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Depth Gauge And The Physics Of It

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Metal detectors often seem to have a 'Depth Gauge'.  How is it calculated? Is it the strength (or inverse of it) of the amplitude of the return signal?  So, for instance, everything else being equal, the 'deep' target would mean either a stronger target at greater depth or a weaker shallow target?

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"Is it the strength of the amplitude of the return signal?"

Yes, it's based on the change in signal strength as the target is swept over. It's not the total signal strength, as that will obviously include the continuous signal from the ground ( and the continuous coil signal that every coil creates due to imperfect nulling of the wires ).

The signal strength varies quite dramatically with the depth of the target. If you're mathematically skilled, a fair practical approximation is that signal strength varies with the inverse 5.5th power of the distance from the coil. This means, for example, that increasing target depth by just 15% (eg. 7" to 8" ) causes the target signal to fall 50%.

I assume you're actually referring to the 'on-the-fly' depth gauge than many machines have, the 'Shallow/Medium/Deep' bar-graph? They will just use a simple number comparator system. If signal-strength is more than xx, show the shallow bar, etc.
If you were talking about the depth indicator in pinpoint mode, it may be the same system, but extended to 16 levels etc, so a signal that's more than '100' and less than '135' would result in '7' being displayed to indicate 7 inches.

Obviously all these scales/bargraphs need some kind of 'calibration standard' target for accuracy ..... and there isn't one. Surprise surprise. It's generally considered that a 'medium-sized' coin is appropriate, something like a USA 5 cent  seems a fair example.
My Fisher F75 has a surprisingly accurate pinpoint-mode depth gauge. I've investigated its calibration, with coins like US 5c and 1c , and it gives very straight-line graphs for 'indicated' vs 'actual' depth. The F75 does most of its signal processing inside a DSP microcontroller, so can presumably perform quite precise and repeatable assessment of strength. Plus, you would typically move the coil slowly in pinpoint-mode, so it may do more signal averaging, to cut down noise and create a more stable reading.

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