{"title":"Talbot (1836)， Montgomery (1967)， Lau(1948)和Wolf(1955)关于光学中的周期性","authors":"A. Lohmann, D. Mendlovic, G. Shabtay","doi":"10.1088/0963-9659/7/5/018","DOIUrl":null,"url":null,"abstract":"If a wave is laterally periodic, then it is also longitudinally periodic. Nevertheless, lateral periodicity is not needed for longitudinal periodicity. Lateral quasi-periodicity is a more general case and sufficient for longitudinal periodicity. These results can be drawn from the Helmholtz equation, if the light is quasi-monochromatic and spatially coherent. For partially coherent light, similar results can be deduced from the Wolf equations. The triple correlation of a complex amplitude obeys a pair of wave equations, which are constructed exactly like the Wolf equations. Hence, the same laws on periodicity are valid. We present a historical and systematic view of all of those periodicity laws.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Talbot (1836), Montgomery (1967), Lau (1948) and Wolf (1955) on periodicity in optics\",\"authors\":\"A. Lohmann, D. Mendlovic, G. Shabtay\",\"doi\":\"10.1088/0963-9659/7/5/018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If a wave is laterally periodic, then it is also longitudinally periodic. Nevertheless, lateral periodicity is not needed for longitudinal periodicity. Lateral quasi-periodicity is a more general case and sufficient for longitudinal periodicity. These results can be drawn from the Helmholtz equation, if the light is quasi-monochromatic and spatially coherent. For partially coherent light, similar results can be deduced from the Wolf equations. The triple correlation of a complex amplitude obeys a pair of wave equations, which are constructed exactly like the Wolf equations. Hence, the same laws on periodicity are valid. We present a historical and systematic view of all of those periodicity laws.\",\"PeriodicalId\":20787,\"journal\":{\"name\":\"Pure and Applied Optics: Journal of The European Optical Society Part A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Optics: Journal of The European Optical Society Part A\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0963-9659/7/5/018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pure and Applied Optics: Journal of The European Optical Society Part A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0963-9659/7/5/018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Talbot (1836), Montgomery (1967), Lau (1948) and Wolf (1955) on periodicity in optics
If a wave is laterally periodic, then it is also longitudinally periodic. Nevertheless, lateral periodicity is not needed for longitudinal periodicity. Lateral quasi-periodicity is a more general case and sufficient for longitudinal periodicity. These results can be drawn from the Helmholtz equation, if the light is quasi-monochromatic and spatially coherent. For partially coherent light, similar results can be deduced from the Wolf equations. The triple correlation of a complex amplitude obeys a pair of wave equations, which are constructed exactly like the Wolf equations. Hence, the same laws on periodicity are valid. We present a historical and systematic view of all of those periodicity laws.
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