Error Analysis, Design and Modeling of an Improved Heterodyne Nano-Displacement Interferometer

A new heterodyne nano-displacement with error reduction is presented. The main errors affecting the displacement accuracy of the nano-displacement measurement system including intermodulation distortion error, cross-talk error, cross-polarization error and phase detection error are calculated. In the designed system, a He-Ne laser having three-longitudinal-mode is considered as the stabilized source. The free spectral range of the 35cm laser cavity is about 435-MHz at 632.8-nm wavelength, which a secondary beat frequency equal to 300-kHz is produced by combining the reference and measurement beams. The resolution of the displacement measurement resulting from intermodulation distortion, cross-talk and cross-polarization errors is limited to 18-pm. Also, the phase detection uncertainty causes an error of only 5.9-pm in the displacement measurement. Furthermore, frequency-path models of two- and three-longitudinal-mode laser interferometers are modeled as the ac interference, ac reference, dc interference and optical power terms. A comparison study between two- and three-longitudinal-mode laser interferometers confirms that the performance of the designed system is considerably improved.