How does an artist become an icon? It helps to have an iconic face. Look at Pablo Picasso and Andy Warhol, or Frida Kahlo and Georgia O’Keeffe. Kahlo had a major exhibition at Tate Modern in 2005; O’Keeffe (1887-1986) is being honoured with one now (until 30 October).

Unlike Kahlo, O’Keeffe did not paint herself. We know her face and body as a young woman from the adulatory photographs taken at the start of her career by her Svengali-like mentor and eventual husband, Alfred Stieglitz. A selection of these striking images hangs in the opening room with examples of her early abstract drawings.

In a later room she looks out at us as an old woman from a cover of Life magazine, her sphinx-like profile silhouetted against the New Mexico landscape that she painted so often it is known as O’Keeffe country.

Portraits of the artist are not the only photographs on display. O’Keeffe was strongly influenced by contemporary photography, which she claimed to find “more living, more vital” than some contemporary painting, and parallels are drawn between her paintings and photographs of similar subjects by Stieglitz, Paul Strand and Ansel Adams.