There's a pretty good Flux Loop for professional tape recorders article actually titled "Magnetic Reproducer Equalization Accuracy or Flatter is Fatter" written by Peter Butt that appeared in Recording Engineer Reproducer magazine in the October 1978 issue. He describes using a flux loop to check the overall playback response of the head and repro amp combination. The repro head naturally exhibits a 6 dB/octave rising response due to Faraday's law of magnetic induction. The head is followed by an integrator amplifier which has a -6 dB/octave characteristic which should ideally bring the frequency response back to normal. In fact the integrator response is made to level off to flat at some frequency which corresponds to one of the various international recording equalization standards using an R-C network. The break frequency of the R-C network is numerically referred to using the time constant "tau" =RxC in seconds. He points out the obvious advantages of using a flux loop to check playback response since the results aren't affected by problems like azimuth, skewing, gap loss, gap non-linearity, spacing loss, fringing effects, noise, and contour effects.
The loop he describes uses 30 turns of 30 gage enameled wire, in series with a resistor (nearly equal to the source resistance) and mounted on a non-ferrous frame of fiberglass vector board, shaped into a rectangular vertical loop with the active face placed directly on center with the gap running vertically across the string of pole pieces. The ones I have made were done on blocks of styrofoam which I was easily able to cut into shape to fit closely over the front of the head. A cable of RG58A is attached securely, and to prevent the wires from scratching the head surface you finish it off with a thin safety epoxy coating on the front face. Because of the many different shapes of playback head covers out there, you will probably need to make special ones to get intimate placement for each tape recorder you work on.
Here's a short synopsis of his test procedure:
1. Monitor the playback signal from the repro amp output, not the tape deck line amp outs (they can have additional frequency rolloffs).
2. Position the flux loop for maximum output at 400 Hz.
3. Sweep the test frequencies up to find the Repro peak and just beyond, to make sure you are not clipping.
4. Here you'll need to consult the recommended playback curves for your chosen standard (15 ips NAB, 30 ips AES, EIA or CCIR). Note the expected dB level for 10 kHz with respect to 400 Hz, and adjust the Hi Freq eq to this setting. Also set the Low Freq eq if available and recheck the 10 kHz level.
5. Calculate the expected theoretical standards levels from 10 kHz and above at 1 kHz intervals past the response peak, and compare these to your actual flux loop measurements. If you find a rise, a maximum and a fall that deviates from the ideal response, you have identified a playback head-to-cable resonance that can be corrected by paralleling a proper damping resistance to the head-cable combination. This is a trial and error effort but Mr Butt suggests resistances in the range of 100 kohms to 430 kohms have worked on tape decks from a variety of manufacturers.
As far as obtaining the response curves for the different international standards, I have seen them included in a manual that was printed by the old Standard Tape Laboratory company. I'm not sure if Magnetic Reference Labs also has these curves available on their website, but it sounds like something they would offer there.
Flux loops can also be used in reverse, that is to pick up the magnetic flux coming out of a record head and monitored on an oscilloscope. The recording process is actually linear (unlike the playback event that has the rising 6 dB/octave characteristic) but as with tape playback standards, the various standards may include deviations from this linear recording event. Again, checking with published record and playback standards graphs is a good idea here.