Physics and Engineering of Radiation Detection

432 Chapter 7. Position Sensitive Detection and Imaging

Image

Multiplication

Spike Function Sampled Data

Frequency Spectrum Spike Function

Convolution

Convoluted Spectrum

Multiplication

(b)

(a)

Transformation

Fourier

Aliasing

Convoluted Spectrum sinc Function

(c)

Reconstructed Spectrum

Figure 7.1.6: (a) Sampling in spatial domain is equivalent to multiplication of the
image by a spike function. (b) Sampling in frequency domain is equivalent to con-
volution of the frequency spectrum with a spike function. (c) Multiplication of the
convoluted frequency spectrum by a sinc function leads to aliasing even if the copies
of the frequency spectrum are well apart. This type of aliasing is therefore solely
due to reconstruction.

wherex 0 represents the center of the function andσis the standard deviation (see
Fig.7.1.9). TheFWHMof this function is given by

FWHM =2

√

2ln2σ

≈ 2. 36 σ. (7.1.11)

A.4 Line Spread Function (LSF)

Line spread function is similar toPSFin the sense that it uses the same technique
to quantify the spatial resolution. However, in this case, the image of an ideal line is
used instead of a point. TheLSFis then drawn perpendicularly through this image.
Since a line can be thought to consist of a large number of closely spaced points,
therefore theLSFproduces a whole profile ofFWHMs instead of a single value as
for thePSF. The resolution of the system at any point can then be deduced from
this profile. AlthoughLSFis a good measure of the system resolution but it is very
difficult to determine experimentally. The main difficulty lies in manufacturing an
ideal line object.