758","article-title":"Using Deep Learning to Identify the Depth of Metal Surface Defects with Narrowband SAW Signals","volume":"157","author":"Ding","year":"2023","journal-title":"Opt. Laser Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"13627","DOI":"10.1364\/OE.486890","article-title":"Automatic Elimination of Phase Aberrations in Digital Holography Based on Gaussian 1\u03c3- Criterion and Histogram Segmentation","volume":"31","author":"Chen","year":"2023","journal-title":"Opt. Express"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3873","DOI":"10.1016\/j.optcom.2009.06.049","article-title":"Phase Aberration Compensation of Digital Holographic Microscopy Based on Least Squares Surface Fitting","volume":"282","author":"Di","year":"2009","journal-title":"Opt. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.optlastec.2013.10.014","article-title":"Automatic Compensation of Phase Aberrations in Digital Holographic Microscopy for Living Cells Investigation by Using Spectral Energy Analysis","volume":"57","author":"Liu","year":"2014","journal-title":"Opt. Laser Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109704","DOI":"10.1016\/j.optlastec.2023.109704","article-title":"Automatic and Accurate Compensation for Phase Aberrations in Digital Holographic Microscopy Based on Iteratively Reweighted Least Squares Fitting","volume":"167","author":"Liu","year":"2023","journal-title":"Opt. Laser Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"110808","DOI":"10.1063\/1.5115079","article-title":"Automatic Compensation of Phase Aberrations in Digital Holographic Microscopy Based on Sparse Optimization","volume":"4","author":"Ren","year":"2019","journal-title":"APL Photonics"},{"key":"ref_22","first-page":"1","article-title":"Interference Fringe Patterns in Documentation on Works of Art: Application on Structural Diagnosis of a Fresco Painting","volume":"2","author":"Tornari","year":"2017","journal-title":"Am. J. Art. Des."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0029-5493(87)90177-4","article-title":"Profile- and Deformation-Measurements with High Axial Resolution Using the Acoustical Holography","volume":"102","author":"Roye","year":"1987","journal-title":"Nucl. Eng. Des."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10921-021-00755-z","article-title":"Active Thermography for Non-Invasive Inspection of an Artwork on Poplar Panel: Novel Approach Using Principal Component Thermography and Absolute Thermal Contrast","volume":"40","author":"Rippa","year":"2021","journal-title":"J. Nondestruct. Eval."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"14746","DOI":"10.1364\/OE.20.014746","article-title":"Thermal Quasi-Reflectography: A New Imaging Tool in Art Conservation","volume":"20","author":"Daffara","year":"2012","journal-title":"Opt. Express"},{"key":"ref_26","first-page":"1","article-title":"Large Viewing Angle Holographic 3D Display System Based on Maximum Diffraction Modulation","volume":"4","author":"Wang","year":"2023","journal-title":"Light Adv. Manuf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1021\/acsphotonics.2c01514","article-title":"High-Quality Holographic 3D Display System Based on Virtual Splicing of Spatial Light Modulator","volume":"10","author":"Wang","year":"2023","journal-title":"ACS Photonics"}],"container-title":["Digital"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2673-6470\/4\/1\/4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:44:14Z","timestamp":1760132654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2673-6470\/4\/1\/4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,29]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["digital4010004"],"URL":"https:\/\/doi.org\/10.3390\/digital4010004","relation":{},"ISSN":["2673-6470"],"issn-type":[{"value":"2673-6470","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,29]]}}}