Shape Measurement Of X-ray Nested Mirror Moulds Based On Stripe Reflection Method

The X-ray optical lens consisting of nested grazing incidence mirrors(nested mirrors)is an important part of X-ray telescope systems.The development of high-performance X-ray optical lenses is of great strategic significance for the X-ray space exploration and resource utilization.Two common types of nested mirrors are the super-paraboloid and the Wolter-I combination system respectively.The thin and high-resolution nested mirror cannot be processed by direct grinding and polishing of shells.Instead,high-precision moulds are manufactured at first,and then mirrors are replicated with which by applying the processing technology,such as the methods of thin Al foil,thin glass foil,replication by electroformed Nickel and so on.The processing and measurement of high-precision moulds is the key to the nested mirror manufacturing technology.In this paper,a surface reconstruction method based on stripe reflection and phase-shifting was proposed for the nested mirror measurement during the transition stages from the fine grinding to coarse polishing.The stripe reflection method,which has the characteristics of full-aperture,non-contact,simple structure,low cost,high dynamic and high sensitivity,effectively links up the profilometers and interferometers during the transition stages.This paper introduces the research background and current status of nested X-ray telescopes in the world,and describes the structures and shape measuring methods of nested grazing incidence mirrors in detail,especially the stripe reflection method,whose focus is on the implementation principle,error sources,and key technologies.The stripe reflection method is generally composed of four parts:phase-shifting,phase unwrapping,surface reconstruction and internal and external parameter calibration.In this paper,various phase unwrapping algorithms and surface reconstruction algorithms were simulated and analyzed in detail,the advantages and disadvantages of which were compared.An improved discrete cosine transform algorithm(IDCT)were proposed,which was suitable for surface reconstruction in the non-uniform grids.The simulation results show that the IDCT reconstruction error reaches sub-nanometer level.According to the given prescription of the nested mirror,the imaging optical paths of the single-reflection super-parabolic mirror system and the second-reflection Wolter-I combined mirror system were optimally designed in the optical design software,as well as the inner and outer surfaces measuring optical paths corresponding to the shape measuring models of nested mirrors and nested mirror moulds respectively.A surface iteration model based on the triangle similarity principle was proposed.The iterative results are consistent with the standard design data,which verifies the applicability of the iteration model for surface reconstruction in the non-uniform grids.An experimental system based on stripe reflection method was built.The shape measuring of the nested mirror mould was carried out with the calibration of internal and external parameters and the IDCT reconstruction algorithm.The experimental results verify the feasibility of the stripe reflection method for the shape measuring of grazing incidence mirror moulds during the transition stages.The work of this paper provides a certain reference value for the shape measuring of nested grazing incidence mirrors.