Toward fast and provably accurate near-field ptychographic phase retrieval
Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to...
Ausführliche Beschreibung
Autor*in: |
Iwen, Mark [verfasserIn] |
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Englisch |
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2023 |
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© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Übergeordnetes Werk: |
Enthalten in: Sampling theory, signal processing, and data analysis - [Cham] : Birkhäuser, 2021, 21(2023), 1 vom: 30. Jan. |
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Übergeordnetes Werk: |
volume:21 ; year:2023 ; number:1 ; day:30 ; month:01 |
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DOI / URN: |
10.1007/s43670-022-00045-3 |
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Katalog-ID: |
SPR049193511 |
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520 | |a Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. | ||
650 | 4 | |a Near-field ptychography |7 (dpeaa)DE-He213 | |
650 | 4 | |a Phase retrieval |7 (dpeaa)DE-He213 | |
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650 | 4 | |a Inverse problems |7 (dpeaa)DE-He213 | |
650 | 4 | |a Wirtinger flow |7 (dpeaa)DE-He213 | |
650 | 4 | |a Weighted angular synchronization |7 (dpeaa)DE-He213 | |
700 | 1 | |a Perlmutter, Michael |4 aut | |
700 | 1 | |a Roach, Mark Philip |0 (orcid)0000-0003-4150-5411 |4 aut | |
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10.1007/s43670-022-00045-3 doi (DE-627)SPR049193511 (SPR)s43670-022-00045-3-e DE-627 ger DE-627 rakwb eng Iwen, Mark verfasserin aut Toward fast and provably accurate near-field ptychographic phase retrieval 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 Perlmutter, Michael aut Roach, Mark Philip (orcid)0000-0003-4150-5411 aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 21(2023), 1 vom: 30. Jan. (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:21 year:2023 number:1 day:30 month:01 https://dx.doi.org/10.1007/s43670-022-00045-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2023 1 30 01 |
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10.1007/s43670-022-00045-3 doi (DE-627)SPR049193511 (SPR)s43670-022-00045-3-e DE-627 ger DE-627 rakwb eng Iwen, Mark verfasserin aut Toward fast and provably accurate near-field ptychographic phase retrieval 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 Perlmutter, Michael aut Roach, Mark Philip (orcid)0000-0003-4150-5411 aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 21(2023), 1 vom: 30. Jan. (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:21 year:2023 number:1 day:30 month:01 https://dx.doi.org/10.1007/s43670-022-00045-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2023 1 30 01 |
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10.1007/s43670-022-00045-3 doi (DE-627)SPR049193511 (SPR)s43670-022-00045-3-e DE-627 ger DE-627 rakwb eng Iwen, Mark verfasserin aut Toward fast and provably accurate near-field ptychographic phase retrieval 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 Perlmutter, Michael aut Roach, Mark Philip (orcid)0000-0003-4150-5411 aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 21(2023), 1 vom: 30. Jan. (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:21 year:2023 number:1 day:30 month:01 https://dx.doi.org/10.1007/s43670-022-00045-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2023 1 30 01 |
allfieldsGer |
10.1007/s43670-022-00045-3 doi (DE-627)SPR049193511 (SPR)s43670-022-00045-3-e DE-627 ger DE-627 rakwb eng Iwen, Mark verfasserin aut Toward fast and provably accurate near-field ptychographic phase retrieval 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 Perlmutter, Michael aut Roach, Mark Philip (orcid)0000-0003-4150-5411 aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 21(2023), 1 vom: 30. Jan. (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:21 year:2023 number:1 day:30 month:01 https://dx.doi.org/10.1007/s43670-022-00045-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2023 1 30 01 |
allfieldsSound |
10.1007/s43670-022-00045-3 doi (DE-627)SPR049193511 (SPR)s43670-022-00045-3-e DE-627 ger DE-627 rakwb eng Iwen, Mark verfasserin aut Toward fast and provably accurate near-field ptychographic phase retrieval 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 Perlmutter, Michael aut Roach, Mark Philip (orcid)0000-0003-4150-5411 aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 21(2023), 1 vom: 30. Jan. (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:21 year:2023 number:1 day:30 month:01 https://dx.doi.org/10.1007/s43670-022-00045-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 21 2023 1 30 01 |
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Enthalten in Sampling theory, signal processing, and data analysis 21(2023), 1 vom: 30. Jan. volume:21 year:2023 number:1 day:30 month:01 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Near-field ptychography</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Phase retrieval</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier ptychography</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Inverse problems</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wirtinger flow</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weighted angular synchronization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Perlmutter, Michael</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Roach, Mark Philip</subfield><subfield code="0">(orcid)0000-0003-4150-5411</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Sampling theory, signal processing, and data analysis</subfield><subfield code="d">[Cham] : Birkhäuser, 2021</subfield><subfield code="g">21(2023), 1 vom: 30. 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Iwen, Mark |
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Iwen, Mark misc Near-field ptychography misc Phase retrieval misc Fourier ptychography misc Inverse problems misc Wirtinger flow misc Weighted angular synchronization Toward fast and provably accurate near-field ptychographic phase retrieval |
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Toward fast and provably accurate near-field ptychographic phase retrieval Near-field ptychography (dpeaa)DE-He213 Phase retrieval (dpeaa)DE-He213 Fourier ptychography (dpeaa)DE-He213 Inverse problems (dpeaa)DE-He213 Wirtinger flow (dpeaa)DE-He213 Weighted angular synchronization (dpeaa)DE-He213 |
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misc Near-field ptychography misc Phase retrieval misc Fourier ptychography misc Inverse problems misc Wirtinger flow misc Weighted angular synchronization |
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toward fast and provably accurate near-field ptychographic phase retrieval |
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Toward fast and provably accurate near-field ptychographic phase retrieval |
abstract |
Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstractGer |
Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstract_unstemmed |
Abstract Ptychography is an imaging technique that involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Similarly, in Fourier ptychography a sample is illuminated at different angles of incidence (effectively shifting the sample’s Fourier transform) after which a lens acts as a low-pass filter, thereby effectively providing localized Fourier information about the sample around frequencies dictated by each angle of illumination. Mathematically, one therefore obtains a similar set of overlapping measurements of the sample in both Fourier ptychography and ptychography, except in the different domains (Fourier for the former, and physical for the latter). In either case, one is then able to reconstruct an image of the sample from the measurements using similar methods. Near-Field (Fourier) Ptychography (NFP) (see, e.g., Stockmar et al. (Sci Rep 3(1):1–6, 2013), Stockmar et al. (Phys Rev Appl 3(1): 014005, 2015) and Zhang et al. (Optics Exp 27(5): 7498–7512, 2019)) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) for specific Point Spread Functions (PSFs) and physical masks which lead to well-conditioned lifted linear systems. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample for these specific PSF and mask pairs. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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container_issue |
1 |
title_short |
Toward fast and provably accurate near-field ptychographic phase retrieval |
url |
https://dx.doi.org/10.1007/s43670-022-00045-3 |
remote_bool |
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author2 |
Perlmutter, Michael Roach, Mark Philip |
author2Str |
Perlmutter, Michael Roach, Mark Philip |
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isOA_txt |
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hochschulschrift_bool |
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doi_str |
10.1007/s43670-022-00045-3 |
up_date |
2024-07-03T23:46:07.631Z |
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|
score |
7.398636 |