Retroreflection Measurement

It seems intuitively correct to measure retroreflection as a ratio of the intensity of light returned in the direction of the driver to the intensity of their car’s headlights. This ratio would give a scale for retroreflection that consisted of a similitude (dimensionless number) between 0 and 1. Unfortunately there are practical problems with this approach. In addition, there must be a system of units to define light flux, intensity and other optical quantities.

Candela Optical Measure of Luminous Intensity

 

This excerpt is taken from the RoadVista Guide to Retroreflectivity, for additional information download the free RoadVista Retroreflectivity Guidebook

 
 
 
 
 
 
 

The first unit that you need to know is that of a ‘solid angle’. A familiar example of a solid angle is an ice cream cone. The tip of the cone is the apex, the distance from the apex to the open end is the radius (r) and the open end has some defined surface area (S). Solid angles are measured in units called steradian (w, the Greek letter omega). Steradians are defined simply as the ratio of the area of the open end of the cone over the radius squared (r²). In strict math terms the area of the opening is a spherical surface, so you can imagine the ice cream cone and a ball just big enough to fit in the open end of the cone. Increasing the size of the cone until it is a flat disk would give you 2π steradians, so there are a total of 4π steradians in a complete sphere around a source. This is analogous to the two-dimensioned case where 2π equals a complete circular angle in a plane around a point.
In Figure 6, the solid angle subtended by the Area “ABCD” is equal to the area of “ABCD” divided by the total area of the concentric sphere multiplied by the total number of steradians in the sphere. The equation looks like:

Steradian Equation

With the understanding of solid angles, the definition of optical quantities can be made. The basic optical quantity is the ‘candela’, which is a measure of luminous intensity. The candela is the luminous intensity of a source emitting a monochromatic radiation in a given direction of frequency 540 x 10¹² Hertz or wavelength 555 nanometers. The radiant intensity of which, in that direction, is 1/683 watts per steradian. This definition, while not helpful for an intuitive grasp of the nature of luminous intensity, does give us a physical means to establish optical units.

Retroreflection Returns Light to its Source

The next important unit is the unit associated with ‘flux’. Flux is a measure of the total light energy emitted per unit of time. The unit of visible flux or ‘luminous flux’ is called the ‘lumen’ (the unit of flux independent of the human eye sensitivity is the watt). One lumen is defined as the amount of light energy flowing through a solid angle of one steradian from a source having a luminous intensity of one candela.
Illuminance is defined as the luminous flux per unit area. It is measured in units of ‘lux’, or lumens per square meter. Thus, when a uniform light flux of one lumen falls on an area of one square meter the illuminance at any point on the surface is one lux. The sphere in Figure 6 has a total area of 4πr² or 12.57 square meters. So if the point source output has an intensity of one candela, the total power output of the source is 12.57 lumens.
The next terms to work with are intensity and illuminance. Intensity measures the flux of a source in a given direction. Illuminance measures the flux density of light on a surface that is illuminated. These are not the same because the emitted light spreads out over a larger and larger region as it radiates through space. The intensity remains constant since the same amount of flux fills the same angular cone, but because the light is spread out with distance over a larger and larger region of space, illuminance gets smaller as the distance to the illuminated surface increases. For a spatially uniform point source the illuminance decreases proportionately to the square of the distance from the source.
Candelas and lumens are identical in the metric and English measurement systems. Illuminance, however, is measured with units of lumens per square foot rather that per square meter. One lumen per square foot is a foot-candle and one foot-candle equals 10.76 lux (lumens per square meter).

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