{"title":"中心光学系统的算子公式","authors":"I. V. Demydenko","doi":"10.15407/ujpe68.5.309","DOIUrl":null,"url":null,"abstract":"Currently, there are many mathematical methods in use in geometric optics. This paper presents a new mathematical apparatus: an operator formalism, which describes centered optical systems in the paraxial approximation. This work is an ideological continuation of author’s previous research. The refraction and reflection operators of spherical surfaces are defined here. The mathematical properties of the operators are studied, and their physical interpretations are established. In addition, the relations between the lensing operator and the refraction operators of a spherical surface are determined. The behavior of rays is also considered, which helped to establish the injectivity and nondegeneracy for points with infinite coordinates. The operator formalism is helpful for finding a centered optical system that performs a given transformation. Moreover, the interchangeability of the optical operators is investigated, and it is found that each operator has a unique effect.","PeriodicalId":23400,"journal":{"name":"Ukrainian Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Operator Formulation for Centered Optical Systems\",\"authors\":\"I. V. Demydenko\",\"doi\":\"10.15407/ujpe68.5.309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Currently, there are many mathematical methods in use in geometric optics. This paper presents a new mathematical apparatus: an operator formalism, which describes centered optical systems in the paraxial approximation. This work is an ideological continuation of author’s previous research. The refraction and reflection operators of spherical surfaces are defined here. The mathematical properties of the operators are studied, and their physical interpretations are established. In addition, the relations between the lensing operator and the refraction operators of a spherical surface are determined. The behavior of rays is also considered, which helped to establish the injectivity and nondegeneracy for points with infinite coordinates. The operator formalism is helpful for finding a centered optical system that performs a given transformation. Moreover, the interchangeability of the optical operators is investigated, and it is found that each operator has a unique effect.\",\"PeriodicalId\":23400,\"journal\":{\"name\":\"Ukrainian Journal of Physics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-07-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ukrainian Journal of Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15407/ujpe68.5.309\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Journal of Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15407/ujpe68.5.309","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Currently, there are many mathematical methods in use in geometric optics. This paper presents a new mathematical apparatus: an operator formalism, which describes centered optical systems in the paraxial approximation. This work is an ideological continuation of author’s previous research. The refraction and reflection operators of spherical surfaces are defined here. The mathematical properties of the operators are studied, and their physical interpretations are established. In addition, the relations between the lensing operator and the refraction operators of a spherical surface are determined. The behavior of rays is also considered, which helped to establish the injectivity and nondegeneracy for points with infinite coordinates. The operator formalism is helpful for finding a centered optical system that performs a given transformation. Moreover, the interchangeability of the optical operators is investigated, and it is found that each operator has a unique effect.
期刊介绍:
Ukrainian Journal of Physics is the general physics edition of the Department of Physics and Astronomy of the National Academy of Sciences of Ukraine. The journal publishes original papers and reviews in the fields of experimental and theoretical physics.