Research On Local Slope Measurement Method Of Sub-nanometer Surface Profile Based On Asymmetric Interference Theory

The development of ultra-precise measurement technique is one of the key criteria for evaluating the national science and technology strength for its critical applications in scientific research and industrial system.For instance,the precision of the optical components employed in extreme ultra-violet photolithography is of sub-nanometer scale and those employed in Synchrotron Radiation X-ray application is of as high as picometer scale due to the short wavelength.However,the precision of current surface profiling methods is limited to 0.1 nm root mean square(RMS)due to the physical limitation and the properties of the components.Therefore,there is an urgent call for developing novel surface profiling methods to break the bottleneck.In this dissertation,the mechanism of asymmetric interferometry is creatively applied in high-precision local slope measurement.The concept of traditional shear interference is expended and a shear-differential asymmetric interferometry is proposed for the first time.By constructing an orthogonal polarized shear differential light path,we convert the space difference of the surface rise of the optical components into the light path difference in the polarization components.The near-orthogonal pre-and postselected polarized projections form an asymmetric interference system with the weak value amplification effect,realizing the ultra-precise measurement of the local slopes of the target components.The theory of shear-differential asymmetric interferometry is established,the parametric simulation is performed and the experimental system is designed and constructed in this dissertation.The precision of surface rise differential measurement is proved to be of picometer scale,and an ultimate local slope measurement with the precision of nano-rad is achieved.Specifically,the dissertation includes:(1)The shear-differential asymmetric interferometry for ultra-precise measurement of the local slope is raised,and the corresponding weak value amplification mechanisms in both frequency domain and space domain are investigated.The quantitative relationships between the pointer shifts in frequency domain/space domain and the target local slope is established,with systemic analysis of the measurement sensitivity and dynamic range.(2)The error in the shear-differential asymmetric measurement system is analyzed,and the theoretical model of the uncertainty is established.To optimize the precision,methods in the aspects of structure design and parameter selection are proposed and testified experimentally.(3)The experimental asymmetric interference measurement systems corresponding to frequency domain and space domain are built,respectively.In both systems,a precision of nano-rad is realized.The correctness and viability of measuring local slope based on the shear-differential asymmetric interferometry are proved.(4)Targeting at needs of surface profiling the ultra-precise deformable reflection mirrors,a surface profiling system based-on dual-path synchronized local slope measurements is build.The single-path differential value is 0.5 mm and the local slope precision measurement repeatability is RMS 9.7 nrad.The distance between the two paths is 2 mm and a minimum resolution of 6.7 nrad is reached,corresponding to a discernability of the local curvature of 2.96 × 105 m in radius.The shear-differential asymmetric interferometry proposed in this dissertation delivers a sensitivity of 7.3 ×10-4 THz/nrad(frequency domain)and 142.0 nm/nrad(space domain)in local slope measurement.In the space domain scheme,the sensitivity is increased by 71-fold comparing to the current highest value acquired by long trace profiler,accompanied by stronger perturbation resistance.The proposed system possesses great potential in achieving surface profiling with the precision of picometer scale,showing a vast prospect in the application of ultra-precise measurement.