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In general there is a electro magnet that can rotate. Around the outside there are many pick up coils. They are wired in two series strings with the coils alternating around the circumfrence. By measuring the ratio of the signals picked up you can detect position of the rotating coil to a fraction of the distance between the two adjacent coils. The whole system is operated on an AC signal in the electromagnet.
By keeping track of the total rotation, the absolute angle of the rotating coil can be determined. If the system is zeroed at a know position the absolute rotation can be calculated.
You might also want to do a search on LVDT (linear variable differential transformer) which is basically a resolver in a linear form. Its output is in DC form, although it's driven with AC. If you want any good resolution you'll need good low-noise amplifiers and AD converters, among many other things.
Perhaps the way to go would nowadays be to use either an absolute encoder with enough bits or an incremental encoder with enough lines, plus an index signal for accurate reference point calibration.
If you can't achieve enough resolution with an incremental encoder disc, you can probably place another sensor head adjacent to the existing one, plus some XOR logic to double the resolution. The placement of the second sensor head is critical, but it can be done.
One good manufacturer of absolute encoders is Stegmann.
I have found a good book reference on the inductosyns. Analog-Digital Conversion Handbook (third edition) by Analog Devices IC company page 449.
The construction is on one surface a zig zag trace in the shape of the graph of a square wave. On the other surface that moves relative to the first surface is another identicla trace that is much shorter. This forms an air core transformer. As the two surfaces move the coupling changes from zero to plus to zero to minus and back to zero. If the square wave type trace has the zigs and zags closely spaced, several thousand can be put around a circle. There is also another pickup zig zag that is displaced from the fist one by a quarter of the zig zag period.
The Analog Devices signal processing claims to be able to resolve one period of movement into 2^12 parts giving seconds of arc resolution.
You can find the explanation on analog divices .They are producing resolver to digital converters 2S82 , 2S83 ,2S84 which can be used in 10,12,14,16 bit mode and thus can not be compared to encoders.* in resolution I mean 16 bit - 65535 impulses HI)