The Chapel Veil or Prayer Veil (or Mantilla)

By coincidence I found a nice picture on the page of

Saint Francis Veil Company, Veneta, Oregon, USA

showing the Vergin Mary covering her head with a veil.

You will find detailed information here.

Caravaggio: Annunciation of the Birth of Jesus, 1608/09

Musée des Beaux-Arts, Nancy, France

Mary with veil

Caravaggio: Ankündigung der Geburt Jesu, 1608/09, Musée des Beaux-Arts in Nancy

Caravaggio: Ankündigung der Geburt Jesu, 1608/09, Musée des Beaux-Arts in Nancy

In church:

© pictures: Orbis Catholicus

In presence of the Pope:

Jacqueline Kennedy and John XIII

Queen Elisabeth II in the Vatican

The Spanish Mantilla is a veil fixed over a high comb (peineta):

© picture: Orbis Catholicus

A free download of Paul K. William's book here.

More information and pictures:

Those headcoverings blog

"Will you mantilla with me?"