as was actually observed on the experimental data (see figure 5.18).
5.4.1.2. Correction o f pixel non-uniformities
The presence of pixel non-uniformities in the CCD makes it necessary to introduce some form of post-processing in the digital images in order to correct for response and dark current variations. It has already been mentioned that fixed pattern noise can be the dominant source of noise at high signal levels. In addition, scintillation detection requires the use of a phosphor screen that, as in this case, may introduce image artefacts. This is particularly important if CCDs are to be used in medical applications, where the imaging task consists of detecting an abnormality without a priori knowledge of its localisation, shape or size. Image artefacts could increase the number of false positive diagnostics and consequently contribute to an increased dose to the patient if repeat exposures are necessary.
The fact that the CCD response is linear over most of its dynamic range allows to use simple computer algorithms to eliminate pixel-to-pixel non-uniformities. The correction process makes use of dark and flat-field images to compensate for background trends and for fixed pattern noise, respectively. In this thesis the corrected pixel data S^{i) were calculated on a pixel by pixel basis using the equation
S»(0 = ( S / ( 0 - 5 , ( 0 ) ^ (5.16)
where S^{i) are the corresponding pixel values of the calibration frame (flat image), S^{i) are the uncorrected pixel data, and S^{i) are the dark frame pixel data. Similar algorithms have been reported by Blouke et al (1987) and Karellas et al (1992).
Using the general equation for error propagation it can be demonstrated that if the uncorrected and the calibration images contain only random noise then the variance in the corrected image would be given by
/ _ \ 2 / - \2 6 2 2 a„ + S. / \ j j y f J (5.17)
Chapter 5 A CCD-based x-ray imaging system
where and are the mean values of the uncorrected and flat images, respectively, andô = ( ^ /0 - ^ /f ) > .
Figures 5.20a shows an uncorrected image of a flat field taken with device FO-2 using the experimental arrangement described in §5.2.1, Visible illumination was used as opposed to x-rays in order to avoid extra sources of random noise such as direct hits in the silicon. The crack pattern of the Csl screen can be clearly seen in this image. Figure 5.20b shows the corresponding corrected image, as obtained using the algorithm described above. The phosphor structure practically disappears after correction, and the total measured standard deviation (see table 5.5) is reduced by a factor of approximately 5.
(a) (b)
Figure 5.20. Correction of fixed pattern noise in a coated device, (a) Noise in the uncorrected image is totally dominated by the crack structure of the phosphor, (b) Noise is reduced by a factor - 5 after correction.
(a) (b)
Figure 5.21. Correction of fixed pattern noise in a deep depletion device. The total noise increases by a factor of -1 .3 after correction (see table 5.5)
Chapter 5___________________________________________________A CCD-based x-ray imaging system
Figures 5.21a and 5.21b show a similar example of the correction procedure for a deep depletion device. In this case an artefact due to a partially blocked column of pixels can be clearly seen in the image. The artefact disappears after correction, although the corrected image looks slightly noisier. The mean signal and standard deviation of all the images presented in figures 5.20 and 5.21 are given in table 5.5. The values for device No-1 are also given in the same table for comparison . It can be observed that in all cases the measured standard deviation in the corrected images ( a j is smaller that the value calculated with equation 5.17 ( a ') , which indicates that all images contained at least a small contribution of non-stochastic noise.
T a b le 5.5. Mean values and standard deviations for a series o f flat im ages taken with three different devices.
5 . 5 . G:
FO-2 172.3 18.0 15.7 172.5 18.1 156.1 3.4 23.3
D D -3 168.6 11.2 12.3 172.7 11.4 156.4 14.4 15.0
No-1 181.9 7.2 17.1 180.6 6.7 164.8 8.6 8.9
5.4.2. T herm al noise
Thermal excitation of valence electrons in the semiconductor lattice gives rise to the generation of some electrical current in the CCD. The thermal contribution to the output signal is present even in the absence of an input signal. When the CCD is operated at room temperature this current not only introduces a dark signal offset, thereby reducing the dynamic range of the CCD, but it also increases the background noise, and therefore limits the system sensitivity at low-signal levels. The main contribution to dark signal current in a CCD is the thermal generation of electron-hole pairs due to surface states at the Si-SiO^ interface (Blouke et al 1987). This current can be expressed as (Knoll 1989)
(5.18)
where is a proportionality constant characteristic of the device, is the absolute temperature (in °K), K is Boltzmann’s constant and is the silicon band gap, which is also temperature dependent and is given by
Chapter 5 A CCD-based x-ray imaging system
£ [eV ] = 1 .1 5 5 7 -[(7 .0 2 1 X 1 0 ^r / )/ ( 1 108 + £ ) ] (5.19)
T he dark signal o f the CC D can therefore be expressed as (H oldsw orth 1990)
S.,JA D U ] = (G,^;'7„21„„i,) + 5,„o ffs e t (5.20)
w here is any deliberate signal offset introduced in the system . This equation
indicates that dark signal is expected to increase linearly with integration tim e. An estim ation o f the dark current contribution to the dark signal in device FO-1 was obtained by shielding the image section o f the C C D from any visible or x-ray input and m easuring the output signal as a function o f the integration tim e. The results of these m easurem ents are shown in figure 5.22.
40 35 Û 30 < g 25 ■S?
^
20 Q 15 10 , 1 , , H 1 1 1 1 1 1 ' ' 1 ' ' ' 1 ' '' ' 1 ' ' ' 1 ' ' ' . p - - . -o' - . O - - - O . . - - : - x < > - - o ' - 1 1 I 1 1 i i 1 1 1 1 1 1 1 1 11 1 1 1 11 1 1 1 , , 1 , - 0 20 40 60 80 100 120 140 160 Integration time [ms]Figure 5.22. Measured dark signal as a function of integration time at room temperature. The dotted line is a linear regression of the data.
The signal offset and the proportionality constant o f equation 5.20 w ere determ ined from linear regression analysis o f the m easured data, and found to be 5"^^, ~ 9 .0 ± 0 .5
A D U and = 0 .20 ± 0 .0 1 A D U /m s, respectively. T he pixel area o f this
device is 4 .8 4 x 1 0 ^ mm^ and the conversion constant is G^==10~^ADU/e", therefore the dark current contribution was 7 „ = 6.69 nA/cm^.
The Poisson shot noise associated with the dark current in term s o f charge equivalent carriers is given by
Chapter 5______________________________________ A CCD-based x-ray imaging system
^thermal ~ ^ss^pixh (5.21)
When the camera is operated in normal video mode the integration time is 20 ms, therefore the thermal noise per field calculated from equation 5.21 is =6 4 e " . This figure compares well with values reported in the literature. Flint et al (1992a) reported a thermal noise of -150 e" for a 100 jim Epi deep depletion device of the same kind as used in this investigation. Holdsworth et al (1990) have measured a thermal noise of -100 e" on a time-delay and integration CCD at 5 °C using an integration time of 0.79 s, which would be approximately equivalent to 50 e“ at room temperature using an integration time of 20 ms.
An important consequence of the dark signal contribution to the total measured signal when the camera is operated in asynchronous mode is that the dynamic range of the system can be severely limited. At the maximum integration time used {tj = 140 ms) the dark signal already accounted for 15% of the total 8 bit ADC range, and full saturation was reached in about 1 second.
5.5. Summary and conclusions
In this chapter a digital x-ray imaging system prototype based on an asynchronous CCD camera and a programmable frame grabber combination has been described, and its main operational parameters have been determined. The system was used in two different x-ray detection modes: direct conversion in the silicon with deep depletion devices, and scintillation detection using standard CCDs fibre-optically coupled to CsI(Tl) screens.
The basic characteristics of the individual components of the system were analysed using standard methods. Although the system is based on a 8-bit ADC, the total gain can be adjusted to extend the effective range of the ADC by a factor of approximately 15. The parameters that control the total gain of the system were found to be accurate to within 3%. Once the system was calibrated under specific illumination conditions the calibration remained stable to better than 1%, but recalibration was required if camera response or illumination conditions changed over time.
Two different calibration methods were used to determine the conversion factors that relate the CCD signal, expressed in terms of charge carriers per pixel, to the frame
Chapter 5___________________________________________________A CCD-based x-ray imaging system