Machine-Ruling Grating’s Line Error And Its Correction Method

With the rapid development of science and technology, large-area andhigh-quality plane diffraction gratings are being demanded more and more urgentlyin the national military, astronomy, nuclear energy, aerospace and civilian areas.Machine-ruling method is one of the major methods for making grating and is thebest choice for making some special gratings, such as low line-density grating forinfrared laser and all echelle gratings etc… For Machine-ruling method, grating’sline error is one of the important factors that effect the performance of large areagrating (diffraction wavefront, stray light and resolving power etc.).In view of uponreasons, the paper, which is funded by the National Key Technologies R&D Programfor the11th Five-year Plan and National R&D Projects for Key ScientificInstruments, is mainly focused on line errors of machine-ruling grating and methodsfor improve the quality of machine-ruling gratings with large areas. The relationshipamong grating’s diffraction wavefront, grating performances, line error andsubstrate’s surface error is analyzed deeply; Influence and revising method ofmachine-ruling grating’s line error on grating performance is studied detailedly; thereal-time revising method of yaw angle error of grating line is also elaborated. Firstly,the relationship among line error, surface error and diffraction wavefront undercondition of cone diffraction is deduced. Grating’s diffraction wavefronts ofsymmetric orders were measured by interferometer, and the separation of grating lineerror and surface error of substrate is realized from measured digitized results.Grating’s diffraction wavefront is analyzed by Two-dimensional fast Fouriertransform method and the influence of grating line error and surface error on gratingperformance is discussed. With the aid of aforesaid method, grating performance can be analyzed by reconstructing grating’s diffraction wavefront, and grating line errorand surface error on the whole surface of grating can be deduced, both of which canprovide a theoretical basis for grating’s substrate processing, grating manufactureand application. Secondly, the paper provides an light-tracing mathematical model inwhich collimated monochromatic light incidents on a plane grating which containsline’s curved error and line location error and corresponding diffraction light isimaged on the focal plane. The influence of above-mentioned grating line errors ongrating performance is studied. Results show that grating line’s curve and locationerror predominately influence grating sagittal and meridional spectral performanceseparately, and line’s curved error has little effect on grating resolving power andscattered light. Upon results may provide guidance for making of machine-rulinggrating. Thirdly, the problem of asymmetry of ruling tool system, stiffness of quartzguide system and rationality of driven approach for ruling tool system, which aresome main reasons for grating’s line curve of CIOMP-2ruling engine in China, areanalyzed by finite element method, and corresponding mechanical correction methodare provided. some correction methods are verified by experiments, and experimentand simulation results are consistent on the changing trend. Fourthly, the structureand mechanical amended the original structure compared to the position error of thegrating lines have decreased significantly, effectively inhibit the grating stray light,and improve the quality of the grating of the grating ruling machine. The mechanicalcorrection method for main grating-line position errors in CIOMP-2ruling engine isstudied. The problem of incomplete grating lines is solved by mechanicallycorrecting the parallelism of the ruling tool system and micro-positioning table. Inorder to solve the problem of instability of ruling tool system, a correction methodfor connection mode of saddle slider and ruling tool is provided by using flexiblehinge instead of the fixed connection, and this method is an effective solution to theproblem of instability of ruling tool system. Compared to the origin ruling toolsystem, the modified ruling tool system’s grating-line position errors is decreasedsignificantly, stray light is effectively suppressed, and grating quality of CIOMP-2ruling engine is improved. Fifthly, relationship among main parameters of themathematical model of micro-positioning table system and dynamic performance ofmicro-positioning table system is analyzed by simulation, and thepositioning-accuracy difference between BP-neural-network PID control andtraditional PID control is compared by experiment analysis. Results show that thedynamic performance of the micro-positioning table can be improved by increasingthe connection stiffness (or damping) between micro-positioning table and macro-positioning table on the general trend, and BP-neural-network PID control ismore suitable for CIOMP-2ruling engine than traditional PID control. Upon analysisresults has some reference significances for the design and improvement ofmacro-micro table of grating ruling engine. Sixthly, in order to solve the problem ofyaw angle of micro-positioning table of ruling engine,a single-PZT correctionmethod is provided. The sources of measurement error of yaw angle is analyzed bymeasurement results from three laser interferometer and one diffraction-wavefrontmeasuring machine of Zygo Company. In final, experimental verification of thesingle-PZT correction method is performed. The results show that the single-PZTcorrection method can effectively suppress yaw errors of grating line. Thesingle-PZT correction method may be applied to correct the yaw angle of gratinglines of large-area and high-quality gratings which are made by grating rulingengines in real time.