0–360 Degrees angular measurements using spatial displacement

The angle measurement is one of the fundamental measurement techniques required for a large number of applications. Many mechanical and optical measurement methods accomplish this task, requiring contact with the object or interference using multiple laser beams. We introduce a measurement for a given arbitrary angle accomplished by the conversion of the angle measurement to a spatial displacement measurement. The resolution of the angular measurement is a microradian, and it is limited only by the resolving power of a pixel. This measurement is almost independent of the specific wavelength, degree of coherence, and measurement distance. Moreover, our method realizes a non-contact and nondestructive angular measurement within the range of 0°–360°. We anticipate it to have important applications in optical communication systems and industry.