Subaperture stitching testing for fine flat mirrors with large apertures using an orthonormal polynomial fitting algorithm

Abstract Interferometry, which measures the difference between a reference surface and a test surface, is widely used in high-precision testing. Usually the reference surface is considered as perfect and the surface errors there can be ignored during the testing. Considering the interferometry for fine optics with large apertures where the error of the reference surface is non-ignorable, we propose a stitching algorithm based on an orthonormal polynomial fitting method that can be used to accomplish the testing of both the reference surface and the surface under test simultaneously. To evaluate the accuracy of the above algorithm, the performance of the proposed method was analyzed by testing the tertiary mirror for the Thirty-Meter Telescope project (TMT project) and utilizing the algorithm in the simulation. Further, a practical experiment was implemented to demonstrate the practicability of the proposed method.

[1]  D. Walker,et al.  Modeling and validation of polishing tool influence functions for manufacturing segments for an extremely large telescope. , 2013, Applied optics.

[2]  G N Lawrence,et al.  Subaperture testing of aspheres with annular zones. , 1988, Applied optics.

[3]  Guang-ming Dai,et al.  Orthonormal polynomials in wavefront analysis: analytical solution , 2007 .

[4]  Osuk Y. Kwon,et al.  Full Aperture Testing With Subaperture Test Optics , 1983, Optics & Photonics.

[5]  Michael DeMarco,et al.  Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VON) , 2010, International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT).

[6]  Haobo Cheng,et al.  Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces. , 2013, Applied optics.

[7]  Gene H. Golub,et al.  Matrix computations , 1983 .

[8]  G N Lawrence,et al.  Method for subaperture testing interferogram reduction. , 1983, Optics letters.

[9]  Dong Liu,et al.  Aspheric subaperture stitching based on system modeling. , 2015, Optics express.

[10]  Katsuyuki Okada,et al.  Measurement of large plane surface shapes by connecting small-aperture interferograms , 1994 .

[11]  Matthias Schock,et al.  Thirty Meter Telescope Detailed Science Case: 2015 , 2015, 1505.01195.

[12]  Donglin Ma.  Recommended conceptual optical system design for China's Large Optical-infrared Telescope (LOT). , 2018, Optics express.

[13]  Feifei Gu,et al.  Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique. , 2014, Optics express.

[14]  Fan Wu,et al.  Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method. , 2007, Optics express.

[15]  Virendra N Mahajan,et al.  Nonrecursive determination of orthonormal polynomials with matrix formulation. , 2007, Optics letters.

[16]  Tilman W. Stuhlinger.  Subaperture Optical Testing: Experimental Verification , 1986, Other Conferences.

[17]  Dong Liu,et al.  Practical methods for retrace error correction in nonnull aspheric testing. , 2009, Optics express.

[18]  James H. Burge,et al.  Stitching of off-axis sub-aperture null measurements of an aspheric surface , 2008, Optical Engineering + Applications.

[19]  Lisong Yan,et al.  Experimental study on subaperture testing with iterative triangulation algorithm. , 2013, Optics express.

[20]  Tao Wei,et al.  Nonnull interferometer simulation for aspheric testing based on ray tracing. , 2011, Applied optics.

[21]  Peng Su,et al.  Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors. , 2010, Applied optics.

[22]  Shengyi Li,et al.  Subaperture stitching test of large steep convex spheres. , 2015, Optics express.