Hemispherical microphone array for capture of sound and radiation pattern
The main problem is how to capture direct sound
in the primary direction of sound radiation regardless its shifting directionality. This can be solved with one of two closely related methods:
- Reposition a single microphone depending on tone to be sampled, positioned to capture direct sound in the known primary radiation direction;
- Uniformly space microphones around the subject, e.g. at the vertices of a polyhedron, to capture sound that can be used to construct an uniform direct sound recording without previous knowledge about the instruments sound radiation pattern.
The first method only require a regular setup for capturing samples but with knowledge about the type of sound field produced by the instrument to be recorded. The second method require a more extensive amount of gear but with the advantage that any type of sound field can be captured without special knowledge about the instrument. Only the second method will be further discussed.
The microphone arrangement will have dual purposes:
- To capture the radiated sound to be processed into an approximated point source;
- To capture the radiation pattern making reconstruction of it possible.
The method require an approximated free-field condition over a reflecting plane to ensure direct sound only capture. A reflecting plane, like concrete, hard wood, parquet or linoleum floor is alright because an orchestra in general lack members with the ability to levitate and move around in the vertical axis. In other words, the distance to the floor is constant and any resulting reflections can be considered part of the approximated point source.
The overall arrangement should not only be limited to capturing of solo instruments, ensembles must work well too, it should just be a matter of scale. The captured ensemble should then be considered as a single instrument on its own.
A source of inspiration is the theory behind the Ambisonics system and its related recording techniques, arrangement of microphone arrays, encoding and decoding of signals. The microphone array itself produce a first set, the A-format, consisting of the signals from the microphone capsules. These signals are not intended to be used without further processing. The A-format is then transformed into the second set of audio signals, the B-format, consisting of the following four signals:
- W, a pressure signal (mono) corresponding to the output from an omni-directional microphone;
- X, the front-to-back directional information, a forward-pointing "figure-of-eight" microphone;
- Y, the side-to-side directional information, a leftward-pointing "figure-of-eight" microphone;
- Z, the up-to-down directional information, an upward-pointing "figure-of-eight" microphone.
Encoding and decoding in the Ambisonics system is thus based on spherical harmonics components.
The basic principle of Ambisonics is in our case being inverted: instead of recording at
one point, we record the
one point. The equivalent of the X
signals can be constructed from pairs of facing cardioid microphones while the W
signal will be constructed from all microphone signals.
Being able to capture a complete sound field is only useful when the recording space provide a completely approximated free-field condition such as in a full anechoic chamber. Because of the hard reflecting floor, acting as an acoustic mirror, any sound radiated downward will be captured as first-order reflections from above. That is actually how such sound is normally heard! So sound reflected by the floor can in practice be considered being part of the upward sound radiation, the floor will become an integrated part of the sampled instrument.
So what is the least number of microphones needed to capture the radiation pattern and to calculate a pressure signal?
As we only have to cover a hemisphere of sound radiation a set of five microphones pointing 90° to each other will be sufficient, one pair of microphones on the x
(front-back) and y
(left-right) axis respectively and one mounted directly from above on the positive z
Encoding is straight forward with the microphones Cartesian representation. A set of signals containing pressure and directionality information are constructed from the signals captured by the uniformly spaced microphones. Sound pressure W
is calculated as the sum of all three signals. The pairs on the x
axis are summed together to create the X
gradient signals respectively, while the single microphone on the z axis signal is kept as Z
) + y1
) + z
By combining the WXYZ
signals in various proportions it is possible to derive any number of direct sounds, radiating in any direction. In our case create any "virtual microphone" on the surface of the unit hemisphere.
being the output signal, with A
being angle and elevation, W
the pressure signal and X
By using a hemispherical microphone array it is possible to encode and decode the radiation pattern of a sampled instrument as well as its sound by the use of spherical harmonics components derived from the theory of Ambisonics. The sampled instrument can then either be treated as an omni-directional point source by ignoring the gradients or having "virtual microphones" placed around it on the surface of the unit hemisphere.