  We report the development of a method for eliminating background-induced
systematic shifts affecting precise measurements of saturation absorption
signals. With this technique, we measured the absolute frequency of the
$6s^2~^1\text{S}_0 \to 6s6p~^3\text{P}_1$ transition in $^{201a}\text{Hg}$
($F=3/2\to F'=5/2$) to be $1181541111051(83)$~kHz. The measurement was
referenced with an optical frequency comb synchronized to the frequency of the
local representation of the UTC. This specific atomic line is situated on the
steep slope of the Doppler background at room temperature, which results in
frequency systematic shift. We determined the dependence of this shift on the
properties of both the spectral line and the background of the measured signal.
