The filtering characteristics of simple grating optical low-pass filters

Abstract.We studied the characteristics of a two-dimensional grating optical low-pass filter (GOLF) theoretically and experimentally. The modulation transfer function (MTF) of an optical system that consists of a lens and a GOLF is theoretically derived by taking all orders of diffracted beams into consideration. The MTFs of a two-phase chess-board-type GOLF and a three-phase GOLF were calculated for various phase differences and compared with that of a birefringent low-pass filter (BLF). The three-phase GOLF with nine center beams of equal strength removes most moiré fringes, but the resolution degradation is severe compared to the BLF. The two-phase GOLF with a phase difference of 180°, which is similar to the BLF in term of beam distribution, has a medium characteristic somewhere between those of the three-phase GOLF and the BLF. Samples of two GOLFs are made and experimented on by attaching them to a digital camera. The experimental result coincides with the theoretical development.