The radiation properties of real world loudspeakers must be determined by measurements made on the surface of the sphere previously described. The loudspeaker is placed in a free-field
- an environment that is free of acoustic reflections. A measurement microphone is placed on-axis and in the far-field of the loudspeaker. In the far field the propagating wavefronts are spherical. A measurement distance of 8 meters satisfies the far-field requirement for all but the largest loudspeakers. The impulse response is measured and recorded, and the measurement angle is incremented by the desired angular resolution, typically 5 degrees, and the measurement repeated. This continues until the microphone is 180 degrees off-axis. The series of 37 measurements is referred to as an “arc.” The loudspeaker is returned to the axial position, rotated 5 degrees about its aiming axis, and another arc is collected. The process is repeated until a sufficient number of arcs have been collected to fully characterize the radiation from the
loudspeaker. The exact number of arcs depends on the required number of quadrants, which in turn depends on the acoustical symmetry of the loudspeaker.
The end result, using 5 degree angular resolution, is a set of over 2600 impulse responses. The IRs can be transformed to the frequency domain to yield the transfer function, or frequency response magnitude and phase, for each measurement position. This data is then processed into a set of loudspeaker balloon plots. There is one balloon plot for each 1/n-octave band, but limited to the frequency bands for which geometric acoustic assumptions apply. One octave resolution is generally used for room acoustics work. One-third octave may be used for loudspeaker coverage mapping.
The balloon data is assumed to represent the directional behavior of the device at 1 meter, even though it was measured at 8 m. This assumption is necessary to allow the balloon data to be accurately extrapolated to remote listener positions using the inverse-square law. A software program extrapolates the balloon until it intersects with an audience plane, and then weights the LP using the balloon data. The resultant LP is presented as a coverage map of the audience area.
To fully evaluate the coverage, the process must be repeated for each frequency band of interest. This makes 1/1-octave a practical frequency resolution for sound system design.