  A sensitive high resolution sub-Doppler detecting spectrometer, based on
noise-immune cavity-enhanced optical heterodyne molecular spectrometry
(NICE-OHMS), for trace gas detection of species whose transitions have severe
spectral overlap with abundant concomitant species is presented. It is designed
around a NICE-OHMS instrumentation utilizing balanced detection that provides
shot-noise limited Doppler-broadened detection. By synchronous dithering the
positions of the two cavity mirrors, the effect of residual etalons between the
cavity and other surface in the system could be reduced. An Allan deviation of
the absorption coefficient of coefficient of $2.2 \times 10^{-13}$
$\text{cm}^{-1}$ at 60 s, which, for the targeted transition in
$\text{C}_{2}\text{H}_{2}$, corresponds to a $3\sigma$ detection sensitivity of
130 ppt, is demonstrated. It is shown that despite significant spectral
interference from $\text{CO}_{2}$ at the targeted transition, which precludes
Db detection of $\text{C}_{2}\text{H}_{2}$, acetylene could be detected in
exhaled breath of healthy smokers.
