  Raman scattering cross sections depend on photon polarization. In the
cuprates nodal and antinodal directions are weighted more strongly in $B_{2g}$
and $B_{1g}$ symmetry, respectively. On the other hand in angle-resolved
photoemission spectroscopy (ARPES), electronic properties are measured along
well-defined directions in momentum space rather than their weighted averages.
In contrast, the optical conductivity involves a momentum average over the
entire Brillouin zone. Newly measured Raman response data on high-quality
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single crystals up to high energies have
been inverted using a modified maximum entropy inversion technique to extract
from $B_{1g}$ and $B_{2g}$ Raman data corresponding electron-boson spectral
densities (glue) are compared to the results obtained with known ARPES and
optical inversions. We find that the $B_{2g}$ spectrum agrees qualitatively
with nodal direction ARPES while the $B_{1g}$ looks more like the optical
spectrum. A large peak around $30 - 40\,$meV in $B_{1g}$, much less prominent
in $B_{2g}$, is taken as support for the importance of $(\pi,\pi)$ scattering
at this frequency.
