We derive an analytic formula for the transmittance of a dielectric la
mella when the interference between successive internal reflections is
only partially spatially coherent. This allows effects such as surfac
e roughness and nonparallelism, which produce cumulative distortions i
n the phase front with each reflection, and which result in a loss of
fringe contrast at high frequencies, to be accounted for quantitativel
y. The transmittance of a Si lamella, measured with a Fourier-transfor
m interferometer over the range 20 to 1000 cm(-1), agrees with our for
mula to within the accuracy of the data, which is dominated by systema
tic instrumental effects.