Dervish headgear, 15th century

Probably the headgear of a Sheikh, considering the quality and the size of it. The hat is made of gold brocade, which was (and is) an exclusive and very expensive fabric.

‘Sheikh’ has a lot of meanings; in this particular case, the man, always an elder, is the spiritual leader of a Sufi brotherhood.

Sufism is defined by some adherents as the inner, mystical dimension of Islam, others contend that it is a perennial philosophy of existence that pre-dates religion, the expression of which flowered within Islam. A practitioner of this tradition is generally known as a sufi. They belong to different "orders" - congregations formed around a master - which meet for spiritual sessions, in meeting places known as ‘zawiyah’ (zaviye), ‘khanqah’ or ‘tekke’.

Regarding the size of the Ottoman male headgear:
In Ottoman culture (and more generally in the Islamic World until the beginning of the 20th century) the size of a man’s headgear was an indication of his social position. The bigger the hat, the more important the person was (or pretented to be). This was especially the case with landed nobility and religious Orders; high state officials had other means of proclaiming their rang.

Correspondent: J.M.Criel, Antwerpen.
Sources: Isabella I. Bird : ‘Journeys in Persia and Kurdistan (1891)’ & Wikipedia .