  Precision laser spectroscopy is key to many developments in atomic and
molecular physics and the advancement of related technologies such as atomic
clocks and sensors. However, in important spectroscopic scenarios, such as
astronomy and remote sensing, the light is of thermal origin and
interferometric or diffractive spectrometers typically replace laser
spectroscopy. In this work, we employ laser-based heterodyne radiometry to
measure incoherent light sources in the near-infrared and introduce techniques
for absolute frequency calibration with a laser frequency comb. Measuring the
solar continuum, we obtain a signal-to-noise ratio that matches the fundamental
quantum-limited prediction given by the thermal photon distribution and our
system's efficiency, bandwidth, and averaging time. With resolving power
R~1,000,000 we determine the center frequency of an iron line in the solar
spectrum to sub-MHz absolute frequency uncertainty in under 10 minutes, a
fractional precision 1/4000 the linewidth. Additionally, we propose concepts
that take advantage of refractive beam shaping to decrease the effects of
pointing instabilities by 100x, and of frequency comb multiplexing to increase
data acquisition rates and spectral bandwidths by comparable factors. Taken
together, our work brings the power of telecommunications photonics and the
precision of frequency comb metrology to laser heterodyne radiometry, with
implications for solar and astronomical spectroscopy, remote sensing, and
precise Doppler velocimetry.
