Metal imaging system

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I'm trying to prototype a metal detector that uses "high" resolution images instead of sound to detect metal.

Cut out the meaningless jargon, and put the words in the right order.
You're trying to form images from an array of sensors that, like most metal detectors, do not involve sound.
Yes?

If you think I'm on the right track,

Sorry I don't.
Lots of things wrong.
For a start a Hall effect sensor will not detect metal. It measures magnetic fields. You might think you get a magnetic field variation in the presence of metal but first off it only works with magnetic metals, iron, nickle and cobalt, it will not work with other metals like copper, zinc, gold, silver, lead, tin and so on. Second the amount of interaction you get between a lump of metal and the Earth's magnetic field is too small to detect with a Hall effect sensor. You need a flux gate magnetometer.

Traditional metal detectors work by sending an electro magnetic field into the ground and picking up disturbances in that field. That works with all metals and in fact all conducting materials.

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Having lots of tiny coils is not going to do anything for you. What happens is that they will all cross couple and you will get the same signal from each coil.
This is why they don't use this method for detecting metal.

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The first step for you is to develop the working sensor, then deal with how to control it from the arduino. Once you have one sensor working, you can look at the possibility of adding more.

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A CD4051 is the bog standard analog multiplexer such as in the patent circuit.

Just hook up one coil or one hall effect sensor and get a feel for how it works. I think you will be disappointed at the range if you can get anything out of the set up at all.
Yes I have worked with eddy current flaw detectors for tubes, those coils are huge and the current was large.l I am talking about 40A coil current with a range of a few mm.

I made a Proton precession magnetometer some years back, before the days of Arduino, when micros were black magic.

They are a lot of work to make, but evidently have a good range.

I dont think you could have an array of them, but you could use a single one to scan a surface ( mine was to scan a beach for treasure shipwreck, but they found the wreck before I finsihed my project, so I dumped it )

At what kind of speed do you want to get your results? You may be better off getting multiple channel external adc's and use spi, then you'll be able to sample faster and do other things while the adcs sample,

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aaronadams3:
My biggest problem is how to plug hundreds of sensors into the arduino.

I suggest you need to get one sensor working and show that it does what you want before you worry about the practicalities of making a hundred of them.

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What sort of effect are you expecting to measure after a second?

aaronadams3:
I put a piece of metal in the cup to pick up the current and hopefully hold the charge long enough for the AO wire to measure a voltage.

Is this a recognised detection technique? It does not strike me as a particularly promising approach.