Выражение встречается в следующем контексте: Corneal transplant surgery: The corneal button is removed and the anterior chamber filled with the preparation until it is level with the surface of the cornea.
покороче -- диск роговицы; подлиннее -- участок роговицы в форме диска
см.: A cylindrical, cookie-cutter type instrument called a trephine is used to remove a round, button-shaped portion of the diseased or damaged cornea. A "button" of similar size is cutr from the donor cornea and placed within the round opening.