Electric Field Simulation And Error Analysis Of Planar Two-Dimensional Nano Time-Grating

Precision measurement technology plays a key role in the fine control of all links of high-end precision equipment manufacturing,and is the technical guarantee to support the high-level development of China’s manufacturing industry.The manufacturing or working process of high-end precision equipment such as lithography machine and two-dimensional precision worktable not only puts forward higher requirements for the precision and resolution of precision displacement measurement,but also requires the provision of large range,planar two-degree-of-freedom measurement information.Therefore,it is particularly urgent to carry out independent research on planar two-dimensional nano-displacement measurement technology under the background of "pinching the neck" of two-dimensional measurement technology and components of high-end precision equipment.On the basis of the previous research on one-dimensional nano time grating,this paper carried out the research on the planar two-dimensional nano time grating sensor,and proposed a new excitation electrode coding method for two-dimensional measurement,which can simultaneously construct a uniform alternating electric field in the x and y directions.In addition,a multi-sensing electrode array method is also proposed,combined with the combined operation of sensing signals to realize the decoupling of signals in the x and y directions.The nonlinear electric field distribution and its effect on the error of planar two-dimensional nano-grid sensor are analyzed,simulated and verified by experiments.Using the PCB manufacturing process,an experimental prototype with an effective range of 200 mm×200 mm was manufactured,and its original measurement accuracy in the x and y directions reached ±8.2 μm and ±6.8 μm respectively,providing a unique way for high-precision two-dimensional displacement measurement A new implementation path based on traditional optical methods.The main research contents and contributions of this paper are listed as follows:1)The sensing structure and principle of planar two-dimensional nano time-grating are proposed and analyzed.The sensor structure is composed of a large-area array of excitation electrodes positioned on a fixed ruler and a small-area array of induction electrodes assembled on a coplanar moving ruler that travels over the fixed ruler at a fixed separation gap.The discrete orthogonal coding method of the proposed excitation electrode can generate the uniform alternating excitation electric field in two measurement directions at the same time.A simplified mathematical model of the sensor is established.The single-cycle two-dimensional sensor model is decomposed into a simplified X model with only x-direction excitation and a simplified Y model with only y-direction excitation.The signal output of a single induction electrode under the two simplified models is analyzed step by step,so as to separate the traveling wave signal output by a single induction electrode.Finally,an array of four induction electrodes with orthogonal spatial phase and the combined summation and difference operations can realize the decoupling of two measurement direction signals.2)The error characteristics of the sensor are analyzed.Based on the structure and sensing mechanism of the sensor,and the influence of the spatial distribution of the nonlinear electric field on the traveling wave signal,the error analysis mathematical model of the planar two-dimensional nano time-grating displacement sensor is established,and the relationship between the spatial harmonic component introduced by the nonlinear electric field and the sensor’s periodic and long-range error characteristics is analyzed.3)The electric field simulation analysis and verification of the sensor are carried out.The electric field simulation model is established according to the sensor structure and sensing mechanism,and the simulation analysis is carried out according to the idea of theoretical error analysis.The simulation verifies the mechanism of the sensor signal generation,the feasibility of the signal decoupling method,and the characteristics of the periodic and long-range error.4)Experimental research was conducted.An experimental testing platform was built and an experimental prototype of the sensor was manufactured.The sensor error tests in different gap cycles,stability and resolution tests,and planar two-dimensional large range error tests were conducted.The feasibility and error characteristics of the sensor measurement method are verified,and the basic performance indicators of the sensor are obtained.In summary,the theoretical analysis of sensor measurement principles and errors in this paper provides theoretical support for electric field simulation analysis and experimental research.The simulation analysis preliminarily verifies the correctness of theoretical derivation,and provides reference and guidance for experimental research.Experimental research further verifies the correctness of theoretical derivation and obtains basic performance indicators of the sensor.