Western Europe and the Ottoman Empire were on roughly comparable technological and scientific levels in most fields until about the late seventeenth century, of course with variations depending on the field. Before that, scietific exchange of texts and techniques was relatively common and went more or less two ways.
Europeans had more or less caught up with the Muslim lands by sometime around 1200-1400 (again depending on the field and place). In the period discussed, the technological expertise generally available to both societies was generally of the same order.