Page 76 - Sensors and Control Systems in Manufacturing

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O n e
Cha p te r

In most practical cases, the following approximation is true:
.
α= 57 3∗ D
L
Example:
distance = 20 feet
image diameter = 5 feet
Exact formula gives the angle = 14.25°
In the case of a “soft edge” light image diameter, it is usually mea-
sured at the point where illumination is 50 percent (beam angle) or
10 percent (field angle) of the center illumination.

1.15.9 Calculating Lumens Output—Luminous Flux
The beam radius is divided into “n” equal parts (radii and illumina-
tion reading values are indexed from 0, at the beam center, to n–1, at
the beam edge). See Fig. 1.23.

1.15.10 Calculating Center and Edge Points—Two Points:

2
.
(
E
P = 21 R E + 05 )
.
1 0
1.15.11 Calculating Center, Middle, and Edge Points—Three
Points:
.
2
.
.
(
P = 13 R E +12 E + 02 E )
2 1 0
Beam Profile
E 0
E 1
E 2

E n – 1

Radius
R = 0 R 1 R 2 R n – 1 = R beam
0
FIGURE 1.23 Calculation of lumens output.