A noncontact optical method has been developed for measuring the linear displacements of an object to within several angstroms by measuring how the intensity of a light beam coming from a three-dimensional transmissive holographic diffraction grating (a hologram) depends on the phase mismatch between the beams incident on the hologram. The phase mismatch between the beams is caused by the displacement of the object, from which one of the beams incident on the grating is reflected. It is shown that, when a He-Ne laser (λ = 633 nm) and a photodetector whose relative error ΔI/I_(max) is 0.5* 10~(-3) is used, the error in measuring the displacement of the object can be brought to about 0.1 nm.
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