{"title":"这只是分解波前像差的充分条件,而不是充分必要条件","authors":"P. Lin","doi":"10.1051/jeos/2022004","DOIUrl":null,"url":null,"abstract":"The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has the form W(h₀,ρ,Φ)=ΣΣΣC(2j+m)(2p+m)m.(h₀)Λ(2j+m). (ρ)Λ(2p+m).(cosΦ)Λm, where j, p and m are non-negative integers, ρ and Φ are the polar coordinates of the pupil, and h₀ is the object height. However, one non-zero component of the primary aberrations (i.e., C133h₀ρ³(cosΦ)³) is missing from this equation when the image plane is not the Gaussian image plane. This implies that the equation is a sufficient condition only, rather than a necessary and sufficient condition, since it cannot guarantee that all of the components of the aberrations can be found. Accordingly, this letter presents a new method for determining all the components of aberrations of any order. The results show that three and five components of the secondary and tertiary aberrations, respectively, are missing in the existing literature.\n","PeriodicalId":674,"journal":{"name":"Journal of the European Optical Society-Rapid Publications","volume":" ","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations\",\"authors\":\"P. Lin\",\"doi\":\"10.1051/jeos/2022004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has the form W(h₀,ρ,Φ)=ΣΣΣC(2j+m)(2p+m)m.(h₀)Λ(2j+m). (ρ)Λ(2p+m).(cosΦ)Λm, where j, p and m are non-negative integers, ρ and Φ are the polar coordinates of the pupil, and h₀ is the object height. However, one non-zero component of the primary aberrations (i.e., C133h₀ρ³(cosΦ)³) is missing from this equation when the image plane is not the Gaussian image plane. This implies that the equation is a sufficient condition only, rather than a necessary and sufficient condition, since it cannot guarantee that all of the components of the aberrations can be found. Accordingly, this letter presents a new method for determining all the components of aberrations of any order. The results show that three and five components of the secondary and tertiary aberrations, respectively, are missing in the existing literature.\\n\",\"PeriodicalId\":674,\"journal\":{\"name\":\"Journal of the European Optical Society-Rapid Publications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2022-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the European Optical Society-Rapid Publications\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://doi.org/10.1051/jeos/2022004\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the European Optical Society-Rapid Publications","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1051/jeos/2022004","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations
The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has the form W(h₀,ρ,Φ)=ΣΣΣC(2j+m)(2p+m)m.(h₀)Λ(2j+m). (ρ)Λ(2p+m).(cosΦ)Λm, where j, p and m are non-negative integers, ρ and Φ are the polar coordinates of the pupil, and h₀ is the object height. However, one non-zero component of the primary aberrations (i.e., C133h₀ρ³(cosΦ)³) is missing from this equation when the image plane is not the Gaussian image plane. This implies that the equation is a sufficient condition only, rather than a necessary and sufficient condition, since it cannot guarantee that all of the components of the aberrations can be found. Accordingly, this letter presents a new method for determining all the components of aberrations of any order. The results show that three and five components of the secondary and tertiary aberrations, respectively, are missing in the existing literature.
期刊介绍:
Rapid progress in optics and photonics has broadened its application enormously into many branches, including information and communication technology, security, sensing, bio- and medical sciences, healthcare and chemistry.
Recent achievements in other sciences have allowed continual discovery of new natural mysteries and formulation of challenging goals for optics that require further development of modern concepts and running fundamental research.
The Journal of the European Optical Society – Rapid Publications (JEOS:RP) aims to tackle all of the aforementioned points in the form of prompt, scientific, high-quality communications that report on the latest findings. It presents emerging technologies and outlining strategic goals in optics and photonics.
The journal covers both fundamental and applied topics, including but not limited to:
Classical and quantum optics
Light/matter interaction
Optical communication
Micro- and nanooptics
Nonlinear optical phenomena
Optical materials
Optical metrology
Optical spectroscopy
Colour research
Nano and metamaterials
Modern photonics technology
Optical engineering, design and instrumentation
Optical applications in bio-physics and medicine
Interdisciplinary fields using photonics, such as in energy, climate change and cultural heritage
The journal aims to provide readers with recent and important achievements in optics/photonics and, as its name suggests, it strives for the shortest possible publication time.