ASTM E808-01(2016)
(Practice)Standard Practice for Describing Retroreflection
Standard Practice for Describing Retroreflection
SIGNIFICANCE AND USE
4.1 This practice applies to any measurement of reflectance in which the angle at the sample between the direction of the incident radiation and the direction of viewing is less than approximately 10°, and the reflected radiation is concentrated in a direction opposite to the direction of incidence.
4.2 The CIE (goniometer) system described in 6.1.1 was developed by the Subcommittee on Retroreflection of Committee 2.3 on Materials of the International Commission on Illumination (Commission International de l'Eclairage, CIE). It is intended to provide a common basis for the measurement of retroreflection, which should be used worldwide.
4.3 This practice provides alternative geometric coordinate systems useful for visualizing relationships between various angles in actual use.
SCOPE
1.1 This practice provides terminology, alternative geometrical coordinate systems, and procedures for designating angles in descriptions of retroreflectors, specifications for retroreflector performance, and measurements of retroreflection.
1.2 Terminology defined herein includes terms germane to other ASTM documents on retroreflection.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E808 −01 (Reapproved 2016)
Standard Practice for
Describing Retroreflection
This standard is issued under the fixed designation E808; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.1 In accordance with the convention appearing in the
Significance and Use section of Terminology E284, the super-
1.1 This practice provides terminology, alternative geo-
script B appearing after [CIE] at the end of a definition
metrical coordinate systems, and procedures for designating
indicates that the given definition is a modification of that cited
angles in descriptions of retroreflectors, specifications for
with little difference in essential meaning.
retroreflector performance, and measurements of retroreflec-
tion.
NOTE 1—The terminology given here describes visual observation of
luminance as defined by the CIE V (λ) spectral weighting function for the
1.2 Terminology defined herein includes terms germane to
photopic observer. Analogous terms for other purposes can be defined by
other ASTM documents on retroreflection.
using appropriate spectral weighting.
1.3 This standard does not purport to address all of the
3.2 Definitions:
safety concerns, if any, associated with its use. It is the
3.2.1 The delimiting phrase “in retroreflection” applies to
responsibility of the user of this standard to establish appro-
each of the following definitions when used outside the context
priate safety and health practices and determine the applica-
of this or other retroreflection standards.
bility of regulatory limitations prior to use.
3.2.2 coeffıcient of line retroreflection, R ,n—of a retrore-
M
flecting stripe, the ratio of the coefficient of luminous intensity
2. Referenced Documents
(R ) to the length (l), expressed in candelas per lux per metre
I
2 –1 –1
2.1 ASTM Standards: (cd·lx ·m ). R = R /l.
M I
E284 Terminology of Appearance 3.2.2.1 Discussion—R depends on the spectral composi-
M
tion of the illumination which is usually CIE illuminant A.
2.2 Federal Standard:
Fed. Std. No. 370 Instrumental Photometric Measurements 3.2.3 coeffıcient of luminous intensity, R,n—of a
I
of Retroreflecting Materials and Retroreflecting Devices retroreflector, ratio of the luminous intensity (I) of the retrore-
flector in the direction of observation to the illuminance (E )
'
2.3 CIE Document:
at the retroreflector on a plane perpendicular to the direction of
CIE Publication No. 54 Retroreflection-Definition and Mea-
–1
the incident light, expressed in candelas per lux (cd·lx ). R =
I
surement
(I/E ).
'
3.2.3.1 Discussion—Inagivenmeasurementoneobtainsthe
3. Terminology
average R over the solid angles of incidence and viewing
I
3.1 Terms and definitions in Terminology E284 are appli-
subtendedbythesourceandreceiverapertures,respectively.In
cable to this standard.
practice, Iisoftendeterminedastheproductoftheilluminance
at the observer and the distance squared (I=E d ). R depends
r I
onthespectralcompositionoftheilluminationwhichisusually
This practice is under the jurisdiction of ASTM Committee E12 on Color and
CIE illuminant A.
Appearance and is the direct responsibility of Subcommittee E12.10 on Retrore-
3.2.3.2 Discussion—Also called coeffıcient of (retrore-
flection.
flected) luminous intensity. Equivalent commonly used terms
Current edition approved Jan. 1, 2016. Published January 2016. Originally
approved in 1981. Last previous edition approved in 2009 as E808 – 01 (2009). are CIL and SI (specific intensity). CIE Publication 54 uses the
DOI: 10.1520/E0808-01R16.
symbol R for R . The ASTM recommendation is to use the
I
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
symbol R .
I
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
3.2.4 coeffıcient of retroreflected luminance, R ,n—the ratio
L
the ASTM website.
of the luminance, L, in the direction of observation to the
Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
normal illuminance, E , at the surface on a plane normal to the
Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http:// '
www.dodssp.daps.mil. incident light, expressed in candelas per square metre per lux
–2 –1
Available from U.S. National Committee of the CIE (International Commission
[(cd·m )·lx ].
on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond
St., Salem, MA 01970, http://www.cie-usnc.org. R 5 L/E 5 R /Acosν 5 I/EAcosν 5 R /cosν (1)
~ ! ~ ! ~ ! ~ !
L ' I A
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E808 − 01 (2016)
where: 3.2.10 datum mark, n—an indication on the retroreflector,
off the retroreflector axis, that establishes the direction of the
A = surface area of the sample, and
datum axis.
ν = viewing angle.
3.2.11 datum half-plane, n—thehalf-planethatoriginateson
3.2.4.1 Discussion—Theunitsmillicandelapersquaremetre
the line of the retroreflector axis and contains the datum axis.
–2 –1
per lux [(mcd·m )·lx ] are usually used to express the R
L
3.2.12 entrance angle, β,n—the angle between the illumi-
values of road marking surfaces. This quantity is also referred
nation axis and the retroreflector axis.
to as specific luminance. Historically the symbol SL was used
3.2.12.1 Discussion—The entrance angle is usually no
for R . In some references CRL is used. These are all
L
larger than 90°, but for completeness its full range is defined as
equivalent, but R is preferred.
L
0°≤β≤180°. In the CIE (goniometer) system β is resolved into
3.2.4.2 Discussion—R dependsonthespectralcomposition
L
two components β and β . Since by definition β is always
1 2
of the illumination which is usually CIE illuminant A.
positive,thecommonpracticeofreferringtothesmallentrance
3.2.5 coeffıcient of (retroreflected) luminous flux, R ,n—the
Φ
angles that direct specular reflections away from the photore-
ratio of the luminous flux per unit solid angle, Φ'/Ω', in the
ceptor as negative valued is deprecated by ASTM. The
direction of observation to the total flux Φ incident on the
recommendation is to designate such negative values as
effective retroreflective surface, expressed in candelas per
belonging to β .
–1
lumen (cd·lm ).
3.2.13 entrance angle component,β ,n—the angle from the
R 5 ~Φ'/Ω'!/Φ 5 I/Φ 5 R /cosβ (2)
Φ A
illumination axis to the plane containing the retroreflector axis
3.2.5.1 Discussion—The units for this photometric quantity,
and the first axis. Range: –180°<β ≤180°.
candelas per lumen, are sometimes abbreviated as CPL.
3.2.14 entrance angle component,β ,n—the angle from the
3.2.5.2 Discussion—R depends on the spectral composi-
Φ
plane containing the observation half-planeto the retroreflector
tion of the illumination which is usually CIE illuminant A.
axis. Range: –90°≤β ≤90°.
3.2.6 coeffıcient of retroreflection, R ,n—of a plane retrore-
3.2.14.1 Discussion—For some measurements it is conve-
A
flecting surface, the ratio of the coefficient of luminous nient to extend the range of β to –180°<β ≤180°. β must then
2 2 1
intensity (R ) to the area (A), expressed in candelas per lux per
be restricted to –90°<β ≤90°.
I
–1 –2
square metre (cd·lx ·m ). R = R /A.
A I
3.2.15 entrance half-plane, n—the half-plane that originates
3.2.6.1 Discussion—The equivalent inch-pound units for
on the line of the illumination axis and contains the retrore-
coefficient of retroreflection are candelas per foot candle per
flector axis.
square foot. The SI and inch-pound units are numerically
3.2.16 first axis, n—theaxisthroughtheretroreflectorcenter
equal, because the units of R reduce to 1/sr. An equivalent
A
and perpendicular to the observation half-plane.
term used for coefficient of retroreflection is specific intensity
3.2.17 fractional retroreflectance, R,n—the fraction of
per unit area, with symbol SIAor the CIE symbol R'. The term T
unidirectional flux illuminating a retroreflector that is received
coefficient of retroreflection and the symbol R along with the
A
at observation angles less than a designated value, α .
SI units of candelas per lux per square metre are recommended max
3.2.17.1 Discussion—R has no meaning unless α is
by ASTM. T max
specified.
3.2.6.2 Discussion—The radiometric BRDF is not the ana-
3.2.17.2 Discussion—For a flat retroreflector R may be
logue of R but rather of R . T
A Φ
calculated as follows:
3.2.6.3 Discussion—R depends on the spectral composi-
A
α π
max
tion of the illumination which is usually CIE illuminant A.
R ~α,ρ!
A
α dαdρ. (3)
* *
cos β
3.2.7 co-entrance angle, e, n—the complement of the angle
α50 ρ52π
between the retroreflector axis and the illumination axis.
For a non-flat retroreflector R may be calculated as
T
3.2.7.1 Discussion—e=90°-β. Range 0°
follows:
zontal road markings, the retroreflector axis is considered to be
α π
max
R ~α,ρ!
the normal to the road surface, making e the angle of
I
* * α dαdρ. (4)
A
inclination of the illumination axis over the road surface.
P
α50 ρ52π
3.2.8 co-viewing angle, a, n—the complement of the angle
A is the area of the retroreflector as projected in the
P
between the retroreflector axis and the observation axis.
direction of illumination. Angles β and ω must remain
s
3.2.8.1 Discussion—a= 90°-ν. Range 0°
fixed through the integration. Angles α and ρ are in radi-
zontal road markings, the retroreflector axis is considered to be
ans: R is unitless. Presentation angle γ may replace ρ in
T
the normal to the road surface, making a the angle of
these formulas. For very small values of β, rotation angle
inclination of the observation axis over the road surface.
ε may replace ρ in these formulas. For example, for β=5°
the resulting error will be less than, usually much less
3.2.9 datum axis, n—a designated half-line from the retrore-
than, 0.5 % of the calculated R .
flector center perpendicular to the retroreflector axis. T
3.2.17.3 Discussion—R is usually expressed in percent.
T
3.2.9.1 Discussion—The datum axis together with the ret-
roreflector center and the retroreflector axis establish the 3.2.18 illumination axis, n—the half-line from the retrore-
position of the retroreflector. flector center through the source point.
E808 − 01 (2016)
3.2.19 illumination distance, n—the distance between the 3.2.30 retroreflective element, n—aminimalopticalunitthat
source point and the retroreflector center. produces retroreflection.
3.2.20 observation angle, α,n—the angle between the 3.2.31 retroreflective material, n—a material that has a thin
illumination axis and the observation axis.
continuous layer of small retroreflective elements on or very
near its exposed surface (for example, retroreflective sheeting,
3.2.20.1 Discussion—The observation angle is never nega-
tive and is almost always less than 10° and usually no more beaded paint, highway sign surfaces, or pavement striping).
than 2°. The full range is defined as 0°≤α<180°.
3.2.32 retroreflective sheeting, n—a retroreflective material
3.2.21 observation axis, n—the half-line from the retrore- preassembled as a thin film ready for use.
flector center through the observation point.
3.2.33 retroreflector, n—a reflecting surface or device from
3.2.22 observation distance, d, n—the distance between the which, when directionally irradiated, the reflected rays are
retroreflector center and the observation point. preferentially returned in directions close to the opposite of the
direction of the incident rays, this property being maintained
3.2.23 observation half-plane, n—the half-plane that origi-
over wide variations of the direction of the incident rays.
nates on the line of the illumination axis and contains the
B
[CIE]
observation axis.
3.2.34 retroreflector axis, n—a designated half-line from the
3.2.24 observation point, n—the point taken as the location
retroreflector center.
of the receiver.
3.2.34.1 Discussion—The direction of the retroreflector axis
3.2.24.1 Discussion—in real systems the receiver has finite
is usually chosen centrally among the intended directions of
size and the observation point is typically the center of the
illumination;forexample,thedirectionoftheroadonwhichor
entrance pupil.
with respect to which the retroreflector is intended to be
3.2.25 orientation angle, ω,n—the angle in a plane per-
s
positioned. When symmetry exists, the retroreflector axis
pendicular to the retroreflector axis from the entrance half-
usually coincides with the axis of symmetry of the retroreflec-
plane to the datum axis, measured counter-clockwise from the
tor. For horizontal road markings the normal to the surface is
viewpoint of the source.
chosen as the retroreflector axis.
3.2.25.1 Discussion—Range –180°<ω ≤180°. In the previ-
s
3.2.35 retroreflector center, n—the point on or near a ret-
ous editions of Practice E808 as well as in CIE Pub. 54, 1982,
roreflector that is designated to be the location of the device.
orientation angle is defined as ω, the supplement of the above
defined orientation angle ω . The change reverses the sense of
3.2.36 rho angle, ρ,n—the dihedral angle from the obser-
s
orientation angle, making it now agree with the counterclock-
vation half-plane to the half-plane that originates on the line of
wise sense of rotation angle, ε, and exchanges the 0° and 180°
the illumination axis and contains the datum axis, measured
points, making it now agree with Fed. Std. No. 370, §2.2.9b.
counter-clockwise from the viewpoint of the source.
3.2.36.1 Discussion—Range –180°<ρ≤180°.
3.2.26 presentation angle, γ,n—the dihedral angle from the
entrance half-plane to the observation half-plane, measured
3.2.37 RM azimuthal angle, b, n—the dihedral angle from
counter-clockwise from the viewpoint of the source.
the half-plane originating on the line of the retroreflector axis
3.2.26.1 Discussion—Range –180°<γ≤180°.
and containing the obverse of the illumination axis to the
half-plane originating on the line of the retroreflector axis and
3.2.27 retroreflectance factor, R , (of a plane retroreflecting
F
containing the observation axis, measured clockwise from a
surface), n—the dimensionless ratio of the coefficient of
viewpoint on the retroreflector axis.
luminousintensity(R )ofaplaneretroreflectingsurfacehaving
I
area A to the coefficient of luminous intensity of a perfect 3.2.37.1 Discussion—Range –180°
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E808 − 01 (Reapproved 2016)
Standard Practice for
Describing Retroreflection
This standard is issued under the fixed designation E808; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.1 In accordance with the convention appearing in the
Significance and Use section of Terminology E284, the super-
1.1 This practice provides terminology, alternative geo-
script B appearing after [CIE] at the end of a definition
metrical coordinate systems, and procedures for designating
indicates that the given definition is a modification of that cited
angles in descriptions of retroreflectors, specifications for
with little difference in essential meaning.
retroreflector performance, and measurements of retroreflec-
tion.
NOTE 1—The terminology given here describes visual observation of
luminance as defined by the CIE V (λ) spectral weighting function for the
1.2 Terminology defined herein includes terms germane to
photopic observer. Analogous terms for other purposes can be defined by
other ASTM documents on retroreflection.
using appropriate spectral weighting.
1.3 This standard does not purport to address all of the
3.2 Definitions:
safety concerns, if any, associated with its use. It is the
3.2.1 The delimiting phrase “in retroreflection” applies to
responsibility of the user of this standard to establish appro-
each of the following definitions when used outside the context
priate safety and health practices and determine the applica-
of this or other retroreflection standards.
bility of regulatory limitations prior to use.
3.2.2 coeffıcient of line retroreflection, R , n—of a retrore-
M
flecting stripe, the ratio of the coefficient of luminous intensity
2. Referenced Documents
(R ) to the length (l), expressed in candelas per lux per metre
I
2 –1 –1
(cd·lx ·m ). R = R /l.
2.1 ASTM Standards:
M I
E284 Terminology of Appearance 3.2.2.1 Discussion—R depends on the spectral composi-
M
tion of the illumination which is usually CIE illuminant A.
2.2 Federal Standard:
Fed. Std. No. 370 Instrumental Photometric Measurements 3.2.3 coeffıcient of luminous intensity, R , n—of a
I
of Retroreflecting Materials and Retroreflecting Devices retroreflector, ratio of the luminous intensity (I) of the retrore-
flector in the direction of observation to the illuminance (E )
'
2.3 CIE Document:
at the retroreflector on a plane perpendicular to the direction of
CIE Publication No. 54 Retroreflection-Definition and Mea-
–1
4 the incident light, expressed in candelas per lux (cd·lx ). R =
I
surement
(I/E ).
'
3.2.3.1 Discussion—In a given measurement one obtains the
3. Terminology
average R over the solid angles of incidence and viewing
I
3.1 Terms and definitions in Terminology E284 are appli-
subtended by the source and receiver apertures, respectively. In
cable to this standard.
practice, I is often determined as the product of the illuminance
at the observer and the distance squared (I = E d ). R depends
r I
on the spectral composition of the illumination which is usually
This practice is under the jurisdiction of ASTM Committee E12 on Color and
CIE illuminant A.
Appearance and is the direct responsibility of Subcommittee E12.10 on Retrore-
3.2.3.2 Discussion—Also called coeffıcient of (retrore-
flection.
flected) luminous intensity. Equivalent commonly used terms
Current edition approved Jan. 1, 2016. Published January 2016. Originally
approved in 1981. Last previous edition approved in 2009 as E808 – 01 (2009). are CIL and SI (specific intensity). CIE Publication 54 uses the
DOI: 10.1520/E0808-01R16.
symbol R for R . The ASTM recommendation is to use the
I
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
symbol R .
I
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
3.2.4 coeffıcient of retroreflected luminance, R , n—the ratio
L
the ASTM website.
of the luminance, L, in the direction of observation to the
Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
normal illuminance, E , at the surface on a plane normal to the
Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http:// '
www.dodssp.daps.mil. incident light, expressed in candelas per square metre per lux
–2 –1
Available from U.S. National Committee of the CIE (International Commission
[(cd·m )·lx ].
on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond
St., Salem, MA 01970, http://www.cie-usnc.org. R 5 ~L/E ! 5 ~R /Acosν! 5 ~I/EAcosν! 5 ~R /cosν! (1)
L ' I A
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E808 − 01 (2016)
where: 3.2.10 datum mark, n—an indication on the retroreflector,
off the retroreflector axis, that establishes the direction of the
A = surface area of the sample, and
datum axis.
ν = viewing angle.
3.2.11 datum half-plane, n—the half-plane that originates on
3.2.4.1 Discussion—The units millicandela per square metre
the line of the retroreflector axis and contains the datum axis.
–2 –1
per lux [(mcd·m )·lx ] are usually used to express the R
L
3.2.12 entrance angle, β, n—the angle between the illumi-
values of road marking surfaces. This quantity is also referred
nation axis and the retroreflector axis.
to as specific luminance. Historically the symbol SL was used
3.2.12.1 Discussion—The entrance angle is usually no
for R . In some references CRL is used. These are all
L
larger than 90°, but for completeness its full range is defined as
equivalent, but R is preferred.
L
0°≤β≤180°. In the CIE (goniometer) system β is resolved into
3.2.4.2 Discussion—R depends on the spectral composition
L
two components β and β . Since by definition β is always
1 2
of the illumination which is usually CIE illuminant A.
positive, the common practice of referring to the small entrance
3.2.5 coeffıcient of (retroreflected) luminous flux, R , n—the
Φ
angles that direct specular reflections away from the photore-
ratio of the luminous flux per unit solid angle, Φ'/Ω', in the
ceptor as negative valued is deprecated by ASTM. The
direction of observation to the total flux Φ incident on the
recommendation is to designate such negative values as
effective retroreflective surface, expressed in candelas per
belonging to β .
–1
lumen (cd·lm ).
3.2.13 entrance angle component, β , n—the angle from the
R 5 Φ'/Ω' /Φ 5 I/Φ 5 R /cosβ (2)
~ !
Φ A
illumination axis to the plane containing the retroreflector axis
3.2.5.1 Discussion—The units for this photometric quantity,
and the first axis. Range: –180°<β ≤180°.
candelas per lumen, are sometimes abbreviated as CPL.
3.2.14 entrance angle component, β , n—the angle from the
3.2.5.2 Discussion—R depends on the spectral composi-
Φ
plane containing the observation half-plane to the retroreflector
tion of the illumination which is usually CIE illuminant A.
axis. Range: –90°≤β ≤90°.
3.2.6 coeffıcient of retroreflection, R , n—of a plane retrore- 3.2.14.1 Discussion—For some measurements it is conve-
A
flecting surface, the ratio of the coefficient of luminous
nient to extend the range of β to –180°<β ≤180°. β must then
2 2 1
intensity (R ) to the area (A), expressed in candelas per lux per be restricted to –90°<β ≤90°.
I
–1 –2
square metre (cd·lx · m ). R = R /A.
A I
3.2.15 entrance half-plane, n—the half-plane that originates
3.2.6.1 Discussion—The equivalent inch-pound units for
on the line of the illumination axis and contains the retrore-
coefficient of retroreflection are candelas per foot candle per
flector axis.
square foot. The SI and inch-pound units are numerically
3.2.16 first axis, n—the axis through the retroreflector center
equal, because the units of R reduce to 1/sr. An equivalent
A
and perpendicular to the observation half-plane.
term used for coefficient of retroreflection is specific intensity
3.2.17 fractional retroreflectance, R , n—the fraction of
per unit area, with symbol SIA or the CIE symbol R'. The term T
unidirectional flux illuminating a retroreflector that is received
coefficient of retroreflection and the symbol R along with the
A
at observation angles less than a designated value, α .
SI units of candelas per lux per square metre are recommended max
3.2.17.1 Discussion—R has no meaning unless α is
by ASTM. T max
specified.
3.2.6.2 Discussion—The radiometric BRDF is not the ana-
3.2.17.2 Discussion—For a flat retroreflector R may be
T
logue of R but rather of R .
A Φ
calculated as follows:
3.2.6.3 Discussion—R depends on the spectral composi-
A
α π
max
tion of the illumination which is usually CIE illuminant A.
R α,ρ
~ !
A
α dαdρ. (3)
* *
cos β
3.2.7 co-entrance angle, e, n—the complement of the angle
α50 ρ52π
between the retroreflector axis and the illumination axis.
For a non-flat retroreflector R may be calculated as
T
3.2.7.1 Discussion—e=90°-β. Range 0°
follows:
zontal road markings, the retroreflector axis is considered to be
α π
max
R α,ρ
~ !
the normal to the road surface, making e the angle of I
α dαdρ. (4)
* *
inclination of the illumination axis over the road surface. A
P
α50 ρ52π
3.2.8 co-viewing angle, a, n—the complement of the angle
A is the area of the retroreflector as projected in the
P
between the retroreflector axis and the observation axis.
direction of illumination. Angles β and ω must remain
s
3.2.8.1 Discussion—a= 90°-ν. Range 0°
fixed through the integration. Angles α and ρ are in radi-
zontal road markings, the retroreflector axis is considered to be
ans: R is unitless. Presentation angle γ may replace ρ in
T
the normal to the road surface, making a the angle of
these formulas. For very small values of β, rotation angle
inclination of the observation axis over the road surface.
ε may replace ρ in these formulas. For example, for β=5°
the resulting error will be less than, usually much less
3.2.9 datum axis, n—a designated half-line from the retrore-
than, 0.5 % of the calculated R .
flector center perpendicular to the retroreflector axis. T
3.2.17.3 Discussion—R is usually expressed in percent.
T
3.2.9.1 Discussion—The datum axis together with the ret-
roreflector center and the retroreflector axis establish the 3.2.18 illumination axis, n—the half-line from the retrore-
position of the retroreflector. flector center through the source point.
E808 − 01 (2016)
3.2.19 illumination distance, n—the distance between the 3.2.30 retroreflective element, n—a minimal optical unit that
source point and the retroreflector center. produces retroreflection.
3.2.20 observation angle, α, n—the angle between the
3.2.31 retroreflective material, n—a material that has a thin
illumination axis and the observation axis. continuous layer of small retroreflective elements on or very
3.2.20.1 Discussion—The observation angle is never nega- near its exposed surface (for example, retroreflective sheeting,
beaded paint, highway sign surfaces, or pavement striping).
tive and is almost always less than 10° and usually no more
than 2°. The full range is defined as 0°≤α<180°.
3.2.32 retroreflective sheeting, n—a retroreflective material
3.2.21 observation axis, n—the half-line from the retrore- preassembled as a thin film ready for use.
flector center through the observation point.
3.2.33 retroreflector, n—a reflecting surface or device from
3.2.22 observation distance, d, n—the distance between the which, when directionally irradiated, the reflected rays are
retroreflector center and the observation point. preferentially returned in directions close to the opposite of the
direction of the incident rays, this property being maintained
3.2.23 observation half-plane, n—the half-plane that origi-
over wide variations of the direction of the incident rays.
nates on the line of the illumination axis and contains the
B
[CIE]
observation axis.
3.2.34 retroreflector axis, n—a designated half-line from the
3.2.24 observation point, n—the point taken as the location
retroreflector center.
of the receiver.
3.2.34.1 Discussion—The direction of the retroreflector axis
3.2.24.1 Discussion—in real systems the receiver has finite
is usually chosen centrally among the intended directions of
size and the observation point is typically the center of the
illumination; for example, the direction of the road on which or
entrance pupil.
with respect to which the retroreflector is intended to be
3.2.25 orientation angle, ω , n—the angle in a plane per-
s
positioned. When symmetry exists, the retroreflector axis
pendicular to the retroreflector axis from the entrance half-
usually coincides with the axis of symmetry of the retroreflec-
plane to the datum axis, measured counter-clockwise from the
tor. For horizontal road markings the normal to the surface is
viewpoint of the source.
chosen as the retroreflector axis.
3.2.25.1 Discussion—Range –180°<ω ≤180°. In the previ-
s
3.2.35 retroreflector center, n—the point on or near a ret-
ous editions of Practice E808 as well as in CIE Pub. 54, 1982,
roreflector that is designated to be the location of the device.
orientation angle is defined as ω, the supplement of the above
defined orientation angle ω . The change reverses the sense of
3.2.36 rho angle, ρ, n—the dihedral angle from the obser-
s
orientation angle, making it now agree with the counterclock-
vation half-plane to the half-plane that originates on the line of
wise sense of rotation angle, ε, and exchanges the 0° and 180°
the illumination axis and contains the datum axis, measured
points, making it now agree with Fed. Std. No. 370, §2.2.9b.
counter-clockwise from the viewpoint of the source.
3.2.36.1 Discussion—Range –180°<ρ≤180°.
3.2.26 presentation angle, γ, n—the dihedral angle from the
entrance half-plane to the observation half-plane, measured
3.2.37 RM azimuthal angle, b, n—the dihedral angle from
counter-clockwise from the viewpoint of the source.
the half-plane originating on the line of the retroreflector axis
3.2.26.1 Discussion—Range –180°<γ≤180°.
and containing the obverse of the illumination axis to the
half-plane originating on the line of the retroreflector axis and
3.2.27 retroreflectance factor, R , (of a plane retroreflecting
F
containing the observation axis, measured clockwise from a
surface), n—the dimensionless ratio of the coefficient of
viewpoint on the retroreflector axis.
luminous intensity (R ) of a plane retroreflecting surface having
I
area A to the coefficient of lum
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E808 − 01 (Reapproved 2009) E808 − 01 (Reapproved 2016)
Standard Practice for
Describing Retroreflection
This standard is issued under the fixed designation E808; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice provides terminology, alternative geometrical coordinate systems, and procedures for designating angles in
descriptions of retroreflectors, specifications for retroreflector performance, and measurements of retroreflection.
1.2 Terminology defined herein includes terms germane to other ASTM documents on retroreflection.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E284 Terminology of Appearance
2.2 Federal Standard:
Fed. Std. No. 370 Instrumental Photometric Measurements of Retroreflecting Materials and Retroreflecting Devices
2.3 CIE Document:
CIE Publication No. 54 Retroreflection-Definition and Measurement
3. Terminology
3.1 Terms and definitions in Terminology E284 are applicable to this standard.
3.1.1 In accordance with the convention appearing in the Significance and Use section of Terminology E284, the superscript
B appearing after [CIE] at the end of a definition indicates that the given definition is a modification of that cited with little
difference in essential meaning.
NOTE 1—The terminology given here describes visual observation of luminance as defined by the CIE V (λ) spectral weighting function for the
photopic observer. Analogous terms for other purposes can be defined by using appropriate spectral weighting.
3.2 Definitions:
3.2.1 The delimiting phrase “in retroreflection” applies to each of the following definitions when used outside the context of
this or other retroreflection standards.
3.2.2 coeffıcient of line retroreflection, R , n—of a retroreflecting stripe, the ratio of the coefficient of luminous intensity (R )
M I
–1 –1
to the length (l), expressed in candelas per lux per metre (cd·lx ·m ). R = R /l.
M I
This practice is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.10 on Retroreflection.
Current edition approved Feb. 1, 2009Jan. 1, 2016. Published February 2009January 2016. Originally approved in 1981. Last previous edition approved in 20012009 as
E808 – 01.E808 – 01 (2009). DOI: 10.1520/E0808-01R09.10.1520/E0808-01R16.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from Standardization Documents Order Desk, DODSSP, Bldg. 4, Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://www.dodssp.daps.mil.
Available from U.S. National Committee of the CIE (International Commission on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond St.,
Salem, MA 01970, http://www.cie-usnc.org.
3.2.2.1 Discussion—
R depends on the spectral composition of the illumination which is usually CIE illuminant A.
M
3.2.3 coeffıcient of luminous intensity, R , n—of a retroreflector, ratio of the luminous intensity (I) of the retroreflector in the
I
direction of observation to the illuminance (E ) at the retroreflector on a plane perpendicular to the direction of the incident light,
'
–1
expressed in candelas per lux (cd·lx ). R = (I/E ).
I '
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E808 − 01 (2016)
3.2.3.1 Discussion—
In a given measurement one obtains the average R over the solid angles of incidence and viewing subtended by the source and
I
receiver apertures, respectively. In practice, I is often determined as the product of the illuminance at the observer and the distance
squared (I = E d ). R depends on the spectral composition of the illumination which is usually CIE illuminant A.
r I
3.2.3.2 Discussion—
Also called coeffıcient of (retroreflected) luminous intensity. Equivalent commonly used terms are CIL and SI (specific intensity).
CIE Publication 54 uses the symbol R for R . The ASTM recommendation is to use the symbol R .
I I
3.2.4 coeffıcient of retroreflected luminance, R , n—the ratio of the luminance, L, in the direction of observation to the normal
L
illuminance, E , at the surface on a plane normal to the incident light, expressed in candelas per square metre per lux
'
–2 –1
[(cd·m )·lx ].
R 5 ~L/E !5 ~R /Acosν!5 ~I/EAcosν!5 ~R /cosν! (1)
L ' I A
where:
A = surface area of the sample, and
ν = viewing angle.
where:
A = surface area of the sample, and
ν = viewing angle.
3.2.4.1 Discussion—
–2 –1
The units millicandela per square metre per lux [(mcd·m )·lx ] are usually used to express the R values of road marking surfaces.
L
This quantity is also referred to as specific luminance. Historically the symbol SL was used for R . In some references CRL is used.
L
These are all equivalent, but R is preferred.
L
3.2.4.2 Discussion—
R depends on the spectral composition of the illumination which is usually CIE illuminant A.
L
3.2.5 coeffıcient of (retroreflected) luminous flux, R , n—the ratio of the luminous flux per unit solid angle, Φ'/Ω',Φ'/Ω', in the
Φ
direction of observation to the total flux Φ incident on the effective retroreflective surface, expressed in candelas per lumen
–1
(cd·lm ).
R 5 Φ'/Ω' /Φ5 I/Φ5 R /cosβ (2)
~ !
Φ A
R 5 ~Φ'/Ω'!/Φ5 I/Φ5 R /cosβ (2)
Φ A
3.2.5.1 Discussion—
The units for this photometric quantity, candelas per lumen, are sometimes abbreviated as CPL.
3.2.5.2 Discussion—
R depends on the spectral composition of the illumination which is usually CIE illuminant A.
Φ
3.2.6 coeffıcient of retroreflection, R , n—of a plane retroreflecting surface, the ratio of the coefficient of luminous intensity (R )
A I
–1 –2
to the area (A), expressed in candelas per lux per square metre (cd·lx · m ). R = R /A.
A I
3.2.6.1 Discussion—
The equivalent inch-pound units for coefficient of retroreflection are candelas per foot candle per square foot. The SI and
inch-pound units are numerically equal, because the units of R reduce to 1/sr. An equivalent term used for coefficient of
A
retroreflection is specific intensity per unit area, with symbol SIA or the CIE symbol R'. The term coefficient of retroreflection and
the symbol R along with the SI units of candelas per lux per square metre are recommended by ASTM.
A
E808 − 01 (2016)
3.2.6.2 Discussion—
The radiometric BRDF is not the analogue of R but rather of R .
A Φ
3.2.6.3 Discussion—
R depends on the spectral composition of the illumination which is usually CIE illuminant A.
A
3.2.7 co-entrance angle, e, n—the complement of the angle between the retroreflector axis and the illumination axis.
3.2.7.1 Discussion—
e=90°-β. Range 0°
making e the angle of inclination of the illumination axis over the road surface.
3.2.8 co-viewing angle, a, n—the complement of the angle between the retroreflector axis and the observation axis.
3.2.8.1 Discussion—
a= 90°-ν. Range 0°
making a the angle of inclination of the observation axis over the road surface.
3.2.9 datum axis, n—a designated half-line from the retroreflector center perpendicular to the retroreflector axis.
3.2.9.1 Discussion—
The datum axis together with the retroreflector center and the retroreflector axis establish the position of the retroreflector.
3.2.10 datum mark, n—an indication on the retroreflector, off the retroreflector axis, that establishes the direction of the datum
axis.
3.2.11 datum half-plane, n—the half-plane that originates on the line of the retroreflector axis and contains the datum axis.
3.2.12 entrance angle, β, n—the angle between the illumination axis and the retroreflector axis.
3.2.12.1 Discussion—
The entrance angle is usually no larger than 90°, but for completeness its full range is defined as 0°≤β≤180°. In the CIE
(goniometer) system β is resolved into two components β and β . Since by definition β is always positive, the common practice
1 2
of referring to the small entrance angles that direct specular reflections away from the photoreceptor as negative valued is
deprecated by ASTM. The recommendation is to designate such negative values as belonging to β .
3.2.13 entrance angle component, β , n—the angle from the illumination axis to the plane containing the retroreflector axis and
the first axis. Range: –180°<β ≤180°.
3.2.14 entrance angle component, β , n—the angle from the plane containing the observation half-plane to the retroreflector
axis. Range: –90°≤β ≤90°.
3.2.14.1 Discussion—
For some measurements it is convenient to extend the range of β to –180°<β ≤180°. β must then be restricted to –90°<β ≤90°.
2 2 1 1
3.2.15 entrance half-plane, n—the half-plane that originates on the line of the illumination axis and contains the retroreflector
axis.
3.2.16 first axis, n—the axis through the retroreflector center and perpendicular to the observation half-plane.
3.2.17 fractional retroreflectance, R , n—the fraction of unidirectional flux illuminating a retroreflector that is received at
T
observation angles less than a designated value, α .
max
3.2.17.1 Discussion—
R has no meaning unless α is specified.
T max
E808 − 01 (2016)
3.2.17.2 Discussion—
For a flat retroreflector R may be calculated as follows:
T
α π
max
R ~α,ρ!
A
* * α dαdρ. (3)
cos β
α50 ρ52π
For a non-flat retroreflector R may be calculated as follows:
T
α π
max
R ~α,ρ!
I
α dαdρ. (4)
* *
A
P
α50 ρ52π
A is the area of the retroreflector as projected in the direction of illumination. Angles β and ω must remain fixed
P s
through the integration. Angles α and ρ are in radians: R is unitless. Presentation angle γ may replace ρ in these formulas.
T
For very small values of β, rotation angle ε may replace ρ in these formulas. For example, for β=5° the resulting error will
be less than, usually much less than, 0.5 % of the calculated R .
T
3.2.17.3 Discussion—
R is usually expressed in percent.
T
3.2.18 illumination axis, n—the half-line from the retroreflector center through the source point.
3.2.19 illumination distance, n—the distance between the source point and the retroreflector center.
3.2.20 observation angle, α, n—the angle between the illumination axis and the observation axis.
3.2.20.1 Discussion—
The observation angle is never negative and is almost always less than 10° and usually no more than 2°. The full range is defined
as 0°≤α<180°.
3.2.21 observation axis, n—the half-line from the retroreflector center through the observation point.
3.2.22 observation distance, d, n—the distance between the retroreflector center and the observation point.
3.2.23 observation half-plane, n—the half-plane that originates on the line of the illumination axis and contains the observation
axis.
3.2.24 observation point, n—the point taken as the location of the receiver.
3.2.24.1 Discussion—
in real systems the receiver has finite size and the observation point is typically the center of the entrance pupil.
3.2.25 orientation angle, ω , n—the angle in a plane perpendicular to the retroreflector axis from the entrance half-plane to the
s
datum axis, measured counter-clockwise from the viewpoint of the source.
3.2.25.1 Discussion—
Range –180°<ω ≤180°. In the previous editions of Practice E808 as well as in CIE Pub. 54, 1982, orientation angle is defined as
s
ω, the supplement of the above defined orientation angle ω . The change reverses the sense of orientation angle, making it now
s
agree with the counterclockwise sense of rotation angle, ε, and exchanges the 0° and 180° points, making it now agree with Fed.
Std. No. 370, §2.2.9b.
3.2.26 presentation angle, γ, n—the dihedral angle from the entrance half-plane to the observation half-plane, measured
counter-clockwise from the viewpoint of the source.
3.2.26.1 Discussion—
Range –180°<γ≤180°.
3.2.27 retroreflectance factor, R , (of a plane retroreflecting surface), n—the dimensionless ratio of the coefficient of luminous
F
intensity (R ) of a plane retroreflecting surface having area A to the coefficient of luminous intensity of a perfect reflecting diffuser
I
of the same area under the same conditions of illumination and observation.
E808 − 01 (2016)
π R
I
R 5 (5)
F
Acosβcosν
3.2.27.1 Discussion—
In the above expression β is the entrance angle and ν is the viewing angle. The quantity, R , is numerically the same as the
F
reflectance factor, R.
3.2.27.2 Discussion—
R depends on the spectral composition of the illumination which is usually CIE illuminant A.
F
3.2.28 retroreflection, n—reflection in which reflected rays are preferentially returned in directions close to the opposite of the
B
direction of the incident rays, this property being maintained over wide variations of the direction of the incident rays. [CIE]
3.2.29 retroreflective device, n—deprecated term; use retroreflector.
3.2.30 retroreflective element, n—a minimal optical unit that produces retroreflection.
3.2.31 retroreflective material, n—a material that has a thin continuous layer of small retroreflective elements on or very near
its exposed surface (for example, retroreflective sheeting, beaded paint, highway sign surfaces, or pavement striping).
3.2.32 retroreflective sheeting, n—a retroreflective material preassembled as a thin film ready for use.
3.2.33 retroreflector, n—a reflecting surface or device from which, when directionally irradiated, the reflected rays are
preferentially returned in directions close to the opposite of the direction of the incident rays, this property being maintained over
B
wide variations of the direction of the incident rays. [CIE]
3.2.34 retroreflector axis, n—a designated half-line from the ret
...
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