“M-maybe he became ill and couldn’t leave the studio!” frets the long-lashed, slender-fingered blonde in black outlines, flat colour surfaces and Ben Day dots in Roy Lichtenstein’s “M-Maybe – a Girl’s Picture”. Since Peter and Irene Ludwig bought this painting in 1968, its dime-comic heroine has been known as “the Mona Lisa of Cologne” and is the trademark of the city’s Ludwig Museum, which owns the greatest collection of American pop art outside the US. Standing between the Rhine, the looming gothic cathedral and the cavernous railway station with its Eau de Cologne neon signs, this museum always impresses with its upbeat contemporary approach. Its current show Roy Lichtenstein: Art as Motif is a model of cool wit and understated scholarship, and almost every room made me laugh out loud.

Famously, Lichtenstein brought cartoon imagery into high art, combining banal subject matter with formal discipline, a flair for composition, and visual unity. In “M-Maybe” you empathise with a series of abstract marks which, put in context, read in an economical, shorthand way as “girl”. Such glamorous-yet-distressed icons of 1960s metropolitan life have always been Lichtenstein’s most popular works. In a recent interview with Jeff Koons, Lichtenstein’s widow Dorothy recalled that “Roy adored women. He was optimistic and positive ... and he did have a lot of empathy ... he had many friends who were troubled. He may even have picked these women because he was so reserved in his own being that this was a way of latching on to the emotional highs and lows of life.”

That reserve-yet-sympathy – something shared, crucially, with Warhol, America’s other great pop pioneer – was essential to Lichtenstein’s entire project, and it is his cerebral, measured, erudite side that this show explores. Complementing the classic comic-book paintings and sculpture – “Takka Takka”, “Mad Scientist”, the bold ceramic “Blonde” – in its permanent collection, the Ludwig has borrowed some hundred works to show how, from the early 1960s, Lichtenstein evolved a new pictorial language using art history itself as a motif.

“Bet you can’t paint as good as that,” one of his sons challenged in the late 1950s, pointing to a Mickey Mouse comic. Lichtenstein responded with ink drawings in abstract expressionist style incorporating Mickey and Donald Duck. The absurdity and impersonality of pop was a vital correction to the high seriousness of Pollock and Co., but Lichtenstein from the start balanced dumb subjects with intellectual pleasures of appropriation and manipulation.

“Golf Ball” (1962) depicts a dimpled black and white sphere on a grey ground – an everyday object which, thus abstracted, recalls certain Mondrian black and white compositions. The game is to test our sense of realism – Lichtenstein shows representation to be a mere code, a system of signs. Later, the golf ball reappears as a painting on the wall in “Still Life with Goldfish”, a loose transcription in Ben Day dots – so called after Benjamin Day, who invented his printing technique based on systems of dots in 1879 – of a celebrated Matisse still life.

From “Rouen Cathedral, seen at three different times of day” (1969), a green, pink and purple stencil-like triptych after Monet, to “Expressionist Head” (1980), a parody of Kirchner, Lichtenstein’s inventiveness in rendering the refinements of modern art within his signature dot style is often very funny. His monumental version of Carlo Carrà’s small gouache “Red Horseman” is a riff on futurist innovations in conveying movement – the subject too of his own dynamic comic paintings such as the Ludwig’s “Explosion No 1”. “Trompe-l’Oeil with Leger Head and Paintbrush” reminds us how much Lichtenstein owed to the block-like figures of the French modernist. “Girl with Tear” reduces his typical all-American girl, via Dalí, to three elements: blond coiffure, wide almond-shaped eye and giant teardrop.

“Lichtenstein always maintained a very clever irony,” says John Currin in the catalogue here. “People in his paintings are acting out a modernist situation ... [the] bubble caption commenting about it not being a proper modernist painting. He saw that making figurative painting was basically a damned state, or an ironic state, banished from modernity. He was pretty dead on: the future of American figuration is this kind of damned state.” This century’s most fashionable artists – Currin, Koons, Hirst – have generally evolved out of pop, and Lichtenstein holds a special place as an intermediary between their ironies and modernism.

His laboriously handmade depictions of the printed Ben Day code are a paradox that admitted what has since become a truism: our visual experiences are mediated by mechanical reproduction and electronic simulation. “His real heroes”, though, Dorothy Lichtenstein notes, “were Cézanne and Picasso, which is why he felt he had to get beyond the level of his own taste.”

As this show documents, he did so by unpicking and developing the vocabulary shared by the 1950s-60s commercial art of advertising and comics with modernism: Picasso’s light and shade, Matisse’s strong but subtle contours, Mondrian’s primary colours. The results can by dry in their precise artifice, but they are never nostalgic. That is why Lichtenstein still looks especially fresh in historic European museums. Here one is aware that only an American could have so courteously, calmly, generously, definitively smashed European modernism, yet assimilated it into the postwar international aesthetic that continues to influence how art is made and seen now.

Until October 3. www.museenkoeln.de

Copyright The Financial Times Limited 2017. All rights reserved. You may share using our article tools. Please don't cut articles from FT.com and redistribute by email or post to the web.