Three-dimensional objects are formed by photo-curing a liquid polymer by exposure to a radiation in a space between a sheet transparent to the radiation and a supporting plate. On a side of the sheet facing towards the photo-curing liquid polymer, a membrane is arranged. The membrane is transparent to the radiation and covered by a layer of liquid lubricant. The membrane is displaceable with respect to an area in which said liquid polymer is undergoing curing by exposure to the radiation, which radiation (e.g., at 410 nm) may be provided by a collimated light source composed of an array of light emitting diode (LED) sources, an array of baffles, and an array of lenses. The baffles limit beam widths of each individual LED source in the array of LED, and the array of lenses is located one focal length from said array of LED sources.