Calculation instead of trial and error
Opticians at the time tried out lenses by trial and error. Petzval, a professor of mathematics in Vienna, calculated his lens precisely. He was helped by artillerymen lent to him by an archduke, so they could cope with the huge amount of calculation done by hand.
An unlucky deal
The lens was made by Peter Voigtländer, who earned a fortune from it, while Petzval received only a small share. The dispute over the rights troubled him for the rest of his life. His lens, however, was made and copied for another hundred years.
Legacy
Today optics has the Petzval field curvature, there is a crater on the Moon named after him, and modern Petzval lenses for enthusiasts imitate his typical swirly background blur. There is a memorial room dedicated to him in Spišská Belá. See also Photography.