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El problema de Dirichlet en un pol´ıgono

5.4.1. Measurement o f glare-to-primary ratio

The glare-to-primary ratio (GPR) is scattering of the secondary quanta within the detector and is described in section 2.9.1. The GPR was measured with a test object comprising a series of 2 mm thick lead discs of diameter 1 -3 mm embedded in a 2 mm thick PMMA sheet (Carton et al 2009, Seibert et al 1984), which was placed on top of the breast support. The exposure was taken at 29 kV, Mo/Rh or W/Rh anode/filter combination with the anti scatter grid in place and a 2 mm Al filter placed at the tube port. The x-ray beam was collimated to 18 cm x 24 cm. Three images of the phantom were acquired, with the phantom shifted slightly between exposures. It was assumed that any signal behind the discs is glare. The image was linearised and the signals in the centre of each lead disc in the image and its surrounding background were measured. The GPR was calculated for each disc and the results fitted linearly against the disc diameter. The final GPR was calculated by extrapolating the measured results back to the zero diameter. Fig. 5.4 shows with results from the measurements for each detector. The calculated GPRs are in table 5.4 with the results of simulations described in section 5.4.3.

0.2 0 -, --- 0 .0 5 - 0.00 1 2 Diameter (mm) 3 0 ASEh ASEs CSI CRc NIPa NIPc

Fig. 5.4. Measured glare-to-primary ratio for six systems

It is difficult to make accurate measurements of GPR. A major issue is that glare is really a special case of blur where the signal travels for long distance within the detector system. In theory glare should be measured as part of the MTF. However it is shown (section 5.4.2) that the glare is not fully encompassed within the measured MTF, but glare and blur cannot be truly measured separately.

With three images the random error of the glare to primary ratio was about 3%. However, the presence of scatter may have caused a systematic error, as scatter will have the same appearance as glare in the image. To reduce the scatter in the image the anti-scatter grid was used and an aluminium filter was used rather than PMMA. The beam was not

collimated to ensure that glare was maximised, unfortunately this also had the adverse effect of increasing scatter. As discussed in section 2.9.2, the scatter will not only be created in the PMMA support o f the test object but also originate within the breast support, grid and detector cover and for practical reasons this was counted as part o f the GPR.

Despite the uncertainties associated with this measurement, from knowledge of the detector design the relative results between the different detectors were as expected. The a- Se systems have relatively low glare as would be expected as there was low spread of signal within the detector. The electric field applied to the a-Se layer reduced the spread of secondary quanta better than the columnar structure of Csl crystal. The largest glare was measured in the CR systems, with the CRc with a turbid phosphor with the largest glare. This was not surprising. During the reading cycle the laser beam is scattered within the phosphor (Rowlands 2002), and causes stimulation of the trapped signal at considerable distance from the initial irradiation area. Although the glare of the NIP systems was lower than the turbid phosphor, it is perhaps surprising that the columnar structure did not reduce the glare further. In addition to the glare within the detector, it may be reasonable to assume that the detector cover needs to be very robust for CR systems compared to the other detectors and so this could be a large source of scatter, which would be incorporated into the glare.

Salvagnini et al (2012) measured the GPR to be around 0.01 and 0.03 for the Hologic and Siemens systems respectively. This is lower than the measurements here, although there were a number o f differences in the techniques. They used much larger lead discs of between 4 and 30 nun, so they have a larger extrapolation than this work, which may increase the uncertainty. Fig. 5.4 shows the measured results and a straight line was a good fit for GPR, but these curves were not shown by Salvagnini et al (2012) to judge the fit of their data over such a wide range of diameters.

Glare can be a relatively large proportion of the signal within an image, in particular for CR systems. Considering the effect that this can have on image quality, it is surprising that little work has been undertaken in this area.

5.4.2. C om parison o f M T F low freq u en cy drop a n d glare-to-prim ary ratio

Veiling glare affects how the input signal is transferred to output and therefore the measurement of presampled MTF should include the effect of glare. As the glare affects the signal over long distances, it should be seen as a low frequency drop (LFD) in the MTF. Fig. 5.5 shows the measured low frequency component of the MTF and indeed a low frequency drop was present in the measured MTF of each of the detectors studied.

.00 0.95 ë o . 9 0 - ASEh ASEs CRc CSI NIPa NIPc 0 . 8 5 - 0.0 0.2 0.4 0.6 0.8 I.O F req u en cy (m m ' )

Fig. 5.5. Measured low frequency MTF of systems studied, average over both directions.

The question therefore arises whether this LFD represents the glare measured for each detector (table 5.4). This was tested using a computer simulation. Glare is dependent on the irradiated area and ideally the irradiated area of the image and the irradiated area for the glare measurement should be similar for accurate simulation. Using MATLAB (Mathworks, Matwick, MA, USA), a 2048 x 2048 array with pixel value equal to one was created. A single disc was added to the centre of the image, the signal behind the disc was zero. A series of such images was created with the disc diameter varying from 1 to 3 mm in steps of 0.5 mm. A two dimensional MTF was created from the x and y one dimensional MTFs (section 5.3). At each spatial frequency in the 2D array, the MTFs were interpolated from the orthogonal one dimensional MTFs and weighted according to angle relative to the axes. The MTFs are assumed to be symmetric in the negative spatial frequencies. The spatial frequency at the edges of the array corresponded to the Nyquist frequency of the original image and zero spatial frequency was in the centre. Each image was multiplied by the 2D MTF for each detector in frequency space and then reconverted back to an image. The results were analysed as for the real images and the GPR calculated. The results are shown in table 5.4. For all of the detectors, the GPR calculated from the simulated images was lower than the measured GPR of the real images. In some of the cases it was less than half the real value. This size of difference could not be ignored and so the MTF will need to be corrected to account for glare. It is difficult to improve on the MTF measurement methodology on a system in clinical use. It may be that any glare which adds a signal evenly across the image will not be seen in the MTF as this signal is lost during the differentiation of the edge spread function. Also the measurement of MTF is collimated so there was less glare to be detected.

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