Theory And Experiment Of Micro-Angle Measurement Based On Two-Dimensional Talbot-Moiré Effect

With the further development of modern metrology optics and the maturity of microoptics studied at the micron and sub-micron scales,more and more researchers are using optical devices,optical principles and optical effects to perform micro-angle measurement research.At the same time,the requirements for the accuracy,long distance,simplicity,and timeliness of micro-angle measurements are getting higher and higher.Microoptical devices can be divided into refractive optical devices and diffractive optical devices by the different ways of light propagation.Gradient index planar microlens array is a refractive optical device,and a binary optical device is a diffractive optical device.Nowadays,the fabrication process of optical precision devices is also becoming more and more perfect.For example,photolithographic ionexchanging technology used to fabricate planar microlens array is also becoming mature.In this rapidly changing and information-driven era,application of microoptical elements plays a pivotal role.At present,microoptical devices have an inestimable role in optical measurement,optical calculation,optical communication,beam shaping,optical imaging characteristics,and optical communication.The measurement of the minute rotation angle is currently widely used in missile tracking,satellite measurement,sensing and detection,robotics applications,ship tracking,drone tracking,CNC machine tools and other aerospace,marine,medical and other fields.However,the current minute angle measurement technology has disadvantages such as low accuracy of measurement results,complicated measurement methods,difficult to process measurement data,and poor timeliness of measurement.Therefore,there is an urgent need to find a simple,efficient and accurate measurement technology.Because the rotation angle is very tiny,there is no specific value range.Generally,a miniature angle sensor is used for measurement.The principle of electromagnetic induction is used to convert the measured angle signal into an electrical signal.Finally,the electrical signal value is output.There are also many measuring methods,such as tangential displacement method and laser autocollimation method etc..Among these methods for measuring minute angles,the optical principle method has advantages of high accuracy and non-contact measurement.In recent years,more and more researchers paid attention to the measurement of micro-angle.An important optical element is used when making measurements using optical princi ples.That is the grating,such as diffraction gratings,scribing gratings,holographic gratings,arrayed waveguide gratings,fiber gratings,Dammann gratings,etc..The diffraction structures of various new types of gratings have the characteristics of spatial periodicity.This dissertation focuses on two-dimensional grids formed by the intersection of crisscross grid lines and shaped like a square array.Aiming at the analysis of the Talbot effect of the two-dimensional transmission grating and the Moiré fringes,the Talbot-Moiré effect method is proposed and can be used for fast,efficient,non-contact,high-precision measurement of small rotation angles.The main works are as follows:(1)In-depth and detailed theory analysis of measuring the micro-rotation angle by using the two-dimensional grid Talbot effect to generate Moiré grid fringes.It includes the Talbot effect of periodic structure objects,the analysis of the Talbot image with the same periodic object and the completely opposite Talbot sub-image;and the dynamic display effect of periodic structure objects overlapping each other to form a Moiré grid fringe.The principle and characteristics of the Moiré fringe pitch is analyzed.That is,the larger the Moiré fringe width,the smaller the angle of the grid line.The measurement principle of micro-rotation angle and experimental verification analysis are put forward to lay the foundation.(2)We use monochromatic parallel light to enter the first two-dimensional grid,which form the same Talbot image at the Talbot distance.Select a suitable Talbot image,and then Moiré stacked fringes are formed with the second two-dimensional grid.At last the Moiré fringes have an enlarged dynamic display effect to perform non-contact long-distance measurement with a small rotation angle.A two-dimensional grid diffraction optical test system and a micro-rotation angle test system were set up for experimental measurement and experimental data processing.The experimental results show that they are consistent with the theoretical analysis.Therefore,it is feasible to measure micro-angles using the Moiré grating fringe generated from the imaging of the periodic object's Talbot effect,and this measurement method using optical principles is called the Talbot-Moiré effect method.In conclusion,results in this article enrich the content of modern metrology optical micro-angle measurement.The method proposed for measuring micro-angles of the amplified Moiré grating fringe produced by the two-dimensional grating Talbot effect has the advantages of high accuracy,non-contact,high sensitivity,high timeliness,etc..