A non-contact angle measuring apparatus includes a matter-wave and energy (MWE) particle source and a detector. The MWE particle source is used for generating boson or fermion particles. The detector is used for detecting a plurality peaks or valleys of an interference pattern generated by 1) the boson or fermion particles corresponding to a slit, a bump, or a hole of a first plane and 2) matter waves' wavefront-split associated with the boson or fermion particles reflected by a second plane, wherein angular locations of the plurality peaks or valleys of the interference pattern, a first distance between a joint region of the first plane and the second plane, and a second distance between the detector and the slit are used for deciding an angle between the first plane and the second plane.
