2.2. Radiolucent Materials

The field generator array is typically created from copper coils [17,22,23,24]. Many conventional coils contain X-ray attenuating materials that are visible in the X-ray images and potentially obscure patient anatomy. The linear attenuation coefficient of dense materials varies approximately as the fourth power of the atomic number for X-ray energies in the diagnostic range [25]. Aluminum (Al), with an atomic number of 13, has, therefore, considerably less X-ray attenuation than copper, with an atomic number of 29. However, copper is a better conductor and easier to work with generally [26].

In order to predict how easily an X-ray will penetrate a material, its attenuation coefficient needs to be considered. The attenuation coefficient characterizes how easily a volume of material can be penetrated by an X-ray or other ionizing energy. For all materials, this is a highly non-linear parameter based on a wide range of photon scattering and absorption processes [25]. However, tables of the attenuation coefficient are readily available [27], which allows comparisons of the relative absorptions of different materials to be analyzed. To predict the absorption of a monochromatic X-ray beam as it traverses a homogenous material with an absorption coefficient µ, the Lambert–Beer law can be used

where the observed intensity I is related to the intersection length of the object x and I0 is the X-ray intensity at its source [28]. If we define the normalized intensity of the X-ray source with distance into a material as:

In order to compare the absorption of two materials, we define a simple ratio of the change in absorption relative to the ideal case where no attenuating materials are present based on the relative attenuation of two materials denoted A and B as follows:

For example, for a 50 μm thick layer of aluminum and copper exposed to an X-ray tube voltage of 80 keV would result in γ=12.338, i.e., the copper is approximately 12 times more attenuating in comparison to the aluminum. The voltages used in diagnostic X-ray tubes range from roughly 20 kV to 150 kV and thus the highest energies of the X-ray photons range from roughly 20 keV to 150 keV [25]. An example of this can be seen in Figure 4. Figure 5 shows a comparison between the relative absorption of copper to aluminum for a range of material thicknesses. At low voltages, the absorption varies significantly at the different material thicknesses but these differences decrease as the voltage increases across the typical diagnostic imaging range.

A comparison of the absorption coefficient for pure copper and aluminum for a range of photon energies. The typically used range for diagnostic imaging is also shown. Within this range, we see that copper has a much greater absorption than aluminum and this trend is more pronounced at lower energy levels [29,30].

A comparison between the relative absorption over copper to aluminum for a range of material thicknesses. At low voltages, the absorption varies significantly at the different material thicknesses but these differences decrease as the voltage increases across the typical diagnostic imaging range [29,30].