Physics and Engineering of Radiation Detection

9.11. Counting Statistics 569

Nb1 Nb2

dd

w

Nb

Ni

v/2 v/2

Figure 9.11.2: Subtraction of background for determination of peak

area.

counts. In the example shown in the figure, the background has a linear trend, which
is not really a representative of the majority of spectra. However, it would serve
well to introduce the reader to a simple method of background elimination.
The first step in elimination of background is to define a region of interest as
shown by shaded portion of the spectrum in Fig.9.11.2. This region has two parts as
depicted by a horizontal line in the figure. The upper part is what we are interested
in. The bottom part is the background that needs to be subtracted from the total
area. The question is, how do we draw that horizontal line? One way to do it
is to simply connect the two ends o f the peak. But this method may not work
very well since the local fluctuations in the background may introduce too large an
uncertainty in the result. Another simple method is to use two other regions to
estimate the background counts as shown in Fig.9.11.2. We first choose two regions
of equal widthsv/2 on either side of the background area. The total area of these
regions isNb 1 +Nb 2. We then assume that the ratio of this total area to the total
width of these regions is equal to the ratio of the background area to the background
area width, that is

Nb

w

≈

Nb 1 +Nb 2

v

(9.11.21)

⇒Nb ≈

w

v

[Nb 1 +Nb 2 ]. (9.11.22)

Having estimatedNb, we can now calculate the area of the peak from

Ni=Nt−Nb, (9.11.23)

whereNtrepresents the total area of the region of interest (shaded portion in
Fig.9.11.2).
We are now interested in determining the error in our measurement of the area.
For that we can use the error propagation formula 9.5.5, according to which the