WFS

Practical constraints prevented Snow from pursuing "full WFS"

He used only a few loudspeakers (3), but laid the theorietical framework

"The acoustic curtain"

“The myriad loudspeakers of the screen, acting as point sources of sound identical with the sound heard by the microphones, would project a true copy of the original sound into the listening area. The observer would then employ ordinary binaural listening, and his ears would be stimulated by sounds identical to those he would hav e heard coming from the original sound source .” (Snow, 1953)

A.J. Berkhout. A holographic approach to acoustic control. Journal of the Audio Engineering Society,36:977–995, December 1988.

Berkhout developed the theoritcal basis for "acoustical holography" applied to seismology

The sound scene does not depend on listening position, because the whole sound field corresponding to the scene is rendered

It doesn't rely on psychoacoustic "tricks"

The relative acoustic perspective adjusts with listener movement. Acoustical analog to motion parallax

Huygen's theorem

Kirchhoff-Helmholz integral

Rayleigh integrals

Discretization

Reduction to a line

Driving function

In practice the dipoles are removed from the KH integral, leaving only monopoles

Also, there is no need to compensate the soundfield outside the rendering volume, which also simplifies some calculations.

Source

Non-focusing

Focusing

Artifacts

Playback

Sound element Spatializer (SES)

WFSCollider

Swonder

Spat

SSR

WFS desginer

SFS toolbox