Conventional figure measurement techniques are inadequate for testing aspheres for grazing incidence applications. Conventional techniques are best suited for optical components in the shape of flats, spheres, or conical surfaces of revolution, used mainly in normal incidence applications . These optics usually have their symmetry axis coincident with the local surface normal direction. Grazing incidence optics, on the other hand, are usually cylindrical, toroidal, or ellipsoidal in shape, with the symmetry axis intersection far outside the clear aperture. Such surfaces are not axisymmetric when viewed along their surface normals. They are highly anamorphic, having vastly different curvatures in the two directions parallel and perpendicular to the symmetry axis. It is extremely challenging to test these optical components during fabrication to insure that they indeed meet the specifications for figure and finish quality. It is because of the extreme difficulties involved in developing reliable tests with conventional interferometric techniques that we decided to use profiling techniques to characterize the figure and finish of synchrotron radiation (SR) optics.
{"title":"Integrating Figure and Finish Measurements with Surface Profiling Instruments","authors":"P. Takacs, E. Church","doi":"10.2172/10137803","DOIUrl":"https://doi.org/10.2172/10137803","url":null,"abstract":"Conventional figure measurement techniques are inadequate for testing aspheres for grazing incidence applications. Conventional techniques are best suited for optical components in the shape of flats, spheres, or conical surfaces of revolution, used mainly in normal incidence applications . These optics usually have their symmetry axis coincident with the local surface normal direction. Grazing incidence optics, on the other hand, are usually cylindrical, toroidal, or ellipsoidal in shape, with the symmetry axis intersection far outside the clear aperture. Such surfaces are not axisymmetric when viewed along their surface normals. They are highly anamorphic, having vastly different curvatures in the two directions parallel and perpendicular to the symmetry axis. It is extremely challenging to test these optical components during fabrication to insure that they indeed meet the specifications for figure and finish quality. It is because of the extreme difficulties involved in developing reliable tests with conventional interferometric techniques that we decided to use profiling techniques to characterize the figure and finish of synchrotron radiation (SR) optics.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126101518","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}
Optical scattering from surface micro irregularities at a specific wavelength is directly related to the RMS-roughness value of the surface1. It is usually measured by a TIS (Total Integrated Scatter) instrument. In its’ conventional application this method can only be used to investigate the front surface of opaque samples. In the case of transparent samples or samples coated with a transparent film, one must handle two scattering interfaces as well as possible interference effects in the film. The resulting light scattering cannot be described by the standard TIS equation. By combining the scalar scattering theory with the Fresnel formalism we have obtained a model which predicts the scattering from a double layer as a function of wavelength. By fitting model calculations to experimental scattering spectra with the interface roughness values as parameters we can extract the rms-roughness values of the two interfaces. The model has been described elsewhere2. Using the scattering spectra and such fitting calculations we can conveniently, and non-destructively, determine the RMS-roughness of a "hidden" interface.
{"title":"Determination of Interface Roughness Using A Wavelength Scanning TIS Instrument","authors":"D. Ronnow, M. Bergkvist, A. Roos, C. Ribbing","doi":"10.1364/surs.1992.stub7","DOIUrl":"https://doi.org/10.1364/surs.1992.stub7","url":null,"abstract":"Optical scattering from surface micro irregularities at a specific wavelength is directly related to the RMS-roughness value of the surface1. It is usually measured by a TIS (Total Integrated Scatter) instrument. In its’ conventional application this method can only be used to investigate the front surface of opaque samples. In the case of transparent samples or samples coated with a transparent film, one must handle two scattering interfaces as well as possible interference effects in the film. The resulting light scattering cannot be described by the standard TIS equation. By combining the scalar scattering theory with the Fresnel formalism we have obtained a model which predicts the scattering from a double layer as a function of wavelength. By fitting model calculations to experimental scattering spectra with the interface roughness values as parameters we can extract the rms-roughness values of the two interfaces. The model has been described elsewhere2. Using the scattering spectra and such fitting calculations we can conveniently, and non-destructively, determine the RMS-roughness of a \"hidden\" interface.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114396935","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}
E. Méndez, R. Espinosa, J. F. Aguilar, H. Escamilla, Z. Gu
The scattering of light from randomly rough surfaces has attracted a great deal of attention in recent years. Despite all this work, several aspects of the problem remain poorly understood. More specifically, analytical progress is difficult in situations when multiple scattering effects are important, when the statistics of the surface are non-Gaussian, and when the surface profile is multiscale (fractal-like). For a number of years, it has been clear that more systematic studies of the problem are required. In particular, for experimental work, it is important to be able to fabricate surfaces with known statistical properties in a more or less controlled way.
{"title":"Light Scattering from Photofabricated Surfaces with non-Gaussian Statistical Properties","authors":"E. Méndez, R. Espinosa, J. F. Aguilar, H. Escamilla, Z. Gu","doi":"10.1364/surs.1992.stua3","DOIUrl":"https://doi.org/10.1364/surs.1992.stua3","url":null,"abstract":"The scattering of light from randomly rough surfaces has attracted a great deal of attention in recent years. Despite all this work, several aspects of the problem remain poorly understood. More specifically, analytical progress is difficult in situations when multiple scattering effects are important, when the statistics of the surface are non-Gaussian, and when the surface profile is multiscale (fractal-like). For a number of years, it has been clear that more systematic studies of the problem are required. In particular, for experimental work, it is important to be able to fabricate surfaces with known statistical properties in a more or less controlled way.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114572810","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}
The introduction of submicron sensitive laser stylus profilometers1,2 based on the compact disk (CD) laser pick-up head and operating by an auto focusing technique, has opened up a new area for non-contact surface roughness measurement in the critical micron range. As many machined surfaces, paper surfaces and painted coatings have surface structures in this roughness range the field for applications is very wide. Careful investigations are therefore needed to show how the laser stylus technique compares with the common technique of contact stylus measurements. This paper, which is related to a thorough study on surface roughness of paper and ceramic materials,3 presents some of the special features observed for the laser stylus instrument.
{"title":"Comparison between laser stylus and contact stylus measurements on rough surfaces","authors":"L. Mattsson, P. Wågberg","doi":"10.1364/surs.1992.smb4","DOIUrl":"https://doi.org/10.1364/surs.1992.smb4","url":null,"abstract":"The introduction of submicron sensitive laser stylus profilometers1,2 based on the compact disk (CD) laser pick-up head and operating by an auto focusing technique, has opened up a new area for non-contact surface roughness measurement in the critical micron range. As many machined surfaces, paper surfaces and painted coatings have surface structures in this roughness range the field for applications is very wide. Careful investigations are therefore needed to show how the laser stylus technique compares with the common technique of contact stylus measurements. This paper, which is related to a thorough study on surface roughness of paper and ceramic materials,3 presents some of the special features observed for the laser stylus instrument.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130052551","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}
Characterization of surface roughness remains today a crucial problem, in particular in the fields of optics and mechanics. Many techniques [1] have been developed in this aim, and involve scatterometers or profilometers. However the measured roughness values may strongly vary from one technique to another, and it becomes necessary to normalize the statistical parameters that describe surface defects. In this paper we present experimental results obtained from 3 techniques that are Angle-Resolved light Scattering measurements (ARS), mechanical profilometer (Talystep) and Atomic Force Microscope (AFM). Moreover, a theoretical tool is provided for a detailed investigation of the apparatus functions relative to the light scattering and Talystep techniques.
{"title":"Theoretical and experimental comparison of different techniques to characterize surface roughness","authors":"C. Amra, L. Bruel","doi":"10.1364/surs.1992.stua5","DOIUrl":"https://doi.org/10.1364/surs.1992.stua5","url":null,"abstract":"Characterization of surface roughness remains today a crucial problem, in particular in the fields of optics and mechanics. Many techniques [1] have been developed in this aim, and involve scatterometers or profilometers. However the measured roughness values may strongly vary from one technique to another, and it becomes necessary to normalize the statistical parameters that describe surface defects. In this paper we present experimental results obtained from 3 techniques that are Angle-Resolved light Scattering measurements (ARS), mechanical profilometer (Talystep) and Atomic Force Microscope (AFM). Moreover, a theoretical tool is provided for a detailed investigation of the apparatus functions relative to the light scattering and Talystep techniques.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"15 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127650886","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}
The integral equation method can be used to obtain exact solutions for scattering from one-dimensional surfaces. Scattering cross sections for randomly rough surfaces can then be found by averaging scattered intensities for many surface realizations. The accuracy of analytical methods for rough surface scattering can then be examined. Traditionally, the perturbation and Kirchhoff approximations have been the most commonly used analytical methods—the former for surfaces with small roughness and the latter for surfaces with smooth roughness. These approaches can be extended systematically to obtain the perturbation series and the multiple scattering series, respectively. The first few terms in the perturbation series can be formally averaged, extending the range of analytic perturbation theory. The terms in the multiple scattering series beyond the lowest order (the Kirchhoff approximation) have not yet been formally averaged. The multiple scattering series is thus implemented as an approximate numerical method. Numerical results will be presented showing the accuracy and limitations of these two series approaches. These results will also clarify how the two complementary series apply when the surfaces have both small and smooth roughness. The relationship of the multiple scattering series to shadowing phenomena and a major shortcoming with the multiple scattering approach will also be addressed. Recently, several new approximations to rough surface scattering have been developed which reduce properly to the perturbation and Kirchhoff approximation limits. These new approaches will be briefly reviewed and their accuracy discussed.
{"title":"Analytical vs. Numerical Methods for Rough Surface Scattering","authors":"E. Thorsos","doi":"10.1364/surs.1992.sma4","DOIUrl":"https://doi.org/10.1364/surs.1992.sma4","url":null,"abstract":"The integral equation method can be used to obtain exact solutions for scattering from one-dimensional surfaces. Scattering cross sections for randomly rough surfaces can then be found by averaging scattered intensities for many surface realizations. The accuracy of analytical methods for rough surface scattering can then be examined. Traditionally, the perturbation and Kirchhoff approximations have been the most commonly used analytical methods—the former for surfaces with small roughness and the latter for surfaces with smooth roughness. These approaches can be extended systematically to obtain the perturbation series and the multiple scattering series, respectively. The first few terms in the perturbation series can be formally averaged, extending the range of analytic perturbation theory. The terms in the multiple scattering series beyond the lowest order (the Kirchhoff approximation) have not yet been formally averaged. The multiple scattering series is thus implemented as an approximate numerical method. Numerical results will be presented showing the accuracy and limitations of these two series approaches. These results will also clarify how the two complementary series apply when the surfaces have both small and smooth roughness. The relationship of the multiple scattering series to shadowing phenomena and a major shortcoming with the multiple scattering approach will also be addressed. Recently, several new approximations to rough surface scattering have been developed which reduce properly to the perturbation and Kirchhoff approximation limits. These new approaches will be briefly reviewed and their accuracy discussed.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132537660","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}
The man-or-woman in the street model of optical surface quality involves two features -- 'figure', which behaves according to geometrical optics, and 'finish', which is treated by diffraction optics.
{"title":"Specification of surface finish in terms of system performance","authors":"E. Church, P. Takacs","doi":"10.1364/surs.1992.sma1","DOIUrl":"https://doi.org/10.1364/surs.1992.sma1","url":null,"abstract":"The man-or-woman in the street model of optical surface quality involves two features -- 'figure', which behaves according to geometrical optics, and 'finish', which is treated by diffraction optics.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128928114","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}
Intensity angular correlations of Light diffusely reflected from random rough surfaces in the case in which the speckle pattern does not follow a Gaussian second order statistics are studied. A new effect is found which constitutes a generalization of the enhanced backscattering and is due to time reversal symmetry.
{"title":"Enhanced Long Range Correlations of Light Reflected from Random Rough Surfaces","authors":"M. Nieto-Vesperinas, J. Sánchez-gil","doi":"10.1364/surs.1992.pd1","DOIUrl":"https://doi.org/10.1364/surs.1992.pd1","url":null,"abstract":"Intensity angular correlations of Light diffusely reflected from random rough surfaces in the case in which the speckle pattern does not follow a Gaussian second order statistics are studied. A new effect is found which constitutes a generalization of the enhanced backscattering and is due to time reversal symmetry.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116430605","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}
The concept of surface impedance has been widely used in electromagnetic theory of scattering. For a 2D scattering problem the impedance Z(x) on a surface ∑ can be defined as (1) where E║ and H║ represent the components of the electric and magnetic fields tangential to surface ∑, x is a coordinate on the surface and n^ the unit vector normal to it. If Z(x) is known, eq. (1) can be used as a boundary condition exactly equivalent to Maxwell’s, but since it is defined in terms of the fields this knowledge requires the complete solution of the scattering problem.
{"title":"Exact calculations of surface impedance for periodic rough surfaces","authors":"V. Brudny","doi":"10.1364/surs.1992.sma5","DOIUrl":"https://doi.org/10.1364/surs.1992.sma5","url":null,"abstract":"The concept of surface impedance has been widely used in electromagnetic theory of scattering. For a 2D scattering problem the impedance Z(x) on a surface ∑ can be defined as (1) where E║ and H║ represent the components of the electric and magnetic fields tangential to surface ∑, x is a coordinate on the surface and \u0000n^ the unit vector normal to it. If Z(x) is known, eq. (1) can be used as a boundary condition exactly equivalent to Maxwell’s, but since it is defined in terms of the fields this knowledge requires the complete solution of the scattering problem.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"251 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134068759","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}
We report angle resolved light scattering characteristics of individual polystyrene spheres on silicon and on a 91.5 nm thick film of oxide on silicon. Scattering was measured as a function of polarization using a He-Ne laser at a 45 degree incident angle.
{"title":"Light Scattering by Sub-Half Micron Spherical Particles on Silicon and Oxide/Silicon Surfaces*","authors":"E. Bawolek, E. Hirleman","doi":"10.1364/surs.1992.pd3","DOIUrl":"https://doi.org/10.1364/surs.1992.pd3","url":null,"abstract":"We report angle resolved light scattering characteristics of individual polystyrene spheres on silicon and on a 91.5 nm thick film of oxide on silicon. Scattering was measured as a function of polarization using a He-Ne laser at a 45 degree incident angle.","PeriodicalId":339350,"journal":{"name":"Surface Roughness and Scattering","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128046323","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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