Design、Manufacture And Error Analysis Of CGH For Ultra-precision Testing Aspheric Surface

With the development of modern science and technology, people are makinghigher demands on the performance of the optical system, the aspheric surface hasincreasingly widely used in a variety of precision optical system or the special opticalsystem. In addition, the development of optical precision processing technology alsomake high-precision aspheric surfaces with large caliber becomes possible.Processing high-precision aspheric surfaces needs to have testing technology whichits precision matches with processing precision. Currently, the interferometric opticaltesting is used for the aspheric surfaces testing generally, wherein, the ComputerGenerated Hologram (CGH) method is used in the high-precision aspheric surfacestesting widely. The basic principle of this method is using the ideal asphericwavefront which is generated by CGH and actual detector wavefront to produceinterference patterns, and then achieve the high-precision testing of the asphericsurfaces. Therefore, how to design the CGH and analyze its impact of the accuracy tothe entire testing accuracy has very important significance.First of all, the basic knowledge of aspheric surface and its testing method areboth introduced. Then, the principle of aspheric with CGH and CGH’s designincluding its production process, particularly the process of using of electron beamdirect writing machine is introduced briefly，it’s the foundation of analysis of thecoding error.Then, the basic theory of CGH、design ideas and specific design method arestudied by ray tracing theory and scalar diffraction theory,in addition, the advantagesand disadvantages of them are compared. All of these provide necessary theoreticalbasis to the CGH design. After that, according to the ray tracing theory，the specificdesign results are given for the concrete aspheric surface by Matlab and Zemaxrespectively, and the two results fit well.At last, using the theory of scalar diffraction and the binary linear grating model combined with the design and the production process of the CGH, Substrate surfacefigure error、Duty-cycle error、Pattern distortion、Etching depth error、Direct writingcoding error are studied respectively. And according to the analysis, the parameters ofCGH such as Duty-cycle、Etching depth are optimized. By the analysis of processerror, we can give the advice of how choose the production parameters in the differentcondition. The results show that,(a) The first-order of the diffracted light should bechoose for the testing light, because we can get the highest diffraction efficiency atthis time and there is no influence to the diffraction wavefront caused by Duty-cycle.(b) According to different processing condition, appropriate parameters of Duty-cycleand Etching depth should be choose to balance the diffraction efficiency and thetesting accuracy. For instance, when the tolerance of the duty cycle, and the etchingdepth are not very much (assuming a tolerance of1%), the etching depth should beselected near0.4λ and the duty cycle should be45-50%, so that both guaranteedsufficiently high diffraction efficiency can we get and we also take into account theimpact of the duty cycle and etch depth fluctuation to the diffraction wavefront.(c)The smaller of the tolerance of E-beam direct writing machine, which means that thesmaller of the etching equipment can etch the minimum line width and the moresupport of etching angle, the higher of the accuracy and the smaller coding error.We explored the design method of CGH in the paper, and analyzed the CGHfabrication error quantitatively. This work can provide a theoretical basis for thehigh-precision aspheric surface testing and has guiding significance for the analysis ofthe testing report.