In a remarkable exhibition at the National Gallery, the late Richard Hamilton, doyen of the Pop Art movement of the 1950s and 1960s, and a leading British artist with an international following, has left a beautiful and startling legacy in an exquisitely executed visual study of the fundamentals of the artist's craft.

When Hamilton died last year, he was working on an exhibition he knew he would never finish. This was to be his valedictory gesture, planned in meticulous detail by the artist himself, and created in the knowledge that he would never see the final exhibition when it opened to the public. Hamilton enjoyed a lifelong engagement with the National Gallery, as a student and later as an influential teacher, and a number of the works in this exhibition are inspired by paintings in the gallery's collection, including a 15th-century Fra Angelico Annunciation and the Arnolfini Portrait. He was also a passionate supporter of free admission to national galleries and museums, and this is one of the reasons he chose the National Gallery to host his final exhibition.

Presented in the Sunley Room, the pictures displayed on stark white walls which allow their subject matter to be seen with even greater clarity, this is an exhibition about the process of making art – an intellectual process for Hamilton. Cool modern interiors, their furnishings redolent of Hamilton's seminal masterpiece of the 1950s, Just what is it that makes today's homes so different, so appealing?, are depicted in rigorous mathematical detail as Hamilton explores single-point perspective and the representation of interior spaces. Seductive and beautiful nude women populate these spaces, whose walls are decorated with representations of works by Marcel Duchamp, Hamilton's artistic hero. These ubiquitous woman are not only objects of desire; they are contemplations of the beauty of the female form, they are the artist's muse, an ancient tradition in Western art, and they are also examples of the artist's experimentation with traditional iconography and the sacred imagery of the Renaissance. For example, in An Annunciation (a), the white lily, a symbol of the Virgin's purity, is replaced with a simple white table lamp. The nudes also connect Hamilton to Marcel Duchamp, in particular The Bride Stripped Bare and Nude Descending a Staircase; Hamilton's take on the latter is a nude reflected in an Art Nouveau mirror (Descending Nude, 2006).

Hamilton also displays his fascination with new technology, in particular the use of the inkjet printer and Photoshop image editing software, which enabled him to conceive of collage and photographic effects in an entirely new way. Hamilton has embraced this digital technology, delighting in its ability to manipulate images and create great subtlety of colours and shadings, while carrying on an ancient artistic traditional of making paintings, no matter how the image is created.

Hamilton was a master technician, obsessed with the "how to" of creating art, and making the production process appear seamless. However, these paintings are not mere exercises in which techniques are refined: many of the pictures are ambiguous, demonstrating an inability to fully communicate one's vision in an artwork, and suggesting a certain temporariness. The subjects may be depicted in graphic detail, but what is Hamilton really trying to say?

The exhibition culminates in a series of preparatory designs for a work based on Balzac's story The Unknown Masterpiece, a tale about the artistic process, which also pays homage to another modernist hero: Balzac's story fascinated Picasso. The Unknown Masterpiece, Balzac (a) + (b) + (c) depicts three masters of painting derived from famous self-portraits: Poussin, Courbet and an aged Titian. All three contemplate a beautiful reclining nude. The images were created on a computer and over-painted by hand, which allowed Hamilton to make ironic connections with the master painters of earlier times in both composition and craft while also considering art, beauty and desire. Taken all together, these three works-in-progress suggest how a final work might have evolved to completion.

Richard Hamilton: The Late Works, at National GalleryFrances Wilson reviews Richard Hamilton: The Late Works at the National Gallery.5