{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:47:13Z","timestamp":1774453633242,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T00:00:00Z","timestamp":1651795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Institute of Rangsit University (RSU)"},{"name":"School of Engineering of King Mongkut\u2019s Institute of Technology Ladkrabang (KMITL)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Quantitative phase imaging has been of interest to the science and engineering community and has been applied in multiple research fields and applications. Recently, the data-driven approach of artificial intelligence has been utilized in several optical applications, including phase retrieval. However, phase images recovered from artificial intelligence are questionable in their correctness and reliability. Here, we propose a theoretical framework to analyze and quantify the performance of a deep learning-based phase retrieval algorithm for quantitative phase imaging microscopy by comparing recovered phase images to their theoretical phase profile in terms of their correctness. This study has employed both lossless and lossy samples, including uniform plasmonic gold sensors and dielectric layer samples; the plasmonic samples are lossy, whereas the dielectric layers are lossless. The uniform samples enable us to quantify the theoretical phase since they are established and well understood. In addition, a context aggregation network has been employed to demonstrate the phase image regression. Several imaging planes have been simulated serving as input and the label for network training, including a back focal plane image, an image at the image plane, and images when the microscope sample is axially defocused. The back focal plane image plays an essential role in phase retrieval for the plasmonic samples, whereas the dielectric layer requires both image plane and back focal plane information to retrieve the phase profile correctly. Here, we demonstrate that phase images recovered using deep learning can be robust and reliable depending on the sample and the input to the deep learning.<\/jats:p>","DOI":"10.3390\/s22093530","type":"journal-article","created":{"date-parts":[[2022,5,8]],"date-time":"2022-05-08T23:27:25Z","timestamp":1652052445000},"page":"3530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of Deep Learning-Based Phase Retrieval Algorithm Performance for Quantitative Phase Imaging Microscopy"],"prefix":"10.3390","volume":"22","author":[{"given":"Sarinporn","family":"Visitsattapongse","sequence":"first","affiliation":[{"name":"Department of Biomedical Engineering, School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}]},{"given":"Kitsada","family":"Thadson","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9105-8627","authenticated-orcid":false,"given":"Suejit","family":"Pechprasarn","sequence":"additional","affiliation":[{"name":"College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand"}]},{"given":"Nuntachai","family":"Thongpance","sequence":"additional","affiliation":[{"name":"College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1038\/s41566-018-0253-x","article-title":"Quantitative phase imaging in biomedicine","volume":"12","author":"Park","year":"2018","journal-title":"Nat. Photonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21191","DOI":"10.1364\/OE.17.021191","article-title":"Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing","volume":"17","author":"Kabashin","year":"2009","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3729","DOI":"10.1364\/OL.44.003729","article-title":"Quantitative phase imaging with molecular vibrational sensitivity","volume":"44","author":"Tamamitsu","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"28039","DOI":"10.1364\/OE.20.028039","article-title":"Surface plasmon microscopic sensing with beam profile modulation","volume":"20","author":"Zhang","year":"2012","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1364\/OPTICA.381729","article-title":"Full optical characterization of single nanoparticles using quantitative phase imaging","volume":"7","author":"Khadir","year":"2020","journal-title":"Optica"},{"key":"ref_6","unstructured":"Popescu, G. (2011). Quantitative Phase Imaging of Cells and Tissues, McGraw-Hill Education."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0091-679X(08)00805-4","article-title":"Quantitative phase imaging of nanoscale cell structure and dynamics","volume":"90","author":"Popescu","year":"2008","journal-title":"Methods Cell Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1364\/OL.41.001427","article-title":"Real-time quantitative phase imaging based on transport of intensity equation with dual simultaneously recorded field of view","volume":"41","author":"Tian","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JSTQE.2018.2827663","article-title":"Quantitative phase imaging (QPI) in neuroscience","volume":"25","author":"Hu","year":"2018","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Brock, N., Hayes, J., Kimbrough, B., Millerd, J., North-Morris, M., Novak, M., and Wyant, J.C. (2005). Novel Optical Systems Design and Optimization VIII. Dynamic Interferometry, SPIE.","DOI":"10.1117\/12.621245"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, D., Loo, J.F.C., Chen, J., Yam, Y., Chen, S.-C., He, H., Kong, S.K., and Ho, H.P. (2019). Recent advances in surface plasmon resonance imaging sensors. Sensors, 19.","DOI":"10.3390\/s19061266"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1776","DOI":"10.1002\/anie.201908806","article-title":"Surface plasmon resonance microscopy: From single-molecule sensing to single-cell imaging","volume":"59","author":"Zhou","year":"2020","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10797","DOI":"10.1364\/OE.24.010797","article-title":"Single shot embedded surface plasmon microscopy with vortex illumination","volume":"24","author":"Chow","year":"2016","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0030-4018(75)90095-4","article-title":"Image formation by phase coincidences in optical waveguides","volume":"13","author":"Ulrich","year":"1975","journal-title":"Opt. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Somekh, M.G., and Pechprasarn, S. (2017). Surface plasmon, surface wave, and enhanced evanescent wave microscopy. Handbook of Photonics for Biomedical Engineering, Springer.","DOI":"10.1007\/978-94-007-5052-4_20"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1364\/JOSAA.11.001272","article-title":"Complex modes in open lossless dielectric waveguides","volume":"11","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"215829","DOI":"10.1117\/12.7972989","article-title":"Phase retrieval and diversity in adaptive optics","volume":"21","author":"Gonsalves","year":"1982","journal-title":"Opt. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1364\/AO.32.001737","article-title":"Phase-retrieval algorithms for a complicated optical system","volume":"32","author":"Fienup","year":"1993","journal-title":"Appl. Opt."},{"key":"ref_19","first-page":"237","article-title":"A practical algorithm for the determination of phase from image and diffraction plane pictures","volume":"35","author":"Gerchberg","year":"1972","journal-title":"Optik"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106187","DOI":"10.1016\/j.optlaseng.2020.106187","article-title":"Transport of intensity equation: A tutorial","volume":"135","author":"Zuo","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Somekh, M.G., Pechprasarn, S., Chen, W., Pimonsakonwong, P., and Albutt, N. (2017). Applied Mechanics and Materials. Back Focal Plane Confocal Ptychography, Trans Tech Publications.","DOI":"10.4028\/www.scientific.net\/AMM.866.361"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"12729","DOI":"10.1364\/OE.389897","article-title":"Rapid tilted-plane Gerchberg-Saxton algorithm for holographic optical tweezers","volume":"28","author":"Cai","year":"2020","journal-title":"Opt. Express"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"19388","DOI":"10.1364\/OE.26.019388","article-title":"Fast phase retrieval in off-axis digital holographic microscopy through deep learning","volume":"26","author":"Zhang","year":"2018","journal-title":"Opt. Express"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"19593","DOI":"10.1364\/OE.423222","article-title":"PhaseGAN: A deep-learning phase-retrieval approach for unpaired datasets","volume":"29","author":"Zhang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.zemedi.2018.12.003","article-title":"A gentle introduction to deep learning in medical image processing","volume":"29","author":"Maier","year":"2019","journal-title":"Zeitschrift f\u00fcr Medizinische Physik"},{"key":"ref_26","unstructured":"Hemanth, D.J., and Estrela, V.V. (2017). Deep Learning for Image Processing Applications, IOS Press."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hassaballah, M., and Awad, A.I. (2020). Deep Learning in Computer Vision: Principles and Applications, CRC Press.","DOI":"10.1201\/9781351003827"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Dong, C., Loy, C.C., He, K., and Tang, X. (2014). European conference on computer vision. Learning a Deep Convolutional Network for Image Super-Resolution, Springer.","DOI":"10.1007\/978-3-319-10593-2_13"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.neunet.2020.01.026","article-title":"Mu-net: Multi-scale U-net for two-photon microscopy image denoising and restoration","volume":"125","author":"Lee","year":"2020","journal-title":"Neural Netw."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zuluaga, F.H.G., Bardozzo, F., Patino, J.I.R., and Tagliaferri, R. (2021, January 1\u20135). Blind microscopy image denoising with a deep residual and multiscale encoder\/decoder network. Proceedings of the 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Jalisco, Mexico.","DOI":"10.1109\/EMBC46164.2021.9630502"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hajiabadi, H., Mamontova, I., Prizak, R., Pancholi, A., Koziolek, A., and Hilbert, L. (2021). Deep-learning microscopy image reconstruction with quality control reveals second-scale rearrangements in RNA polymerase II clusters. bioRxiv.","DOI":"10.1101\/2021.12.05.471272"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-021-95593-4","article-title":"Deep learning-based single-shot phase retrieval algorithm for surface plasmon resonance microscope based refractive index sensing application","volume":"11","author":"Thadson","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12859-017-1757-y","article-title":"A deep convolutional neural network approach to single-particle recognition in cryo-electron microscopy","volume":"18","author":"Zhu","year":"2017","journal-title":"BMC Bioinform."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1093\/icesjms\/fsz171","article-title":"Developing a microscopic image dataset in support of intelligent phytoplankton detection using deep learning","volume":"77","author":"Li","year":"2020","journal-title":"ICES J. Mar. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-022-06065-2","article-title":"Measurement precision enhancement of surface plasmon resonance based angular scanning detection using deep learning","volume":"12","author":"Thadson","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4370","DOI":"10.1103\/PhysRevB.6.4370","article-title":"Optical constants of the noble metals","volume":"6","author":"Johnson","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1063\/1.555536","article-title":"Refractive index of alkali halides and its wavelength and temperature derivatives","volume":"5","author":"Li","year":"1976","journal-title":"J. Phys. Chem. Ref. Data"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.phpro.2011.06.139","article-title":"Fabrication of refractive index tunable polydimethylsiloxane photonic crystal for biosensor application","volume":"19","author":"Raman","year":"2011","journal-title":"Phys. Procedia"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1021\/cm000937z","article-title":"High-refractive-index thin films prepared from trialkoxysilane-capped poly (methyl methacrylate)\u2212 titania materials","volume":"13","author":"Lee","year":"2001","journal-title":"Chem. Mater."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Suvarnaphaet, P., and Pechprasarn, S. (2018). Enhancement of long-range surface plasmon excitation, dynamic range and figure of merit using a dielectric resonant cavity. Sensors, 18.","DOI":"10.3390\/s18092757"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"10628","DOI":"10.1109\/JSEN.2021.3063136","article-title":"Analysis of Open Grating-Based Fabry\u2013P\u00e9rot Resonance Structures With Potential Applications for Ultrasensitive Refractive Index Sensing","volume":"21","author":"Sasivimolkul","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_42","unstructured":"Yu, F., and Koltun, V. (2015). Multi-scale context aggregation by dilated convolutions. arXiv."},{"key":"ref_43","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Chen, D., He, M., Fan, Q., Liao, J., Zhang, L., Hou, D., Yuan, L., and Hua, G. (2019, January 7\u201311). Gated context aggregation network for image dehazing and deraining. Proceedings of the 2019 IEEE winter conference on applications of computer vision (WACV), Waikoloa, HI, USA.","DOI":"10.1109\/WACV.2019.00151"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/TIP.2011.2173206","article-title":"On the Mathematical Properties of the Structural Similarity Index","volume":"21","author":"Brunet","year":"2012","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"075401","DOI":"10.1088\/1361-6501\/ab7def","article-title":"Defocus leakage radiation microscopy for single shot surface plasmon measurement","volume":"31","author":"Chow","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1364\/BOE.448085","article-title":"Analysis of the surface plasmon resonance interferometric imaging performance of scanning confocal surface plasmon microscopy","volume":"13","author":"Tontarawongsa","year":"2022","journal-title":"Biomed. Opt. Express"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"7388","DOI":"10.1364\/OE.20.007388","article-title":"Confocal surface plasmon microscopy with pupil function engineering","volume":"20","author":"Zhang","year":"2012","journal-title":"Opt. Express"},{"key":"ref_49","unstructured":"Hong, P. (2018). Customizing optical patterns via feedback-based wavefront shaping. arXiv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1364\/OPEX.12.001665","article-title":"Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping","volume":"12","author":"Sinclair","year":"2004","journal-title":"Opt. Express"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1038\/s41591-019-0539-7","article-title":"An augmented reality microscope with real-time artificial intelligence integration for cancer diagnosis","volume":"25","author":"Chen","year":"2019","journal-title":"Nat. Med."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1038\/s41591-019-0715-9","article-title":"Near real-time intraoperative brain tumor diagnosis using stimulated Raman histology and deep neural networks","volume":"26","author":"Hollon","year":"2020","journal-title":"Nat. Med."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.optcom.2017.08.035","article-title":"Adaptive optics compensation of orbital angular momentum beams with a modified Gerchberg\u2013Saxton-based phase retrieval algorithm","volume":"405","author":"Chang","year":"2017","journal-title":"Opt. Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3530\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:06:51Z","timestamp":1760137611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3530"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":53,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22093530"],"URL":"https:\/\/doi.org\/10.3390\/s22093530","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,6]]}}}