1、Designation: E 2387 05Standard Practice forGoniometric Optical Scatter Measurements1This standard is issued under the fixed designation E 2387; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in
2、parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice describes procedures for determining theamount and angular distribution of optical scatter from asurface. In particular it focuses
3、 on measurement of the bidi-rectional scattering distribution function (BSDF). BSDF is aconvenient and well accepted means of expressing opticalscatter levels for many purposes. It is often referred to as thebidirectional reflectance distribution function (BRDF) whenconsidering reflective scatter or
4、 the bidirectional transmittancedistribution function (BTDF) when considering transmissivescatter.1.2 The BSDF is a fundamental description of the appear-ance of a sample, and many other appearance attributes (suchas gloss, haze, and color) can be represented in terms ofintegrals of the BSDF over sp
5、ecific geometric and spectralconditions.1.3 This practice also presents alternative ways of present-ing angle-resolved optical scatter results, including directionalreflectance factor, directional transmittance factor, and differ-ential scattering function.1.4 This practice applies to BSDF measureme
6、nts on opaque,translucent, or transparent samples.1.5 The wavelengths for which this practice applies includethe ultraviolet, visible, and infrared regions. Difficulty inobtaining appropriate sources, detectors, and low scatter opticscomplicates its practical application at wavelengths less thanabou
7、t 0.2 m (200 nm). Diffraction effects start to becomeimportant for wavelengths greater than 15 m (15 000 nm),which complicate its practical application at longer wave-lengths. Measurements pertaining to visual appearance arerestricted to the visible wavelength region.1.6 This practice does not apply
8、 to materials exhibitingsignificant fluorescence.1.7 This practice applies to flat or curved samples ofarbitrary shape. However, only a flat sample is addressed in thediscussion and examples. It is the users responsibility to definean appropriate sample coordinate system to specify the mea-surement
9、location on the sample surface and appropriate beamproperties for samples that are not flat.1.8 This practice does not provide a method for ascribingthe measured BSDF to any scattering mechanism or source.1.9 This practice does not provide a method to extrapolatedata from one wavelength, scattering
10、geometry, sample loca-tion, or polarization to any other wavelength, scattering geom-etry, sample location, or polarization. The user must makemeasurements at the wavelengths, scattering geometries,sample locations, and polarizations that are of interest to his orher application.1.10 Any parameter c
11、an be varied in a measurement se-quence. Parameters that remain constant during a measurementsequence are reported as either header information in thetabulated data set or in an associated document.1.11 The apparatus and measurement procedure are generic,so that specific instruments are neither excl
12、uded nor implied inthe use of this practice.1.12 For measurements performed for the semiconductorindustry, the operator should consult Practice SEMI ME 1392.1.13 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user
13、of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 284 Terminology of AppearanceE 308 Practice for Computing the Colors of Objects byUsing the CIE SystemE 1331 Tes
14、t Method for Reflectance Factor and Color bySpectrophotometry Using Hemispherical Geometry2.2 ISO Standard:ISO 13696 Optics and Optical InstrumentsTest Methodsfor Radiation Scattered by Optical Components32.3 Semiconductor Equipment and Materials International(SEMI) Standard:1This practice is under
15、the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.03 on Geometry.Current edition approved Jan. 1, 2005. Published February 2005.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at se
16、rviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from International Organization for Standardization (ISO), 1 rue deVaremb, Case postale 56, CH-1211, Geneva 20, Switzerland.1Copyright ASTM International, 10
17、0 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.ME 1392 Practice for Angle Resolved Optical Scatter Mea-surements on Specular and Diffuse Surfaces43. Terminology3.1 Definitions:3.1.1 Definitions of terms not included here will be found inTerminology E 284.3.2 Defini
18、tions of Terms Specific to This Standard:3.2.1 absolute normalization method, na method of per-forming a scattering measurement in which the incident poweris measured directly with the same receiver system as is usedfor the scattering measurement.3.2.2 angle of incidence, ui, npolar angle of the sou
19、rcedirection, given by the angle between the source direction andthe surface normal; see Fig. 1.3.2.2.1 DiscussionSee Discussion of scatter polar angle.3.2.3 aspecular angle, a, nthe angle between the speculardirection and the scatter direction, the sign of which is positivefor backward scattering a
20、nd negative for forward scattering.3.2.3.1 DiscussionFor scatter directions in the plane ofincidence (with fs= 0 and fi= 180), the aspecular angle isgiven by:a5ui2us(1)A more general expression for the aspecular angle, valid forall incident and scattering directions, is given by:a5cos21cosuicosus2 s
21、inuisinuscosfs2fi!# (2)Since the arccosine of a value is always positive, the signmust be separately chosen so that it is positive when thescattering direction is behind the specular direction and nega-tive when the scattering direction is forward of the speculardirection. The convention adopted her
22、e is that it is positive if:sinuscosfs2fi! . sinui(3)and negative otherwise. Fig. 2 illustrates the regions of positiveand negative aspecular angles.3.2.4 beam coordinate system, na coordinate system par-allel to the sample coordinate system, whose origin is thegeometric center of the sampling regio
23、n, used to define theangle of incidence, the scatter angle, the incident azimuthangle, and the scatter azimuth angle.3.2.5 bidirectional reflectance distribution function, BRDF,nthe sample BSDF measured in a reflective geometry.3.2.6 bidirectional scattering distribution function BSDF,nthe sample ra
24、diance Ledivided by the sample irradiance Eefor a uniformly-illuminated and uniform sample:BSDF 5LeEesr21# (4)3.2.6.1 DiscussionBSDF is a differential function depen-dent on the wavelength, incident direction, scatter direction,and polarization states of the incident and scattered fluxes. TheBSDF is
25、 equivalent to the fraction of the incident flux scatteredper unit projected solid angle:BSDF 5limV0PsPiVcosussr21# (5)The BSDF of a lambertian surface is independent of scatterdirection. The BSDF of a specularly reflecting surface has asharp peak in the specular direction. If a surface scattersnon-
26、uniformly from one position to another then a series ofmeasurements over the sample surface must be averaged toobtain suitable statistical uncertainty.3.2.7 bidirectional transmittance distribution function,BTDF, nthe sample BSDF measured in a transmissivegeometry.4Available from Semiconductor Equip
27、ment and Materials International (SEMI),3081 Zanker Rd., San Jose, CA 95134.FIG. 1 Angle ConversionsE23870523.2.8 BSDF instrument signature, nthe mean scatter leveldetected when there is no sample scatter present expressed asBSDF.3.2.8.1 DiscussionThe BSDF instrument signature isgiven by the DSF ins
28、trument signature divided by cosus. TheBSDF instrument signature depends upon scattering angle.Because of the factor cosus, if it is not below the noiseequivalent BSDF, it diverges to infinity at us= 90.3.2.9 colorimetric BSDF, nthe angle-resolved multi-parameter color specification function which i
29、s scaled so thatthe luminance factor Y corresponds to the photometric BSDF.3.2.9.1 DiscussionThe colorimetric BSDF consists ofthree color coordinates as a function of the scattering geometry.One of color coordinates corresponds to the luminance factor Yand is usually expressed as the ratio of the lu
30、minance of aspecimen to that of a perfect diffuser. For the colorimetricBSDF, this color coordinate is replaced by the photometricBSDF. The specific illuminant (for example, CIE StandardIlluminant D65), set of color matching functions (for example,CIE 1931 Standard Colorimetric Observer), and the co
31、lorsystem (for example, CIELAB) must be specified and includedwith any data.3.2.10 differential scattering function, DSF, nthe fractionof incident light scattered per unit solid angle, given by:DSF 5limV0PsPiV5 BSDF cosus(6)3.2.11 directional transmittance factor, Td, nthe ratio ofthe BTDF to that f
32、or a perfectly transmitting diffuser (definedas 1/p), given by:Td5pBTDF (7)3.2.12 directional reflectance factor, Rd, nthe ratio of theBRDF to that for a perfect reflecting diffuser (defined as 1/p),given by:Rd5pBRDF (8)3.2.13 DSF instrument signature, nthe mean scatter leveldetected when there is n
33、o sample scatter present expressed asa DSF.3.2.13.1 DiscussionThe DSF instrument signature pro-vides an equivalent DSF for a perfectly reflecting specularsurface as measured by the instrument. The instrument signa-ture includes contributions from the size of the incident lightbeam at the receiver ap
34、erture, the diffraction of that beam, andstray scatter from instrument components. For high-sensitivitysystems (those whose NEDSF strives for levels below about10-6sr-1), the limitation on instrument signature is normallyRayleigh scatter from molecules within the volume of theincident light beam tha
35、t is sampled by the receiver field ofview. The instrument signature can be measured by removingthe sample and scanning the receiver through the incident beamin a transmission configuration. The signature can also bemeasured by scanning a reference sample, whose scatter isexpected to be significantly
36、 lower than that of the specimenbeing studied, in which case the signature is adjusted bydividing by the reference sample reflectance. It is necessary tofurnish the instrument signature when reporting BSDF data sothat the user can decide at what scatter direction the measuredsample BSDF or DSF is lo
37、st in the signature. Preferably thesignature is at least a few decades below the sample data andcan be ignored. The DSF instrument signature depends uponthe receiver solid angle and the receiver field of view.FIG. 2 Definition of the Sign of the Aspecular AngleE23870533.2.14 incident azimuth angle,
38、fi, nthe angle from the XBaxis to the projection of the source direction onto the X-Yplane; when not specified, this angle is assumed to be 180; seeFig. 1.3.2.14.1 DiscussionSee Discussion for scatter polarangle.3.2.15 incident direction, nthe central ray of the incidentflux specified by uiand fiin
39、the beam coordinate system,pointing from the illumination to the sample.3.2.15.1 DiscussionThe incident direction is the oppositeof the source direction.3.2.16 incident power, Pi, nthe radiant flux incident on thesample.3.2.16.1 DiscussionFor relative BSDF measurements, theincident power is not meas
40、ured directly. For absolute BSDFmeasurements it is important to verify the linearity, and ifnecessary correct for any nonlinearity, of the detector systemover the range from the incident power level down to thescatter level which may be as many as 13 to 15 orders ofmagnitude lower. If the same detec
41、tor is used to measure theincident power and the scattered flux, then it is not necessary tocorrect for the detector responsivity; otherwise, the signal fromeach detector must be normalized by its responsivity. In allcases, the absolute power is not needed, so long as the unit ofpower is the same as
42、 that used to measure the scattered powerPs.3.2.17 noise equivalent BSDF, NEBSDF, nthe root meansquare (rms) of the noise fluctuation expressed as equivalentBSDF.3.2.17.1 DiscussionThe noise equivalent BSDF is givenby the DSF divided by cos us. Because of the factor cos us, theNEBSDF depends upon sc
43、attering angle and diverges toinfinity at us= 90. The NEBSDF is inversely proportional tothe collection solid angle.3.2.18 noise equivalent DSF, NEDSF, nthe root meansquare (rms) of the noise fluctuation expressed as equivalentDSF.3.2.18.1 DiscussionMeasurement precision is limited bythe acceptable
44、signal to noise ratio with respect to thesefluctuations. Unlike the NEBSDF, the NEDSF should beindependent of scattering geometry and is evaluated by re-peated measurements with the source beam blocked. TheNEDSF is given by the rms of the repeated measurementsdivided by the incident power. The NEDSF
45、 is inverselyproportional to the collection solid angle.3.2.19 photometric BSDF, nthe sample luminance di-vided by the sample illuminance for a uniformly-illuminatedand uniform sample.3.2.20 plane of incidence, PLIN, nthe plane containingthe sample normal and central ray of the incident flux.3.2.21
46、relative normalization method, na method forperforming a scattering measurement in which a diffuselyreflecting sample of known BRDF is used as a reference.3.2.22 receiver, na system that generally contains aper-tures, filters, focusing optics, and a detector element thatgathers the scatter flux over
47、 a known solid angle and providesa measured signal.3.2.23 receiver solid angle, V, nthe solid angle subtendedby the receiver aperture stop from the center of the samplingaperture.3.2.24 sample coordinate system, na coordinate systemfixed to the sample and used to specify position on the samplesurfac
48、e.3.2.24.1 DiscussionThe sample coordinate system (X, Y,Z) is application and sample specific. The cartesian coordinatesystem shown in Fig. 3 is recommended for flat samples. Theorigin is at the geometric center of the sample face with the Zaxis normal to the sample. A fiducial mark must be shown at
49、the periphery of the sample; it is most conveniently placedalong either the X or Y axes. If the sample fiducial mark is notan X axis mark, the intended value should be indicated on thesample. The incident and scatter directions are measured in thebeam coordinate system (XB, YB, ZB). Th Z and ZB axes arealways the local normal to the sample face.3.2.25 sample irradiance, Ee, nthe radiant flux incidenton the sample surface per unit area.3.2.25.1 DiscussionIn practice, Eeis an average calcu-lated from the incident power, Pi, divided by
