**5. Quasi monochromatic X-ray beam imaging**

#### **5.1 Generation of quasi monochromatic beams using diffraction**

Different methods have been developed to approximate monochromatic beams i.e. to provide quasi monochromatic beams, which consist of not a single X-ray energy but a narrow range of X-ray energies.

Contrast Enhancement in Mammography Imaging Including K Edge Filtering 139

The spatial resolution of such a system was analyzed by Gambaccini et al. (Gambaccini, Tuffanelli et al. 2001) who found that along the direction perpendicular to the diffraction plane the resolution properties of the imaging system mainly depend on the x-ray tube focal spot size and position. Along the diffraction plane the spatial resolution depends on mosaic

There is another method of generating small energy bandwidth X-ray radiation. It is known that in addition to the Brehmstrahlung radiation, materials bombarded with electrons produce characteristic radiation which increases the intensity of the X-ray radiation at energy levels specific to each material. For instance, a typical X-ray radiation spectrum for a Tungsten (W) anode using 100 kV anode-cathode potential and a 2 mm Al window is shown in Figure 4. As before, the lowest energy X-rays are absorbed by the Al output window. The sharp peeks in the X-ray spectrum are characteristic for the anode material. These peeks are the result of the electron structure of a given material and they show the energy differences

For example, W has 3 electron shells that play a role in its use as a K edge filter. The 3 innermost electron shells are designated "K", "L", "M", where K is the innermost shell, and M the outermost. For W, K has an energy of 70keV, L has an energy of 11keV, and M has an energy of 3keV. The characteristic peaks for W will occur at "L minus K" and "M minus K" or at 59keV (designated the K peak) and 67keV (designated the K peak). W also has a second electron in its K shell with a slightly different binding energy which explains the

The same phenomenon works in the opposite way; materials absorb X-ray photons which are above their binding energy. This is the basis of the K edge filters. Generally at these (energy) levels the X-ray absorption of the material jumps (increases) when the material is used as an X-ray filter. Figure 5 shows the X-ray spectrum for the same W anode and the same X-ray tube voltage as in Figure 4 but with an added 0.2 mm W sheet as a filter. This

crystal characteristics and on the geometry of the setup.

between electron shells of the atomic structure.

Fig. 4. W anode spectra with low energy filter of 2 mm Al.

**6. K edge filters** 

doublets in Figure 4.

**6.1 Theory of K edge filters** 

One method utilizes mosaic crystals to produce quasi-monochromatic X-ray beams. When an X-ray hits the crystalline structure of a material, constructive interference takes place in accordance with the Bragg equation:

$$\mathbf{2d} \times \sin \theta = \lambda \times \mathbf{n} \tag{3}$$

where, is the exiting X-ray photon wavelength, d is the spacing between atomic planes of the crystal and is the diffraction angle and n is an integer. The d-spacings are substancespecific and like the have an inverse relationship with the energy of the output beam. At different , different X-ray energy photons are reflected back from the crystal. This is called Bragg reflection and this method was proposed by Baldelli et al. (Baldelli, Taibi et al. 2003) to generate monochromatic X-rays. However, this method has some drawbacks. First of all, because it is a Bragg reflection from a plain surface it provides only a monochromatic fan beam and not a cone beam; furthermore, the intensity of the diffracted beam is very low because only a very small portion of the total incoming X-ray spectrum is reflected back. Moreover, because of the variation of crystal angle in the mosaic crystal and the finite width of the slits the X-ray beam is only quasi monochromatic with an energy bandwidth of ~E.

Fig. 3. Quasi monochromatic X-ray beam by X-ray diffraction.

A prototype of a quasi monochromatic diffraction system has also been developed for mammography (Baldelli and et al. 2005). Advantages of the system are that it is tunable in the range of 18-24keV, and according to the authors, the dose can be decreased by half. Disadvantages are that it uses little of the available X-ray flux and requires scanning, as it produces only a sheet beam, so the scanning time is a few seconds long (possible motion blur). The resolution of the system is also lower than the best digital mammo systems can produce.

#### **5.2 Applications for quasi monochromatic beams**

A similar system to that of Baldelli's (Baldelli and et al. 2005) was developed for a combined breast SPECT – CT system (Gambaccini, Fantini et al. 2001). It had the same advantages and disadvantages as the mammography system.

The spatial resolution of such a system was analyzed by Gambaccini et al. (Gambaccini, Tuffanelli et al. 2001) who found that along the direction perpendicular to the diffraction plane the resolution properties of the imaging system mainly depend on the x-ray tube focal spot size and position. Along the diffraction plane the spatial resolution depends on mosaic crystal characteristics and on the geometry of the setup.
