Elimination Of Periodic Nonlinearity In Heterodyne Interferometry With Two Spatially Separated Balanced Beams

With development of ultra-precision engineering and nanotechnology, heterodyne laser interferometry is tending to high-speed, high acceleration, sub-nanometer accuracy. Influence factors of sub-nanometer accuracy is numerous, but periodic nonlinearity error of several even to over ten nanometers is a key factor which limits development of sub-nanometer accuracy.This subject mainly studied on an integrated models of periodic nonlinearity error, analysed the mechanism of error source affecting periodic nonlinearity error, looked for ways to fundamentally reduce periodic nonlinearity error, and proposed a novel method for construction of a heterodyne interferometer with two spatially separated balanced beams. The main works are as follows:To solve the problem of no integrated model, according to 5 error sources from various aspects of a heterodyne laser interferometry system, an integrated periodic nonlinearity error model was established to completely describe the comprehensive relationship among various error sources in this thesis, which could provide a necessary theoretical basis for analysis, decrease and measurement of periodic nonlinearity error. Through analysing and simulating the relationships between error sources and first-order, second-order & high-speed error, the results showed that three fundamental error sources to contribute periodic nonlinearity error were namely elliptically polarization of two laser beams, non-orthogonal polarization axis of two laser beams, and angle error between polarization axis and polarizing beam splitter. In low-speed measurement, first-order error is the main error. And in high-speed measurement, first-order and high-speed error were the main error. Then analysed the properties of periodic nonlinear error using vector analysis method. Results showed that the value of periodic nonlinear error is equal to the ratio of error component amplitude and ideal component amplitude, which provide a basis for rapidly estimating periodic nonlinearity error. Finally, using the integrated model, effects of three compensation techniques for periodic nonlinearity error were analyzed. Results showed, compensation techniques could reduce periodic nonlinearity error to 0.1~1nm without changing structure, which provide reference for further decreasing periodic nonlinear error.To solve the problem of unbalanced optical path causing thermal error in the reported interferometers with two spatially separated beams, a construction method of a heterodyne interferometer with two spatially separated balanced beams was proposed. That is, two spatially separated beams parallelly incidence to a traditional coaxial heterodyne interferometer, and two output beams was recombined into one beam using PBS or BS to constitute a heterodyne interferometer. Due to non-coaxiality and balance of two beams, a constructed interferometer could eliminate both periodic nonlinearity error and thermal error. Generally, the interferometer could eliminate periodic nonlinearity error within ±50pm. Then, with the proposed method, a linear-single-axis interferometer and a single-axis plane mirror interferometer were improved, and a three-axis plane mirror heterodyne interferometer was developed.To solve the problem of unable to measure pm-level periodic nonlinearity error accurately in a heterodyne interferometer with two spatially separated beams, the quadrature demodulation measurement method was improved, and an accurate calculation model was designed. The calculation model included solution phase and amplitude, solution amplitude error, filtering, down sampling and averaging, adding window function, and FFT. The improved model could greatly reduce error and noise, and could measure pm-level periodic nonlinearity error. Experimental results showed that first-order&second-order periodic nonlinearity error had been measured out, the measurement accuracy was ±3.5pm, and 85% of noise was reduced.Finally, both a 4-subdivision single-axis heterodyne interferometer with two spatially separated balanced beams and a dual-beam laser source with adjustable frequency-difference were designed, and then an experimental system of periodic nonlinearity error measurement was built. In high-speed displacement experiment, the periodic nonlinearity error was observed and measured using spectrum measurement method. There was no identified error at first-harmonic or second-harmonic Doppler frequency. In low-speed experiment, experimental data was calculated using the quadrature demodulation method. Results showed that there was still residual error attributed to "ghosting" reflection, the first-order was ±35.6pm, and the second-order error was ±9.4pm. At the same time, thermal drift experimental results showed that the thermal error was 6.5nm/°C. Under the temperature control accuracy of 0.02°C, the proposed interferometer could meet 0.6nm measurement accuracy demand of the lithography equipments.