X-Ray Phase-Contrast Tomography by Luca Brombal

Author:Luca Brombal
Language: eng
Format: epub
ISBN: 9783030604332
Publisher: Springer International Publishing

PhR

1.52 m

2.72 m

6.44 m

SNR

No

1.63 (0.02)

1.63 (0.03)

1.62 (0.01)

Yes

8.45 (0.13)

13.3 (0.3)

33.8 (0.7)

Contrast (%)

No

48.9 (0.5)

44.1 (0.5)

50.0 (0.4)

Yes

48.6 (0.3)

44.2 (0.1)

49.1 (< 0.1)

FWHM (px)

Yes

2.1 (0.5)

2.3 (0.3)

2.4 (0.2)

The quantitative results of the image analysis are reported in Table 5.2. As predicted by the theory (see Table 5.1) the SNR, calculated according to Eq. 5.11, does not vary significantly with the propagation distance if no PhR is applied, while its increase due to PhR is greater than a factor of 20 when considering 6.44 m of propagation distance. In addition, it must be noted that only little contrast variations (below 6%) are observed when changing the distance while, at a given position, no relevant contrast alterations are associated to the PhR algorithm whose action is limited to image noise. The latter observation is of great importance in sight of the clinical application of this technique, since the image appearance will look ‘familiar’ to the clinician’s eye, who will not require a specific training to read the images, as it may occur for other phase-contrast techniques. Furthermore, considering phase-retrieved images, the FWHM measured in pixel units does not vary significantly with the propagation distances and, in all cases, it was found to be slightly higher than 2 pixels (120 m on the detector plane). This implies that, taking into account the magnification, the actual spatial resolution slightly improves at longer distances (FWHM 100 m) at the expense of a smaller field of view.

With the aim of a better data visualization, the measured SNR gain, contrast and spatial resolution concerning the phase-retrieved images (points) and the theoretical predictions (lines) are plotted as a function of the propagation distance in Fig. 5.4. From the top panel it can be seen that the measured SNR gain is in remarkable agreement with the model results obtained via numerical integration considering realistic detector and reconstruction parameters (solid line). Interestingly, if the analytical formula given in Eq. (5.10) is followed instead of numerical integration, the predicted SNR gain factor (dashed line) is about 2-fold higher than the measured one. This can be easily explained taking into account the number of simplifications made in deriving that expression, the fundamental one being the rather unrealistic assumption of a detector featuring a constant MTF up to the Nyquist frequency: for this reason the values predicted according to the analytical formula constitute, in practice, an upper limit in terms of SNR gain when compared with experimental data. At the same time, it is worth mentioning that the factor of 2 difference between the two different approaches is almost constant at all the propagation distances, hence, even if Eq. (5.10) does not provide an accurate estimate of SNR gain factors in absolute terms, it still provides the correct trend with respect to the propagation distance. In addition, when comparing phase-retrieved images, a 4-fold increase in SNR is observed at 6.44 m with respect to the shortest propagation distance (1.52 m): remarkably, at a fixed propagation distance, such SNR increase would correspond to a 16-fold higher radiation dose.

Fig. 5.4Comparison between

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