We developed a far-infrared Fabry-Perot filter constructed from a sing
le silicon substrate. The limiting resolving power caused by beam dive
rgence of a silicon-gap Fabry-Perot filter is approximately 10 times h
igher than that of a vacuum-gap Fabry-Perot filter because of the larg
e index of refraction of silicon. The filter thus permits compact, hig
h-throughput optical systems. Metal mesh patterns microlithographed on
each face provide enhanced, wavelength-dependent face reflectivity. W
e tested the performance of filters with metal mesh patterns consistin
g of inductive crosses and capacitive squares. A Fabry-Perot filter de
veloped for a rocketborne astrophysics experiment with a capacitive sq
uare metal mesh pattern achieves a resolving power of lambda/Delta lam
bda(FWHM) = 160 at lambda = 158 mu m, with a peak transmittance of 37%
over an active aperture of 6.9 mm for an f/3.8 optical beam at 15 deg
rees incidence. The absorptivity of a 240-mu m thick silicon substrate
patterned with capacitive metal mesh is A less than or similar to 1%
per pass, including loss in both the silicon and the metal mesh.