Research On Ultra-precise Aspheric Surface Testing

In optical design, the radius of curvature (ROC) is used as the only variable parameterfor optimizing a sphere surface. By contrast, a conic constant and many high-orderaspheric coefficients can be used as variables for optimizing an aspheric surface.Therefore, aspheric surfaces are commonly used in the high numerical aperture (NA)projection objectives to decrease the complexity and to improve the imagingperformance. However, its applications are limited by the testing level despite ofmany superior optical features. Especially the ultra-precision aspheric surface testinghas become a challenge that we have to deal with. Usually, Annular stitching orsub-aperture stitching method can test an asphere with a mild departure from the bestfit radius (BFR), but the testing precision is restricted by the mechanical positioningerror and the retrace error of the interferometer. Stigmatic null testing can test a conicsurface, but with the center usually obscured. Thus, null lens compensator is the bestchoice for testing a high-order aspheric surface. Furthermore, the testing precisionshould be less than1nm RMS in order to meet the surface precision requirements ofasphere elements in high NA projection objectives.Aiming at the requirements of ultra-precision aspheric surface testing in high NAprojection objectives, this dissertation focuses on the research of computer-generatedhologram (CGH) and null lens as compensators and contains the following sections:1. Designing high precise CGH. The thesis analyses the CGH working principle,CGH working modes and diffraction efficiency; gives the calculatingmethods of CGH phase and CGH spatial frequency. For a general even highorder asphere in high-NA projection objectives, the thesis discusses thedesign method of null CGH and alignment CGH in detail, and then analysesthe reason how the diffracting ghosts turn up, and proposed a method toavoid them. According to the methods described in this thesis, a programbased on Matlab platform is compiled to complete the CGH design for theaspheres in the high-NA projection objective.2. Error analysis of aspheric testing with CGH and calibrating methods. Thethesis analyses the substrate error, etching error, alignment error betweenCGH and asphere, imaging distortion and the influence of temperature andpressure fluctuation. The thesis gives the calibration methods for thesubstrate error of CGH and builds a model to correct the imaging distortion of CGH precisely. The thesis also gives an effective method to restrict thealignment errors such as spherical aberration and coma. Using the nonlinearleast-square method, the vertex radius of curvature is acquired whenmeasuring the aspheric surface. To improve the testing precision, therotational asymmetric surface is calibrated absolutely using the multi-angleaveraging method.3. Designing high precise null lens and tolerance analysis. Compared to otherdesigns, the design which uses the parallel beam illuminating the null lenscould be easily aligned (need not to take the axial and decenter alignment)and avoid the alignment errors for aspheric surface testing. Furthermore, thefabricating tolerance of ROC and center thickness, and the aligning toleranceof spacing will be much loosened by using the optical redesign method in thefabricating and aligning process. This will be very favorable for opticalfabrication and alignment.4. The results comparing and experimental verification. A paraboloid is testedprecisely using stigmatic null test and CGH null test respectively. Theprecision of CGH is verified experimentally by comparing the two testingresults.