The show spans her earliest days with Rolling Stone - then an irreverent, pop stars 'n' dope heads' magazine - through the Reagan years, whose denizens she captured like gaudy butterflies for Vanity Fair, ending with her mature work, altogether more cerebral and pensive. She is pleased with the way her 146 pictures are displayed.
'I love this beautiful, dignified low light for photographs. It's very British. Photography is the study of light, and one of the interesting things about going to Sarajevo was that there was no electricity - so I went back to natural light.' Given the complicated lighting set-ups she normally uses, it was ironic that I found the pictures from Sarajevo the best in the show. She flinched. 'That has a double edge - a bitter-sweet feel to it. Yes, to me they are the most moving pictures. I was trying to crawl back to where I started, the purity of the early work.'
Annie Leibovitz is the highest-paid photographer in the US, capable of earning at least pounds 1m a year. Her style is so famous that she doesn't need to sign her portraits. They lent discreet class to the retail giant Gap, whose clients she photographed for one campaign, and to American Express, for which she did another. Advertisers do not care what she costs. Even at dollars 50,000 a day, she's worth it.
She is very difficult, I was warned, she'll be rude, impatient, arrogant - typical criticisms levelled at successful women. To assistants she is a slave driver, her perfectionism lashing them on to longer days and greater efforts, as she stage manages her shots like one-act plays whose props, costumes and lighting must be flawless. To her subjects she is all charm and persuasion, for they must be cajoled. She is very much in control. I may have been lucky, but she could not have been kinder or more accommodating.
She started using a camera the way most people do, to take photographs of her family. The show begins with pictures of her parents, touching in their affectionate intimacy. One shows her father in profile at the wheel of the family car. 'That's him driving me to the airport after a visit. It's typical of my father that he never talked to me until that ride. Then he'd say, 'When're you gonna get married, Annie? When're you gonna get a real job?' ' She laughs.
Annie Leibovitz is a third-generation American whose great-grandparents were Russian Jews. Her mother grew up in New York in an educated middle-class family. Her father's parents had emigrated from Romania, and his family spoke Yiddish, while he was 'a rough kinda guy' whose prospective in-laws disapproved of his factory job. Annie's parents married despite this opposition and, with the advent of the Second World War, her father joined the air force. When it ended he had a brief spell in business before returning to the air force - 'a very unusual career for someone Jewish' - and having six children. Annie, born in 1949, is the third.
'It was a wonderful upbringing because we got to travel all over the United States, living out of a station wagon. My sister pointed out that my first frame was the car windshield, looking down the highway. My parents let us know we were loved, which is the important thing. You can't get through life without that.' She is still close to her family. Is being Jewish important to her? 'I'm not a practising Jew, but I feel very Jewish.'
Leibovitz expresses herself best through her pictures. Put her in front of them, and she is fluent and informative. Sit her away from them and she starts twiddling her hair and twisting her long, strong hands. Photography is said to be her life, leaving her no time for anything else. Is this true? She frowns and mutters indecipherably, 'Uh-hmm . . .' which could mean yes or no. I wait.
'When one has a career or an art like this, it does dominate your life. It doesn't start at 9am and stop at 6pm. You think about it all the time. This is a wonderful but very demanding life. I can't separate what's personal from what's work. I don't live with anybody but I have some great friendships. I have a great apartment; I collect photographic books and furniture; I love looking at buildings; then there's the studio . . .' Her voice trails away.
She has the strong, clever, austere look of successful Jewish women, such as Susan Sontag, a good friend, Gloria Steinem or Barbra Streisand. Leibovitz is lanky, six feet tall, funnier and more beautiful than most photographs suggest. She wears no make-up and there is no self-portrait in the show. She seems without vanity; perhaps because she has photographed many professional beauties, some ageing ungracefully under layers of 'slap'. She looks anonymous-expensive; her clothes relaxed. She always dresses in black, for simplicity, comfort and understated authority. It's very effective.
Leibovitz started out thinking she was going to be a painter, and attended the San Francisco Art Institute. 'I was a very bad hippie but it was that time in the late Sixties, during Vietnam, when it was pretty confusing to have a father in the military, so I spent a year in Israel on a kibbutz, with the idea that I might not come back. I learnt Hebrew for five or six months; I learnt discipline and the work ethic. It straightened me out; I went back to school and the next semester I submitted my portfolio to Rolling Stone.'
The magazine took her on aged 20 and, in the 13 years that followed, Leibovitz became their chief photographer and the chronicler of the Seventies. She toured with the Rolling Stones, doing what pop people did, sharing their risks and addictions, but always with a camera in one hand. She left behind an incomparable record of sleaze and unmade hotel beds on which are sprawled pop stars, their wives and girlfriends, singed by the hot light of fame.
Leibovitz went on to become the chronicler of the Eighties - a decade she calls 'rich, fat and vulgar'. Together with Tina Brown at Vanity Fair, she created a new look for the magazine that made it essential reading for celebrities and nobodies alike. The middle section of her show displays the icons of that period: Arnold Schwarzenegger, impossibly muscular; the Trumps before their break- up, all glitter, pout and sulk. Most of the famous VF cover-shots are here. But the Nineties are under way, and Leibovitz hopes she has moved on.
The final section of the exhibition starts with three portraits of women with HIV/Aids. Next is a portrait composed of 15 magnetic resonance images: brain scans, which disclose the skull slice by slice. The first small section looks like a foetus with a large ear. Gradually the head grows until the central scan is gnarled and toothy, like an old man or an angry ape. The images dwindle again to a curled up, pearly, new-born skull. It is a quite brilliant rendering of the progress from ape to angel, infant to old crone. The subject is that weird singer-cum-artist in electronics, Laurie Anderson - which is why the rather strange photographs are so apt.
Leibovitz has a huge studio in downtown Manhattan and several assistants, but the ideas behind the portraits are her own and the photographic means often unexpectedly simple. She tries to reproduce what the human eye would see. 'I don't like long lenses, I prefer to retain the human distance.'
Is she tempted to make films?
'I did a series of little films for the Brooklyn Academy of Dance and realised then that the still image is silent; that we work with line and form to create emotion, and that's what makes it so interesting. I actually like the limitations of the still photograph. The mystery of photography: that's enough to work with. I don't have any other ambitions but to figure this out. There are so many variables - light; what your subject is like; and how you interact.
'Jacques-Henri Lartigue was a very big influence on me, because of his longevity. He made me realise the importance of work as a body and that's why I'm completely dedicated to doing it over a lifetime.'
Her detractors call Leibovitz an opportunist. In the Seventies, they point out, she photographed mainly the world of sex and drugs and rock 'n' roll; in the Eighties she photographed the overblown world of the mega-rich and famous. When in the Nineties her work takes on a more serious and reflective note, does this make her a vicar of Bray, turning with each passing phase, or a sensitive barometer of her own times?
'I know that I'm affected by my times - by what I watch on TV and who I talk to. It's not just my eye that goes into it. Your work and art is something you have to take care of. You have to feed it and keep it alive - but what a wonderful thing to do]'
Back to the pictures from Sarajevo. How did she come to take that curving bloodstain like a giant brush-stroke with only a collapsed bicycle and no victim to be seen? 'I was so upset that I thought I was photographing in colour but it was black- and-white film, and about three times over-exposed. We chanced upon it as we were driving along. A mortar went off and three people were killed, including the boy on the bicycle. He was put in the back of our car and died on the way to hospital.
'Sarajevo is unbelievably rich in life and death; a place where the people have no walls, literally, and no skin, and everyone knows exactly who they are. All veneer has been rubbed off and you see a microcosm of life.'
This indeed is what her photographs have always done: stripped off the protective skins to reveal a microcosm of life.
'Annie Leibovitz: Photographs 1970-1990' is at the National Portrait Gallery from tomorrow until 30 May, admission pounds 3.50. The exhibition will be reviewed in the 'Independent' on 9 March.