  Traceability of precision instrument and measuring method is the core issue
in metrology science. In the field of nanometer length measurement, the laser
interferometers are usually used to trace the measurement value to the laser
wavelength, but the laser wavelength is sensitive to the environment
disturbance. Chromium self-traceable grating is an ideal nanometer length
reference grating with pitch traceability, fabricated by the atomic lithography
technique. The new nanometer length traceability chain can be established based
on the pitch traceability of chromium self-traceable grating, which is often
used to calibrate the systematic error of the atomic force microscope. In this
paper, the metrological self-mixing grating interferometer based on the
chromium self-traceable grating (SMGI-Cr) is firstly established, whose
interfere phase is traceable to the pitch of the chromium self-traceable
grating directly and traceable to the chromium atomic transition frequency of
energy level 7 S 3 to 7 P 4 indirectly. The nanometer displacement measurement
is also achieved by the SMGI-Cr. The measurement error is no more than 0.2366%,
compared to a commercial interferometer.
