Context : Discovered in the last decade as overdensities of resolved stars , the ultra-faint dwarfs ( UFDs ) are among the least luminous , most dark-matter dominated , and most metal-poor galaxies known today .
They appear as sparse , loose objects with high mass-to-light ratios .
Hercules is the prototype of the UFD galaxies .
To date , there are still no firm constraints on its total luminosity due to the difficulty of disentangling Hercules bona-fide stars from the severe Galactic field contamination .

Aims : To better constrain Hercules properties , we aim at removing foreground and background contaminants in the galaxy field using the proper motions of the Milky Way stars and the colour-colour diagram .

Methods : We have obtained images of Hercules in the r _ { Sloan } , B _ { Bessel } and U _ { spec } bands with the Large Binocular Telescope ( LBT ) and LBC-BIN mode capabilities .
The r _ { Sloan } new dataset combined with data from the LBT archive span a time baseline of about 5 yr , allowing us to measure proper motions of stars in the Hercules direction for the first time .
The U _ { spec } data along with existing LBT photometry allowed us to use colour-colour diagram to further remove the field contamination .

Results : Thanks to a highly-accurate procedure to derive the r _ { Sloan } -filter geometric distortion solution for the LBC-red , we were able to measure stellar relative proper motions to a precision of better than 5 mas yr ^ { -1 } down to r _ { Sloan } \simeq 22 mag and disentangle a significant fraction ( > 90 % ) of Milky Way contaminants .
We ended up with a sample of 528 sources distributed over a large portion of the galaxy body ( \sim 0.12 deg ^ { 2 } ) .
Of these sources , 171 turned out to be background galaxies and additional foreground stars from the analysis of the U _ { spec } - B _ { Bessel } vs . B _ { Bessel } - r _ { Sloan } colour-colour diagram .
This leaves us with a sample of 357 likely members of the Hercules UFD .
We compared the cleaned colour-magnitude diagram ( CMD ) with evolutionary models and synthetic CMDs , confirming the presence in Hercules of an old population ( t = 12 \pm 2 Gyr ) with wide spread metallicity ( -3.3 < [ Fe/H ] < -1.8 ) .

Conclusions : Our procedure to estimate star proper motions proved to be a very effective way to identify likely members for stellar systems as far as 130 kpc .
The present selection , based on both proper motions and colour-colour diagram , provides a robust identification of Hercules members and a new target list for more spectroscopic investigations .