# ASTM E808-01 (Reapproved 2016)

Designation: E808 − 01 (Reapproved 2016)Standard Practice forDescribing Retroreflection1This standard is issued under the fixed designation E808; 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 parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides terminology, alternative geo-metrical coordinate systems, and procedures for designatingangles in descriptions of retroreflectors, specifications forretroreflector performance, and measurements of retroreflec-tion.1.2 Terminology defined herein includes terms germane toother ASTM documents on retroreflection.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user 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:2E284 Terminology of Appearance2.2 Federal Standard:Fed. Std. No. 370 Instrumental Photometric Measurementsof Retroreflecting Materials and Retroreflecting Devices32.3 CIE Document:CIE Publication No. 54 Retroreflection-Definition and Mea-surement43. Terminology3.1 Terms and definitions in Terminology E284 are appli-cable to this standard.3.1.1 In accordance with the convention appearing in theSignificance and Use section of Terminology E284, the super-script B appearing after [CIE] at the end of a definitionindicates that the given definition is a modification of that citedwith little difference in essential meaning.NOTE 1—The terminology given here describes visual observation ofluminance as defined by the CIE V (λ) spectral weighting function for thephotopic observer. Analogous terms for other purposes can be defined byusing appropriate spectral weighting.3.2 Definitions:3.2.1 The delimiting phrase “in retroreflection” applies toeach of the following definitions when used outside the contextof this or other retroreflection standards.3.2.2 coeffıcient of line retroreflection, RM,n—of a retrore-flecting stripe, the ratio of the coefficient of luminous intensity(RI) to the length (l), expressed in candelas per lux per metre(cd·lx–1·m–1). RM= RI/l.3.2.2.1 Discussion—RMdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.3 coeffıcient of luminous intensity, RI,n—of aretroreflector, ratio of the luminous intensity (I) of the retrore-flector in the direction of observation to the illuminance (E )at the retroreflector on a plane perpendicular to the direction ofthe incident light, expressed in candelas per lux (cd·lx–1). RI=(I/E ).3.2.3.1 Discussion—In a given measurement one obtains theaverage RIover the solid angles of incidence and viewingsubtended by the source and receiver apertures, respectively. Inpractice, I is often determined as the product of the illuminanceat the observer and the distance squared (I=Erd2). RIdependson the spectral composition of the illumination which is usuallyCIE illuminant A.3.2.3.2 Discussion—Also called coeffıcient of (retrore-flected) luminous intensity. Equivalent commonly used termsare CIL and SI (specific intensity). CIE Publication 54 uses thesymbol R for RI. The ASTM recommendation is to use thesymbol RI.3.2.4 coeffıcient of retroreflected luminance, RL,n—the ratioof the luminance, L, in the direction of observation to thenormal illuminance, E , at the surface on a plane normal to theincident light, expressed in candelas per square metre per lux[(cd·m–2)·lx–1].RL5 ~L/E ! 5 ~RI/Acosν! 5 ~I/EAcosν! 5 ~RA/cosν! (1)1This practice is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.10 on Retrore-flection.Current edition approved Jan. 1, 2016. Published January 2016. Originallyapproved in 1981. Last previous edition approved in 2009 as E808 – 01 (2009).DOI: 10.1520/E0808-01R16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://www.dodssp.daps.mil.4Available from U.S. National Committee of the CIE (International Commissionon Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 PondSt., Salem, MA 01970, http://www.cie-usnc.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1where:A = surface area of the sample, andν = viewing angle.3.2.4.1 Discussion—The units millicandela per square metreper lux [(mcd·m–2)·lx–1] are usually used to express the RLvalues of road marking surfaces. This quantity is also referredto as specific luminance. Historically the symbol SL was usedfor RL. In some references CRL is used. These are allequivalent, but RLis preferred.3.2.4.2 Discussion—RLdepends on the spectral compositionof the illumination which is usually CIE illuminant A.3.2.5 coeffıcient of (retroreflected) luminous flux, RΦ,n—theratio of the luminous flux per unit solid angle, Φ /Ω , in thedirection of observation to the total flux Φ incident on theeffective retroreflective surface, expressed in candelas perlumen (cd·lm–1).RΦ5 ~Φ /Ω !/Φ 5 I/Φ 5 RA/cosβ (2)3.2.5.1 Discussion—The units for this photometric quantity,candelas per lumen, are sometimes abbreviated as CPL.3.2.5.2 Discussion—RΦdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.6 coeffıcient of retroreflection, RA,n—of a plane retrore-flecting surface, the ratio of the coefficient of luminousintensity (RI) to the area (A), expressed in candelas per lux persquare metre (cd·lx–1·m–2). RA= RI/A.3.2.6.1 Discussion—The equivalent inch-pound units forcoefficient of retroreflection are candelas per foot candle persquare foot. The SI and inch-pound units are numericallyequal, because the units of RAreduce to 1/sr. An equivalentterm used for coefficient of retroreflection is specific intensityper unit area, with symbol SIA or the CIE symbol R . The termcoefficient of retroreflection and the symbol RAalong with theSI units of candelas per lux per square metre are recommendedby ASTM.3.2.6.2 Discussion—The radiometric BRDF is not the ana-logue of RAbut rather of RΦ.3.2.6.3 Discussion—RAdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.7 co-entrance angle, e, n—the complement of the anglebetween the retroreflector axis and the illumination axis.3.2.7.1 Discussion—e=90°-β. Range 0°e, the receiver over the source, for testing.FIG. 7 RM (Road Marking) SystemE808 − 01 (2016)7several angles, can no longer be applied. Therefore, byconvention, β1=β; β2=0°; ε=ωs; γ=0°; and ρ= the projection ofωsinto a plane perpendicular to the illumination axis, that is,ρ=tan–1(tanωs/cosβ).7.3 When β = 0°, the illumination axis and the retroreflectoraxis coincide. In this special case, the definition of the entrancehalf-plane, which is used in the definition of two angles, ωsandγ, can no longer be applied. Therefore, by convention,ωs= 0°; γ =–ρ =-ε.8. Specification Conventions8.1 If the retroreflector has a datum mark and the rotationangle ε is unspecified, it has been a common practice toconsider ε = 0°. This practice is deprecated by ASTM becausethe presence of a datum mark indicates that the retroreflector issensitive to rotation. ASTM recommends that the conditionsdesired for test be completely specified.8.2 When the entrance angle β alone is specified withoutreference to components, it has been a common practice in theUnited States to consider β2=0° and β1=β. Because the use ofsuch conventions results in misunderstandings and conflictingstandards, ASTM deprecates the use of this convention andrecommends that the conditions desired for test be completelyspecified. Note in particular that for sign sheeting β2=0°, β1=βis a poor representation of the road scenario and may result inmisapplication of some materials.9. Aperture Description Conventions9.1 Since the efficiencies of retroreflectors are often rapidlyvarying functions of the observation angle α and the rho angleρ, it is usually important to describe the apertures of the sourceand receiver that are to be used in a measurement. Thefollowing conventions for describing apertures are based on theassumptions that: (1) the luminance of the source in thedirection of the retroreflector is uniform over the sourceaperture stop, (2) the illumination axis passes through thecenter of the source aperture stop, (3) the responsivity of thereceiver in the direction of the retroreflector is uniform over thereceiver aperture stop, and (4) the observation axis passesthrough the center of the receiver aperture stop.9.1.1 Circular Aperture—The angular size of a circularaperture, either source or receiver, should be described bygiving the angle subtended at the retroreflector center by adiameter of the aperture.9.1.2 Rectangular Aperture—If a rectangular aperture, ei-ther source or receiver, has one side parallel to the observationhalf-plane, then its angular size should be described by givingfirst the angle subtended at the retroreflector center by the sideparallel to the observation half-plane and second the anglesubtended at retroreflector center by the side perpendicular tothe observation half-plane. For example, a 0.1° by 0.2°rectangular aperture has its short side parallel to the observa-tion half-plane.10. Keywords10.1 Application system; CIE (goniometer) system; en-trance angle; Intrinsic system; observation angle; orientationangle; presentation angle; retroreflection; rotation angleAPPENDIX(Nonmandatory Information)X1. TRANSFORMATION TABLESX1.1 Equations for transformation from the 1959 BrusselsCIE coordinate system (α, E, V, H) to the CIE (goniometer)system (α, β1, β2, ε).NOTE X1.1—The symbol E is used to designate the rotation angle in the1959 Brussels system to avoid confusion.α 5 αcos β 5 cos VcosHsin β152 sin V~sin2V1 cos2V cos2H!1/2cos β15cos VcosH~sin2V1 cos2V cos2H!1/2sin β252sin HcosVcos ε 5cos E cos H1 sin E sin V sin H~ sin2V1 cos2V cos2H!1/2sin ε 5cos E sin H sin V 2 sin E cos H~ sin2V1 cos2V cos2H!1/2X1.1.1 Special cases: when V =0°andH = 6 90°then β25790° ~note sign reversal!β15 0°ε 52EX1.2 Equations for transformation from CIE (goniometer)system (α, β1, β2, ε) to the 1959 Brussels CIE coordinatesystem (α, E, V, H).α 5 αsin V 52sin β1cos β2sin H 52 sin β2~sin2β21 cos2β1cos2β2!1/2cos H 5cos β1cosβ2~sin2β21 cos2β1cos2β2!1/2cos E 5sin ε sin β1sin β21 cos ε cos β1~sin2β21 cos2β1cos2β2!1/2sin E 5cos ε sin β1sin β22 sin ε cos β1~sin2β21 cos2β1cos2β2!1/2E808 − 01 (2016)8X1.2.1 Special cases: when β2=0°andβ1= 6 90°then H 5 0°V 5790°E 52εX1.3 In the SAE J594f system, the transformations are thesame as in Sections X1.1 and X1.2, with the followingconventions:E = εSAE(εSAEis rotation angle in SAE J594f)β10 =down SAE J594f angleβ10 =right SAE J594f angleβ20, sgn(x)=+1; sgn(0)=0. This agreeswith most software, but some define sgn(0)=+1.X1.4.1 Equations for transformation from Intrinsic systemto CIE system are as follows:β15 tan21~tan β· cos γ! (X1.1)β25 sin21~sin β· sin γ! (X1.2)ε 5 ωs2 tan21~tan γ· cos β! 2 90°·~1 2 sgn~cos γ!! (X1.3)X1.4.2 Equations for transformation from CIE system toIntrinsic system are as follows:β 5 cos21~cos β1· cos β2! (X1.4)ωs5 ε1 tan21Ssin β2tan β1D190°·~1 2 sgn~β1!! (X1.5)γ 5 tan21Stan β2sin β1D190°·~1 2 sgn~β1!! (X1.6)X1.4.2.1 For the special case β1=0°≠β2, makeωs= ε + 90°· sgn(β2).For the special case β1=0°=β2, make ωs= 0°.X1.4.2.2 For the special case β1=0°≠β2, makeγ = 90° · sgn(β2).For the special case β1=0°=β2, make γ =-ε.X1.4.3 Equations for transformation from Application sys-tem to CIE system are as follows:β15 sin21~sin β· cos ~ωs2 ε!! (X1.7)β25 tan21~tan β· sin ~ωs2 ε!! (X1.8)X1.4.4 Equations for transformation from CIE system toApplication system are as follows:β 5 cos21~cos β1· cos β2! (X1.9)ωs5 ε1 tan21Ssin β2tan β1D190°·~1 2 sgn~β1!! (X1.10)X1.4.4.1 For the special case β1=0°≠β2, makeωs= ε + 90°· sgn(β2).For the special case β1=0°=β2, make ωs= 0°.X1.4.5 Equation for transformation from Intrinsic system toApplication system is as follows:ε 5 ωs2 tan21~tan γ cos β! 2 90°·~1 2 sgn~cos γ!! (X1.11)X1.4.5.1 For the special cases where tan γ is infinite, makeε=ωs–γ.X1.4.6 Equation for transformation from Application sys-tem to Intrinsic system is as follows:γ 5 tan21Stan ~ωs2 ε!cos βD190°·~1 2 sgn~cos ~ωs2 ε!!!(X1.12)X1.4.6.1 For the special cases where tan(ωs–ε) is infinite,make γ=ωs–ε.X1.4.7 Equations for transformation from RM system toApplication system are as follows:α 5 cos21~sin a sin e 2 cos a cos b cos e! (X1.13)β 5 90°2e (X1.14)ε 5 d 2 tan21Stan a sin btan e1 tan a cos bD190°·~1 1 sgn ~tan e1 cos a cos b!! (X1.15)ωs5 d 2 b1180° (X1.16)X1.4.8 To transform from RM system to CIE system, firstuse the equations in X1.4.7 to transform to the Applicationsystem, then use the equations in X1.4.3 to transform to theCIE system.X1.4.9 Equations for transformation from CIE system toRM system are as follows:a 5 sin21~cos ~β12 α! cos β2!(X1.17)b 5 180°1sgn~β2!cos21(X1.18)Ssin2β2cos β1cos~β12 α!1 sin β1sin~β12 α!= 1 2 cos2β1cos2β2=1 2 cos2~β12 α! cos2β2De 5 sin21~cos β1cos β2! (X1.19)d 5 ωs1b 2 180° (X1.20)X1.4.9.1 To use Eq X1.20 requires first using Eq X1.18 toobtain b and equation Eq X1.5 to obtain ωs.X1.4.10 Equations for transformation between rotationangle and rho angle are as follows:ρ 52tan21Stan ~ωs2 ε!cos βD1 tan21Stan ωscos βD(X1.21)190°·~sgn~cos ~ωs2 ε!! 2 sgn~cos ωs!!ε 5 ωs2 tan21Stan ωscos β 2 tan ρ cos2βcos β1 tan ωstan ρD1Q (X1.22)Make Q=0° or Q=180° so as to produce ε in the samequadrant as ρ.E808 − 01 (2016)9ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. 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