Analysis And Modeling For Moire Pattern Of Ronchi Grating

Moiré measurements are widely used for displacement and angle measurement and have applications for geometric measurement and monitoring.They are highly precise,and have wide-range,anti-interference,and digital output properties.As the global manufacturing industry accelerates the digitization process and China’s integrated optical,mechanical,electrical products and equipment gain increasing prevalence,there is rapid growth in the domestic and foreign demand for grating sensors continue to improve in precision and reliability.Therefore,it is important to research the measurement theory of Moiré pattern of Ronchi grating and explore the development of new grating sensors.This paper uses information optical theory to research and analyze the use of widely-used measurements of transmission-type black-and-white grating(Ronchi grating),focusing on the grating Optical Transmission Function(OTF)and creating a distributional mathematical description for relative motion grating couples Moiré fringe generates on optical fields.This helps establish a complete mathematical model of the Moiré Pattern(Complete Transmittance Model of Moiré Pattern,or CTMMP).On this basis,implicit function analysis and numerical fitting of the mathematical model completes the establishment of the Moiré fringe computer simulation model.Because the comprehensive model fully reflects the Moiré pattern’s harmonic characteristics of the diffraction properties,it holds strong significance in both theory and application.Preliminary testing and validation indicate: the model not only provides accurate forecasting for transmission characteristics of the optical field under various grating parameters on the horizontal and vertical Moiré fringe,but also for errors related to grating,light source,such as collimation of other characteristics of the sensor,thereby helping lay the foundation for future expansion of the grating sensor device.Firstly,the paper describes the grating and measurement of Moiré fringe indicators and parameters.Optical projection ordinal theory helps lay out the analysis of the traditional equation of “grating – periodic relationships formula of the Moiréfringe cycle.” Convolution relationships for grating OTP provides the mathematical definition of its function and the auto-correlation function characteristics of the Moiréfringe profile provides the mathematical analysis to reveal the triangular wave property of the Moiré fringe’s wave function.Further,Fourier series and transformation are used to analyze the diffraction properties of grating and grating couples and the laws are used to,reinforcing the validity and support of posterior mathematical modeling of the theory.In respect to errors evidenced in the previous process of grating transmission,the study introduces graphics image processing theory,using graphics and the two-dimensional rotation matrix rotating graphics function domain invariance principle to verify the function of rotating coordinate system to draw the variable substitution rules.In this way,the complete grating transmittance function expression and CTMMP are educed based on the rules.Further research cannot directly establish a simulation model of the problem for the CTMMP transcendental equation as the implicit function form of the series.Through the application of MATLAB handle graphics functions,extraction of coordinates of the curves grating vector,and use of fitting algorithms,the implicit function of the transcendental equation becomes a explicit function of the form of Moiréfringe numerical model,and ultimately establishes the Moiré fringe computer simulation model of transmission.The paper analyzes and verifies the model’s accuracy and convergence.Finally,the paper describes three key findings of the study of available computer models of Moiré fringe measurement of the grating system simulation technology:(1)the light radiation angle simulation results show that the light source on the performance of grating sensors have a profound impact as sensors need to minimize the use of highly collimated light source;(2)the superposition principle of linear systems helps identify errors produced in short-term simulation of grating.Results show that short-term grating errors have a significant SNR on the output signal wave form,but the filter can eliminate short-term measurement error and their adverse effects on results;(3)Moirévertical stripes on the first simulation show the output signal of its triangular wave form profile,which is in line with the ideal output waveform of Moiré metrology.At the same time,grating provides the specific parameters and the impact of deflection errors on the waveform.The simulation shows that the vertical Moiré fringe is a promising method of displacement measurement and rectifies errors in domestic understanding of this measurement method.In conclusion,the analysis and modeling of transmission gratings and Moiréfringe show a more accurate description of the theoretical characteristics of the Moiréfringe patterns.At the same time,the model for grating measurement systems provides new design possibilities for the analysis and design of new sensors.The breadth and depth of Moiré metrology theory strengthen its practicality.Therefore,the paper concludes that there are still many issues remaining that require further research and practice.