We have collected a considerable amount of measurement data on sound source directivities: https://github.com/AppliedAcousticsChalmers/sound-source-directivities
Most directivity data that are available are incomplete in one way or another. For example, a given directivity might only be available at a limited discrete set of frequencies or along limited contours like circles or the like. This technically prevents the popular spherical harmonic (SH) representations to be computed from the data.
We describe in the article
J. Ahrens and S. Bilbao, “Computation of Spherical Harmonic Representations of Source Directivity Based on the Finite Distance Signature,” IEEE Transactions on Audio, Speech and Language Processing 29, pp. 83-92, 2021 [ pdf ]
how such SH representations can actually be obtained by means of interpolation of the magnitude and manual fitting of a suitable phase. The result are what we term complete directivities, i.e., directivites that are valid at every frequency, angle, and distance. Actually, we even store the directivities in time domain, which is usually not possible with incomplete representations.
A large part of our database bases on measurement data that are publicly available. We also have a considerable data that you cannot find for download anywhere else.