THEORETICAL CHARACTERISATION POSSIBILITIES

The objective of this article is to examine the theoretical Possibilities available for characterising anomalies using coil based induction detectors designed to analyse received frequencies. These theoretical possibilities are based on the various phenomenons and effects that an anomaly can experience. Consequently, the reading of this article should be in conjunction with the reading the article on Phenomenons.

Phenomenons characterise anomalies. Most phenomenons cause distortions of the waveforms or cause intermodulation effects. Distortions of the waveforms result in harmonics in the received signal.

The results of many phenomenons can be the change in another property of an anomaly and the change of this other property may well result in causing a further phenomenon or phenomenons. Inter-phenomenon effects will generally show up with the production of specific intermodulation frequencies on the receive signal. Possible examples of this are shown in the Self Modulation and Intermodulation sections below.

It should be noted that a number of the possibilities specified in this article are ones that the author has never known to be actually implemented in a metal detector. As with any new unimplemented ideas, the likelihood that these ideas will turn out to be useful, is not high. Some of this has been written as much in documenting underlying principles as in documenting ideas to be implemented. The research oriented design specified as an early priority of this project should make it easy to try out ideas like this.

SINGLE FREQUENCY

With a single frequency being output on the transmit coil, the normal rule is that the external soil and anomalies will modify the waveform such that all available information that can be used to characterise the coil's surroundings, is found in the phase and amplitudes of that frequency (the primary frequency) when read back from the receive coil and in the phase and amplitudes of each its harmonics when read back from the receive coil.

The above rule, that the only frequencies of interest are integer multiples of the primary frequency, has an unusual exception with magnetics. This is discussed further in the section entitled NON HARMONICS.

Primary Frequency:

Traditional VLF metal detectors have performed most of their characterisation on the phase shift and amplitude change of the primary frequency. In particular, the phase shift or the phase shift in relation to the change in amplitude created by the anomaly tends to be characteristic of the particular metal and the change in amplitude tends to give an indication of size and/or distance. Various designers have released phase diagrams where they have various objects such as rusty nails, cans and bottle tops showing in various parts of a pie diagram (ie circle cut into slices) based on the typical phase shifts for the objects.

When the phase plus amplitude waveform specification is converted to its equivalent inphase and quadrature component specification it's easier to equate the received waveform to the physics involved. For the easiest physics, the inphase should be based on the phase of the current waveform through the Transmit coil. In this case, the change in the inphase component is considered to be due to the anomalies resistance and the change in quadrature component is considered to be due to the anomalies impedance. The anomalies impedance is due to characteristics such as inductance and capacitance that change the phase of the waveform. While the objects resistance is mainly the objects actual electrical resistance, it can also be due to phenomenons that cause a similar loss of energy and result in an analogous voltage drop per current.

While in most cases the frequency examined is the primary frequency, there has been detectors which have just examined the harmonic at three times the frequency of the primary. Presumably the reason that only the primary is examined is due to the wealth of information in the primary frequency alone and the difficulty and cost of using electronics to also examine the harmonics,

Harmonics

Harmonics are frequencies that are integer multiples of a Transmitted frequency.

Once the full waveform is input as a Pulse Code Modulated (PCM) data stream and we have a sufficiently powerful computer, it's not too hard to extract the harmonics. Various phenomenons that make up the characteristics of the anomaly will result in various harmonics as well as different phases and amplitude relationships of these harmonics.

Odd Harmonics

We refer to frequencies where the multiple of the primary frequency is an odd number as odd harmonics. For example, 3, 5, 7, 9 etc times the primary frequency. The majority of harmonics seen are likely to be odd harmonics and the low order harmonics are likely to be larger than the higher multiples of the primary frequency.

Non linearities in the property relationships of the anomalies cause odd harmonics in the received signal. Non linearities in the property relationships of the detector itself and of the ground will also cause odd harmonics in the received signal and these have to be subtracted before using the non linearity information to characterise the anomaly.

With an AC input waveform, the response that occurs when a value of a relationship is increasing can be different to the response that occurs when the value of a relationship is decreasing. This is referred to as hysteresis. Hysteresis of relationships can occur under both a changing magnetic field and a changing electric field but the best known hysteresis is the large hysteresis effect that occurs in the relationship between magnetic field strength (H) and resultant magnetic flux density (B) when ferromagnetic materials are under the influence of an AC magnetic field.

The phase and amplitude of the harmonic and relative proportions of low order to high order odd harmonics all go towards characterising the non linearity and hysteresis and consequently characterising the anomaly. For example, hysteresis will give large phase changes in the harmonic compared to harmonics generated from non linearities that do not involve hysteresis.

Even Harmonics

While even harmonics are generally smaller than odd harmonics, there is a variety of phenomenons that can cause even harmonics. These phenomenons can be grouped into phenomenon groups that have specific property types that are possible of causing even harmonics. The property types that can cause even harmonics include the following:

Asymmetry

Lack of symmetry (asymmetry) produces even harmonics. This is typical in magnetic systems due to anisotropic properties. By anisotropic properties we mean properties of a material that depend on a direction.

One of the main examples of this occurs with the remanent magnetism that many of the buried anomalies have. This magnetism has a specific direction with each buried anomaly that is magnetised.  That is, each has its own north and south poles. The direction of this will make increasing the magnetic field easier in one direction and harder in another and similarly make decreasing the magnetic field more difficult in one direction and easier in the other.

The result of this asymmetry, or any other asymmetry, will be seen with the production of even harmonics in the received signal.

Magnitude Only Response

Where the response to a change of a property is dependant on magnitude only, the result of an AC waveform stimulus is to produce a waveform at double the frequency of the original waveform. Several of the phenomenons that occur with electromagnetic systems have this type of frequency doubling property.

One example occurs with magnetostriction. Since unmagnetised ferromagnetic materials shorten in length irrespective of the direction of magnetisation, these materials will shorten in length both as the magnetic field has maximum positive amplitude and with maximum negative amplitude. This causes an oscillation of its length at double the frequency of the magnetic field causing it. As there are a number of phenomenons relating to property changes under the influence of stress, this doubling of frequency may be impressed on or modulate a number of further properties of an anomaly.

Self Modulation

In the case of the single Transmit frequency so far assumed, true intermodulation should not be seen due to the lack of frequencies but self modulation can cause a similar effect. This is sometimes referred to as self intermodulation. Ignoring the contradiction in terms, a possible example might occur with Magnetoresistance. Assume an oscillating Magnetic field of frequency f acting on an anomaly that generates eddy currents across an average resistance R combined with a magnetoresistance effect where the resistance varies from R by plus and minus delta_R. The effect of this is to create a resistance factor with respect to time of the following form:

1 + ((delta_R / R ) sin(360 f t))

Since current and hence magnetic field produced by the anomaly is proportional to 1/R, the magnetic field is divided by the above factor. So long as delta_R/R is very small, division by the above factor approximates to multiplication by the following:

1 - ((delta_R / R ) sin(360 f t))

That is, division by 1 point 0 0 0 ... 1 approximates multiplication by 0 point 9 9 9 ... and division by 0 point 9 9 9 ... approximates multiplication by 1 point 0 0 0 ... 1 where each of these factors and divisors have the same number of significant digits.

The above multiplication of the Transmit waveform modulates the waveform with a sine waveform multiplied by a sine waveform that results in an AC waveform component at twice the transmit frequency. See http://humanise.org/demining/underlying-maths for more information on how this multiplication results in doubling the frequency. Note that as we also multiply the Transmit waveform by one, the original waveform of frequency f remains as the dominant waveform received.

As the division of the resistance factor only approximates multiplication, this produces further distortions that would be seen in higher order even harmonics. The greater the proportion of delta_R to R is, the greater the proportion of these higher order even harmonics.

Rectification

Rectification can cause even harmonics. Rectification occurs due to the use of components that act as one way valves. Diodes in electronic circuits are designed for this purpose. Although rectification is common in electronic circuits, it's not likely to be seen in humanitarian demining anomalies unless the anomaly is a discarded electronic circuit.

NON HARMONICS

The normal rule that the only frequencies of interest are integer multiples of the primary frequency, has an unusual exception with magnetics. This occurs due to the Barkhausen Effect.

A slow, smooth increase of a magnetic field applied to a piece of ferromagnetic material, such as iron, causes it to become magnetized, not continuously but in minute steps or discontinuous jumps in magnetization. The material magnetizes in fits and starts with the amount of resultant Barkhausen noise for a given material being linked with the amount of impurities, crystal dislocations, etc. The consequence of this effect is that the response to a Transmitted single frequency waveform can include frequencies that are not an integer multiple of the applied frequency.

The Barkhausen Effect creates further possibilities for characterising an anomaly. It's expected that measurement of the Barkhausen Effect would be easier with a relatively slow single frequency. Noise on the input that is due to the Barkhausen Effect should be easily recognised as different from other noise as it occurs as the magnetization of the anomaly is increasing in each direction but not when the magnetization is at its positive and negative crests. Other forms of noise would be continuous through out.

A possible algorithm to extract noise, assuming there is only one Transmit frequency, may be as follows:

The PCM data stream is examined by the Digital Signal Processing (DSP) module which outputs the phase and amplitude of the primary frequency plus the phase and amplitude of any significant harmonics.

The Barkhausen Effect module receives the output of the DSP module as well as receiving the original input signal as a PCM data stream. Using the output of the DSP module it creates a PCM data stream containing just the clean primary and significant harmonics. It now subtracts each of the values in its created data stream from the values in the input data stream and converts these differences to magnitude only. These differences represent the noise in the input signal.

The Barkhausen Effect module groups each of the individual noise values into those occurring at a time when Barkhausen Effect is likely (ie increasing magnetisation) and those occurring when Barkhausen Effect is unlikely (ie crests of magnetisation). It adds each of the values into group totals over a window or bucket period. It may also perform weighted bucket algorithms similar to the DSP module. See http://humanise.org/demining/averaging for more information on this. After this the Barkhausen Effect module would output the resultant group totals to the Analysis and Display modules.

The Barkhausen Effect module would provide a further tool for characterising an anomaly. It's expected that it will work best with just one single slow Transmit frequency. As will be seen in the following, there are many reasons for a humanitarian detector to use multiple frequencies. Full characterisation may not be needed until after an anomaly is identified. Consequently there's no need to run it while searching for anomalies. This module could be implemented as a tool that's applied by the detector's operator only while the detector is stationary over an anomaly.

One problem with this concept is that previous to converting the analog input to digital by the A/D, the electronics will have a low pass filter to filter off high frequencies. There is a requirement to filter off frequencies higher than half the sampling rate. See our Hardware page at http://humanise.org/demining/hardware for more information on this.

Even if our interface electronics doesn't do this, most sound cards will have some filtering of these high frequencies before the A/D. Should most of the Barkhausen Effect be seen as frequencies higher than our low pass filter then most of the effect will be filtered off. In this case we may need an additional A/D which has a higher sampling rate, in order to implement this Barkhausen Effect module.

MULTIPLE FREQUENCIES

Change in Response with Change in Frequency

Both the received primary frequency and the received harmonics change as the Transmit frequency changes. This can be due to a number of effects but they include effects due to typical grain size of soil versus that of anomalies that should help to separate ground effect from anomaly response. If there are three or more Transmit frequencies over a wide range of frequencies then we can not only examine the change in response with change in frequency but also look at the linearity / non linearity in this relationship.

Information that has previously been easier found with Pulse Induction (PI) detectors should be available by examination of the change in response with change in frequency. See http://humanise.org/demining/metal-detector-types for more information.

Intermodulation

This form of distortion normally occurs when two sine waves of frequencies f₁ and f₂ are present at the input, resulting in the creation of several other frequency components, whose frequencies include (f₁+f₂), (f₁-f₂), (2f₁-f₂), (2f₂-f₁), and generally (mf₁ ± nf₂) for integer m and n. Generally the size of the unwanted output falls rapidly as m and n increase.

A larger range of characterising information becomes available while examining intermodulation harmonics resulting from multiple Transmit frequencies than the information available from a single Transmit frequency. This allows better separation of effects from various phenomenons or phenomenon groups.

An example of this can be seen with magnetostriction. As previously mentioned, an oscillation of the length of an unmagnetised ferromagnetic anomaly occurs at double the frequency of the AC magnetic field that causes it.

Initially, let us just assume a single oscillating magnetic field of frequency f acting on an unmagnetised ferromagnetic anomaly. If the changing of length occurring at the frequency of 2f modulates another parameter, such as modulates the resistance, then the result will be a sine waveform of frequency 2f multiplying a sine waveform of frequency f. The result of this is to produce sine waveforms of frequency (2f-f) and (2f+f). That is, the result ends up in the primary frequency (2f-f=f)and in the lowest odd harmonic (2f+f=3f). As a number of other phenomenons cause these frequencies, it makes it difficult to separate effects.

Now let us instead assume the oscillating Magnetic field Transmitted comprises two frequencies. We denote the lower frequency as f₁ and the higher frequency f₂. Less us also assume that f₂ is greater than twice f₁.

From this, it's possible to get a large range of intermodulation frequencies. The change in length will occur at both the frequencies of 2f₁ and 2f₂. When this length change modulates the anomalies electrical resistance, as well as modulating their own frequencies they can modulate the opposite frequencies. This results in sines waveforms of f₁ being multiplied by 2f₂ and sine waveforms of f₂ being multiplied by 2f₁. The modulation of opposite frequencies provides waveforms with frequencies of (f₂ - 2f₁), (2f₂ - f₁), (f₂ + 2f₁) and (2f₂ + f₁). Normally the lower frequency (f₂ - 2f₁) is the easiest to examine.

While the above response is easily distinguishable from the phenomenons that cause simple harmonics, it's not the only set of phenomenons that can cause that response. For example, electrostriction also causes a length change at double the frequency of its excitation frequency. In this case the excitation would be a AC electric field such as that creating the eddy currents. As this length change would modulate the anomalies resistance exactly the same as for magnetostriction the resulting response would be in the same intermodulation frequencies.

With several phenomenon intermodulation combinations able to create a waveform of frequency f₂ - 2 f₁, the amplitude and phase of this particular frequency is one of the most important frequencies to examine for anomaly characterisation.

A similar situation occurs in the case where f₂ is larger than f₁ but instead of being more than twice the frequency of f₁ it's between f₁ and twice f₁. In this case the lowest intermodulation frequency of interest is the waveform at a frequency of 2f₁ - f₂.

There are a larger number of phenomenons that don't involve a frequency doubling. Many of these can also modulate another property in a similar manner to that just described except without the frequency doubling. These will also result in intermodulation frequency responses. The largest effect for these will be seen in the (f₂ - f₁) and the (f₂ + f₁) frequencies.

Utilizing Fluxgate Effect for Characterisation

The Fluxgate effect can occur when you apply both a static magnetic field and an alternating magnetic field to a ferromagnetic material. The fluxgate effect can be observed by examination of the harmonic at double the frequency of the alternating field.

In common uses of the fluxgate effect such as the fluxgate magnetometer, the fluxgate compass and Electronic Article Surveillance (EAS), very specific ferromagnetic material is chosen and the material is placed either within the coil or very close to the coil that creates the alternating magnetic field. The closeness of the coil and the choice of material results in the alternating magnetic field driving the material into alternating saturation. Under these circumstances, the static field that creates the asymmetry can be extremely minute yet still create an easily detectable effect.

With a coil based detector being used for underground anomalies, we cannot chose the material or utilize such a strong AC field but we can use a larger magnetic field for our static field and we can use more sensitive transducers such as the 24 or 32 bit audio cards that allow us to detect extremely small amounts of the resultant even harmonics.

Instead of using a static field we can use a slow AC field. If the frequency of this is orders of magnitude smaller than the other AC field then it can act as a static DC field that regularly changes its direction. The advantages of doing that is that we then can recognise and differentiate effects that occur as a result of the fluxgate effect and effects of other phenomenons that also cause even harmonics.

The fluxgate effect would result in even harmonics only while the slow AC signal is near it maximum or minimum values and not while is was near its zero value. Further, the resultant even harmonic would have a large phase change with each half of the slow AC cycle. Even harmonics generated from other effects would not be following this pattern.

MULTIPLE COILS

Depth/Distance/Placement Measurements

Utilising traditional analysis based on phase of the primary frequency, the phase effects are relatively impervious to size of anomaly and distance of the anomaly from the coil. This is unlikely to continue to be the case when examining the harmonics and intermodulation frequencies and other effects that can occur due to the various phenomenons. The size of any change in phase or change in amplitude is likely to be related to both the anomalies size (particularly size of surface area) and its distance from the coils. Analysis of characteristics is more likely to give consistent results if the distance from the coils is taken into account.

The size of the effect decreases very fast with depth or distance from the coils. A second coil can be installed at a small height above the standard coils. An anomaly at a considerable distance from both coils will have have proportionally similar effect on both coils as the difference in distance from the coils is a small proportion of the total distance. An anomaly close to the coils will have a proportionally greater difference in its effects between the coils at different heights.

In principle, multiple coils provides a precise way to measure distance of an anomaly from the coils. Mathematical equations for distance from coil are relatively complex. They depend on size of coil and act differently in the area close to the coils where the effect is related to each side of the coil and deeper where the coils act more like single point sources. Equations are given in various papers within the technical literature but these generally only relate to anomalies directly under the coil. Implementation of distance calculations is likely to be easier through the use of lookup tables.

Calculation of magnetic feild at a distance from a loop by use of the Biot-Savart law are shown at the following link:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c3

As distance calculations are not the same for an anomaly near but not under the coils as for an anomaly directly under the coils, the algorithm can be greatly improved by having information on the position of the anomaly. This can be achieved by either changing the near ground Transmit coil to three coils or changing the near ground Receive coil to three coils.

Any of the additional coils, either as used for height above the standard coils or those used for position, can be an additional Transmit Coil, transmitting a different frequency from other transmit coils. Alternatively, any of the additional coils can be an additional Receive coil, which would be picking up the same frequencies as the other receive coils.

Greater Depth/Smaller Size Anomalies

Multiple coils can also be used to give better results from the point of view of working to a greater depth while at the same time being able to recognise smaller anomalies. Large coils tend to allow detection to a greater depth and give a greater width of coverage. Smaller coils are able to detect smaller near surface anomalies and are better at pin pointing the exact location of an anomaly. A mixture of both could provide the best of both worlds.

Creating an additional perpendicular field

A number of the phenomenons involve magnetic fields perpendicular to other fields such as perpendicular to an electric field. If we wish to use these phenomenons to characterise anomalies then we may need to have a coil at a distance away from the standard coils or perhaps a pair of coils, one to either side of the standard coils.

In some cases the phenomenons effect is seen with a static magnetic field. This could be created with a steady current through a coil or coils. Alternatively, a very slow alternating field can act as a slowly changing static field. If a slow alternating magnetic field is used, responses due to this are easier differentiated from responses from other effects as the response due to the slow alternating field will only occur while that field is there and not while it's changing or, depending on the phenomenons causing it, while that field is changing and not while it is at its maximums and minimums.

Subtracting Out External Interference

One question that this design might look at is whether there is a better way of handling the external interference problem than using shielding. An alternative to shielding from interference from outside radiation is to try to counteract the ambient electromagnetic noise by measuring it and reversing it out.

Magnetometers often utilise two transducers with one held above the user to measure the ambient magnetic field so that this can be subtracted from the values being measured by the transducer near the ground. An additional coil at a height above the Transmit and Receive coils could be used in a similar way for a otherwise standard Induction Balance detector.

The subtracting out of the external interference can be done by inputting it on a different channel of the audio card and then using the computer to subtract it from the regular PCM stream. Alternatively, it can be inverted and added in the interface electronics previous to either signal going to the audio card.

Array of Coils used for Imaging

Use of a large number of coils is generally referred to as an array of coils. It's possible using such an array of coils to provide imaging of underground anomalies. This is projected to be a later project for the Humanise.org. See our Provisional Roadmap at http://humanise.org/demining/roadmap