In Ann (1982) by Alex Katz, a woman looks straight at us. Her head, framed by a dark bob that falls to the shoulders, fills almost the whole height of the linen, and at more than three times life size the face has the presence of a billboard and the stillness of an icon. Nothing competes with it: a flat ground of warm beige, two gold earrings, a black blouse scattered with white birds and patches of magenta, rose, blue and yellow.

At first sight the painting belongs entirely to its author. The economy of means, the frontal pose, the cropping, the smooth passages of flesh and the sweeping strokes of the hair are the marks of a manner Katz had been refining for three decades. Yet Ann is not one of his portraits of poets, dancers and painters from the downtown circle, nor one of the many images of his wife Ada. It is a commission: a picture made for a sitter who did not belong to the artist’s world, and who expected, as sitters always have, to recognise herself. Every commissioned portrait is a negotiation between the painter’s style and the patron’s face, between what art wants and what likeness owes. Ann conducts that very old negotiation in a resolutely modern idiom, and shows how a painter who claimed to care above all about style could produce one of the most quietly intense faces of his decade.

The sitter is Ann Frasher, who with her husband Edward Randall Hudson Jnr was a collector and patron of the arts. In the second half of the 1960s Randall Hudson presided over the Fort Worth Art Association, the body from which the Modern Art Museum of Fort Worth descends. In 1967 he was among the men who secured Picasso’s Femme couchée lisant for the Fort Worth Art Center at auction, and in 1968 he welcomed a panel Roy Lichtenstein had painted for the Artists’ Peace Tower in Los Angeles. He would later sit on the boards of the Kimbell Art Foundation, the Whitney Museum of American Art, the J. Paul Getty Trust and the National Gallery of Art, among many others.