Max Leo Leidl , Benedikt Diederichs , Carsten Sachse , Knut Müller-Caspary
{"title":"损耗函数和电子剂量对使用 Wirtinger 流程进行二维材料层析成像的影响","authors":"Max Leo Leidl , Benedikt Diederichs , Carsten Sachse , Knut Müller-Caspary","doi":"10.1016/j.micron.2024.103688","DOIUrl":null,"url":null,"abstract":"<div><p>Iterative phase retrieval is based on minimising a loss function as a measure of the consistency of an initial guess and underlying experimental data. Under ideal experimental conditions, real data contains Poissonian noise due to counting statistics. In this work, we use the Wirtinger Flow concept in combination with four common loss functions, being the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> loss, the mean-squared error (MSE), the amplitude loss and the Poisson loss. Since only the latter reflects the counting statistics as an asymmetric Poisson distribution correctly, our simulation study focuses on two main cases. Firstly, high-dose momentum-resolved scanning transmission electron microscopy (STEM) of an MoS<sub>2</sub> monolayer is considered for phase retrieval. In this case, it is found that the four losses perform differently with respect to chemical sensitivity and frequency transfer, which we interprete in terms of the substantially different signal level in the bright and dark field part of diffraction patterns. Remedies are discussed using further simulations, addressing the use of virtual ring detectors for the dark field, or restricting loss calculation to the bright field. Secondly, a dose series is presented down to 100 electrons per diffraction pattern. It is found that all losses yield qualitatively reasonable structural data in the phase, whereas only MSE and Poisson loss range at the correct amplitude level. Chemical contrast is, in general, reliably obtained using the Poisson concept, which also provides the most continuous spatial frequency transfer as to the reconstructed object transmission function.</p></div>","PeriodicalId":18501,"journal":{"name":"Micron","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0968432824001057/pdfft?md5=7092d16b4b135a202c8d0c20480d3752&pid=1-s2.0-S0968432824001057-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Influence of loss function and electron dose on ptychography of 2D materials using the Wirtinger flow\",\"authors\":\"Max Leo Leidl , Benedikt Diederichs , Carsten Sachse , Knut Müller-Caspary\",\"doi\":\"10.1016/j.micron.2024.103688\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Iterative phase retrieval is based on minimising a loss function as a measure of the consistency of an initial guess and underlying experimental data. Under ideal experimental conditions, real data contains Poissonian noise due to counting statistics. In this work, we use the Wirtinger Flow concept in combination with four common loss functions, being the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> loss, the mean-squared error (MSE), the amplitude loss and the Poisson loss. Since only the latter reflects the counting statistics as an asymmetric Poisson distribution correctly, our simulation study focuses on two main cases. Firstly, high-dose momentum-resolved scanning transmission electron microscopy (STEM) of an MoS<sub>2</sub> monolayer is considered for phase retrieval. In this case, it is found that the four losses perform differently with respect to chemical sensitivity and frequency transfer, which we interprete in terms of the substantially different signal level in the bright and dark field part of diffraction patterns. Remedies are discussed using further simulations, addressing the use of virtual ring detectors for the dark field, or restricting loss calculation to the bright field. Secondly, a dose series is presented down to 100 electrons per diffraction pattern. It is found that all losses yield qualitatively reasonable structural data in the phase, whereas only MSE and Poisson loss range at the correct amplitude level. Chemical contrast is, in general, reliably obtained using the Poisson concept, which also provides the most continuous spatial frequency transfer as to the reconstructed object transmission function.</p></div>\",\"PeriodicalId\":18501,\"journal\":{\"name\":\"Micron\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0968432824001057/pdfft?md5=7092d16b4b135a202c8d0c20480d3752&pid=1-s2.0-S0968432824001057-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Micron\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0968432824001057\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MICROSCOPY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Micron","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0968432824001057","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MICROSCOPY","Score":null,"Total":0}
Influence of loss function and electron dose on ptychography of 2D materials using the Wirtinger flow
Iterative phase retrieval is based on minimising a loss function as a measure of the consistency of an initial guess and underlying experimental data. Under ideal experimental conditions, real data contains Poissonian noise due to counting statistics. In this work, we use the Wirtinger Flow concept in combination with four common loss functions, being the loss, the mean-squared error (MSE), the amplitude loss and the Poisson loss. Since only the latter reflects the counting statistics as an asymmetric Poisson distribution correctly, our simulation study focuses on two main cases. Firstly, high-dose momentum-resolved scanning transmission electron microscopy (STEM) of an MoS2 monolayer is considered for phase retrieval. In this case, it is found that the four losses perform differently with respect to chemical sensitivity and frequency transfer, which we interprete in terms of the substantially different signal level in the bright and dark field part of diffraction patterns. Remedies are discussed using further simulations, addressing the use of virtual ring detectors for the dark field, or restricting loss calculation to the bright field. Secondly, a dose series is presented down to 100 electrons per diffraction pattern. It is found that all losses yield qualitatively reasonable structural data in the phase, whereas only MSE and Poisson loss range at the correct amplitude level. Chemical contrast is, in general, reliably obtained using the Poisson concept, which also provides the most continuous spatial frequency transfer as to the reconstructed object transmission function.
期刊介绍:
Micron is an interdisciplinary forum for all work that involves new applications of microscopy or where advanced microscopy plays a central role. The journal will publish on the design, methods, application, practice or theory of microscopy and microanalysis, including reports on optical, electron-beam, X-ray microtomography, and scanning-probe systems. It also aims at the regular publication of review papers, short communications, as well as thematic issues on contemporary developments in microscopy and microanalysis. The journal embraces original research in which microscopy has contributed significantly to knowledge in biology, life science, nanoscience and nanotechnology, materials science and engineering.