  The advent of the laser frequency comb as the wavelength calibration unit
allows us to measure the radial velocity at $cm\ s^{-1}$ precision level with
high stability in long-term, which enable the possibility of the detection of
Earth-twins around solar-like stars. Recent study shows that the laser
frequency comb can also be used to measure and study the precision of the
instrumental system including the variations of line profile and the systematic
uncertainty and instrumental drift. In this paper, we present the stringent
analysis of a laser frequency comb(LFC) system with 25GHz repetition frequency
on a R$\sim$50,000 spectrograph with the wavelength spanning from 5085\AA \ to
7380\AA. We report a novel fitting model optimized for the comb line profile,
the constrained double Gaussian. The constraint condition is set as
$\left|\mu_{1,2} - \mu \right| <\sqrt{2ln2}\sigma$. We introduce Bayesian
information criterion to test various models. Compared to the traditional
Gaussian model, the CDG(Constrained Double Gaussians) model provides much
better goodness of fit. We apply the CDG model to the observed comb data to
demonstrate the improvement of RV precision with CDG model. We find that the
improvement of CDG model is about 40\%$\sim$60\% for wavelength calibration
precision. We also consider the application to use the LFC and CDG model as a
tool to characterize the line shape variation across the detector. The
motivation of this work is to measure and understand the details of the comb
lines including their asymmetry and behaviors under various conditions, which
plays a significant role in the simultaneous calibration process and
cross-correlation function method to determine the Doppler shift at high
precision level.
