This paper presents a set of Green's functions for Neumann and Dirichl
et boundary conditions for the Helmholtz equation applied to the inter
ior of a cylindrical cavity which are based on evanescent wave expansi
ons instead of the usual normal mode expansions. The evanescent expans
ion capitalizes on the known physics of the shell-fluid interaction, g
iven a cavity with flexible walls, providing a pressure field which de
cays exponentially (in the Limit of small wavelength) into the interio
r of the cavity when the wall vibration is subsonic, Due to this decay
the evanescent Green's functions converge much faster than the conven
tional Green's functions which are built up out of the interior eigenm
odes of a rigid (or pressure release) cavity. Furthermore, these evane
scent Green's functions can be inverted in a fairly straightforward wa
y to provide the foundations for solving the inverse holography proble
m, that is, the reconstruction of the normal surface velocity from a m
easurement of the pressure in tile interior. [S0001-4966(97)05012-1].