7.1. Some Important Terminologies and Quantities 437
whereνis the spatial frequency anddis the pixel size. This expression does not
take into account the variation in image quality due to pixel to pixel spacing. The
MTF due only to these spacings can also be represented by a similar sinc function
given by
MTF(ν)sp=sin(pνπ)
pνπ. (7.1.19)
Hereprepresents the pixel spacing. We can now used equation 7.1.18 to determine
the overall MTF of the detector. This gives
MTF(ν)total = MTF(ν)pixMTF(ν)sp=sin(dνπ)sin(pνπ)
pdν^2 π^2. (7.1.20)
This shows that the MTF of a pixel detector can be improved by decreasing the size
of the pixels and the pixel-to-pixel spacings. In the limit that these parameters tend
to zero, the MTF tends to unity. That is
lim
p,d→ 0MTF(ν)total=1. (7.1.21)Of course, this does not represent apracticalphysical limit onMTFsince it is almost
impossible to design a detector that satisfies this condition. The physical limit is
still governed by the actual pixel width and the pixel-to-pixel spacing according to
the relation 7.1.20.
7.1.B Efficiency
Efficiency of any detection system characterizes its usefulness for a particular task.
Any position sensitive or imaging system consists of a number of individual elements
working together. For example a nuclear imaging system consists of a radioactive
source, collimation setup, imaging detector array (generally a charged coupled de-
vice), data acquisition and storage system, and image processing software. Each of
these elements has its own efficiency, which must be taken into account to obtain a
realistic measure of the signal-to-noise ratio. Since a complete discussion of all such
efficiencies is out of the scope of this book, we will restrict ourselves to the quantum
efficiency, which is related directly to the process of detection.
B.1 QuantumEfficiency
Quantum efficiency is traditionally used to quantify the efficiency of x-ray based
systems. However it can, in principle, be used for any photon based system. Since
most imaging systems use photons as incident radiation therefore it deserves some
attention. Before we go on to its mathematical formalism, a point worth noting
is that the actual definition of quantum efficiency is dependent on the underlying
physical processes. For example during our discussion on photomultiplier tubes
we saw that quantum efficiency of photocathode is described in terms of number of
incident photons and the number of generated photoelectrons. In this chapter we will
define quantum efficiency to characterize how efficiently x-ray photons get absorbed
in the material through which they pass. That is how efficiently the photons are
absorbed in the detection material. The rationale behind this definition is that the