Although indoor lighting is expressed by illuminance, road lighting is also expressed by brightness, so it is necessary to know the conversion relationship between illuminance E and brightness L. The author has not found the conversion relationship between illuminance E and luminance L so far, so I can only find the conversion relationship between illuminance E and luminance L from the relevant optical definitions.
related definition
Definition and Reasoning of Luminous Intensity I
Definition of luminous intensity I: The luminous flux emitted by a point light source in a unit solid angle in a given direction is defined as the luminous intensity of the light source in this direction. The symbol is I, and the unit is Candela (cd).
I=dφ/dΩ
In the formula, φ is the luminous flux, lm; Ω is the solid angle, sr (sphere area/radius square, Ω=4πR2/R2=4πsr for the entire spherical surface).
Its unit relationship: 1cd=1 lm/ sr
The author's reasoning: when all directions emit light uniformly
1cd=4πlm/4πsr (the numerator and denominator of the above formula are multiplied by 4π)
dΩ= 4πsr (corresponding to the luminous flux emitted by a point light source located at the center of a sphere with a radius of 1m dφ=4πlm), that is, dΩ also means that the solid angle formed by the entire spherical surface is 4πsr.
That is, an isotropic point light source: 1 candela (cd), emitting luminous flux φ=4πlm to the surroundings.
Note: The luminous intensity was earlier called "candlelight", and after 1948, the luminous intensity was officially named as candela (cd). As mentioned above, the luminous flux emitted by a 1cd uniform point light source is 4πlm.
The definition and reasoning of illuminance E and brightness L
(Light) Definition of illuminance E: expressed by the area density of luminous flux in the illuminated place. The symbol is E, and the unit is lux (lx).
E= dφ/dA (E is the illuminance, the unit is lm/m2, named lux, its symbol is lx; A is the area, the unit is m2)
The international unit of illuminance E is Lux (lx). 1 lux means the illuminance value of uniform distribution of 1lm luminous flux on an area of 1m2. Or it is a uniformly luminous point source with a luminous intensity of 1 cd. On the inner surface of a sphere with a radius of 1m centered on it, the illuminance value E formed by each point is 1lx. So Lux is also called Mi-Candela.
The definition of brightness (photon brightness) L: the luminous flux emitted by the unit projection surface of the light source in a certain direction in the unit solid angle, (the author reasoned: if the 1m2 inner surface of a sphere with a radius of 1m receives the light from the center of the sphere All diffuse reflection (reflection coefficient p=1), that is, the 1m2 inner surface of a sphere with a radius of 1m (that is, the unit projection surface) receives all the luminous flux from the center of the sphere in a unit solid angle and is diffusely reflected, then 1cd/m2( 1 nit) is equivalent to 1m2 unit projection surface emission (actually all diffuse reflection, that is, the diffuse reflection coefficient is 1) 4πlm luminous flux, that is, E=4πlx, which is called the brightness in a certain direction. The symbols are L, L =I/dA, the unit is cd/m2 (the unit used to be called nit (nt) has been abolished).
The relationship between illuminance E and brightness L
The author deduces the quantitative relationship between illuminance E and brightness L from the above definition: Please note that I, E, and L are all proportional to luminous flux. For the 1m2 inner surface of a sphere with a radius of 1m and the center point of the sphere to form a solid angle 1sr, that is, the luminous intensity at the center of the sphere is just equal to the illuminance on the inner surface of a sphere with a radius of 1m: I1 = E1 . If the luminance on the inner surface of a sphere with a radius of 1m is L=1cd/m2, because cd is numerically proportional to the luminous flux φ, the luminous flux φ on the inner surface of a sphere with a radius of 1m=4π·E, that is, the luminous flux φ can be obtained product. Therefore, it should be natural: to satisfy the brightness L=1cd/m2 on the inner surface of a sphere with a radius of 1m, the total cd value K=4πm2×1cd/m2=4πcd on the inner surface of a sphere with a radius of 1m (like the luminous flux φ In that way, the product can be calculated), this 4πcd can only come from the center point light source I of the sphere with a radius of 1m, and the luminous intensity I value of this point light source can only be 4πcd. The brightness L=1cd/m2= illuminance E formed on the inner surface of a sphere with a radius of 1m, the illuminance E=4π1x formed on the inner surface of a sphere with a radius of 1m, it can be seen that in the same diffuse reflection The value of E on the surface is 4π times the value of L.
