Systematic error analysis and parameter design of a vision-based phase estimation method for ultra-precision positioning.

Ultra-precision position measurement is increasingly important in advanced manufacturing such as the semiconductor industry and fiber optics or photonics. A vision-based phase estimation method we proposed previously performs position measurement by imaging a 2D periodic pattern. In this paper, systematic errors of this method are analyzed and derived mathematically, which are classified into two types: spectrum leakage error caused by image truncation and window function modulation, and sub-pixel error resulting from discrete Fourier transform (DFT) intensity interpolation. Key design parameters are concluded including pattern period T, camera pixel size t and resolution N, as well as the type of window function used. Numerical simulations are conducted to investigate the relationship between the phase errors and design parameters. Then an error reduction method is proposed. Finally, the improved performance of parameter optimization is validated by a comparative experiment. Experimental results show the measurement errors of the prototype are within ∼2 nm in X or Y axis, and ∼1 µrad in axis, which reaches the sub-pixel accuracy better than 10-3pixel.

Forward fiber Fourier transform spectrometer modeling and design with PZT phase modulation real-time compensation.

Piezoelectric ceramic transducers (PZTs) are often applied in all-fiber Fourier transform spectrometers (FFTSs) to realize phase modulation. Combining a PZT and optical fiber features, a theoretical FFTS modeling is established. We systematically deduced the main causes of spectral errors and the factors of the instrumental resolution, then designed a new FFTS system and provided real-time compensation methods for spectral errors. We creatively employed two Mach-Zehnder interferometers by winding the sensing arms of the two on the same PZT cylinder to realize the dual optical path experiencing the same and simultaneous phase modulation. A processing circuit is designed to achieve selective sampling of the test interferogram, avoiding the spectral artifacts generated by the PZT phase discontinuities. The narrow line width of the reference spectrum is obtained at the same time for real-time calibration of spectral shift resulting from dispersion and other phase errors. By the comparison of the original interferogram and spectrum with those after compensation, the experiments validated that the system design could effectively compensate for the spectral errors caused by PZT and optical fiber physical limitations. Finally, the improved ideas are discussed if the FFTS prototype is to be applied to test a real-time gas spectrum.