Abstract

An optical measurement method to get the in-plane and out-of-plane displacements of a local surface using a laser is proposed. The proposed method simultaneously derives the in-plane and out-of-plane displacements by measuring the shift of interference fringes formed by scattered beams. The average errors of the in-plane and out-of-plane displacement measurements are significantly smaller than 10nm. Moreover, the proposed method uses only low-cost optical elements.

© 2009 Optical Society of America

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References

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  1. C. M. Vest (Wiley, 1979).
  2. K. J. Gasvik, Optical Metrology, 3rd ed. (Wiley, 2002).
    [CrossRef]
  3. Y. Y. Cheng and J. C. Wyant, Appl. Opt. 24, 804 (1985).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).
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    [CrossRef]
  7. Y. Bitou, Appl. Opt. 47, 6219 (2008).
    [CrossRef] [PubMed]
  8. M. Francon, Laser Speckle and Applications in Optics (Academic, 1979).

2008 (1)

2007 (1)

1985 (2)

Bitou, Y.

Cervants, F. G.

Cheng, Y. Y.

Creath, K.

Danzmann, K.

Francon, M.

M. Francon, Laser Speckle and Applications in Optics (Academic, 1979).

Gasvik, K. J.

K. J. Gasvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

Heinzel, G.

Jennrich, O.

Kreis, T.

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).

Marin, A. F. G.

Steier, F.

Vest, C. M.

C. M. Vest (Wiley, 1979).

Wand, V.

Wyant, J. C.

Appl. Opt. (4)

Other (4)

M. Francon, Laser Speckle and Applications in Optics (Academic, 1979).

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).

C. M. Vest (Wiley, 1979).

K. J. Gasvik, Optical Metrology, 3rd ed. (Wiley, 2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the proposed method.

Fig. 2
Fig. 2

Setup for simultaneous measurement of the in-plane and out-of-plane displacements of a local surface.

Fig. 3
Fig. 3

Interference fringes corresponding to u = ( a ) 0 nm , (b) 60 nm , (c) 120 nm , and (d) 180 nm .

Fig. 4
Fig. 4

Relationship between the input displacement u and the measured displacement u * .

Fig. 5
Fig. 5

Interference fringes corresponding to w = ( a ) 0 nm , (b) 60 nm , (c) 120 nm , and (d) 180 nm .

Fig. 6
Fig. 6

Relationship between the input displacement w and the measured displacement w * .

Equations (3)

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u = λ Δ n u 2 sin θ ,
v = λ Δ n v 2 sin ϕ ,
w = λ Δ n w 2 ,

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