# ASTM E808-01 (Reapproved 2016)

Designation E808 01 Reapproved 2016Standard 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 perance, 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 Standards2E284 Terminology of Appearance2.2 Federal StandardFed. Std. No. 370 Instrumental Photometric Measurementsof Retroreflecting Materials and Retroreflecting Devices32.3 CIE DocumentCIE 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 1The terminology given here describes visual observation ofluminance as defined by the CIE V spectral weighting function for thephotopic observer. Analogous terms for other purposes can be defined byusing appropriate spectral weighting.3.2 Definitions3.2.1 The delimiting phrase “in retroreflection” applies toeach of the following definitions when used outside the contextof this or other retroreflection standards.3.2.2 coeffcient of line retroreflection, RM,nof a retrore-flecting stripe, the ratio of the coefficient of luminous intensityRI to the length l, expressed in candelas per lux per metrecdlx1m1. RM RI/l.3.2.2.1 DiscussionRMdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.3 coeffcient of luminous intensity, RI,nof aretroreflector, ratio of the luminous intensity I of the retrore-flector in the direction of observation to the illuminance Eat the retroreflector on a plane perpendicular to the direction ofthe incident light, expressed in candelas per lux cdlx1. RII/E.3.2.3.1 DiscussionIn 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 IErd2. RIdependson the spectral composition of the illumination which is usuallyCIE illuminant A.3.2.3.2 DiscussionAlso called coeffcient 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 coeffcient of retroreflected luminance, RL,nthe 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 luxcdm2lx1.RL5 L/E 5 RI/Acos 5 I/EAcos 5 RA/cos 11This 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 serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standards 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 States1whereA surface area of the sample, and viewing angle.3.2.4.1 DiscussionThe units millicandela per square metreper lux mcdm2lx1 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 DiscussionRLdepends on the spectral compositionof the illumination which is usually CIE illuminant A.3.2.5 coeffcient of retroreflected luminous flux, R,ntheratio of the luminous flux per unit solid angle, /, in thedirection of observation to the total flux incident on theeffective retroreflective surface, expressed in candelas perlumen cdlm1.R5 // 5 I/ 5 RA/cos 23.2.5.1 DiscussionThe units for this photometric quantity,candelas per lumen, are sometimes abbreviated as CPL.3.2.5.2 DiscussionRdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.6 coeffcient of retroreflection, RA,nof a plane retrore-flecting surface, the ratio of the coefficient of luminousintensity RI to the area A, expressed in candelas per lux persquare metre cdlx1m2. RA RI/A.3.2.6.1 DiscussionThe 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 DiscussionThe radiometric BRDF is not the ana-logue of RAbut rather of R.3.2.6.3 DiscussionRAdepends on the spectral composi-tion of the illumination which is usually CIE illuminant A.3.2.7 co-entrance angle, e, nthe complement of the anglebetween the retroreflector axis and the illumination axis.3.2.7.1 Discussione90-. Range 0e, the receiver over the source, for testing.FIG. 7 RM Road Marking SystemE808 01 20167several angles, can no longer be applied. Therefore, byconvention, 1; 20; s; 0; and the projection ofsinto a plane perpendicular to the illumination axis, that is,tan1tans/cos.7.3 When 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, sand, can no longer be applied. Therefore, by convention,s 0; -.8. Specification Conventions8.1 If the retroreflector has a datum mark and the rotationangle is unspecified, it has been a common practice toconsider 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 alone is specified withoutreference to components, it has been a common practice in theUnited States to consider 20 and 1. 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 20, 1is 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 and the rho angle, 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 uni 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 uni over thereceiver aperture stop, and 4 the observation axis passesthrough the center of the receiver aperture stop.9.1.1 Circular ApertureThe 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 ApertureIf 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 0.2rectangular 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 angleAPPENDIXNonmandatory InationX1. TRANSATION TABLESX1.1 Equations for transation from the 1959 BrusselsCIE coordinate system , E, V, H to the CIE goniometersystem , 1, 2, .NOTE X1.1The symbol E is used to designate the rotation angle in the1959 Brussels system to avoid confusion. 5 cos 5 cos VcosHsin 152 sin Vsin2V1 cos2V cos2H1/2cos 15cos VcosHsin2V1 cos2V cos2H1/2sin 252sin HcosVcos 5cos E cos H1 sin E sin V sin H sin2V1 cos2V cos2H1/2sin 5cos E sin H sin V 2 sin E cos H sin2V1 cos2V cos2H1/2X1.1.1 Special cases when V 0andH 6 90then 25790 note sign reversal15 0 52EX1.2 Equations for transation from CIE goniometersystem , 1, 2, to the 1959 Brussels CIE coordinatesystem , E, V, H. 5 sin V 52sin 1cos 2sin H 52 sin 2sin221 cos21cos221/2cos H 5cos 1cos2sin221 cos21cos221/2cos E 5sin sin 1sin 21 cos cos 1sin221 cos21cos221/2sin E 5cos sin 1sin 22 sin cos 1sin221 cos21cos221/2E808 01 20168X1.2.1 Special cases when 20and1 6 90then H 5 0V 5790E 52X1.3 In the SAE J594f system, the transations are thesame as in Sections X1.1 and X1.2, with the followingconventionsE SAESAEis rotation angle in SAE J594f10 down SAE J594f angle10 right SAE J594f angle20, sgnx1; sgn00. This agreeswith most software, but some define sgn01.X1.4.1 Equations for transation from Intrinsic systemto CIE system are as follows15 tan21tan cos X1.125 sin21sin sin X1.2 5 s2 tan21tan cos 2 901 2 sgncos X1.3X1.4.2 Equations for transation from CIE system toIntrinsic system are as follows 5 cos21cos 1 cos 2 X1.4s5 1 tan21Ssin 2tan 1D1901 2 sgn1 X1.5 5 tan21Stan 2sin 1D1901 2 sgn1 X1.6X1.4.2.1 For the special case 102, makes 90 sgn2.For the special case 102, make s 0.X1.4.2.2 For the special case 102, make 90 sgn2.For the special case 102, make -.X1.4.3 Equations for transation from Application sys-tem to CIE system are as follows15 sin21sin cos s2 X1.725 tan21tan sin s2 X1.8X1.4.4 Equations for transation from CIE system toApplication system are as follows 5 cos21cos 1 cos 2 X1.9s5 1 tan21Ssin 2tan 1D1901 2 sgn1 X1.10X1.4.4.1 For the special case 102, makes 90 sgn2.For the special case 102, make s 0.X1.4.5 Equation for transation from Intrinsic system toApplication system is as follows 5 s2 tan21tan cos 2 901 2 sgncos X1.11X1.4.5.1 For the special cases where tan is infinite, makes.X1.4.6 Equation for transation from Application sys-tem to Intrinsic system is as follows 5 tan21Stan s2 cos D1901 2 sgncos s2 X1.12X1.4.6.1 For the special cases where tans is infinite,make s.X1.4.7 Equations for transation from RM system toApplication system are as follows 5 cos21sin a sin e 2 cos a cos b cos e X1.13 5 902e X1.14 5 d 2 tan21Stan a sin btan e1 tan a cos bD1901 1 sgn tan e1 cos a cos b X1.15s5 d 2 b1180 X1.16X1.4.8 To trans from RM system to CIE system, firstuse the equations in X1.4.7 to trans to the Applicationsystem, then use the equations in X1.4.3 to trans to theCIE system.X1.4.9 Equations for transation from CIE system toRM system are as followsa 5 sin21cos 12 cos 2X1.17b 5 1801sgn2cos21X1.18Ssin22cos 1cos12 1 sin 1sin12 1 2 cos21cos221 2 cos212 cos22De 5 sin21cos 1cos 2 X1.19d 5 s1b 2 180 X1.20X1.4.9.1 To use Eq X1.20 requires first using Eq X1.18 toobtain b and equation Eq X1.5 to obtain s.X1.4.10 Equations for transation between rotationangle and rho angle are as follows 52tan21Stan s2 cos D1 tan21Stan scos DX1.21190sgncos s2 2 sgncos s 5 s2 tan21Stan scos 2 tan cos2cos 1 tan stan D1Q X1.22Make Q0 or Q180 so as to produce in the samequadrant as .E808 01 20169ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. 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