Measurement based on the principle of radiation absorption is mainly used to deter­mine the thickness of rolled metals. The intensity of the radiation penetrating a

Counter Recorder

Figure 11.21 Continuous level indication with point radiation sources and a linear detector.

material depends on the elemental composition, thickness, and density of the mate­rial placed in the path of the radiation. For thickness measurements, the material must have a permanent chemical composition and density.

The intensity change caused by a material layer is described by the following formula (see also Eq. (5.46)):

f = exp(-ME)0 (П.27)

10

where I0 is the intensity of radiation entering, I is the intensity of radiation leaving the material, p,(E) is the linear absorption coefficient, and I is the thickness of the material layer.

The upper part of Figure 11.22 shows a measuring arrangement based on radia­tion absorption, while the bottom part shows a measuring arrangement based on radiation reflection. The measuring technique based on reflection is mostly applied when access to both sides of the equipment is impossible due to the mechanical arrangement of the equipment.

Radiation sources used for thickness measurements include gamma — and beta — emitter nuclides. The radiation energy is selected to match the material density. As detectors, ionization chambers and proportional counters are applied.

To obtain the best sensitivity for the thickness measurements by absorption, optimal measuring conditions are applied by selecting the best radiation source (with given p(E)). The conditions of the optimazation measurements can be deduced from Eq. (5.48) as follows: where I0 is the intensity of radiation entering, I is the intensity of radiation leaving the substance, p, is the mass-absorption coefficient, p is the density, I is the thick­ness, and d is the surface density of the paper layer.

Absorption Electronic Recorder Detector device Reflection

Electronic Detector device Recorder Figure 11.22 Measuring principles based on radiation absorption and reflexion.

The optimal value of д is obtained using the relative measuring sensitivity (Q), which is defined as:

AI

(11.29)

d

For simplification, AI is expressed by the difference quotient of Eq. (11.28):

AI = I1 Ad (11.30)

and

AI = — fiI0 exp(——ud)Ad (11.31)

By substituting Eq. (11.31) into Eq. (11.29), we obtain:

^I0 exp(—ud)Ad

Q = A0 = ^d exp(—^d) (11:32)

d

The differential quotient of the relative measuring sensitivity Q, according to the mass-absorption coefficient p, is:

Q1 = = d exp(-ppl) — pd2 exp(-pd) (11.33)

dp

The function (Eq. (11.33)) has a maximum if Q = 0. From here, d exp(—ppl) = pd2 exp(-pd) (11.34)

From Eq. (11.34), we obtain:

p=d (11.35)

In conclusion, the sensitivity of the thickness measurement is the best if Eq. (11.35) is fulfilled.

For the thickness measurement by backscattering, a similar equation to Eq. (11.35) can be derived from Eq. (5.69).

Examples of applying industrial thickness-measuring systems include the following:

• Continuous thickness measurement on paper-manufacturing machines with beta-emitting radionuclides.

• Continuous thickness measurement of metal sheets on cold rolling machines.

• Thickness measurement of hot rolled steel sheets.

• Thickness measurement of surface layers deposited on thick basic sheets (coatings).

• Thickness measurement gauges on plate glass production lines.

• Thickness measurement of concrete at construction of containers.