  The infrared spectra of the quasi-two-dimensional organic conductors
$\alpha$-(BEDT-TTF)$_2$$M$Hg(SCN)$_4$ ($M$ = NH$_4$, Rb, Tl) were measured in
the range from 50 to 7000 \cm down to low temperatures in order to explore the
influence of electronic correlations in quarter-filled metals. The
interpretation of electronic spectra was confirmed by measurements of pressure
dependant reflectance of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ at T=300 K. The
signatures of charge order fluctuations become more pronounced when going from
the NH$_4$ salt to Rb and further to Tl compounds. On reducing the temperature,
the metallic character of the optical response in the NH$_4$ and Rb salts
increases, and the effective mass diminishes. For the Tl compound, clear
signatures of charge order are found albeit the metallic properties still
dominate. From the temperature dependence of the electronic scattering rate the
crossover temperature is estimated below which the coherent charge-carriers
response sets in. The observations are in excellent agreement with recent
theoretical predictions for a quarter-filled metallic system close to charge
order.
