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Jasper Johns is so perplexingly rare a presence in London's art galleries that any exhibition of the 84-year-old American artist's work — in this case Regrets, opening at the Courtauld tomorrow — has to be regarded as an event.

Few living artists have influenced the course of art as profoundly as Johns has done. He’s the last surviving member of that revolutionary New York milieu that also included the composer John Cage, choreographer Merce Cunningham, and Johns’s lover and fellow artist Robert Rauschenberg, all of whom in their different ways brought everyday life and art into closer connection.

Pop art simply wouldn’t have happened without Johns’s iconic Fifties paintings of the American flag, targets and numbers, together with his sculpted beer cans and paintbrushes. Today, few artists command the brush with such flair and fluency as he continues to do. And yet we haven’t had a Johns retrospective in London for close to 25 years, while far lesser painters have been granted the honour.

While we wait for the Tate to wake up, we have this fascinating vignette of an exhibition, dedicated to a recent burst of activity in Johns’s studio in Sharon, Connecticut. It shows that he’s as relentlessly probing and inventive as ever, in intriguing communion with artists in the recent and distant past and confronting mortality with power and wit.

The genesis of this group of works is a battered, stained and torn photograph of Lucian Freud that Johns came across while browsing through a Christie’s auction catalogue. Taken by John Deakin, it was found in Francis Bacon’s studio after the painter’s death.

Bacon, who always worked from photographs rather than life, used Freud’s pose in the image as the basis for his Study for Self-Portrait (1964), joining his own head onto his friend’s body. He regularly melded figures in this way to create a deeper intimacy with his subject (in this case some have read it as a projection of his desire for Freud). Bacon clearly studied the photograph intensely: his paint flecks and smudged fingerprints are all over it.

Freud’s pose in the photo is intriguing and ambiguous: he could be in a moment of existential crisis or simply flicking his hair from his eyes. It clearly inspired Bacon, and has now grabbed Johns. In the 11 works displayed at the Courtauld we see how he dissected it, pushing and pulling its elements with pencil, oil, watercolour and ink.

While Bacon focused on the contents of the photo as he made his self-portrait, Johns’s interest is in the image as an object — the folds, stains and void left by a torn section are as important as Freud’s body, sitting on the bed.

Johns abstracted the photo from the start, creating apparently arbitrary segments of colour, a patchwork of bright hues that recall his 1961 painting of the map of the United States. He then created a mirror image on a separate piece of paper, painting it in watercolour. When he put the two pages together a remarkable thing happened: the image of a skull with an abyss beneath it appeared at the join, like a nightmarish Rorschach blot.

When you look at the original photo you couldn’t imagine this would happen, but there it is, clear as day. Johns has always exploited chance and unconscious events — his Stars and Stripes paintings came to him in a dream — and the skull dominates the rest of this series.

The biographical readings here — an ageing artist working with a picture connected to two artist peers, one recently dead, and finding a skull in the image — are irresistible. In looking to the art of the past Johns has often linked ideas of human mortality with the immortality of artistic creation, but never so nakedly.

His feelings about the British artists are unclear — these are by no means homages. Johns owns a Freud portrait and met Bacon briefly but claims that the photograph itself, and not the artists, were uppermost in his mind when he made them.

But it’s difficult not to see more than this: in two of the works, a large oil painting and a watercolour, he has isolated segments in bold primary colours which form the profile of a new Freud-like figure, who seems to turn towards the skull, as if contemplating his own inevitable death. Perhaps Johns latched onto the skull because, at 84, it reflects his feelings about his own mortality.

But his art has always been elusive. In many ways Bacon and Freud sit at the opposite end of the spectrum to Johns. They are all about visceral human feeling, a direct engagement with the human body and psychology, while Johns’s art is more cerebral and poetic. Freud’s and Bacon’s lives, and particularly Bacon’s homosexuality, are writ large in their work, while Johns largely avoids autobiography and has always refused to discuss his relationship with Rauschenberg.

Indeed, the connection between these pictures and the work of another artist is greater: in the margin of one drawing Johns has written “Goya? Bats? Dreams?”, suggesting he has connected Freud’s pose with Francisco de Goya’s The Sleep of Reason Produces Monsters, depicting an artist slumped, head on hands, surrounded by the winged creatures of his unconscious. It’s as if the skull in Johns’s paintings and drawings is the monster of his figure’s imagination.

But the works are far from morbid. Johns has called the series Regrets, which conjures a mood of ruefulness, but is in fact something of a joke. He used to return unsolicited correspondence stamped with a mock-handwritten message saying “Regrets, Jasper Johns”. While making the first work in the series he found the stamp and pressed it into the corner, and it appears in almost all the works, a small but insistent detail that punctures any sense of melancholy.

The image has given him licence to explore the full range of his artistic powers — from the liquid marbling of ink on plastic to drips, cross-hatches, dashes and zig-zags of oil paint on canvas. Johns clearly kept himself guessing throughout the process, unpacking, reworking and breathing new life into Bacon’s photograph. What makes this small show so rewarding is a sense of joining a modern master on a profound visual journey.

Jasper Johns: Regrets is at the Courtauld, WC2 (020 7848 2526, courtauld.ac.uk), from tomorrow to December 14.