Portraits of the artists: Abe Frajndlich turns his lens on the greats of photography

Abe Frajndlich has spent two decades capturing the likenesses of the greats of photography. The results speak volumes about his relationship with his subjects – and their evasiveness when the camera is focused on them

Abe Frajndlich is what you might call a photographer's photographer. And not just because his colleagues admire his work – but because they are his work. For several decades, Frajndlich has turned his camera on the faces of those usually found behind their own. What began as a series of portraits of "Grandes Dames of Photography" for Life in 1988 was picked up and supported with funds from Kodak as an ongoing, globe-trotting project. These portraits have now been published as a book, Penelope's Hungry Eyes. The glossy volume contains more than 100 shots, intimately revealing some of the biggest names in the history of photography, from the other side of the lens.

Frajndlich's background is in English literature, from which he drew that allusive title. He wrote his thesis on Ulysses, deciding that the crucial character in James Joyce's retelling of Homer's Odyssey was the Penelope figure, k Molly. For Frajndlich, Penelope herself has "all these years of waiting [as the faithful wife of Odysseus, abroad at the Trojan War] but simultaneously building this kind of intensity... I jumped from that to the intensity I feel with every photographer – they're always hungry for more pictures."

Of course, Penelope was an arch evader, too: she ducked the advances of numerous suitors during Odysseus's 10-year absence. And Frajndlich's subjects are also slippery creatures – many avoid a direct gaze, opting for closed eyes or turned backs, framing themselves or offering a reflection.

But as much can be revealed by artful evasiveness as by full-frontal honesty, and Frajndlich stages his images to hint at his subjects' idiosyncrasies. Bill Brandt, for example, is seen peering through a magnifying glass, referencing the way Brandt used super-wide-angle lenses to distort the nude figures in his influential photographs of the 1940s.

Frajndlich adds that many photographers he snapped were introverted: "You can gain a passport with a camera in front of your face, but you don't want to be the subject. Some people absolutely refuse to be photographed. I always want to respect these people's own space but at the same time say something that opens up their work, and them."

His portrait of the fashion photographer Louise Dahl-Wolfe is a case in point, with Frajndlich shooting her in the closet of her apartment, "with her clothes, and that wild dress on", as a reference to her own career.

Not everyone played ball, though: Frajndlich wanted the artist Gerhard Richter to lie with his head poking out of his own patterned rug. "He looked at me like, 'Are you crazy? I'm not going to lie in my artwork.'" In the end, he used a secretary instead, Richter standing over her, smoking.

A book, then, that says almost as much about his subjects as it does Frajndlich's own talents. For an odyssey in photography and its arch proponents, set sail here.

'Penelope's Hungry Eyes' by Abe Frajndlich is published by Schirmer/Mosel, priced £49.95