Abstract

We propose a novel common-path non-null interference system for the surface measurement of complex optics. Because of the common-path structure, systematic errors are mostly eliminated and the complexity of system calibration is reduced for the proposed setup. However, optical design of common-path non-null interference systems is of great difficulty because many off-axis beams are used to compensate for the local gradient of the measured piece. Different from the classical common-path interferometers, which pay more attention to the beam quality of the on-axis field of view (FOV), the proposed system requires better quality for both on-axis and off-axis outgoing beams. In the proposed setup, the lens groups with wide FOVs afford wave aberrations better than 0.1λ for the on-axis and off-axis FOVs. Simultaneously, the off-axis beams are prevented from generating pseudo reference beams by optimizing the parameters of the lenses and the aperture. In addition, multiple tilted test beams are generated by a point-source generator based on a fiber array, which is more versatile than a lens-array-type point-source generator. Further, a universal measurement system with high accuracy and time savings is formed, as evidenced by the measurement results of a parabolic mirror and different types of cylindrical mirrors.

© 2019 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer

Qun Hao, Shaopu Wang, Yao Hu, Yifeng Tan, Tengfei Li, and Shanshan Wang
Appl. Opt. 57(17) 4743-4750 (2018)

Interferometer for precise and flexible asphere testing

Eugenio Garbusi, Christof Pruss, and Wolfgang Osten
Opt. Lett. 33(24) 2973-2975 (2008)

Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements

Qun Hao, Shaopu Wang, Yao Hu, Hanglin Cheng, Meng Chen, and Tengfei Li
Appl. Opt. 55(35) 9992-10001 (2016)

References

  • View by:
  • |
  • |
  • |

  1. X. Fu, F. Duan, J. Jiang, T. Huang, L. Ma, and C. Lv, “Astigmatism-corrected echelle spectrometer using an off-the-shelf cylindrical lens,” Appl. Opt. 56, 7861–7868 (2017).
    [Crossref]
  2. K. M. Hampson, I. Munro, C. Paterson, and C. Dainty, “Weak correlation between the aberration dynamics of the human eye and the cardiopulmonary system,” J. Opt. Soc. Am. A 22, 1241–1250 (2005).
    [Crossref]
  3. L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nano-displacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt. 51, 2379–2387 (2012).
    [Crossref]
  4. C. H. Liu and Z. H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47, 3968–3972 (2008).
    [Crossref]
  5. H. F. Johnson and H. D. Wolpert, “Cylindrical optics: how to test them,” Photon. Spectra 4, 55–60 (1984).
  6. D. Malacara, Optical Shop Testing (Wiley, 2007).
  7. A. Alatawi and P. J. Reardon, “Absolute interferometric test of cylindrical wavefront with a fiber optic,” Opt. Eng. 53, 114104 (2014).
    [Crossref]
  8. Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
    [Crossref]
  9. J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” Proc. SPIE 5252, 264–272 (2004).
    [Crossref]
  10. E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
    [Crossref]
  11. E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33, 2973–2975 (2008).
    [Crossref]
  12. H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].
  13. H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
    [Crossref]
  14. G. Baer, J. Schindler, C. Pruss, J. Siepmann, and W. Osten, “Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces,” Opt. Express 22, 31200–31211 (2014).
    [Crossref]
  15. J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
    [Crossref]
  16. H. P. Stahl, “Aspheric surface testing techniques,” Proc. SPIE 1332, 66–76 (1990).
    [Crossref]
  17. J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
    [Crossref]

2018 (1)

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

2017 (2)

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

X. Fu, F. Duan, J. Jiang, T. Huang, L. Ma, and C. Lv, “Astigmatism-corrected echelle spectrometer using an off-the-shelf cylindrical lens,” Appl. Opt. 56, 7861–7868 (2017).
[Crossref]

2016 (1)

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

2015 (1)

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

2014 (2)

2013 (1)

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

2012 (1)

2008 (2)

2007 (1)

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

2005 (1)

2004 (1)

J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” Proc. SPIE 5252, 264–272 (2004).
[Crossref]

1990 (1)

H. P. Stahl, “Aspheric surface testing techniques,” Proc. SPIE 1332, 66–76 (1990).
[Crossref]

1984 (1)

H. F. Johnson and H. D. Wolpert, “Cylindrical optics: how to test them,” Photon. Spectra 4, 55–60 (1984).

Alatawi, A.

A. Alatawi and P. J. Reardon, “Absolute interferometric test of cylindrical wavefront with a fiber optic,” Opt. Eng. 53, 114104 (2014).
[Crossref]

Baer, G.

Chen, L.

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

Dainty, C.

Duan, F.

Fu, X.

Gao, J.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

Garbusi, E.

E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33, 2973–2975 (2008).
[Crossref]

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

Hampson, K. M.

Huang, T.

Huang, Y.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Jiang, J.

Johnson, H. F.

H. F. Johnson and H. D. Wolpert, “Cylindrical optics: how to test them,” Photon. Spectra 4, 55–60 (1984).

Kuang, C. F.

Li, B.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

Li, J.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

Li, L.

Li, Z. H.

Liesener, J.

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” Proc. SPIE 5252, 264–272 (2004).
[Crossref]

Liu, C. H.

Liu, M. C.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Liu, X.

Lu, Q.

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

Luo, D.

Lv, C.

Ma, J.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Ma, L.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).

Munro, I.

Osten, W.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

G. Baer, J. Schindler, C. Pruss, J. Siepmann, and W. Osten, “Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces,” Opt. Express 22, 31200–31211 (2014).
[Crossref]

E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33, 2973–2975 (2008).
[Crossref]

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

Paterson, C.

Pruss, C.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

G. Baer, J. Schindler, C. Pruss, J. Siepmann, and W. Osten, “Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces,” Opt. Express 22, 31200–31211 (2014).
[Crossref]

E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33, 2973–2975 (2008).
[Crossref]

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

Reardon, P. J.

A. Alatawi and P. J. Reardon, “Absolute interferometric test of cylindrical wavefront with a fiber optic,” Opt. Eng. 53, 114104 (2014).
[Crossref]

Rong, S.

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

Schindler, J.

Shen, H.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

Siepmann, J.

Stahl, H. P.

H. P. Stahl, “Aspheric surface testing techniques,” Proc. SPIE 1332, 66–76 (1990).
[Crossref]

Sun, W. Y.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Sun, Y.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

Tiziani, H. J.

J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” Proc. SPIE 5252, 264–272 (2004).
[Crossref]

Wang, J.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

Wolpert, H. D.

H. F. Johnson and H. D. Wolpert, “Cylindrical optics: how to test them,” Photon. Spectra 4, 55–60 (1984).

Yuan, C. J.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Zhu, R.

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

Zhu, R. H.

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Act. Opt. Sin. (1)

H. Shen, J. Li, R. Zhu, and S. Rong, “Design of non-null interferometer based on point source array for testing freeform surface,” Act. Opt. Sin. 33, 1222003 (2013) [in Chinese].

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

J. Li, H. Shen, R. Zhu, J. Gao, Y. Sun, J. Wang, and B. Li, “Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm,” Opt. Commun. 417, 67–75 (2018).
[Crossref]

Opt. Eng. (3)

H. Shen, R. Zhu, L. Chen, and J. Li, “Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm,” Opt. Eng. 54, 074105 (2015).
[Crossref]

A. Alatawi and P. J. Reardon, “Absolute interferometric test of cylindrical wavefront with a fiber optic,” Opt. Eng. 53, 114104 (2014).
[Crossref]

Y. Huang, J. Ma, C. J. Yuan, C. Pruss, W. Y. Sun, M. C. Liu, R. H. Zhu, and W. Osten, “Absolute test for cylindrical surfaces using the conjugate differential method,” Opt. Eng. 55, 114104 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Photon. Spectra (1)

H. F. Johnson and H. D. Wolpert, “Cylindrical optics: how to test them,” Photon. Spectra 4, 55–60 (1984).

Proc. SPIE (4)

J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” Proc. SPIE 5252, 264–272 (2004).
[Crossref]

E. Garbusi, C. Pruss, J. Liesener, and W. Osten, “New technique for flexible and rapid measurement of precision aspheres,” Proc. SPIE 6616, 661629 (2007).
[Crossref]

J. Li, H. Shen, R. Zhu, and Q. Lu, “New technique for generating light source array in tilted wave interferometer,” Proc. SPIE 10329, 1032928 (2017).
[Crossref]

H. P. Stahl, “Aspheric surface testing techniques,” Proc. SPIE 1332, 66–76 (1990).
[Crossref]

Other (1)

D. Malacara, Optical Shop Testing (Wiley, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1. Schematic of the proposed interferometer. L, laser source; FCOS, mainly composed of fiber couplers and optical switches; FA, fiber array; BS, beam splitter; C, collimator; S, transmission sphere; B, interferometer aperture; I, imaging lens; TS, test surface.
Fig. 2.
Fig. 2. Point-source array and fringes obtained by CGW technology for different measurement objects. (a) Point sources for measuring a parabolic surface, with the corresponding interferograms in (d). (b) Point sources for measuring a cylinder surface, with the corresponding interferograms in (e) and (f). (c) Point sources for measuring a freeform surface, with the corresponding interferograms in (g).
Fig. 3.
Fig. 3. Positions of detectable areas corresponding to the sub-interferograms in Fig. 2(d) for parabolic mirror measurement. The blue areas represent the detectable area of the off-axis light sources, and the red area represents the detectable area of the on-axis light source.
Fig. 4.
Fig. 4. Structure diagram of a collimator and transmission sphere. Beam a denotes the light emitted from the on-axis point source. Beams b and c denote the beams emitted from the off-axis point sources.
Fig. 5.
Fig. 5. Spot diagrams of on-axis and off-axis point sources. (a) Spot diagram of an on-axis point source. (b) and (c) Spot diagrams of off-axis point sources.
Fig. 6.
Fig. 6. Wavefronts of on-axis and off-axis point sources. (a) Wavefront of an on-axis point source. (b) and (c) Wavefronts of off-axis point sources.
Fig. 7.
Fig. 7. Positions of on-axis and off-axis beams reflected by the final optical element of the transmission sphere. Beam a represents the light emitted from the on-axis point source, and the returning light beam a returns along the original beam path. Beams b and c denote the light beams emitted from the off-axis point sources, and their offsets are L and l, respectively. Beams b and c denote the returning light beams corresponding to b and c, with their offsets being L and l, respectively.
Fig. 8.
Fig. 8. (a) Surface deviation of a standard spherical mirror. (b) Wavefront quality of the reference in the common-path system.
Fig. 9.
Fig. 9. (a) Schematic of measuring parabolic mirror A with the method of stigmatic null test. (b) Surface deviation of the parabolic surface. (c) Interferograms obtained by an interferometer for measuring a parabolic mirror with the method of stigmatic null test.
Fig. 10.
Fig. 10. Surface deviations of a parabolic surface. (a) Measurement acquired by means of the proposed setup. (b) Measurement acquired by non-common-path TWI. (c) Interferograms obtained when measuring the parabolic mirror with an off-axis test beam. (d) Interferograms obtained when measuring the parabolic mirror with an on-axis test beam.
Fig. 11.
Fig. 11. Measurement of cylindrical mirror A with use of the proposed setup. (a) The plus symbol denotes locations of point sources for measuring cylindrical mirror A. (b) Surface deviation obtained with proposed setup. (c) Interferograms obtained when measuring the cylindrical mirror A with an off-axis test beam. (d) Interferograms obtained when measuring cylindrical mirror A with an on-axis test beam.
Fig. 12.
Fig. 12. Schematic of measuring cylindrical mirror A with use of CGH.
Fig. 13.
Fig. 13. Measurement results of cylindrical mirror A. (a) Surface deviation of cylindrical mirror A with use of the CGH method. (b) Residual error between results of the CGH method and the proposed setup.
Fig. 14.
Fig. 14. Measurement of cylindrical mirror B with use of the proposed setup. (a) The plus symbol denotes locations of point sources for measuring cylindrical mirror B. (b) Experiment result for cylindrical mirror B.
Fig. 15.
Fig. 15. Measurable area of point sources for testing cylindrical mirrors A and B with different NAs.