The two mic noise cancelling idea is well known and very common in many sound applications
-- most notably aircraft comms headsets -- but rarely these days in live sound / PA.
The idea is to have two microphones spaced a short distance apart (something
between 1 and 2 inches usually) in front of the mouth (or whatever the sound source is).
Both mics should be able to hear the sound source directly -- so if they are cardioids
they both need to face the sound source, although this is more usually done with omni mics
in general practice.
The ambient noise, being inherently diffuse sound will be
captured equally in level by both mics -- their near spacing will make no significant
difference to the ambient sound level they capture.
The wanted sound must be
very muich in the nearfield of both mics, but provided the front mic is very close, the
inverse square law of sound energy dispersion means that the slightly more distant mic
will receive significantly less energy of the close sound source than the front mic.
This is also why omni mics are preferred -- because otherwise one mic would have a
stronger bass response because of the proximity effect.
By combining the
outputs of both mics at equal gains but in opposite polarities, the similar level of
ambient noise from each will cancel to a very large degree, whereas the significantly
different levels of the wanted close sound will hardly cancel at all.
There
will be a slight level reduction of wanted sound in comparison to using the close mic on
its own, but given the 30dB+ of ambient noise reduction this is a loss well worth
suffering when working in very noisy conditions.
The physical spacing between
the two mics will affect the frquency response of the wanted close sound because of the
inherent comb filtering such an arrangement creates, but if the distance is only an inch
or so the first comb notch will be well above any significant important component of the
human voice.
..but to return the the original question, this noise cancelling
technique really requires two identical mics spaced a precise distance apart. Most of
those festival photos show dissimilar mics mounted with their capsulesmore or less
coincident -- which lends weight to the suggestion that they were for separate recording
and PA feeds, rather than exotic noise cancelling techniques.
Such techniques
were required for the Grateful Dead because of the unconventional PA arrangaments they
used to employ. I blame John Meyer

Hugh
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Technical Editor, Sound On Sound