A flexible sheet-form optical system, referenced to as a daylighting fabric, which has a fabric-like behavior and light redirecting properties. The daylighting fabric comprises a soft and flexible sheet of optically transmissive material, such as plasticized polyvinyl chloride. A surface of the flexible sheet includes a plurality of parallel slits having spaced-apart walls configured to reflect light by means of a total internal reflection. At least a portion of daylight incident onto the sheet is internally redirected at angles other than the angle of incidence which is exploited to enhance daylight harvesting and illumination of a building interior. Disclosed also are a method and apparatus for making the daylighting fabric. The method includes steps of mechanical slitting of the flexible sheet with a blade, elastic stretch-elongation of the sheet along a direction perpendicular to the slits, and making at least a portion of the sheet elongation irreversible.