In one embodiment, a fingerprint sensing system includes a sheet prism having a sensing surface and a number of prismlets positioned opposite to the sensing surface. Each prismlet has an entrance surface and an exit surface, and is adjacent to another prismlet. The width of the sheet is more than ten times the maximum thickness of any one of the prismlets. When a finger is positioned on the sensing surface, a portion of the radiation entering a number of the entrance surfaces and incident at the sensing surface is reflected through total internal reflection. The reflected radiation emits from a number of the exit surfaces to create an image of the fingerprint. In another embodiment, the system further includes a second sheet prism stacked together with the previously described sheet prism. The second sheet prism has a flat surface and a number of prismlets positioned opposite to the flat surface, which faces the prismlets of the previously described sheet prism. The image formed with two sheet prisms can have lower distortion. In yet another embodiment, the fingerprint sensing system is incorporated into a flat-profile package using mirrors to fold radiation and to compress the height of the package.