For measurement of .. . 
| uw 
BY TRANSMISSION 
on a 
ry 
i 
' 
| 
i 
THICKNESS 
LQ 
NX 
N 
N 
—o 
CONCENTRATION 
~ 9 
> / 
N 
BY REFLECTION 
. . . this article tells how to get... 
BY REFLECTION 
The Best Performance 
from Beta Gages 
By L. R. ZUMWALT 
Tracerlab, Inc. 
Berkeley, California 
INDUSTRIAL PROCESS controls with beta 
gages as the primary indicators can be 
made most useful when the character- 
istics of the gages are known quan- 
titatively. This article presents a 
means of analyzing the application of 
a beta gage to any particular process. 
Thicknesses of continuously moving 
materials and the. concentrations of 
process solutions are the quantities 
most commonly measured with beta 
gages (1-5). Measurements are based 
on two principles. The absorption of 
beta radiation as it passes through a 
material provides an indication of the 
material’s thickness. The degree of 
backscattering of beta rays from a sub- 
stance can be used to determine either 
thickness or concentration. 
Mathematical Formulation 
A quantitative analysis of beta-gage 
sensitivity, accuracy, and response 
time requires the mathematical formu- 
lation of beta-ray transmission and 
reflection. 
Approximate relationships between 
the observed current from the ioniza- 
tion chamber and the thickncss or con- 
centration (variables that deterinine 
the number of beta particles entering 
the ionization chamber) are given in 
this section. 
Thickness-by-transmission. When 
the material measured is between the 
radiation source and the ionization 
chamber 
AI = He = Io => —I,(1 = e7 Her) 
With reference (meter zeroed) at 
s=x2' 
AI =I —I, 
= —I[ eH?’ (1 — e7Ha(z—2’)) 
165 
