Distribution of the luminous intensity of artificial light sources

The luminance of lamps or lights is rarely constant in all directions in space. Luminous intensity distributions are indicated by the manufacturers in polar diagrams in different sections. Usually the absolute luminous intensity in candelas refers to a fixed lamp light-flux.

If in Equation (8.14) the luminance of the sender surface is replaced by the luminous intensity per unit area with

the result for the illuminance is

E dФ ;T ed^ г dI (e,) e dA, cose, r dt(e, e (8 17)

Er = =1 L, coseed^2 =1 coser S 2 – =1 5 coser (8.17)

dA * j dA, cose, r Jr

with Єг as the angle between the receiving surface and solid angle dQ.2.

With the usual constancy of the luminous intensity over the radiating surface As, the photometric distance law is obtained:

E dФ 1 (e,) e

E =——- = cose

r dAr r2 r

However, the functional characteristic of the illuminance, which decreases in inverse proportion to the square of the radius, only applies starting from the so-called photometric minimum distance, which is about 10 times as large as the largest linear dimension of the lighting surface.

Example 8.4

Calculation of the illuminance on an 80 cm high work surface lit by a Lambert emitting lamp at a height of 2.5 m and a lateral distance of 0.5 m with a luminous intensity I(0) = 500 cd.

The angle 9r between the recipient-surface normal and the light is obtained from the lamp height and lateral distance,

( 0.5m

9r = arctan I—–

r I 1.7m

the distance is 1.77 m. The luminous intensity of the light toward the recipient surface is

I (0)cos0s = 500 cd x cos16.4 = 480 cd

so the result is an illuminance of

8.3.3 Units and definitions

An overview of the definitions and units in lighting technology is given in Table 8.4.

Table 8.4: Units in lighting technology. Photometric unit Symbol Definition Unit Luminous energy Qv II lm s Luminous flux Ф – lm Luminous exitance Mv Mv = ^ v dA1 lm m-2 Luminous intensity Iv II cd Luminance Lv L dФ v d QdA1cose1 cd m-2 Illuminance Ev Ev = 1 Lv cose1dQ 2n sr lx Luminous exposure Hv h = dQ dA2 lx s

Artificial and daylight sources can be characterised by the following efficiencies.

Table 8.5: Efficiency definitions in lighting technology.

Efficiency	Symbol	definition	Unit
Radiative efficiency	Пє	Фе/Р	– (W/W)
Luminous efficiency	nv	0v/P	lm/W
Photometric radiation equivalent	K	Ф ФЄ	lm/W
Optical efficiency	O	f—dA/Ф 3 dX Iе	–
Visual efficiency	V	Ф k Ф m e	–