Design Proposal of a Metal Detector for Humanitarian Demining

Abstract—In this research work, a novel design of a metal detector is proposed. To fulfill this, several results obtained with an edge based FEM simulator, and an analytical model were used. The main objective of the proposed detector is to diminish the influence of the soil in the detector performance, given that this is an important problem on landmine detection[1]. By using numerical modeling could be demonstrated the feasibility of the proposed design.


METHODS
The influence of soils in metal detector performance has been studied previously. Theoretically, by using analytical models in [2] , [3] y [4], by using a numerical modeling. These studies, allow to conclude that the electromagnetic properties of soils are highly influent in the detector performance, especially when soils have relative magnetic permeability different from 1. It was experimentally confirmed in [1], these results show that a detector can decrease its probability of detection and increase its false alarms rate, when the soil is magnetic. Taking into consideration that a detector needs a strategy to diminish the effect of soil in its performance.
In order to calculate the induced field of a buried metal a finite elements simulator was developed. In this simulator the model presented in [6] was implemented using the Matlab software This design proposal aims to vanish the voltage induced directly by the transmitter coil, and the voltage induced by soil, in order to avoid a pair of calibrations.
To fulfill this, it is needed to analyze the induced magnetic fields behavior in the scenario of Fig.1, a horizontal coil over a half space. The magnetic field induced by the coil in the air (Fig.1) at the , position can be calculated with the equations ( 1 ), ( 2 ), ( 5 ) and ( 6 ), and the magnetic field induced by the homogenous soil under a variable magnetic field produced by an horizontal transmitter coil, could be calculated with equations ( 3 ), ( 4 ), ( 7 ) and ( 8 ): If

RESULTS
Since one of the main objectives of this design proposal is to vanish the voltage induced directly by the coil transmitter, a good choice is to place the receiver coil perpendicularly to the transmitter coil. According to Fig.2, the induced field in Z direction by the transmitter coil will not be sensed, given that no magnetic field lines pass through the receiver loop.  Whereas Fig.3 shows that the induced magnetic field in X and Y direction is zero if the receiver coil is placed exactly in the middle and perpendicularly to the transmitter coil (Fig.4). If the receiver coil is placed at the plane X=0, the receiver coil would sense the field in direction X, but there is not a component of the induced magnetic field in X (Fig.5), the induced field only has component in Z direction, and it does not cross the receiver coil. This configuration makes it possible to eliminate the field induced by the transmitter coil, and additionally, it works well to eliminate the induced field by an homogenous soil and soil calibration could be avoided. The following figures show the magnetic field induced by a soil when it is excited by a horizontal coil.
From Fig.6 toFig.8, it can be seen that the field lines in Z direction will not be sensed by a receiver coil located in plane X=0, and the field lines in X direction will overlap cancelling each other.    Last results allow to observe that a receiver coil placed in plane X=0, above or below the transmitter coil, will not sense the field induced by the soil and the transmitter coil ( Fig.9, Fig.10). Even, this condition is kept if instead of a receiver coil, several receiver coils are placed in the plane X=0 m (Fig.11, Fig.12).   The distribution of coils proposed avoid the fields induced by the soil and the transmitter coil to be measured. However, it has not been defined if it is feasible to detect buried metals. The detection is feasible in case that the buried metal generates magnetic field lines in direction X crossing the receiver coil. According to the results obtained, these field lines were effectively generated. Nonetheless, in order to analyze the detection feasibility in greater depth, another set of simulations was made, using the edge based numerical model.
The greatest magnitude of the magnetic field in X direction, appears when the center of the transmitter coil has not reached the buried target position. Therefore, it is arbitrarily assigned X=-0,02 m as the transmitter location and the plane where the receiver is placed, to get the results of Fig.13 and the subsequent figures. Fig.13 describes the imaginary and the real part of the magnetic field induced in X direction by a metallic cube, that is buried in a non-magnetic, conductive soil (0,01 S/m), and is exposed to a variable magnetic field, generated by a 5 cm radius transmitter coil powered by a 1 A current at 50 kHz. The following figures (Fig.14-Fig.16) show the magnitude of the magnetic field induced by the buried cube, which cross the receiver located in the middle of transmitter coil. These results allow to conclude that there is indeed an induced magnetic field in X direction that could be sensed to detect a buried target, and therefore this design propose is feasible for a metal detector.    In accordance with the results previously obtained, it is feasible to detect buried metal, by placing the receiver coil perpendicularly to the transmitter coil. This detector senses the magnetic field induced by the buried object in X direction and avoids the magnetic field induced by the soil and transmitter coil.
The following results, show the behavior of the magnetic field induced in X direction, as a function of the height of the coils, in order to establish the optimal receiver location. Fig.17 shows, how the induced magnetic field in X direction, decreases when the transmitter coil height increases, assuming that the receiver is located at the same height of the transmitter. Clearly, when the height of the transmitter and the receiver becomes higher, the induced magnetic field decreases, it suggests that the transmitter and receiver coils should be as close to the soil as possible. It excludes the configuration of the next figure because the transmitter coil needs to be as high as the radius of the receiver coil. Considering the above, it is proposed to use receiver coils with a flat side (Fig.19) instead of a circular coil, seeking to keep transmitter and receiver coils very close to the soil.   Initially, it is analyzed the rectangular receiver coil, for this geometry it is needed to determine the width and high of the rectangular coil to get the greatest induced voltage. To do so, it is necessary to calculate the magnetic vector potential over the line that forms the rectangle (Fig22-Fig23), and doing the integration of the equation ( 13 ) numerically as a sum of the potential in many points separated∆ . In order to get results with a higher resolution ( ∆ ), it was used a 2D interpolation to obtain the potential A, at any position in the simulation scenario (Fig24), this allows to calculate the voltage induced in a coil of any shape.  Fig28. Ideal size of the rectangular receiver coil of a detector that senses the induced magnetic field in X direction.
With a procedure similar to the above, a semicircular receiver coil was analyzed; in this case, it is needed to calculate A in direction at many points of the semicircle, and on the bottom part of the coil it is enough to calculate A in Y direction. To calculate A in direction, it is needed to do a coordinate transformation ( 15 ).
( 15 ) By doing numerical integration, were obtained the results fromFig29, and it can be concluded that the greatest induced voltage is obtained when the semicircle radius is around 4.5 cm. .

IV. CONCLUSIONS
This investigation proposes a novel design of metal detector for humanitarian demining based on simulations made with numerical and analytical models.
The main objective of the proposed design is minimizing the effect of the soil in the detector performance, which is currently a known important problem in demining.
By using numerical and analytical modeling, is possible to determine that the electromagnetics properties of the soil are highly influentialin the performance of the metal detector.
According to the experiments carried out, magnetic soils represent the greatest challenge for the metal detectors used in demining, since in the proposed detector the field induced by the ground is not measured, it is taking advantage of the magnetic and conductive soils, since the field induced by buried objects increases in this type of soil Additionally, this detector avoids the magnetic field induced directly by the transmitter coil. To do this, a receiver in quadrature with the transmitter was proposed, and it was probed that this configuration could detect metal buried objects. The dimensions of the receiver were defined, in order to guarantee the maximum magnitude of induced voltage.