There used to be a Carpet Museum adjacent to the Sultan Ahmet Mosque. I must have slides of some carpets somewhere that I may scan someday.
At any rate, to my great delight I found it had reopened, now in the former Imaret of the Haghia Sophia complex. I was told that the display is changed from time to time, as there are more carpets than room to show them. One of the richest sources was the Ulu Cami in Divriği, which itself is a wonderful building. Some other carpets come from elsewhere, often from places where goods from religious buildings were collected in case they were restored or lost their function. A couple are very ancient.

More carpets are in the Türk ve Islam Eserleri Museum.