X-RAY DETECTORS - Two-Dimensional X-Ray Diffraction - page 93

can be obtained by multiplying the relative standard deviation, s/N, by 100 percent
to give the percent standard deviation as

p
N % ¼

N

100
N

100
Rt

s % ¼ 100 p % ¼ p % ð4 : 3Þ

Apparently, a larger number of counts or a larger count rate results in a better
precision based on Eqs (4.2) and (4.3). Figure 4.2(b) shows how the percent standard
deviation improves as the number of counts increases. At N¼1, s%¼100%; at
N¼100, s%¼10%; at N¼10,000, s%¼ 1%; and at N¼1,000,000, s%¼0.1%.
The Eqs (4.2) and (4.3) assume no background in the number of counts. Since the
probable error of the counts above the background is a combination of the probable
errors of both the total counts and backgrounds counts. The standard deviation
of counts with background is given by

p

N p þN b

s ¼ ð4:4Þ

where N p is the total number of counts (including background counts) and N b is
the background counts. The relative standard deviation of the counts above the
background is given by

p
N p N b %

N p þN b

s % ¼ 100 ð4 : 5Þ

This equation can be used to calculate the uncertainty of the integrated intensity
counts with background correction. However, care must be taken that an appropriate
2u range is selected. A wide 2u range may unrealistically increase the contribution
of the background counts so as to overestimate the standard deviation. A 2u range of
twice the full width at half maximum (FWHM) can have 98 percent peak counts
covered assuming the peak has Gaussian distribution.

4.3.2 Detective Quantum Efficiency and Energy Range

The detective quantum efficiency, alternatively referred to as the detector quantum
efficiency or quantum counting efficiency, is measured by the percentage of incident
photons that are converted by the detector into electrons that constitute a measurable
signal. For an ideal detector, in which every X-ray photon is converted to a detectable
signal without additional noise added, the DQE is 100 percent. The DQE of a real
detector is less than 100 percent because not every incident X-ray photon is detected,
and because there is always some detector noise. The DQE is a parameter defined as
the square of the ratio of the output and input signal-to-noise ratios [11,12].

2

ðS = NÞ out

DQE ¼ ð4 : 6Þ

ðS = NÞ in

A detector's DQE is affected by many variables—for example, X-ray wavelength,
transmission of the detector window, geometric design, the choice of the filling gas