Acoustic Holography

Brüel & Kjær has long since been a pioneer in the field of acoustic holography offering solutions both for stationary and non-stationary sound fields.

Spatial Transformation of Sound Fields (STSF)
The name "Spatial Transformation of Sound Fields (STSF)" gives a good indication of the capabilities of the technique. Based on a measurement over a "scan plane" using a microphone array, or a robot positioned row of microphones, close to the sound source, the sound field can be calculated over parallel planes in the near-field region. The measured 2D sound field data can be "transformed" to other surfaces enabling a complete 3D description of the sound field. STSF can calculate any sound field descriptor such as sound pressure, sound intensity, or particle velocity as a function of position. Contribution analysis can be performed so that you can investigate the effects in the far field of changes to the sound source.

Non-stationary STSF
Non-stationary STSF can calculate any sound field descriptor such as sound pressure, sound intensity or particle velocity as a function of position and time. Results are typically displayed as animated maps to illustrate how a specific property changes as a function of time.

Further reading
For a deeper understanding of the theory, mathematics and implementation of STSF read "Nearfield Acoustic Holography (NAH) I - Theory of Generalised Holography and the Development of NAH", by JD Maynard, E.G. Williams and Y. Lee.

And

"Nearfield Acoustic Holography (NAH) II - Holographic Reconstruction Algorithms and Computer Implementation", by W.A. Veronesi and J.D. Maynard.