In a laser line projection apparatus, six spaced-apart unpolarized laser-beams are plane-polarized with low loss by a combination of a thin-film polarizer, a reflector, and two polarization rotators. Two beams are polarized in each of three polarization-orientations. Two of the polarization-orientations are orthogonally aligned with each other in P and S orientations. The other polarization-orientation is non-orthogonally aligned in an intermediate orientation. The beams are intensity-homogenized and projected into a line of radiation. Any point on the line of radiation is formed from rays with an angular distribution of polarization-orientation from S to P through the intermediate orientation and back to S through the intermediate orientation.