Abstract

A shearing interferometer based on using broadband light source, Savart plate, and angular scanning technique is proposed for slope contour measurements in this Letter. Of which, the Savart plate divides the wavefront reflected from the detected surface into two laterally displaced ones, the interference pattern generated by the interference of the divided wavefronts is modulated by an envelope function, and the slope contour of the detected surface is determined by examining the shifting of the darkest fringe as the shear plate is angularly scanned. A setup for realizing the interferometer is constructed. The experimental results of using this setup agree the validity and feasibility of the proposed interferometer.

© 2012 Optical Society of America

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References

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  1. J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
    [CrossRef]
  2. Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
    [CrossRef]
  3. D. Malacara, in Optical Shop Testing, 3rd ed. (Wiley2007), pp 104–106, 122–184.
  4. M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
    [CrossRef]
  5. Y. Y. Hung and J. Q. Wang, Opt. Lasers Eng. 24, 403 (1996).
    [CrossRef]
  6. V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
    [CrossRef]
  7. S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
    [CrossRef]
  8. E. Mihaylova, M. Whelan, and V. Toal, Opt. Lett. 29, 1264 (2004).
    [CrossRef]
  9. S. Nakadate, Opt. Lasers Eng. 26, 331 (1997).
    [CrossRef]
  10. H. H. Lee, J. H. You, and S. H. Park, Opt. Lett. 28, 2243 (2003).
    [CrossRef]
  11. J. B. Song, Y. W. Lee, I. W. Lee, and Y. H. Lee, Appl. Opt. 43, 3989 (2004).
    [CrossRef]
  12. D. W. Griffin, Opt. Lett. 26, 140 (2001).
    [CrossRef]
  13. S. Zhao and P. S. Chung, Opt. Eng. 45, 105606 (2006).
    [CrossRef]
  14. S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
    [CrossRef]
  15. V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
    [CrossRef]
  16. X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
    [CrossRef]
  17. L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
    [CrossRef]
  18. D. W. Robinson and D. C. Williams, Opt. Commun. 57, 26 (1986).
    [CrossRef]
  19. K. J. Gasvik, in Optical Metrology (Wiley2002), pp 56–61, 290–296.
  20. C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
    [CrossRef]
  21. http://www.halbo.com/sav_plat.htm .
  22. A. Yariv and P. Yeh, in Optical Wave in Crystals (Wiley1984), pp. 121–129.

2010 (1)

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

2009 (1)

X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
[CrossRef]

2007 (2)

S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
[CrossRef]

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

2006 (3)

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

S. Zhao and P. S. Chung, Opt. Eng. 45, 105606 (2006).
[CrossRef]

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

2005 (2)

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
[CrossRef]

2004 (2)

2003 (1)

2001 (1)

1998 (1)

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

1997 (2)

S. Nakadate, Opt. Lasers Eng. 26, 331 (1997).
[CrossRef]

M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
[CrossRef]

1996 (1)

Y. Y. Hung and J. Q. Wang, Opt. Lasers Eng. 24, 403 (1996).
[CrossRef]

1986 (1)

D. W. Robinson and D. C. Williams, Opt. Commun. 57, 26 (1986).
[CrossRef]

Asundi, A.

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Barnes, T. H.

Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
[CrossRef]

Chung, P. S.

S. Zhao and P. S. Chung, Opt. Eng. 45, 105606 (2006).
[CrossRef]

Feng, H. N.

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

Gasvik, K. J.

K. J. Gasvik, in Optical Metrology (Wiley2002), pp 56–61, 290–296.

Griffin, D. W.

Guo, X.

X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
[CrossRef]

Habraken, S.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Huang, H.

X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
[CrossRef]

Hung, M. Y. Y.

M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung and J. Q. Wang, Opt. Lasers Eng. 24, 403 (1996).
[CrossRef]

Lee, H. H.

Lee, I. W.

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

J. B. Song, Y. W. Lee, I. W. Lee, and Y. H. Lee, Appl. Opt. 43, 3989 (2004).
[CrossRef]

Lee, J. U.

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

Lee, Y. H.

Lee, Y. W.

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

J. B. Song, Y. W. Lee, I. W. Lee, and Y. H. Lee, Appl. Opt. 43, 3989 (2004).
[CrossRef]

Li, Y.

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

Liao, Y. C.

S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
[CrossRef]

Lin, K. T.

S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
[CrossRef]

Lin, S. T.

S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
[CrossRef]

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

Lion, Y.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Liu, L.

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Lo, Y. H.

Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
[CrossRef]

Long, K. W.

M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
[CrossRef]

Luan, Z.

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Malacara, D.

D. Malacara, in Optical Shop Testing, 3rd ed. (Wiley2007), pp 104–106, 122–184.

Michel, F.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Mihaylova, E.

Moreau, V.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Murukeshan, V. M.

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Nakadate, S.

S. Nakadate, Opt. Lasers Eng. 26, 331 (1997).
[CrossRef]

Park, S. H.

Peng, Z.

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

Renotte, Y.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Robinson, D. W.

D. W. Robinson and D. C. Williams, Opt. Commun. 57, 26 (1986).
[CrossRef]

Rosso, V.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Seng, O. L.

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Shih, S. H.

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

Somervell, A. R. D.

Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
[CrossRef]

Song, J. B.

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

J. B. Song, Y. W. Lee, I. W. Lee, and Y. H. Lee, Appl. Opt. 43, 3989 (2004).
[CrossRef]

Sun, J.

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Tilkens, B.

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

Toal, V.

Tsai, T. C.

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

Wang, J. Q.

M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
[CrossRef]

Y. Y. Hung and J. Q. Wang, Opt. Lasers Eng. 24, 403 (1996).
[CrossRef]

Wang, L.

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Whelan, M.

Williams, D. C.

D. W. Robinson and D. C. Williams, Opt. Commun. 57, 26 (1986).
[CrossRef]

Xiangli, B.

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, in Optical Wave in Crystals (Wiley1984), pp. 121–129.

Yeh, P.

A. Yariv and P. Yeh, in Optical Wave in Crystals (Wiley1984), pp. 121–129.

You, J. H.

Zeng, A.

X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
[CrossRef]

Zhang, C.

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

Zhao, B.

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

Zhao, S.

S. Zhao and P. S. Chung, Opt. Eng. 45, 105606 (2006).
[CrossRef]

Zhou, Y.

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Appl. Opt. (1)

Opt. Commun. (2)

S. T. Lin, K. T. Lin, and Y. C. Liao, Opt. Commun. 276, 201 (2007).
[CrossRef]

D. W. Robinson and D. C. Williams, Opt. Commun. 57, 26 (1986).
[CrossRef]

Opt. Eng. (3)

V. Rosso, Y. Renotte, S. Habraken, Y. Lion, F. Michel, V. Moreau, and B. Tilkens, Opt. Eng. 46, 105601 (2007).
[CrossRef]

S. T. Lin, S. H. Shih, H. N. Feng, and T. C. Tsai, Opt. Eng. 45, 125602 (2006).
[CrossRef]

S. Zhao and P. S. Chung, Opt. Eng. 45, 105606 (2006).
[CrossRef]

Opt. Laser Technol. (1)

V. M. Murukeshan, O. L. Seng, and A. Asundi, Opt. Laser Technol. 30, 527 (1998).
[CrossRef]

Opt. Lasers Eng. (4)

Y. H. Lo, A. R. D. Somervell, and T. H. Barnes, Opt. Lasers Eng. 43, 33 (2005).
[CrossRef]

M. Y. Y. Hung, K. W. Long, and J. Q. Wang, Opt. Lasers Eng. 27, 61 (1997).
[CrossRef]

Y. Y. Hung and J. Q. Wang, Opt. Lasers Eng. 24, 403 (1996).
[CrossRef]

S. Nakadate, Opt. Lasers Eng. 26, 331 (1997).
[CrossRef]

Opt. Lett. (3)

Optik (1)

L. Wang, L. Liu, Z. Luan, J. Sun, and Y. Zhou, Optik 121, 358 (2010).
[CrossRef]

Proc. SPIE (3)

C. Zhang, B. Zhao, B. Xiangli, Y. Li, and Z. Peng, Proc. SPIE 6150, 615001 (2006).
[CrossRef]

X. Guo, A. Zeng, and H. HuangProc. SPIE 7160, 71602D-1 (2009).
[CrossRef]

J. B. Song, Y. W. Lee, I. W. Lee, and J. U. Lee, Proc. SPIE 5638, 902 (2005).
[CrossRef]

Other (4)

D. Malacara, in Optical Shop Testing, 3rd ed. (Wiley2007), pp 104–106, 122–184.

K. J. Gasvik, in Optical Metrology (Wiley2002), pp 56–61, 290–296.

http://www.halbo.com/sav_plat.htm .

A. Yariv and P. Yeh, in Optical Wave in Crystals (Wiley1984), pp. 121–129.

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of the proposed shearing interferometer.

Fig. 2.
Fig. 2.

The interference patterns corresponding to (a) 0, (b) 44.69, (c) −89.38, (d) 134.07, (e) 178.76, and (f) 223.45 arc-sec rotations of the rotation stage. The numbers in (a) represent the orders of the fringes.

Fig. 3.
Fig. 3.

(a) interference pattern with zeroth-order fringe passing through its center; (b) the measured contour of the slope of the grating sample.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Eem=MARπ/4MSPMSMSPRπ/4MpEin.
Eem=[VXVY],
Ein=[V0V0],
Mp=[1000],
MA=[0001],
MSP=[ejΦ/400ejΦ/4],
MS=[ejϕ/200ejϕ/2].
I=12V02(1cosδ).
I=12V02(1γcosδ).
δ=Φϕ.
Φ=4πλcSΔα.
ϕ=4πλcW(x,y)xS.
W(x,y)x=Δα.

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