Thankfully, although it's a fatal blow to absolute sonic realism, realization of the illusory nature of stereophonic reproduction doesn't inhibit the willing suspension of disbelief necessary for our sonic enjoyment.
With regards to what's actually going on, can anyone here point me to any polar measurements of actual M/S arrays? Not the ubiquitous theoretical plots, but measurements made from real microphones setup in actual M/S implementations, showing the deviations from the idealized plots?
Closest I've ever found was this paper:
A More Realistic View of Mid/Side Stereophony by Trevor Owen de Clercq -
http://www.midside.com/pdf/nyu/masters_thesis.pdfThat paper contains polar plots of the L/R output of M/S arrays using the Neumann KM100 series, two U89, and the SM69. I was very excited when I came across it years ago. However, my excitement was greatly diminished when I discovered the data was not sourced from actual measurements of real-world M/S setups using those microphones, but rather mathematically extrapolated from the published polar plots for each microphone capsule/pattern. The results estimate the M/S polar distortions due to variations in the individual polars of each of the microphones in combination, but the calculations still assume perfect coincidence. Because of that, they do not reflect actual real-world implementations which are not, and can never be perfectly coincident. Realworld measurements are likely to be further distorted in pattern, especially at high frequencies.
Here's the relevant quote from the above linked paper concerning it's methodology-
The data used to calculate these sum and difference polar patterns versus frequency response graphs was extracted from the polar patterns freely available for download at Neumann’s English web site: http://www.neumann.com. Each gif file was opened in Photoshop to make exact measurements. At ten degree intervals, the decibel reduction (calculated in pixels) for each test frequency was recorded. This data was then mapped onto a 0 – 1 scale for use in number crunching programs. The result was a 19 X 8 matrix with each row representing a different test frequency (starting with 125 Hz) and each column representing a different angle of sound incidence (starting at zero degrees). The compiled data is available in the appendix. All Mid/Side to Left/Right conversions of this data were conducted in the FORTRAN programming environment of MATLAB. With MATLAB, advertised as numerical visualization software, the resulting matrixes of Left/Right information could be easily graphed on a polar plot with separation for individual frequencies.