438 Chapter 7. Position Sensitive Detection and Imaging
absorption efficiency is directly related to the efficiency of generation of charge pairs,
which in turn determines the efficiency of signal generation.
We saw in chapter 3 that the passage of photons through matter can be fairly
accurately described through an exponential of the form
I=I 0 e−μx,whereIis the photon intensity at a depthxandI 0 is the incident intensity. μis
the attenuation coefficient, which depends on the photon energy. Let us write this
equation in a slightly different form.
I 0 −I
I 0=1−e−μxHere the numerator (I 0 −I) is simply the number of photons absorbed per unit time
in the material as the beam traverses the distancex. The ratio of this quantity with
the incident photon intensityI 0 is calledquantum efficiency(QE)ofthematerial.
Hencewecanwrite
QE=1−e−μx. (7.1.22)
From this definition it is clear that the quantum efficiency actually represents the
efficiency of the material to absorb the incoming particles. Whether this absorption
is useful or not for generating a detectable signal in a detector is another story. In a
semiconductor detector, for example a part of the incident radiation gets consumed
in increasing the lattice vibrations, something that can be termed asparasitic ab-
sorptionfor radiation detection purposes. This is also true for gas filled detectors
where some of the incident radiation may be absorbed by the walls of the chamber or
by some other elements in the gas without creating charge pairs. However, generally
speaking most of the absorbed radiation does actually generate detectable signal and
with proper calibration this signal can be fairly accurately related to the energy of
the incident radiation. Since in a radiation detector the height of the output signal
depends on the energy absorbed in the material therefore the efficiency of absorp-
tion is directly related to the efficiency of the detector. Same is true for an imaging
system where it is desired that the system has as high a quantum efficiency in the
energy range of interest as possible. Looking at the above equation it is apparent
that this efficiency can be increased in two ways: by increasing the thickness of the
active detection material and by using material with a higher attenuation coefficient.
The energy dependence of attenuation coefficient shows more or less similar be-
havior for most of the materials of interest. The coefficient is high at lower energies
and decreases with energy. If the energy range of interest contains the atomic absorp-
tion edge of the material, then the coefficient will show a sharp dip. Consequently
there will be a peak in quantum efficiency at that level. Such an energy region can
be utilized to create images of high contrast if the region of interest is filled with
such a material. In fact this has been tried in experiments of non-invasive angiogra-
phy where the patient receives potassium intravenously and synchrotron radiation
around the K-edge of potassium is used to create the images of the arteries.
B.2 Spatial Detective Quantum Efficiency (DQE(f))
The detective quantum efficiency is perhaps the most widely used parameter for
characterizing the effectiveness of imaging systems. The reason is that it determines