{"title":"具有充分断开支持的函数的相位检索","authors":"T. Crimmins, J. Fienup","doi":"10.1364/JOSA.73.000218","DOIUrl":null,"url":null,"abstract":"The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|2. This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1983-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"63","resultStr":"{\"title\":\"Phase Retrieval for Functions with Sufficiently Disconnected Support\",\"authors\":\"T. Crimmins, J. Fienup\",\"doi\":\"10.1364/JOSA.73.000218\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|2. This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.\",\"PeriodicalId\":279385,\"journal\":{\"name\":\"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1983-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"63\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1364/JOSA.73.000218\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1364/JOSA.73.000218","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Phase Retrieval for Functions with Sufficiently Disconnected Support
The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|2. This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.