Women dominate the frame in Man Ray exhibition

It's not that the surrealist photographer Man Ray didn't take pictures of the men he knew. Visit the new exhibition of his portraits at the Scottish National Portrait Gallery in Edinburgh and there they all are, the painters, the writers, the filmmakers, the musicians, the architects, the surrealists; all the nobodies in the act of becoming somebody in 1920s Paris (and beyond). Look one way and there's a fresh-faced Ernest Hemingway in 1923, woollen tie tight to the collar, neat little moustache tight to his lip. Look another and there's Picasso in the same year, hair slicked back like a schoolboy who's having his picture taken. James Joyce, Erik Satie, Arnold Schoenberg, Le Corbusier, they're all here, caught in the silvery light of Man Ray's lens.

But I'm not sure these are the images you will take away with you. It's the women you remember. Kiki De Montparnasse's naked back adorned by facing violin f holes, turning her body into an instrument; Coco Chanel all pearls and cigarette; and again and again, the swan neck and modernist, streamlined beauty of model and photographer Lee Miller.

Man Ray's story can be told through his relationships with women. He nurtured them, encouraged them, seduced them, loved them, objectified them and sometimes tried to control them. And he photographed them. Continuously. Obsessively. He reduced their bodies to torsos or heads, transformed them with surrealist tropes – sometimes deliberate (there's a portrait of Dora Maar, Picasso's lover and herself a photographer, from 1936, a headshot in which tiny ceramic hands are tucked beneath her chin), sometimes accidental (his 1922 portrait of Marchesa Casati is memorable for the unplanned double exposure that gives her two sets of eyes). In short, he displayed his satisfactions on film.

Born Michael Emmanuel Radnitzky in Philadelphia in 1890, he cut up his name (as he would later cut up images) when he was 21, reducing it to Man Ray, the same year he sailed for France and the artistic demi-monde of Montparnasse in Paris where he would meet and mix with many of the 20th century's nascent greats, often taking their portrait for the likes of Vanity Fair, Vogue and Harper's Bazaar.

He met Kiki De Montparnasse in a cafe. By then Kiki was already a familiar Parisian face. A cabaret singer at Le Jockey Bar, she would sing bawdy comic songs and hoist her skirts to show her legs (and sometimes more).

Kiki, orignally Alice Prin, she moved to Paris aged 12, and soon landed her first job binding copies of the Kama Sutra. By the early 1920s she was posing for artists including Chaim Soutine, Andre Derain, Jules Pascin and Per Krogh. She initially resisted Man Ray's request for her to pose for photographs. "But she posed nude, I insisted, and the paintings were always on exhibition, sometimes with her name as the title," Man Ray recalled in his autobiography, Self Portrait. "Well, she replied, a painter could always modify the appearance of things whereas a photograph was too factual. Not mine, I replied."

He did more than modify his photographs of her. He modified Kiki herself. "Man Ray had designed Kiki's face for her," Kiki's friend and contemporary, the novelist Kay Boyle once wrote. "He would begin by shaving her eyebrows off ... and then putting other eyebrows back, in any colour he might have selected for her mask that day."

Man Ray and Kiki were together for six years. She was his lover and his muse. It was an explosive, at times violent relationship (Man Ray writes of being slapped by her and hitting her back), but he also encouraged her when she took an interest in painting. But that famous image of Kiki's naked back, Le Violon d'Ingres – a French expression that means hobby – says much of his attitude towards women. In the picture Kiki is transformed into a plaything.

You can see the same attitudes at play in his relationship with the model Lee Miller. Miller, who had been discovered in New York by Conde Nast himself, sailed to Paris in 1929, aged 22. She said later that she deliberately sought out Man Ray. "He looked like a bull with an extraordinary torso and very dark eyebrows and dark hair," she told Home Journal in 1975. "I said 'My name is Lee Miller, and I'm your new student.' Man said, 'I don't have students.' He was leaving for Biarritz the next day, and I said, 'So am I.' I never looked back." She was 17 years his junior.

"To begin with, it was extremely volatile," explains Antony Penrose, Miller's son. "They were absolutely passionate about each other and adored each other. It was an unlikely match. People would say openly, 'What do you see in Man Ray? He's little, he's ugly and he's Jewish.' And she would say, in fact I know that she said this, 'It's not always the good-looking ones that you want to sleep with.' So it was a very unlikely relationship. But it was one that had a kind of catalytic quality. They both sparked each other. She was brilliant at getting him to produce the best he could."

Miller represented something new to Man Ray. "She was," according to her biographer Carolyn Burke, "the incarnation of that provocative French figure, the garconne, an independent young woman who plans to enjoy her freedom."

She brought to the role a New World self-assurance. And that was part of her appeal to Man Ray. She embodied the present. There's a portrait of her in the exhibition from 1929, a tightly cropped image from just behind her shoulders in which she leans forward, eyes closed, an art deco hood ornament in flesh and blood.

And, like Kiki and another lover, the artist Meret Oppenheim – whom he'd photograph in the early 1930s naked beside a printing press, the ink covering her forearm and hand, and matching the colour of her pubic and underarm hair – Miller, in Man Ray's work, became an object of desire. Sometimes through a darkened lens.

"When you look at some of the images he took of her she was always snipped up. He'd shear her head off or just photograph her breasts or something that was reductive," says Penrose, "as though that was a way of getting control over her."

And that desire stretched beyond the frame. Which was a problem for Miller, who felt she should live like the men who surrounded her. "She didn't see why she shouldn't have the same freedoms as the men and go to bed with whoever she wanted," explains Penrose, "and he thought very differently. He wanted to marry her, he wanted to have the exclusivity on her, and she wasn't going to stand for that."

And yet, also like Kiki, he encouraged Miller's creative side. And there was much to encourage. Miller would later become one of the great war photographers, applying her Man Ray-inspired surrealist eye to what she saw in the London Blitz. For the three years they were together, she was instrumental in Man Ray's work. He let her print his images and it was she who made the accidental discovery of the solarisation process, that resulted in a partial reversal of black and whites – a process that became one of Man Ray's trademarks.

"I think the key thing was the way they both understood the other's creativity and encouraged each other," says Penrose. "Not only then, when they were young and ardent, but much later. Man Ray was one of the people who understood Lee the best and he remained supportive of her."

But by 1932 their creative alliance was being ground down by his carnal jealousy. "He wanted to control her and to have her only to himself and she was not about to be controlled by anybody," says Penrose.

He sent her a final demand: "You must arrange to live as my wife, married or not." She ignored him. She then picked up one of his discarded negatives from the bin, cropped it and made it her own work. Infuriated by this he threw her out. She returned to find an image of her neck slashed with a razor and covered in red ink. She bought a one-way ticket to New York. In return, he bought a pistol, not sure if he was going to use it on himself or her. It appears in a self-portrait that also sees him with a rope around his neck and a bottle of poison beside him. It would take another five years before they were reconciled, though in later years, Penrose remembers, they were great friends.

There would be other muses. Oppenheim, then Ady Fidelin and, when he moved back to America, the former dancer Juliet Browner, who would become his wife for 30 years until his death in 1976. In America he returned to painting, but he continued to take photographs.

The last in the exhibition is from 1968, from when he was once again living in Paris; a portrait of Catherine Deneuve in a surrealist set made of items from the artist's studio, with the actress wearing huge earrings, gold-plated whorls that later sold for a five-figure sum at Sotheby's. It was his last magazine assignment.

Almost to the end you could tell Man Ray's story through the women in his life. And in return, he framed theirs. Earlier this year, Deneuve said she only kept one or two images of herself in her home. One of them was Man Ray's.

Man Ray Portraits opens on June 22 and runs until September 8 at the Scottish National Portrait Gallery, Edinburgh, www.nationalgalleries.org