Leibovitz says she wants to pay homage to the first “Women” project, which culminated in a book published in 1999 of more than 100 photographs she took of women in myriad situations and roles. Sontag, a towering intellect who died in 2004, may or may not have had a romantic relationship with Leibovitz (the two kept the public guessing), but the author of On Photography, among many other books, undoubtedly had a major influence on Leibovitz.

When Sontag first suggested a major collection of portraits of women, Leibovitz was ambivalent, thinking the subject matter was simply too broad. But Sontag’s strong preface in the book shows that the somewhat random list of women was actually one of its main strengths. “This celebration of variety, of individuality, of individuality as style, saps the authority of gender stereotypes, and has become an inexorable counterforce to the bigotry that still denies women more than token access to many occupations and experiences,” she wrote.

The book contains some of the most powerful images Leibovitz has taken: a shocking black and white image of a battered wife; an unforgettable portrait of Leibovitz’s mother, looking pensive. These are testament to her range as a photographer, even if she is best known for the staged, theatrical shots of celebrities for Vanity Fair and Rolling Stone magazines that have earned her a place in the pantheon of great photographers.

In Tokyo, Leibovitz explains to the dozens of journalists and public relations people trailing behind her that the rough-and-ready display of the new portraits is intended to be “democratic”, with no subject being bigger than any other, and is styled as a “pop-up” since it is an “installation” of a still-continuing project focusing on women she admires.

As Johan Jervoe, UBS’s chief marketing officer, explains, the exhibition is just part of the Swiss bank’s multi-year contract with Leibovitz. There’s the global advertising campaign she has shot to help the bank rebrand its image as a caring institution that values diversity, as well as this continuation of the “Women” project. UBS, as “exclusive commissioning partner”, will acquire a number of portraits she takes from 2015 to 2017, the year the global exhibition is expected to make its last stop in Zurich.

Leibovitz says that in Japan, Empress Michiko is on the list of people she wants to photograph. She hasn’t named any potential subjects in Hong Kong yet, although it’s hard to imagine anyone here turning down an opportunity for their picture to appear among images of women such as Myanmese democracy figure Aung San Suu Kyi and British primatologist Jane Goodall.

The board is covered in faces of inspiring women, including young Pakistani activist Malala Yousafzai in her classroom in Birmingham in the UK; Misty Copeland, the first black American to be appointed principal female dancer by the American Ballet Theatre; Amy Schumer, the acerbic feminist comic; US Senator Elizabeth Warren; Facebook’s chief operating officer, Sheryl Sandberg; Adele, the singer; and Gloria Steinem, the American feminist who has guided Leibovitz on her selection of women.

Many are American, and like the 1999 book, Leibovitz says the current exhibition remains an “American project”. “I’ve been very careful especially with the first project. Originally we thought, ‘Let’s make it about the world.’ But I thought, being an American, it would be very hard to do that. And I have of course ventured out to the rest of the world and done photographs of people from all over the world. But it’s definitely with an American point of view. There’s no two ways about it,” she says.

It is also a very personal selection which not everyone will agree with. For example, next to Warren’s picture is the portrait of a chic-looking Wendi Deng, looking like a winner despite a bitter and highly public divorce from Rupert Murdoch.

“The truth is, she has an incredible story. She came out of nowhere. It’s part of being a woman and how we make our way. We are actually friends and we see each other from time to time. She’s pretty gutsy. I think she’s been in a very tough position, but I think she’s a real fighter and that’s part of being a woman too,” says Leibovitz, who went through a pretty tough patch herself a few years ago, when her father and Sontag died, and poor financial management took the single mother of three to the brink of bankruptcy.

Another controversial addition is Caitlyn Jenner, the former Olympic gold medallist and television celebrity who was born Bruce Jenner. Here, she is shown in nothing but the white corset that she wore for the famous “Call me Caitlyn” Vanity Fair cover shoot. Why shove a new woman into a demure, sexualised pose unless it was an ironic swipe at the stereotypes that Sontag railed against?

“It’s my tongue-in-cheek spin on a clichéd Vanity Fair cover – I’m not saying it’s good, and I’m not saying it’s bad. Caitlin wanted to really go out there. She wanted something that would surprise people. She had everything money could buy as far as her face and her breasts go – she has beautiful breasts – and she’s very proud of her body,” she says.

Compared with the 1999 “Women” collection, there is also an absence of the “everyday woman” here. That is partly because Leibovitz doesn’t want to replicate the shots included in the original project, she says.

“With this project I want to photograph women who I admire. It’s always supposed to be an addition to the ‘Women’ project. The project had very good bones. It already had a very good basis. That work really stands up. I don’t want to go and photograph a soldier again right now. I don’t want to go photograph a school teacher right now. I want to catch up on the women who I admire, who I think are interesting, right now,” she says. She and Steinem are working on a couple of “issues” that will result in more gritty images over the next year, she says.

Leibovitz has created many empowering images of women, including those of a nearly nude Schumer and tennis star Serena Williams for the Pirelli calendar which show that women of substance, and a woman who is all muscle, are beautiful. But there are many images – such as that of pop star Rihanna, lying in bed with a come-hither look, captured during a recent Cuban shoot for Vanity Fair – that seem to submit to, rather than challenge, male fantasies.

But Staci Ford, honorary associate professor in the department of history and the American Studies Programme at the University of Hong Kong who has written widely on the cross-cultural representation of women in mass media, says Leibovitz isn’t known particularly for having a feminist approach to her work.

“As Audre Lorde said, the master’s tools will never dismantle the master’s house. Leibovitz is using the master’s tools and she thinks she’s dismantling the master’s house. She’s not,” says Ford. Still, while she has played a complicit role in the “prettying-up of feminism, the adoption of Hollywood, commercial aesthetics by powerful women”, she has created some unforgettable images of strong women. Even if they are repackaged and airbrushed, she has helped made the “F” word more acceptable to the world, adds Ford.

For more information, visit ubs.com/annieleibovitz