Some highly technical work on this subject has been published, but a recent short video by Benjamin Kantor does a great job of explaining the basics in very simple terms.
For a more technical discussion, see either of the following:
• Gignac, Francis (1976), A Grammar of the Greek Papyri of the Roman and Byzantine Periods: Vol. 1 Phonology, Milan: Instituto Editoriale Cisalpino-La Goliardica, ASIN B0006CVTGQ
• Teodorsson, Sven-Tage (1977), The phonology of Ptolemaic Koine, Göteborg: Göteborg University, ISBN 91-7346-035-4
There’s also a fairly detailed discussion on Wikipedia.
And, of course, there’s Benjamin Kantor’s own discussion of the topic on the same page where he published the video.