CHARACTERISATION OF AN X-RAY IMAGING SETUP FOR DIGITAL
MAMMOGRAPHY BASED ON A SILICON MICROSTRIP DETECTOR
Tadej Mali1, Vladimir Cindro1, 2, Marko Mikuž1, 2, Dejan Križaj3, Danilo Vrtačnik3, Urban
Zdešar4
1
Jožef Stefan Institute, Ljubljana, Slovenia
2
Faculty of Physics and Mathematics, University of Ljubljana, Slovenia
3
Faculty of Electrical Engineering, University of Ljubljana, Slovenia
4
Institute of Occupational Safety, Ljubljana, Slovenia
Table of contents
Introduction
Materials and Methods
Setup
Modulation transfer function (MTF) measurement
Noise power spectrum
Detective quantum efficiency
Results
Summary
Abstract: A silicon microstrip detector was designed and fabricated. "Edge-on" geometry
was used to assemble it into a slit-scanning X-ray imaging system, resulting in a linear pixel
detector with a pixel size of 0.100×0.220 mm2. Single photon counting was realized using the
CASTOR 1.0 ASIC. The line response function in the direction of scanning was measured
and the corresponding modulation transfer function (MTF) calculated. Noise power spectrum
was obtained and the detective quantum efficiency (DQE) evaluated.
Introduction
Several approaches to digital image acquisition are under consideration. The first approach
utilises integration mode detectors, e. g. photostimulable phosphorus, amorphous silicon and
scintillator-coupled CCD (overview given in Säbel and Aichinger 1996, Yaffe 1998). There
the charge generated by impinging radiation is integrated over exposure time.
Another approach is to use detectors operating in single photon counting mode, with
individual photons detected and counted. There are several groups implementing this
technique either using silicon microstrip detectors (Arfelli et al. 1998, Beuville et al. 1998,
Mali et al. 1999a, 1999b) or gallium arsenide pixel detectors (Amendolia et al. 1997).
The advantage of single photon counting systems compared to integrating ones is that using
appropriate readout electronics, the acquisition can be practically free of detector and
electronic noise. The only source of noise in the image are fluctuations in the number of
impinging photons with a Poissonian distribution. The response of silicon detectors is linear
over an effectively infinite dynamic range (Turchetta et al. 1998). Together with high
efficiency of semiconductor detectors, this contributes to good sensitivity of such detectors as
well as to a reduction of dose.
Materials and methods
Absorption length of 20 keV photons in silicon is approx. 1 mm. Therefore 3 mm of silicon
are sufficient to absorb 95 % of radiation. Since silicon microstrip detectors are produced on
thin (several hundred microns) wafers, they must be used in an "edge-on" geometry (Arfelli
et al. 1998, Beuville et al. 1998, Mali et al. 1999a, 1999b), where photons hit the detector
from the side and the photons are absorbed along the whole length of the strip (figure 1). In
this way only the dead volume between the edge and the active volume limits the quantum
efficiency (QE).
The detector acts as a linear pixel detector with pixel dimensions given by the strip pitch and
the detector thickness. Images of large objects are obtained by scanning in the direction
perpendicular to the detector plane. This approach is called scanning slit radiography or slot
scanned radiography and has the additional benefit of efficiently suppressing scattered
radiation detection (Yaffe 1993, Barnes et al. 1993, Stres et al. 2000).
Figure 1: Silicon microstrip detector used in the ‘edge-on’ geometry. X-ray photons emerge
from the source on the right hand side of the figure.
Setup
The detector with a strip pitch of 0.100 mm was fabricated on 0.220 mm thick, high
resistivity silicon, resulting in a pixel size of 0.100×0.220 mm2. Details of design and
fabrication are described elsewhere (Vrtačnik et al. 1999). A total of 32 strips were wire
bonded to the CASTOR 1.0 readout integrated circuit, covering a total area of 3.2×0.22 mm2.
The readout circuit CASTOR 1.0 is a multichannel, mixed analog-digital, low-noise
integrated circuit. It enables simultaneous photon detection and counting without false photon
hits for photon energies above 12 keV (Comes et al. 1996). Phantom and test objects were
positioned on a table moved by a stepping motor, while the position of the detector and
source were kept fixed.
The X-ray source was an X-ray tube with a tungsten anode operated at single phase 32 kV
peak voltage, the tube current was 5 mA. The first half value of aluminum was measured to
be 0.8 mm. The source to detector distance was 60 cm.
Modulation transfer function (MTF) measurement
Modulation transfer function characterizes the spatial resolution of the system. For an ideal
pixel detector with dimensions x  y one expects:
sin xu sin yv 
MTF u, v  
xu
yv
where u and v are spatial frequencies along x and y-axis. Since MTF falls off inversely
proportional to pixel dimensions, the spatial resolution increases as the pixel size is reduced.
In the case of silicon microstrip detectors, the pixel size can be reduced by smaller strip pitch
(denoted y), while the pixel size in the direction of scanning (denoted x) is limited by wafer
thickness to approx. 0.200 mm. Therefore our research is focused into possible improvements
of the spatial resolution in the direction of scanning (Mali et al. 1999b). Since only the MTF
in the direction of scanning is investigated, it can be obtained from the line spread function
(LSF), which was obtained as the derivative of measured edge response function (ERF). A
thin (0.05 mm) lead foil, embedded into plastic was used to obtain the ERF.
Noise power spectrum (NPS)
The noise power spectrum can be calculated analytically. Suppose that on average N photons
are detected in a pixel at intervals of x (scanning step x needs not be equal to pixel width
x ). The noise in the image is a random variable  x  , describing fluctuations in the number
of detected photons N / x  at each scan position x. It has zero mean and standard deviation
equal to the square root of the number of detected photons per scan:    N / x . The
space function of measured quantum fluctuations can be represented as a piecewise constant
function over an interval of x . The values in neigbouring intervals are totally uncorrelated,
therefore the autocorrelation function (ACF) of the noise equals:
 N 
x 
, if x  x
1 X /2
 2 1 
ACF x   lim
 x    x  x dx    x  x 

X  X  X / 2
0, elsewhere

To obtain the NPS, the Fourier transform of the ACF must be calculated. It should be stressed
that in digital systems the image is sampled at discrete points separated by x . According to
the sampling theorem, the noise components with frequency above 1 / 2x will be mapped
into lower frequencies interval. The discrete Fourier transform of the above ACF is:
NPS (u )   ACR(nx) exp  inxux
n
The result is NPS u   N / x , since only ACF(0) is different from 0. This result implies that
white noise is expected in single photon counting systems.
Detective quantum efficiency (DQE)
DQE is defined as:
QE 2  MTF 2  N in / x
DQE 
NPS
where QE equals quantum efficiency of the detector with the number of incident photons N in
connected to the number of detected photons via N  QE  N in . If the image noise follows
the predicted constant power spectrum, DQE differs from MTF 2 only by the factor of QE.
Note that in digital systems DQE vanishes at frequencies larger than Nyquist frequency,
because the high frequency signal components are aliased to into the low frequency interval.
Results
To accurately measure the MTF, it is necessary to reduce the sampling step to such extent,
that the MTF is negligible outside the Nyquist interval. In our study the scanning step was set
to 0.025 mm, resulting in Nyquist frequency of 20 cycles/mm.
The measured LSF of the system has a full width at half maximum of 0.227 mm, which is
close to the pixel dimensions in the direction of scanning (0.220 mm). The corresponding
MTF is shown in figure 2, together with a MTF of an ideal pixel detector with a pixel size of
0.220 mm. It can be seen, that the system MTF is lower than the ideal one. Effectively the
measured MTF can be described as a product of the ideal MTF and a Gaussian curve with
  4.6 cycles/mm . This corresponds to a LSF of an ideal pixel detector blurred with a
Gausian with   0.03 mm .
It has been shown (Mali et al. 1999b) that X-ray test patterns are stil visible at frequencies,
where the MTF drops to 0.01. In addition, using appropriate image processing, the distortions
due to LSF could also be restored up to frequencies where MTF=0.01 (Mali et al. 1999b).
Therefore our conclusion is, that the current system is capable of showing details with spatial
frequencies above 10 cycles/mm, with some additional room for improvement.
Figure 2: The modulation transfer function of the system.
In the contrast to MTF measurements, in the case of NPS the scanning step can not be
reduced to such extent as to prevent aliasing, since the ACF depends on the sampling rate
x and its Fourier transform is always non-negligible outside the Nyquist interval.
To evaluate the NPS a 1024 steps long flood image was taken. It was corrected for gain and
tube current variations. After these corrections the mean and standard deviation of pixel
values were estimated. The Poissonian relation between mean and standard deviation was
confirmed. Then the NPS was measured in the following way. The 1024 samplings of each of
the 30 pixels were Fourier transformed (using the fast Fourier transform algorithm) and the
transforms were averaged over the pixels. In the resulting spectrum 8 neighbouring bins were
averaged. The resulting error in NPS estimate is then 6.5%. Within this error the NPS is
indeed constant over the whole frequency interval from 0 to Nyquist frequency (figure 3).
Figure 3. Noise power spectrum of the system. Average number of detected photons per pixel
is approx. 4100.
Due to a frequency independent NPS, the DQE of the system is simply OE  MTF 2 as
explained previously. Assuming a 0.200 mm thick dead region, the resulting QE at 20 keV
amounts to 0.80.
Summary
A silicon microstrip detector was designed, fabricated and assembled into a X-ray imaging
system. The system was characterized by means of MTF, NPS and DQE. Comparison to
previous results (Mali et al. 1999b) shows, that the system is capable of resolving details with
spatial frequency above 10 cycles/mm, when an appropriate scanning step is chosen and
image processing applied.
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