Abstract

We present a novel optical configuration of a phase-shifting interferometer for high-accuracy figure metrology of large dioptric convex spherical surfaces. The conformation and design considerations according to measurement accuracy, practicability, and system errors analysis are described. More in detail, we show the design principle and methods for the crucial parts. Some are expounded upon with examples for thorough understanding. The measurement procedures and the alignment approaches are also described. Finally, a verification experiment is further presented to verify our theoretical design. This system gives full-aperture and high-precision surface testing while maintaining relatively low cost and convenient operation.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Ohmura, “The optical design for microlithographic lenses,” Proc. SPIE 6342, 63421T (2007).
    [CrossRef]
  2. T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
    [CrossRef]
  3. 3. http://www.qedmrf.com/metrology/products/ssi-a .
  4. P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O'Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper OFWC2.
  5. M. Bray, “Stitching interferometry–the long and winding road,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMA5.
  6. P. Zhang, H. Zhao, X. Zhou, and J. Li, “Sub-aperture stitching interferometry using stereovision positioning technique,” Opt. Express 18(14), 15216–15222 (2010).
    [CrossRef] [PubMed]
  7. J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
    [CrossRef]
  8. S. Chen, S. Li, Y. Dai, L. Ding, and S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
    [CrossRef] [PubMed]
  9. Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
    [CrossRef]
  10. A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express 16(16), 11975–11986 (2008).
    [CrossRef] [PubMed]
  11. L. Ekstrand and S. Zhang, “Three-dimensional profilometry with nearly focused binary phase-shifting algorithms,” Opt. Lett. 36(23), 4518–4520 (2011).
    [CrossRef] [PubMed]
  12. H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
    [CrossRef]
  13. V. N. Chekal', Y. I. Chudakov, and S. E. Shevtsov, “The use of coordinate-measurement machines to optimize the technology of automatic shaping of optical surfaces,” J. Opt. Technol. 75(11), 755–759 (2008).
    [CrossRef]
  14. J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
    [CrossRef]
  15. B. M. Robinson and P. J. Reardon, “Distortion compensation in interferometric testing of mirrors,” Appl. Opt. 48(3), 560–565 (2009).
    [CrossRef] [PubMed]
  16. N. Bobroff, “Residual errors in laser interferometry from air turbulence and nonlinearity,” Appl. Opt. 26(13), 2676–2682 (1987).
    [CrossRef] [PubMed]
  17. C. Zhao and J. H. Burge, “Vibration-compensated interferometer for surface metrology,” Appl. Opt. 40(34), 6215–6222 (2001).
    [CrossRef] [PubMed]
  18. Z. Shi, J. Zhang, Y. Sui, J. Peng, F. Yan, and H. Yang, “Design of algorithms for phase shifting interferometry using self-convolution of the rectangle window,” Opt. Express 19(15), 14671–14681 (2011).
    [CrossRef] [PubMed]
  19. R. Jóźwicki, “Propagation of an aberrated wave with nonuniform amplitude distribution and its influence upon the interferometric measurement accuracy,” Opt. Appl. 20, 229–252 (1990).
  20. S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).
  21. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
    [CrossRef] [PubMed]
  22. K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29(22), 3280–3285 (1990).
    [CrossRef] [PubMed]
  23. G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
    [CrossRef]
  24. Zygo is a registered trademark of Zygo Corporation.

2011 (3)

2010 (1)

2009 (1)

2008 (4)

2007 (1)

Y. Ohmura, “The optical design for microlithographic lenses,” Proc. SPIE 6342, 63421T (2007).
[CrossRef]

2006 (2)

T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
[CrossRef]

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

2005 (1)

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

2003 (1)

2001 (1)

1995 (1)

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[CrossRef]

1990 (2)

R. Jóźwicki, “Propagation of an aberrated wave with nonuniform amplitude distribution and its influence upon the interferometric measurement accuracy,” Opt. Appl. 20, 229–252 (1990).

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29(22), 3280–3285 (1990).
[CrossRef] [PubMed]

1987 (1)

1949 (1)

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Bobroff, N.

Burge, J. H.

J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
[CrossRef]

C. Zhao and J. H. Burge, “Vibration-compensated interferometer for surface metrology,” Appl. Opt. 40(34), 6215–6222 (2001).
[CrossRef] [PubMed]

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[CrossRef]

Cao, X.

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

Chekal', V. N.

Chen, S.

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, and S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

Chudakov, Y. I.

Dai, Y.

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, and S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

Deck, L. L.

Devries, G.

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

Ding, L.

Dumas, P.

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

Ekstrand, L.

Elster, C.

Fan, T.

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

Forbes, G.

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

Hu, H.

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

Jing, H.

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

Józwicki, R.

R. Jóźwicki, “Propagation of an aberrated wave with nonuniform amplitude distribution and its influence upon the interferometric measurement accuracy,” Opt. Appl. 20, 229–252 (1990).

Kuang, L.

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

Li, J.

Li, S.

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

S. Chen, S. Li, Y. Dai, L. Ding, and S. Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
[CrossRef] [PubMed]

Matsuyama, T.

T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
[CrossRef]

Murphy, P.

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

O'Donohue, S.

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

Ohmura, Y.

Y. Ohmura, “The optical design for microlithographic lenses,” Proc. SPIE 6342, 63421T (2007).
[CrossRef]

T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
[CrossRef]

Okada, K.

Ose, T.

Peng, J.

Reardon, P. J.

Robinson, B. M.

Sakuta, H.

Schulz, M.

Shevtsov, S. E.

Shi, Z.

Su, P.

J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
[CrossRef]

Sui, Y.

Tsujiuchi, J.

Wassermann, G. D.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Wiegmann, A.

Williamson, D. M.

T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
[CrossRef]

Wolf, E.

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Yan, F.

Yang, H.

Zeng, S.

Zhang, J.

Zhang, P.

Zhang, Q.

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

Zhang, S.

Zhao, C.

J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
[CrossRef]

C. Zhao and J. H. Burge, “Vibration-compensated interferometer for surface metrology,” Appl. Opt. 40(34), 6215–6222 (2001).
[CrossRef] [PubMed]

Zhao, H.

Zhou, X.

Appl. Opt. (5)

J. Opt. Technol. (1)

Opt. Appl. (1)

R. Jóźwicki, “Propagation of an aberrated wave with nonuniform amplitude distribution and its influence upon the interferometric measurement accuracy,” Opt. Appl. 20, 229–252 (1990).

Opt. Eng. (1)

Y. Dai, S. Chen, S. Li, H. Hu, and Q. Zhang, “Stylus profilometry for steep aspheric surfaces with multisegment stitching,” Opt. Eng. 50(1), 013601 (2011).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Proc. Phys. Soc. B (1)

G. D. Wassermann and E. Wolf, “On the theory of aplanatic aspheric systems,” Proc. Phys. Soc. B 62(1), 2–8 (1949).
[CrossRef]

Proc. SPIE (6)

J. H. Burge, P. Su, and C. Zhao, “Optical metrology for very large convex aspheres,” Proc. SPIE 7018, 701818 (2008).
[CrossRef]

H. Jing, L. Kuang, T. Fan, and X. Cao, “Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process,” Proc. SPIE 6148, 61480I (2006).
[CrossRef]

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[CrossRef]

S. O'Donohue, G. Devries, P. Murphy, G. Forbes, and P. Dumas, “Calibrating interferometric imaging distortion using subaperture stitching interferometry,” Proc. SPIE 5869, 156–158 (2005).

Y. Ohmura, “The optical design for microlithographic lenses,” Proc. SPIE 6342, 63421T (2007).
[CrossRef]

T. Matsuyama, Y. Ohmura, and D. M. Williamson, “The lithographic lens: its history and evolution,” Proc. SPIE 6154, 615403 (2006).
[CrossRef]

Other (4)

3. http://www.qedmrf.com/metrology/products/ssi-a .

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O'Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper OFWC2.

M. Bray, “Stitching interferometry–the long and winding road,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMA5.

Zygo is a registered trademark of Zygo Corporation.

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

Data of our 12 inch F/0.82 transmission sphere lens.

Fig. 2
Fig. 2

Mainframe of our new type of test bed for large convex surface.

Fig. 3
Fig. 3

Curved object imaged through diverger.

Fig. 4
Fig. 4

Layout of optical design results for f/0.8 diverger lens in our measurement system.

Fig. 5
Fig. 5

Test setup to measure the figure of a large dioptric convex spherical surface with our measurement system. The testing process is composed of two main steps. (a) Step 1: SACA and the lens to be tested are installed and adjusted through monitoring interferograms, which are produced by the back bare surface of the optical flat and the test surface. (b) Step 2: move the optical flat out of light path, install and adjust the reference sphere, and measure figure of test surface by wavelength phase shifting.

Fig. 6
Fig. 6

Sketch map of single-surface refraction.

Fig. 7
Fig. 7

Spherical aberrations introduced in four types of test lenses; the test surface is perpendicular to the rays, so it has no spherical aberrations. (a) Concentric lens, (b) meniscus lens, (c)plano-convex lens, (d) bi-convex lens.

Fig. 8
Fig. 8

Lens having a convex surface to be tested and its three types of aplanatic spherical aberration compensation lenses; (a) L = 0, (b) I = I’ = 0, (c)L = (n + n’)r/n, L’ = (n + n’)r/n’.

Fig. 9
Fig. 9

Spherical aberration compensation lens design for a 260 mm f/1.0 convex spherical surface.

Fig. 10
Fig. 10

SACS design for a 260 mm 500 mm curvature radius convex spherical surface.

Fig. 11
Fig. 11

CGH-type SACs design for a 260 mm 500 mm curvature radius convex spherical surface of a bi-convex lens.

Fig. 12
Fig. 12

Photograph of new system’s experimental setup.

Fig. 13
Fig. 13

Photograph of integration of the SACS and the lens enclosed by the test surface.

Fig. 14
Fig. 14

Photograph of traditional system.

Fig. 15
Fig. 15

Experiment results. (a) The result from the new system. (b) The result from the traditional system. (c) The difference of the figure maps measured by both systems.

Tables (4)

Tables Icon

Table 1 Lens System Prescription for f/0.8 Diverger

Tables Icon

Table 2 Data of 260 mm f/1.0 Convex Surface and Its Spherical Aberration Compensation Lens

Tables Icon

Table 3 Lens System Prescription for Designing a SACs of a 260 mm 500 mm Curvature Radius Convex Spherical Surface

Tables Icon

Table 4 Data of a CGH Type SACs for a 260 mm 500 mm Curvature Radius Convex Spherical Surface of a Bi-convex Lens

Metrics