Desktop version

Home arrow Mathematics

  • Increase font
  • Decrease font


<<   CONTENTS

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51375488) and the National Basic Research Program of China

(Grant No. 2011CB013200). The authors are very grateful to Dr. Chunyu Zhao at the University of Arizona for his help and comments on near-null stitching test.

References

  • 1. D. Malacara, Optical Shop Testing, 3rd ed., John Wiley & Sons, New Jersey (2007).
  • 2. J. C. Wyant, “Optical testing course,” http://fp.optics.arizona.edu/jcwyant/Short_Courses.htm (2008)
  • 3. J. D. Briers, “Optical testing: a review and tutorial for optical engineers,” Opt. Lasers Eng. 32, 111-138 (1999).
  • 4. C. Kim and J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).
  • 5. J. Thunen and O. Kwon, “Full aperture testing with sub-aperture test optics,” Proc. SPIE 351, 1 (1982).
  • 6. W. W. Chow and G. N. Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8, 468-470 (1983).
  • 7. S. C. Jensen, W. W. Chow, and G. N. Lawrence, “Subaperture testing approaches: a comparison,” Appl. Opt. 23, 740-745 (1984).
  • 8. V. N. Mahajan, “Zernike polynomials and wavefront fitting,” in Optical Shop Testing, 3rd ed., pp. 498-546, John Wiley & Sons, New Jersey (2007).
  • 9. T. W. Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118-127 (1986).
  • 10. M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626-635 (1991).
  • 11. W. M. Cheng and M. Y. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32, 1947-1950 (1993).
  • 12. M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444-447 (1992).
  • 13. M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608-613 (1994).
  • 14. M. Bray, “Stitching interferometer for large plano optics using a standard interferometer,” Proc. SPIE 3134, 39-50 (1997).
  • 15. M. Bray, “Stitching interferometer for large optics: recent developments of a system,” Proc. SPIE 3492, 946-956 (1999).
  • 16. S. H. Tang, “Stitching: high-spatial-resolution microsurface measurements over large areas,” Proc. SPIE 3479, 43-49 (1998).
  • 17. J. C. Wyant and J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691-698 (1998).
  • 18. R. D. Day, T. A. Beery, and G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334-341 (1986).
  • 19. G. N. Lawrence and R. D. Day, “Interferometric characterization of full spheres: data reduction techniques,” Appl. Opt. 26, 4875-4882 (1987).
  • 20. U. Griesmann, J. Soons, and Q. Wang, “Measuring form and radius of spheres with interferometry,” CIRPAnn. Manuf. Technol. 53, 451-454 (2004).
  • 21. M. Y. Chen and D. Z. Wu, “Multiaperture overlap-scanning technique for Moire metrology,” Proc. SPIE 2861, 107-112 (1996).
  • 22. J. Peng, Y. Yu, and H. Xu, “Compensation of high-order misalignment aberrations in cylindrical interferometry,” Appl. Opt. 53, 4947-4956 (2014).
  • 23. J. Peng et al., “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26, 025204 (2015).
  • 24. P. Murphy et al., “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38-43 (2003).
  • 25. J. Fleig et al., “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296-307 (2003).
  • 26. M. Tricard et al., “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. Manuf. Technol. 59, 547-550 (2010).
  • 27. Y. M. Liu, G. N. Lawrence, and C. L. Koliopoulo, “Subaperture testing of aspheres with annular zones,” Appl. Opt. 27, 4504-4513 (1988).
  • 28. M. J. Tronolone et al., “Method of testing aspherical optical surfaces with an interferometer,” U.S. Patent 5,416,586 (1995).
  • 29. X. Hou et al., “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15(20), 12890-12899 (2008).
  • 30. M. F. Kuchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
  • 31. S. Chen, S. Li, and Y. Dai, “Iterative algorithm for subaperture stitching interferometry for general surfaces,” J. Opt. Soc. Am. A 22(9), 1929-1936 (2005).
  • 32. S. Chen et al., “Iterative algorithm for subaperture stitching test with spherical interferometers,” J. Opt. Soc. Am. A 23(5), 1219-1226 (2006).
  • 33. S. Chen et al., “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760-4765 (2008).
  • 34. S. Chen et al., “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44(5), 1543-1550 (2012).
  • 35. S. Chen et al., “Testing of large optical surfaces with subaperture stitching,” Appl. Opt. 46(17), 3504-3509 (2007).
  • 36. S. Chen et al., “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047-29058 (2015).
  • 37. S. Chen et al., “Fast and precise registration of quasi-planar free-form wavefronts,” J. Opt. Soc. Am. A 27(7), 1655-1659 (2010).
  • 38. S. Chen et al., “Surface registration-based stitching of quasi-planar free-form wavefronts,” Opt. Eng. 51(6), 063605 (2012).
  • 39. S. Chen et al., “Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates,” Appl. Opt. 51(17), 3817-3825 (2012).
  • 40. S. Chen et al., “Stitching algorithm for subaperture test of convex aspheres with a test plate,” Opt. Laser Technol. 49, 307-315 (2013).
  • 41. S. Chen et al., “Reconfigurable optical null based on counterrotating Zernike plates for test of aspheres,” Opt. Express 22(2), 1381-1386 (2014).
  • 42. S. Chen et al., “Lattice design for subaperture stitching test of concave paraboloid surface,” Appl. Opt. 45(10), 2280-2286 (2006).
  • 43. S. Chen et al., “Calculation of subaperture aspheric departure in lattice design for subaperture stitching interferometry,” Opt. Eng. 49(2), 023601 (2010).
  • 44. P. Zhang et al., “Sub-aperture stitching interferometry using stereovision positioning technique,” Opt. Express 18(14), 15216-15222 (2010).
  • 45. L. Yan et al., “Experimental study on subaperture testing with iterative triangulation algorithm,” Opt. Express 21(19), 22628-22644 (2013).
  • 46. L. Zhang et al., “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Opt. 53(25), 5755-5762 (2014).
  • 47. Y. Wen and H. Cheng, “Measurement of aspheric surfaces using annular subaperture stitching interferometry based on an automatic positioning method: theory and application,” Opt. Eng. 53(7), 074104 (2014).
  • 48. C.-W. Liang et al., “Vibration modulated subaperture stitching interferometry,” Opt. Express 21(15), 18255-18260 (2013).
  • 49. H.-S. Chang et al., “Measurement improvement by high overlapping density subaperture stitching interferometry,” Appl. Opt. 53(29), H102-H108 (2014).
  • 50. S. Chen, S. Li, and G. Wang, “Subaperture test of wavefront error of large telescopes: error sources and stitching performance simulations,” Proc. SPIE 9298, 929817 (2014).
  • 51. K. Z. Smith et al., “Current concepts for cryogenic optical testing of the JWST secondary mirror,” Proc. SPIE 5494, 141-151 (2005).
  • 52. F. Yan et al., “Measurement of large convex hyperbolic mirrors using hindle and stitching methods,” Opt. Lasers Eng. 51, 856-860 (2013).
  • 53. J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
  • 54. G. A. Smith et al., “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).
  • 55. G. A. Smith and J. H. Burge, “Subaperture stitching tolerancing for annular ring geometry,” Appl. Opt. 54(27), 8080-8086 (2015).
  • 56. S. Chang and A. Prata, Jr., “Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes,” J. Opt. Soc. Am. A 22, 2454-2464 (2005).
  • 57. R. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotics Manipulation, CRC Press, Florida (1994).
  • 58. E. Acosta and S. Bara, “Variable aberration generators using rotated Zernike plates,” J. Opt. Soc. Am. A 22, 1993-1996 (2005).
  • 59. J. P. Mills et al., “Conformal dome aberration correction with counter-rotating phase plates,” Proc. SPIE 3705, 201-208 (1999).
  • 60. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Lincoln Lab. Tech. Rep. 854, MIT Lincoln Laboratory, Lexington, Massachusetts (1989).
  • 61. M. Fruit, P. Antoine, and J.-L. Vann, “Development of the SOFIA silicon carbide secondary mirror,” Proc. SPIE 4857, 2744-285 (2003).
  • 62. D. Golini, G. Forbes, and P. Murphy, “Method for self-calibrated sub-aperture stitching for surface figure measurement,” U.S. Patent 6,956,657,B2, QED Technologies Inc. (2005).
  • 63. S. Chen et al., “Parametric registration of cross test error maps for optical surfaces,” Opt. Commun. 346, 158-166 (2015).
  • 64. G. H. Gloub and C. F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore and London (1996).
  • 65. W. X. Liu et al., Solution Methods for Large-Scale Sparse Linear Equations, National Defense Industry Press, Beijing (1981) (in Chinese).
  • 66. G. A. Smith and J. H. Burge, “Subaperture stitching tolerancing for annular ring geometry,” Appl. Opt. 54, 8080-8086 (2015).
  • 67. K. L. Shu, “Ray-trace analysis and data reduction methods for the Ritchey-common test,” Appl. Opt. 22, 1879-1886 (1983).
  • 68. J. E. Yellowhair, “Advanced technologies for fabrication and testing of large flat mirrors,” PhD Dissertation, The University of Arizona, Tucson, Arizona (2007).
  • 69. M. Bray, “Stitching interferometry for the wavefront metrology of x-ray mirrors,” Proc. SPIE 4501, 450107 (2001).
  • 70. J. A. Lipa and G. J. Siddal, “High precision measurement of gyro rotor sphericity,” Precis. Eng. 2, 123-128 (1980).
  • 71. S. Buchman et al., “Cryogenic gyroscopes for the relativity mission,” Physica B 280, 497-498 (2000).
  • 72. T. Kanada, “Estimation of sphericity by means of statistical processing for roundness of spherical parts,” Precis. Eng. 20, 117-122 (1997).
  • 73. Z. Tian et al., “A high-accuracy and convenient figure measurement system for large convex lens,” Opt. Express 20(10), 10761-10775 (2012).
  • 74. B. J. Bauman et al., “Update and image quality error budget for the LSST camera optical design,” Proc. SPIE 7733, 77332W (2010).
  • 75. J. Gou, Y. Chu, and Z. Li, “A geometric theory of form, profile, and orientation tolerances,” Precis. Eng. 23, 79-93 (1999).
 
<<   CONTENTS