# I Calculating Magnetic Field from FFT Amplitude

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1. Mar 10, 2017

### MxwllsPersuasns

So a little bit of background: I work in an undergraduate lab at UMass Amherst and am currently building/optimizing a faraday magnetometer for use in the Muon g-2 experiment at Fermilab. The magnetometer works as follows. A laser is shone through a crystal with a particular Verdet Constant at the same time the crystal is in a cylinder wrapped with wiring to create a magnetic field of known strength down the central axis of the crystal (the direction of propagation of the light) the resulting light has its plane of polarization rotated by a certain amount (usually something of order 10^-4 radians) which results in a loss of intensity on the two photodetectors which are positioned after a beamsplitter such that each recieves ~50% of the total light. After that we collect the data through a little subtractor circuit and in our DAQ Assist Box where we use labview to analyze and transform the data.

One of the transforms we use is the FFT, to look at the strength of various individual frequencies. For example we have our function generator set to a frequency of 100 Hz, we also know that 15 and 60 Hz signals will be in abundance at Fermilab and need to account for those as well, among other things.

What I want to know how to do is take the amplitude for, say, 60 Hz and be able to calculate the magnetic field from that amplitude. Now I don't need people to explain to me how exactly to calculate the magnetic field per say. Rather if someone could provide me with a notion of how to go from the amplitude of a Fourier Transform at a particular frequency to the Voltage of the signal which came in and was transformed. From there I can work backwards in my calculation of the magnetic field strength. Thanks to all who feel so inclined to answer! :)

2. Mar 10, 2017

### .Scott

In the simplest of cases, the energy at a "bin" in the discrete FFT is equal to the energy of the signal at that frequency. In practice, there is all sorts of scaling both obvious and subtle reasons. For example, the analog-to-digital converted applies a de facto scaling. You may be using a window to reduce aliasing - thus a frequency-dependent scaling. So you can only rely on it being proportional. But all this means is that you will need to do a calibration.

Inject a sine wave of a selected frequency, perform the FFT, and look at the amount of energy in the bins that are affected. There will usually be 2 bins affected - but sometimes 1 or 3. Take the square root of the sum of the squares of the absolute values. When you double the amplitude (voltage) of the sine wave, you will double that value derived from the FFT.