Lighting and Mathematics

Lighting design is a kind of artistic creation, which is our consensus. The realization of art lighting design, has always been inseparable from the technology. Art is emotional, technology is rational, the perfect combination of the two, in order to produce good works.

Mathematics is the cornerstone of all kinds of technology. Mathematics is closely related to aesthetics and philosophy. Careful people may find beauty in many mathematical formulas, and even quite abstruse philosophy. To say "mathematics is the language of God" is not an exaggeration.

Lighting design in the analysis and calculation, the same can not be separated from mathematics. The use of mathematical tools, not only will make the lighting design more scientific, more accurate, but also allows us to see a lot of the nature of the problem, rather than stay on the surface.

Here is an example.

Beam angle (beam angle), is one of the most familiar, the most commonly used lighting designers to concept, refers to one of the vertical beam centerline plane, the light intensity is equal to 50% of the maximum intensity (usually center intensity) the angle between two directions. What is the relationship between the luminous flux and the luminous intensity of the lamp? How are these relationships reflected in the light distribution curve? The use of mathematical knowledge, it can be a good solution to these problems.

L calculation premise and hypothesis

In order to simplify the calculation o, only on the axial symmetric light lamps, the heart light intensity is Io;

The light source initial flux is phi o;

The lamp beam angle of 2 beta;

The lamp efficiency.

The calculation of L output luminous flux

L Lambertian source

Lambertian source is a source of widespread in nature. The sun, the frosted glass lampshade, the snow, the white wall and so on can be regarded as Lambertian light source, and many LED chips are very close to Lambertian light source.

The relationship between L beam angle and luminous flux and light intensity of the center

Light beam angle of 2 beta lamps, I beta is equal to I0 of 50%, namely,

I / I0= =0.5 beta

So,

M=lg0.5/lgcos beta (7)

L data relation table

According to the curve of light distribution, the initial luminous flux of the light source is 0 1klm ().

Because the lighting efficiency and I 0, I0 linear relationship, here may wish to take a unified 100%. In practical application, I lamps can be multiplied by the value of theta eta.

According to the above formula, we can get the data table of I theta /I0, m and beta.

L light distribution curve

According to several typical light distribution curve of the data in Table 1 describe as listed in table 2.

Table 2 light distribution curve (unit: cd/klm)

Application of L

It is convenient to integrate the data of all kinds of light emitting lamps. When a specific design project is encountered, the effect of different lamps can be easily compared. The following is a specific example of the application:

In the design of an industrial park building model as shown in figure 3.

In the middle of the two vertical grille prepared from oblique corner hit a beautiful rhythm with two narrow beam of light. Can choose a variety of beam angle from the lamp database in the light of the projection analysis of the trial program, select the effect of satisfactory lamps. 35W 5 degree and 20 degree beam angle projection effect renderings contrast figure.

Source: 2012 7/8, No52 lighting design "magazine"

Author: Shanghai early awakening Lighting Design Co., Ltd.

Key words: lighting design company lighting engineering company