From 'Catholic Encyclopedia': 'Two kinds of canopy are employed in processions of the Blessed Sacrament. One of small dimensions and shaped like an umbrella--except that it is flat and not conical is called an ombrellino. It is provided with a long staff by which it is held'.
Videos from papal solemn Vespers and Te Deum in 2007, 2008, 2009:
And from Corpus Christi Feast (22.05.2008):