  Fourier transform (FT) spectroscopy is a versatile technique for studying the
infrared (IR) optical response of solid-, liquid-, and gas-phase samples. In
standard FT-IR spectrometers, a light beam passing through a Michelson
interferometer is focused onto a sample with condenser optics. This design
enables us to examine relatively small samples, but the large solid angle of
the focused infrared beam makes it difficult to analyze angle-dependent
characteristics. Here we design and construct a high-precision angle-resolved
reflection setup compatible with a commercial FT-IR spectrometer. Our setup
converts the focused beam into an achromatically collimated beam with an angle
dispersion as high as 0.25$^\circ$. The setup also permits us to scan the
incident angle over ~8$^\circ$ across zero (normal incidence). The beam
diameter can be reduced to ~1 mm, which is limited by the sensitivity of an
HgCdTe detector. The small-footprint apparatus is easily installed in an FT-IR
sample chamber. As a demonstration of the capability of our reflection setup we
measure the angle-dependent mid-infrared reflectance of two-dimensional
photonic crystal slabs and determine the in-plane dispersion relation in the
vicinity of the $\Gamma$ point in momentum space. We observe the formation of
photonic Dirac cones, i.e., linear dispersions with an accidental degeneracy at
$\Gamma$, in an ideally designed sample. Our apparatus is useful for
characterizing various systems that have a strong in-plane anisotropy,
including photonic crystal waveguides, plasmonic metasurfaces, and molecular
crystalline films.
