Lighting theory

Light distribution curves, illumination diagrams and isolux diagrams

Careful planning work is required to solve lighting tasks. The necessary information about the properties of luminaires is given in light distribution curves, illumination and isolux diagrams. We provide the necessary knowledge on this page.

Light distribution curves specify in what direction and with what intensity a luminaire emits light. The luminous intensity value in candela (cd) for a given luminaire is obtained by multiplying the value in cd/klm read from the diagram by the total luminous flux in kilolumens (klm) of the lamps used in the luminaire. 

The diagrams also show the half beam angles (solid line, C 180 - C 0° β = 28° and dotted line, C 270 - C 90° β = 92°). 

The luminous intensity values are plotted on the vertical axis and the beam angles on the horizontal axis. In a polar representation, the diagram specifies what sections through the luminaire (C-levels) the curves refer to.

Light distribution curves are usually presented in a polar coordinate system.

For floodlights, we specify the light distributions in Cartesian coordinates

Illumination diagrams for floodlights (Fig. 3) indicate the dimensions of the area bounded by the two half beam angles (Fig. 4) and the average degree of illuminance of this area in relation to the distance. Using the parameters “floodlight – area – horizontal axis” it is possible to take the following readings:

  • the height (solid line, C 0 - C 180  β = 27°) and the width (dotted line, C 270 - C 90° β = 76°) of the delimited area on the vertical axis to the right
  • the average degree of illuminance (parabola) in lux on the vertical axis on the left

Example: At a distance of 12 m, the half beam angles of the floodlight 84 503 delimit an area 5 m high and 15 m wide. The median degree of illuminance on this area is 240 lx. Uniform illumination is achieved when the distances between the floodlights correspond to the width of the area delimited by the half beam angles. When a façade is illuminated from the ground, only about 1/3 of the specified illuminance is achieved.

Isolux diagrams (Fig. 5) specify the distribution of the illuminance on a visible surface. Points with the same degree of illuminance are connected by curves (isolux lines). The luminaire is perpendicular to the drawing plane at the mounting height (h) above the coordinate origin. Depending on the type of luminaire, the mounting height (h) or the corresponding pole height (H) is specified.

The light point interval is approximately twice the distance at which the isolux line runs at half the value of the desired minimum illuminance.

Example: In the isolux diagram shown, the 0.5 lx line runs laterally at a distance of 15 m from the coordinate origin. If a path is to be illuminated (Emin ≥ 1 lx), then a light point spacing of approx. 30 m must be selected. In the case of luminaires with rotationally symmetrical light distribution, the resulting isolux lines are concentric circles.


Determining the distance of a floodlight to the illuminated surface using a light distribution curve

The façade to be illuminated has a height of 8 m (blue line) and a width of 18 m (red line). The High-performance floodlight 84 503 with flat beam light distribution has a half beam angle of 27° and 76°. At a distance of 16 m, the half beam angles cover the dimensions of the façade exactly. The parabola indicates the average degree of illuminance in lux. These values can be read off on the light distribution curve y-axis on the left. The average degree of illuminance on this reference surface is therefore 150 lx. Changes in the distance between the floodlights influence not only the average degree of illuminance but also the size of the illuminated surface. It must be noted that the diffuse light illuminates more than the previously calculated surface. The façade would still be well illuminated with a size of 10 x 22 m.

Determining the luminaire spacing “a” for pathway lighting of Emin = 1 lx using the isolux diagram

When planning pathway lighting, 1 lx is defined as the standard minimum degree of illuminance. Consequently, the 0.5-lx line in the isolux diagram is relevant for determining the luminaire spacing. This 0.5 lx must add up to 1 lx illuminance on the assessed surface to define the luminaire spacing. The result is a light point spacing of 6.5 m. During planning, local conditions like the colour and characteristics of the ground must also be considered. These factors have an enormous influence on the reflective behaviour of the light and can lead to a visually inadequate lighting impression even with a standard-compliant degree of illuminance. An illumination test at the installation site is therefore recommended for optimal planning results.

Determining the luminaire spacing “a” for square illumination with BEGA Light building element 84 737 using the isolux diagram

For luminaires with rotationally symmetrical light distribution, the isolux diagram shows one quarter of the total luminous intensity. The average degree of illuminance for a square situation should be 10 lx. About 20 lx is reached directly at the luminaire. In order to obtain an average of 10 lx, the minimum illuminance between two luminaires should be about 2 to 3 lx. In the diagram, the red circles indicate these values. Consequently, luminaire spacing is 19 m.

Determining the luminaire spacing “a” for square illumination with BEGA Pole-top luminaires 99 515 using the isolux diagram

The same principle applies for asymmetrical light distribution. The luminaires are positioned along the edge of the square in a single arrangement and within the square in a double arrangement.