## 3 Results and Discussion
### Physics of X-ray imaging
Outside this area, the number of recorded quanta is of the order or less than the quantum noise in the central pixel of beam incidence. The digital and digitized mammograms under study were deconvolved in the spatial domain using the PSF as defined in Table 3, rather than running the discrete Fourier transform in the spectral domain. As such, errors introduced by truncation and aliasing were circumvented at the expense of some extra computational power. Now assume that a detector has \(100\%\) efficiency and only the quantum noise is considered. Then eq. (60) holds for the smallest detail to be imaged down to the dimension of one pixel. For objects which are different from the pixel size, a more complex equation must be used:  
\[C_{m}=\frac{1}{\sqrt{N/A}}\cdot\frac{k(a)}{\sqrt{a}} \tag{61}\]  
where \(k(a)\) is a rather complex function of the object area, and \(C_{m}\) is the minimum contrast which can be detected using a given number of photons per unit area and which could ideally be achieved \begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline
**Columns** & **(0)** & **(1)** &..... & **(xsize-2)** & **(xsize-1)** \\
**Rows** & & & & & \\ \hline (**0**) & 0 & 1 &..... & xsize-2 & xsize-1 \\ \hline (**1**) & xsize & xsize+1 &..... & 2*xsize-2 & 2*xsize-1 \\ \hline (**2**) & 2*xsize & 2*xsize+1 &..... & 3*xsize-2 & 3*xsize-1 \\ \hline : &..... &..... &..... &..... &....... \\ \hline (**ysize-2**) & (ysize-2)*xsize & (ysize-2)*xsize+1 &..... & (ysize-1)*xsize-2 & (ysize-1)*xsize-1 \\ \hline (**ysize-1**) & (ysize-1)*xsize & (ysize-1)*xsize+1 &..... & ysize*xsize-2 & ysize*xsize-1 \\ \hline \end{tabular}
\end{table} 
Table 2: Indexes of the receptor matrix elements: _ysize_ stands for rows and _xsize_ for columns. with a \(100\%\) efficient noiseless detector [43]. Both of the above expressions, eqs. (60) and (61), show that contrast varies inversely with the square root of the superficial dose (which is proportional to the number of photons per unit surface impinging on the detector). Qualitatively, if a small object is to be detected, then it must have a large contrast, whereas large objects may be imaged with a relatively smaller contrast. However, practical detectors (with their electronic parts included) have an efficiency less than \(100\%\), thereby reducing \(N/A\) and adding noise to the photon counters. If \(R\) is the ratio between the total noise (including the detector noise) and the intrinsic quantum noise, than the minimum detectable contrast becomes:  
\[C=\frac{R}{\sqrt{\epsilon}}\cdot C_{m} \tag{62}\]  
where \(\epsilon\) is the detector efficiency. As eq. (62) indicates, a poor efficiency (small values of \(\epsilon\)) as well as a noisy detector (small values of \(R\)) entail a minimum detectable contrast higher than the ideal case \(C_{m}\) and, consequently, degrades the performance of the detection system. Several reports have pointed out the superiority of digital detectors over conventional films in three directions, at least. A valuable characteristic of most digital receptors is a constant sensitivity over a much wider range of exposures (latitude) than radiographic films. Secondly, the phantoms routinely used as test objects in mammography are already visible at a fluence with 3 order of magnitude lower by the digital recorders [42]. An increase in fluence corresponds to an increase in image contrast, which amounts to an increase in object visibility. Thirdly, once a digital detector came out with an image as a set of numerical data, the grey scale can be adapted as to enhance the contrast, and even more, tones of greys can be substituted by false colors.