Equipment: Road Surfaces - Road Lighting: Fundamentals, Technology and Application - page 166

Fig. 12.3 Reflection
indicatrices. Arrows indicate
q(

q(0,0) q(0,63) q(0,0) q(0,63)

ʲ = 0, ʳ = 0) and

q( ʲ = 0, ʳ = 63).

S1 /q(0,0).

Left : same S1 but different
Q 0 . Right : different S1 but
similar Q 0

= q(0,63)*cos3 ʳ

ʳ ʳ

ʲ = 180° - 0° plane ʲ = 180° - 0° plane

AlowQ 0 value represents a dark road surface and a high Q 0 value a light surface. A
low S1 value represents a diffuse surface (low glossiness) and a high value a more-
shiny surface (high specularity). The numerical values of Q 0 and S1 can be calculated
from the reflection table. Q 0 as the solid angle weighted average of all the luminance
coefficients and S1 as the ratio of two R values:

1
∗

Q 0 = qdʲdʳ

ʩ

R ( ʲ = 0, tan ʳ = 2)

S 1 =

R ( ʲ = 0, tan ʳ = 0)

with being the solid angle measured from the point on the surface containing
all those directions from which light is incident and contributes to reflection. The
boundaries of these directions of light incidence are standardized (CIE 2001 ). Based
on these boundaries Appendix C gives a table with weighting factors which can be
used as multipliers for the R-Table of a road surface to get its Q 0 value (Sørensen and
Nielsen 1974 ; CIE 2001 ). The tangent of 2 equals 63 ⓦ and thus R( ʲ = 0, tan ʳ = 2)

corresponds to steep angle of light incidence. That also means that R( 2)

in the definition of the specular factor S1, corresponds in the reflection indicatrix to
a position near to the peak of the indicatrix, and thus indeed is representative for the
specular reflection of the road surface (Fig. 12.3 ).
That Q 0 and S1 are indeed suitable for describing the road surface is illustrated
in Fig. 12.4 , which shows four different road surfaces. The two road surfaces shown
on the left have a different lightness but the same specularity. That means that their
reflection indicatrices have a similar shape (Fig. 12.3 left).The two surfaces at the
top of Fig. 12.4 have the same lightness but different specularity, and consequently
a different indicatrix shape (Fig. 12.3 right). In fact Q 0 is indicative for the volume
of the indicatrix. Similarly, the two surfaces on the right of Fig 12.4 have the same
degree of specularity (more shiny than the two on the left), while the two surfaces
on the bottom have the same lightness (darker than the two top ones) but different
specularities. Each particular road surface is, for practical luminance calculations,
sufficient-well characterized by its lightness (i.e. Q 0 ) and specularity (i.e. S1).
The fact that for the determination of Q 0 all 396 values of an R table are required,
makes the actual measurement difficult and time consuming. This will be discussed
in some detail in Sect. 12.2.4. Several methods have therefore been proposed to

ʲ = 0, tan ʳ =