https://www.macworld.com/article/2048514/the-iphone-5s-fingerprint-reader-what-you-need-to-know.html
A capacitance fingerprint reader leverages a handy property of your skin: The outer layer of your skin (your dermis), where your fingerprint is, is non-conductive, while the subdermal layer behind it is conductive. When you touch the iPhone’s fingerprint sensor, it measures the minuscule differences in conductivity caused by the raised parts of your fingerprint, and it uses those measurements to form an image..
The article says that the capacitance reader has a resolution of about 500 dpi - though it uses the home button, not the screen.
500 dpi? That would be enough to get an image of a finger print, but it is astonishing that they can measure the differential between peaks and valleys of the skin on your fingers. I guess they have made some progress since I last looked at this technology.