Simple optical method for small angular displacement measurement based on the astigmatic effect

We propose a novel small-angle measuring optical method based on the astigmatic effect of two orthogonally placed cylindrical lenses. According to the one-to-one correspondence between the laser spot shape and the angle, the angle is determined. We theoretically analyze the measuring range and demonstrate that a longer distance between the rotating axis and the optical axis leads to a smaller measuring range, but better sensitivity. Also, an associated experimental system is established and a measuring range of 0.94 mrad (cubic fit r = 0.9993) as well as a good linear range of 0.37 mrad (linear fit r = 0.9994) with a resolution of 8 mu rad is achieved.