Pub Date : 2019-12-19DOI: 10.1017/9781108769914.025
{"title":"The circle polynomials of Zernike (§9.2.1)","authors":"","doi":"10.1017/9781108769914.025","DOIUrl":"https://doi.org/10.1017/9781108769914.025","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124205968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.016
{"title":"Scattering from inhomogeneous media","authors":"","doi":"10.1017/9781108769914.016","DOIUrl":"https://doi.org/10.1017/9781108769914.016","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130225995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.005
{"title":"Electromagnetic potentials and polarization","authors":"","doi":"10.1017/9781108769914.005","DOIUrl":"https://doi.org/10.1017/9781108769914.005","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133134298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.004
{"title":"Basic properties of the electromagnetic field","authors":"","doi":"10.1017/9781108769914.004","DOIUrl":"https://doi.org/10.1017/9781108769914.004","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115020793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.029
{"title":"Energy conservation in scalar wavefields (§13.3)","authors":"","doi":"10.1017/9781108769914.029","DOIUrl":"https://doi.org/10.1017/9781108769914.029","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127208344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.020
{"title":"Light optics, electron optics and wave mechanics","authors":"","doi":"10.1017/9781108769914.020","DOIUrl":"https://doi.org/10.1017/9781108769914.020","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121004293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1017/9781108769914.026
{"title":"Proof of the inequality |μ12(v)| ⩽ 1 for the spectral degree of coherence (§10.5)","authors":"","doi":"10.1017/9781108769914.026","DOIUrl":"https://doi.org/10.1017/9781108769914.026","url":null,"abstract":"","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"08 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127259692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In geometrical optics, light is described by rays that propagate according to three laws: rectilinear propagation, refraction, and reflection. Their direction of propagation indicates the direction of the flow of light energy. They are normal to a wavefront. They are not a physical entity in the sense that we cannot isolate a ray, yet they are very convenient for describing the process of imaging by a system. We begin this chapter with a brief introduction of the Cartesian sign convention for the distances and heights of the object and image points, and the angles of incidence and refraction or reflection and slope angles of the rays. We discuss Fermat’s principle that the optical path length of a ray from one point to another is stationary, and derive the laws of rectilinear propagation in a homogeneous medium, refraction by a refracting surface, and reflection by a reflecting surface (first in 2D and then in 3D). These laws are used to obtain ray-tracing equations representing the propagation of a ray exactly from a certain point to a point on a refracting or a reflecting surface, or refraction or reflection of the ray by the surface, and propagation of the refracted or reflected ray to the next surface. The purpose of exact ray tracing is to determine the aberrations of a system consisting of a series of refracting and/or reflecting surfaces that generally have a common axis of rotational symmetry called the optical axis. Such a system is called a centered or a rotationally symmetric system. Its surfaces bend light rays from an object according to the three laws to form its image.
{"title":"Foundations of geometrical optics","authors":"V. Mahajan","doi":"10.1117/3.1002529.ch1","DOIUrl":"https://doi.org/10.1117/3.1002529.ch1","url":null,"abstract":"In geometrical optics, light is described by rays that propagate according to three laws: rectilinear propagation, refraction, and reflection. Their direction of propagation indicates the direction of the flow of light energy. They are normal to a wavefront. They are not a physical entity in the sense that we cannot isolate a ray, yet they are very convenient for describing the process of imaging by a system.\u0000\u0000We begin this chapter with a brief introduction of the Cartesian sign convention for the distances and heights of the object and image points, and the angles of incidence and refraction or reflection and slope angles of the rays. We discuss Fermat’s principle that the optical path length of a ray from one point to another is stationary, and derive the laws of rectilinear propagation in a homogeneous medium, refraction by a refracting surface, and reflection by a reflecting surface (first in 2D and then in 3D). These laws are used to obtain ray-tracing equations representing the propagation of a ray exactly from a certain point to a point on a refracting or a reflecting surface, or refraction or reflection of the ray by the surface, and propagation of the refracted or reflected ray to the next surface. The purpose of exact ray tracing is to determine the aberrations of a system consisting of a series of refracting and/or reflecting surfaces that generally have a common axis of rotational symmetry called the optical axis. Such a system is called a centered or a rotationally symmetric system. Its surfaces bend light rays from an object according to the three laws to form its image.","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"318 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128495780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-10-01DOI: 10.1017/CBO9781139644181.030
M. Born, E. Wolf
IT was mentioned in §3.1.1 that the eikonal equation of geometrical optics is identical with an equation which describes the propagation of discontinuities in an electromagnetic field. More generally, the four equations §3.1 (lla)-(14a) governing the behaviour of the electromagnetic field associated with the geometrical light rays may be shown to be identical with equations which connect the field vectors on a moving discontinuity surface. It is the purpose of this appendix to demonstrate this mathematical equivalence. Relations connecting discontinuous changes in field vectors In §1.1.3 we considered discontinuities in field vectors which arise from abrupt changes in the material parameters £ and fi, for example at a surface of a lens. Discontinuous fields may also arise from entirely different reasons, namely because a source suddenly begins to radiate. The field then spreads into the space surrounding the source and with increasing time fills a larger and larger region. On the boundary of this region the field has a discontinuity, the field vectors being in general finite inside this region and zero outside it. We shall first establish certain general relations which hold on any surface at which the field is discontinuous. For simplicity we assume that at any instant of time t > 0 there is only one such surface; the extension to several discontinuity surfaces (which may arise, for example, from reflections at obstacles present in the medium) is straightforward.
{"title":"Propagation of discontinuities in an electromagnetic field (§3.1.1)","authors":"M. Born, E. Wolf","doi":"10.1017/CBO9781139644181.030","DOIUrl":"https://doi.org/10.1017/CBO9781139644181.030","url":null,"abstract":"IT was mentioned in §3.1.1 that the eikonal equation of geometrical optics is identical with an equation which describes the propagation of discontinuities in an electromagnetic field. More generally, the four equations §3.1 (lla)-(14a) governing the behaviour of the electromagnetic field associated with the geometrical light rays may be shown to be identical with equations which connect the field vectors on a moving discontinuity surface. It is the purpose of this appendix to demonstrate this mathematical equivalence. Relations connecting discontinuous changes in field vectors In §1.1.3 we considered discontinuities in field vectors which arise from abrupt changes in the material parameters £ and fi, for example at a surface of a lens. Discontinuous fields may also arise from entirely different reasons, namely because a source suddenly begins to radiate. The field then spreads into the space surrounding the source and with increasing time fills a larger and larger region. On the boundary of this region the field has a discontinuity, the field vectors being in general finite inside this region and zero outside it. We shall first establish certain general relations which hold on any surface at which the field is discontinuous. For simplicity we assume that at any instant of time t > 0 there is only one such surface; the extension to several discontinuity surfaces (which may arise, for example, from reflections at obstacles present in the medium) is straightforward.","PeriodicalId":426885,"journal":{"name":"Principles of Optics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130657224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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