Interferometric etalons are of interest as wavemeters in the visible and the near IR to measure Doppler shifts from laser illuminated moving objects. Signal processing for estimating Doppler shifts is discussed in the context of three etalon-based methods of practical interest: the scanning Fabry-Perot interferometer, the 'edge' method, and the Fizeau interferometer. The semiclassical theory of photodetection is used to model the statistical properties of signal and background noise. Using the probability density functions that tend to govern the signal- and background-induced photocounts, we derive: the theoretical performance limit on unbiased estimators of the signal frequency (Cramer-Rao bound), as well as the maximum likelihood estimators, whose performance may approach this limit. Performance of the estimators is analyzed as a function of signal and background levels for the photocounts statistics. The paper provides a framework for the further development of signal processing theory for etalon wavemeters that operate in the low-light limit of the so-called photocounting regime.