Abstract

Multiwavelength shearing interferometry, a full-field, real-time, and vibration-insensitive method with enhanced accuracy, is proposed. Theoretically, the more wavelengths that are used for shearing interferometers, the higher the precision that can be achieved in the measurement of slopes, curvatures, and the shapes of reflective surfaces. A spherical mirror with specified curvature radius is used to calibrate this method, and then the nonuniform deformation and shape of the TiNi film/Si substrate system are obtained experimentally.

© 2013 Optical Society of America

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  1. L. B. Freund, J. Mech. Phys. Solids 48, 1159 (2000).
    [CrossRef]
  2. X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
    [CrossRef]
  3. T. S. Park and S. Suresh, Acta Mater. 48, 3169 (2000).
    [CrossRef]
  4. X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
    [CrossRef]
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    [CrossRef]
  6. X. L. Dong, X. Feng, K.-C. Hwang, S. Ma, and Q. Ma, Opt. Express 19, 13201 (2011)
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
    [CrossRef]
  11. J. A. Floro and E. Chason, Appl. Phys. Lett. 69, 3830 (1996).
    [CrossRef]
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    [CrossRef]
  13. T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
    [CrossRef]
  14. X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
    [CrossRef]
  15. K. Qian, Opt. Lasers Eng. 45, 304 (2007).
    [CrossRef]
  16. H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
    [CrossRef]
  17. H. V. Tippur, Appl. Opt. 31, 4428 (1992).
    [CrossRef]
  18. Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
    [CrossRef]
  19. K. Iizuka, Engineering Optics (Springer, 2008).
  20. G. Birkhoff and H. Garabedian, J. Math. Phys. 39, 258 (1960).

2013

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

2011

S. Xia and M. Mello, Exp. Mech. 51, 653 (2011).
[CrossRef]

X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
[CrossRef]

X. L. Dong, X. Feng, K.-C. Hwang, S. Ma, and Q. Ma, Opt. Express 19, 13201 (2011)
[CrossRef]

2008

X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
[CrossRef]

2007

M. A. Brown, A. J. Rosakis, and X. Feng, Int. J. Solids Struct. 44, 1755 (2007).
[CrossRef]

K. Qian, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

2006

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

2003

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

2001

A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
[CrossRef]

2000

T. S. Park and S. Suresh, Acta Mater. 48, 3169 (2000).
[CrossRef]

L. B. Freund, J. Mech. Phys. Solids 48, 1159 (2000).
[CrossRef]

1998

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

1997

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

1996

J. A. Floro and E. Chason, Appl. Phys. Lett. 69, 3830 (1996).
[CrossRef]

Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
[CrossRef]

1992

1991

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
[CrossRef]

1960

G. Birkhoff and H. Garabedian, J. Math. Phys. 39, 258 (1960).

Birkhoff, G.

G. Birkhoff and H. Garabedian, J. Math. Phys. 39, 258 (1960).

Blech, I. A.

A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
[CrossRef]

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

Brown, M. A.

M. A. Brown, A. J. Rosakis, and X. Feng, Int. J. Solids Struct. 44, 1755 (2007).
[CrossRef]

Chason, E.

J. A. Floro and E. Chason, Appl. Phys. Lett. 69, 3830 (1996).
[CrossRef]

Dong, X.

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
[CrossRef]

Dong, X. L.

Feng, X.

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
[CrossRef]

X. L. Dong, X. Feng, K.-C. Hwang, S. Ma, and Q. Ma, Opt. Express 19, 13201 (2011)
[CrossRef]

X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
[CrossRef]

M. A. Brown, A. J. Rosakis, and X. Feng, Int. J. Solids Struct. 44, 1755 (2007).
[CrossRef]

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

Finot, M.

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

Floro, J. A.

J. A. Floro and E. Chason, Appl. Phys. Lett. 69, 3830 (1996).
[CrossRef]

Freund, L. B.

L. B. Freund, J. Mech. Phys. Solids 48, 1159 (2000).
[CrossRef]

Fujimoto, H.

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

Garabedian, H.

G. Birkhoff and H. Garabedian, J. Math. Phys. 39, 258 (1960).

Giannakopoulos, A. E.

A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
[CrossRef]

Huang, Y.

X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
[CrossRef]

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

Hwang, K.

X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
[CrossRef]

Hwang, K.-C.

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

X. L. Dong, X. Feng, K.-C. Hwang, S. Ma, and Q. Ma, Opt. Express 19, 13201 (2011)
[CrossRef]

Iizuka, K.

K. Iizuka, Engineering Optics (Springer, 2008).

Jiang, H. Q.

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

Kolawa, E.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Krishnaswamy, S.

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
[CrossRef]

Lambros, J.

Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
[CrossRef]

Lee, Y. J.

Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
[CrossRef]

Ma, Q.

Ma, S.

Mello, M.

S. Xia and M. Mello, Exp. Mech. 51, 653 (2011).
[CrossRef]

Moore, N. R.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Ngo, D.

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

Park, T. S.

T. S. Park and S. Suresh, Acta Mater. 48, 3169 (2000).
[CrossRef]

Park, T.-S.

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

Qian, K.

K. Qian, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Rosakis, A. J.

X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
[CrossRef]

M. A. Brown, A. J. Rosakis, and X. Feng, Int. J. Solids Struct. 44, 1755 (2007).
[CrossRef]

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
[CrossRef]

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
[CrossRef]

Ryu, J.

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

Singh, R. P.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Suresh, S.

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
[CrossRef]

T. S. Park and S. Suresh, Acta Mater. 48, 3169 (2000).
[CrossRef]

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

Tippur, H. V.

H. V. Tippur, Appl. Opt. 31, 4428 (1992).
[CrossRef]

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
[CrossRef]

Tsuji, Y.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Xia, S.

S. Xia and M. Mello, Exp. Mech. 51, 653 (2011).
[CrossRef]

Zhang, C.

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

Acta Mater.

A. E. Giannakopoulos, I. A. Blech, and S. Suresh, Acta Mater. 49, 3671 (2001).
[CrossRef]

T. S. Park and S. Suresh, Acta Mater. 48, 3169 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. A. Floro and E. Chason, Appl. Phys. Lett. 69, 3830 (1996).
[CrossRef]

Exp. Mech.

X. Dong, C. Zhang, X. Feng, and K.-C. Hwang, Exp. Mech. 53, 959 (2013).
[CrossRef]

S. Xia and M. Mello, Exp. Mech. 51, 653 (2011).
[CrossRef]

Int. J. Fract.

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, Int. J. Fract. 48, 193 (1991).
[CrossRef]

Int. J. Solids Struct.

M. A. Brown, A. J. Rosakis, and X. Feng, Int. J. Solids Struct. 44, 1755 (2007).
[CrossRef]

J. Appl. Mech.

X. Feng, Y. Huang, and A. J. Rosakis, J. Appl. Mech. 75, 021022 (2008).
[CrossRef]

J. Appl. Phys.

M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 3457 (1997).
[CrossRef]

J. Math. Phys.

G. Birkhoff and H. Garabedian, J. Math. Phys. 39, 258 (1960).

J. Mech. Mater. Struct.

X. Feng, Y. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, J. Mech. Mater. Struct. 1, 1041 (2006).
[CrossRef]

J. Mech. Phys. Solids

L. B. Freund, J. Mech. Phys. Solids 48, 1159 (2000).
[CrossRef]

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, J. Mech. Phys. Solids 51, 2191 (2003).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

Y. J. Lee, J. Lambros, and A. J. Rosakis, Opt. Lasers Eng. 25, 25 (1996).
[CrossRef]

K. Qian, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Thin Solid Films

X. Dong, X. Feng, and K. Hwang, Thin Solid Films 519, 2464 (2011).
[CrossRef]

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore, Thin Solid Films 325, 42 (1998).
[CrossRef]

Other

K. Iizuka, Engineering Optics (Springer, 2008).

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Figures (4)

Fig. 1.
Fig. 1.

Circle fringes from bifurcation of W film/Si substrate in equilibrium, obtained by CGS method. Reprinted from J. Mech. Phys. Solids, 51, T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” pp. 2191–2211 (2003), with permission from Elsevier.

Fig. 2.
Fig. 2.

(a) Schematic diagram of multiwavelength shearing interferometer. (b) Principle of multiwavelength shearing interferometry.

Fig. 3.
Fig. 3.

(a) Schematic diagram of multiwavelength shearing interference. (b) Slopes f,x of the spherical mirror. Contour levels are in 1×104rad.

Fig. 4.
Fig. 4.

Surface topography of the microfilm. (a) Slope f, x in lateral direction. (b) Slope f, y in vertical direction. (c) κxx. (d) κyy. (e) Twist curvature κxy. (f) Topography.

Equations (6)

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

{f,x(xni(x),yni(x))=ni(x)p2Δλi4p,ni(x)=0,±1,±2,f,y(xni(y),yni(y))=ni(y)p2Δλi4p,ni(y)=0,±1,±2,i=1,2,,k,
{Sx(xni(x),yni(x))=f,x(xni(x),yni(x))Sy(xni(y),yni(y))=f,y(xni(y),yni(y)),
{|f,xSx|=O(lx4)|f,ySy|=O(ly4),
{κxx=Sx(x,y)xκyy=Sy(x,y)yκxy=Sx(x,y)y,
z=f(x,y)=Sxdx+(SydSxdxdy)dy.
{f,x=x(x2+y22D)=xDf,y=y(x2+y22D)=yD,

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