## 4 Conclusions and Discussion  
Nondestructive evaluation of various conductive objects through metal enclosures is investigated by using ELF/VLF magnetic fields. In the presence of an incident field, the hidden objects create field distortions that can be measured outside the enclosure. The field distortion is primarily observed for the normal component of the field on the shield surface and is quantified using the gain G. The gain is shown to be sensitive to the size, conductivity, and permeability of objects, which could provide support for imaging applications. The G value is shown to decrease with increasing distance of the measurement plane from the base of the hidden object with a spatial profile that is consistent with simplified analytical theory. As shown in Figure 5, the projection of the fields on different measurement planes is quite sensitive to the distance from the base of the box. It is apparent that the distance of the measurement plane is an important parameter in determining the spatial resolution on the _xy_ plane. In general, the closer the measurement is to the object, the higher the lateral resolution. As the distance of the measurement plane is increased, the fields will more closely approximate that of a single spherical object, and high spatial resolution will become difficult to attain. When the conductivities of the outer shell are \(10^{6}\) to \(10^{8}\) S/m, the imaged size of the PEC box is almost the same as the actual PEC box size. Several actual materials lie in the range of conductivities utilized in this study. Some representative materials and corresponding conductivity values are nickel (1.28 \(\times\)\(10^{6}\) S/m), aluminum (3.5 \(\times\)\(10^{7}\) S/m), copper (5.8 \(\times\)\(10^{7}\) S/m), and silver (6.3 \(\times\)\(10^{7}\) S/m) [17]. The G value decreases when the conductivities of the inside box decrease \(10^{8}\) to \(10^{6}\) S/m. The distorted field vanishes at far from \(z=-0.3\) m. It is shown that objects with conductive materials and low permeability tend to induce a \"magnetic field shadow\" below the object. In contrast, high permeability materials tend to show an enhancement in the magnetic field at a measurement location below the object. These opposed results also show nondestructive evaluation through a conductive outer shell. The polarity of the surface current is dependent on the radius of sphere material, frequency, and relative permeability. The difference of both conductivities in the inside  
Figure 7: \(H\) fields on _xy_ plane at \(z=-0.005\) m for (**a**,**c**,**e**,**g**,**i**,**k**) conductive (\(\mu_{r}=1\)) material and (**b**,**d**,**f**,**h**,**j**,**l**) ferromagnetic (\(\mu_{r}=1000\)) material through an outer shell at 50 Hz signal. The conductivities of the outer shell and inside box are in the range of \(10^{6}\) to \(10^{8}\) S/m. The inside object in cube geometry has lengths 0.6 with the center and the outer shell has 2.7 mm thickness. and outer shell are also considered. A hidden object can be detected as the conductivity of the inside object is higher than that of the outer enclosure. The results can be utilized for the practical and fundamental limits to nondestructive imaging of conductive objects through metal enclosure using ELF/VLF magnetic fields. Several practical considerations should be kept in mind when selecting the appropriate frequency (or frequency range) for specific applications. The first relevant variable involves information on material properties within the application at hand. For instance, if imaging inside enclosures akin to a shipping container is desired, the frequency must be chosen to be low enough to penetrate the material but not so low that the response of hidden objects is not observable (this will likely be in the sub 100 Hz range). A second important variable is the noise characteristics of the application environment. In the ELF/VLF band, the dominant sources of noise are atmospheric noise (typically from lightning radiation), nearby electronics, and power line harmonics.