[1] Born in Sønderborg in the south of Jutland, Hansen attended the Technical School in Odense before studying painting under Aksel Jørgensen at the Royal Danish Academy of Fine Arts from 1950 to 1954.
He travelled to Italy on a study trip in 1951 and went to France, Spain and North Africa in 1953.
[2] His work in the 1950s was inspired by Jørgensen and Erik Hoppe, leading to dark earthy tones though his landscapes tended towards shades of red and orange.
[2] Many of his works contain motifs such as clowns, skulls, masks and boats, all covered in a naturalistic mode, sometimes approaching a non-figurative style.
Carstensen has also worked with stained glass mosaics (for example in the theatre in Sønderborg) as well as an illustrator.