Frequency domain spectroscopy allows an experimenter to establish optical
properties of solids in a wide frequency band including the technically
challenging 10 THz region, and in other bands enables metrological comparison
between competing techniques. We advance a method for extracting the optical
properties of high-index solids using only transmission-mode frequency domain
spectroscopy of plane-parallel Fabry-Perot optical flats. We show that
different data processing techniques yield different kinds of systematic error,
and that some commonly used techniques have inherent systematic errors which
are underappreciated. We use model datasets to cross-compare algorithms in
isolation from experimental errors, and propose a new algorithm which has
qualitatively different systematic errors to its competitors. We show that our
proposal is more robust to experimental non-idealities such as noise or
apodization, and extract the complex refractive index spectrum of crystalline
silicon as a practical example. Finally, we advance the idea that algorithms
are complementary rather than competitive, and should be used together as part
of a toolbox for better metrology.Comment: 21 pages, 11 figures, 4 appendice
