  Transit spectroscopy is one of the most commonly used techniques for
exoplanet atmosphere characterisation. This technique has been used to detect
ionized and neutral species in exoplanet atmospheres by comparing the observed
stellar lines in and out of transit. The centre-to-limb variation (CLV) of the
stellar lines across the stellar disk is an important effect for transmission
spectroscopy, since it results in a change of stellar line depth when the
planet transits different parts of the stellar disk. We reanalyse the transit
data of HD 189733b taken with the HARPS spectrograph to study the CLV effect
during transit. The transmission light curve of the Na i D line so obtained
shows a clear imprint of the CLV effect. We use a one-dimensional non-LTE
stellar spectral model to simulate the CLV effect. After applying the
correction, the measurement of the Na i absorption in the atmosphere of HD
189733b becomes better determined. We compare the CLV effect of HD 189733b to
that of HD 209458b. The CLV effects are different for these two benchmark
planetary systems and this is attributed to their different stellar effective
temperatures and transit impact parameters. We then explore the general CLV
effect that occurs during exoplanet transits. Normally, a star with a lower
effective temperature exhibits a stronger CLV effect and its CLV feature
extends over a relatively broad wavelength range. The transit impact parameter
(b) describes the transit trajectory on the stellar disk and thus determines
the actual manifestation of the CLV effect. We introduce a b-diagram which
describes the behavior of the CLV effect as the function of different impact
parameters. With improving observational precision, a careful modeling and
correction of the CLV effect is necessary for exoplanet atmosphere
characterisation using transit spectroscopy.
