Even the waiter is bemused. “Will Ms Lange be coming back?” he asks, eyeing the cutlery resting on a not-quite-demolished plate of beetroot salad. No, actually. She left the restaurant so fast that I’m worried for her health – or at least her manners. I had my fork in my mouth when she checked her watch and said in her soft, drawly voice: “Well, it’s 10 to 7. I’ve got to meet my daughter. Sorry to eat and run.” Then, shyly, “I hope there wasn’t anything else,” as she gathered her things. I was still chewing my mouthful of frisee salad when she kissed me fragrantly goodbye. I sat back down, gaping slightly. Then I realised. The past 80 minutes has been leading up to this point.

She pushes through the heavy glass door, and is greeted like an old friend by the staff at Knickerbocker Bar & Grill in Greenwich Village, New York. I’m waiting at a corner table described by the waitress as “Jessica’s usual”. The restaurant is dim and chilly, almost empty, but outside the August air is thick and the streets are crammed with noisy students from nearby NYU. As she crosses the restaurant in expensive-looking heels, a black sweater and blue jeans, her smile cools to the professional greeting she clearly saves for journalists. We shake hands as she slides into the booth opposite me.

“Hello. Nice to meet you,” she says, smiling the white smile. She seems wary – the brown, ringless hands giving her away. They’re never still, self-consciously brushing back her fine shoulder-length hair, first this hand, then that, then both. She fiddles constantly: gesticulating as she speaks, straightening the cutlery, opening and refolding the napkin, then back to combing her hair. When she touches the too-smooth forehead the hands betray her 59 years. In contrast, her lovely face, bare of make-up, is almost lineless.

I had suggested that we meet at the Museum of Modern Art, which has an outstanding photography collection, but that was politely resisted by her office – it seems you don’t suggest to Ms Lange. She moved the date of our interview three times, and the time twice. She also chose the restaurant, a few blocks from her home. I discover she’s done publicity interviews for films here before, probably at the same table. There’s a sense she’s going through familiar motions.

We’re here today because she’s releasing a book: 50 Photographs by Jessica Lange. Photography has been a lifelong interest of hers, less celebrated than her acting but perhaps closer to her heart, something in between a hobby and a compulsion. “I wouldn’t call it a hobby; it’s more than that, but it’s not something I look to do professionally, which is nice because it takes the pressure off,” she says. “I remember going through boxes of photographs, even as a child, and being intrigued by them – that ability to capture a fleeting instant on film as a record of time and space.”

Lange has always collected photography, particularly Josef Koudelka and Henri Cartier-Bresson, and takes her camera on all her travels, but she has never exhibited her work. She’s excited about the book – her first – and beams as she talks about it. “I always took photographs without any intention of showing or publishing them. There was no endgame for me – I just love taking photographs. You have this kind of relationship, this communion with the camera. It’s all about what you see. It’s not a performance.”

Is it a relief to find herself the other side of the lens? “It’s the perfect counterpoint to working in film or theatre because it’s so solitary. I love it. I love the anonymity, where you’re just… watching, not being watched, you know?” She looks at me and narrows her feline eyes, trying to gauge my understanding, and continues: “Which, of course, is all I’m used to – it’s the essence of acting.”

Does it bother her being looked at? “Well, I’m quite shy by nature,” she says. I point out that acting is an odd career choice for someone who is shy of the public gaze. “I know. But the great thing about acting is that it’s not you. It’s a disguise, a masquerade. You’re pretending to be someone else. It’s what made it easy for me.” She lowers her eyes again, twirls the straw in her iced tea, and I wonder if Jessica Lange is wearing her disguise this afternoon.

Lange was born in 1949, the third of four children, and grew up in Cloquet, Minnesota. She has spoken frequently about her late, larger-than-life father, who encouraged her to be independent and whose approval she desperately sought as a child. “With my father, nothing I did was ever good enough,” she has said. “With my mother, everything I did was enchanted. What I got somewhere in between was a real strong sense of myself. The ability to remove myself when things got tough was my survival technique.”

In 1967, aged 18, Lange won a scholarship to study photography at the University of Minnesota. While there she felt oddly dissatisfied – “Yearning, and I didn’t know what I yearned for.” So she left in the middle of term with her boyfriend and tutor, the Spanish photographer Paco Grande. Without telling her parents, Lange travelled with Grande to Europe and arrived in Paris in May 1968 during the student riots. “I thought, ‘This is so exciting. It’s where I want to be’.” She lived a bohemian fairy tale, hanging out with an elite band of photographers and artists, and trained as a mime artist. She and Grande married in 1970, but Lange has said she “never took marriage seriously”.

As the relationship became increasingly troubled, Lange felt herself “drawn towards acting, that flight into the imagination where you can turn the fantasy into reality”. She returned to the US and waited tables in New York while she launched herself as an actress and model.

Does she regret giving up on photography as a career? “It wasn’t something I was serious about then, and I wish I had been,” she says. “In Paris I was in the company of some of the greatest photographers of the time – Robert Frank, Danny Lyon. It wasn’t that I was put off or intimidated – I just didn’t have the passion for it that they did. I wish I had; it would’ve been great to have been paying attention.”

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