Emperor
The first Austrian Emperor was the last Holy Roman Emperor Francis II. In the face of aggressions by Napoleon, Francis feared for the future of the Holy Roman Empire. He wished to maintain his and his family's Imperial status in the event that the Holy Roman Empire should be dissolved, as it indeed was in 1806 when an Austrian-led army suffered a humiliating defeat at the Battle of Austerlitz. After which, the victorious Napoleon proceeded to dismantle the old "Reich" by severing a good portion from the empire and turning it into a separate Confederation of the Rhine. With the size of his imperial realm significantly reduced, Francis II, "Holy Roman Emperor" became Francis I, "Emperor of Austria". The new imperial title may have sounded less prestigious than the old one, but Francis' dynasty continued to rule from Austria and a Habsburg monarch was still an emperor ("Kaiser"), and not just merely a king ("König"), in name.
Roman emperor
This line of Emperors lasted until 1806 when Francis II dissolved the Empire during the Napoleonic Wars. Despite the existence of later potentates styling themselves "emperor", such as the Napoleons, the Habsburg Emperors of Austria, and the Hohenzollern heads of the German Reich, this marked the end of the Western Empire. Although there is a living heir, Karl von Habsburg, to the Habsburg dynasty, as well as a Pope and pretenders to the positions of the electors, and although all the medieval coronation regalia are still preserved in Austria, the legal abolition of all aristocratic prerogatives of the former electors and the imposition of republican constitutions in Germany and Austria render quite remote any potential for a revival of the Holy Roman Empire.