Abstract

We present an integrated sensor based on a grating interferometer (GI) for in-plane displacement measurement in microregions of large engineering structures. The system concept and design, based on a monolithic version of Czarnek’s GI, is discussed in detail. The technology chain of the GI measurement head (MH), including the master fabrication and further replication by means of hot embossing, is described. The numerical analyses of the MH by means of geometric ray tracing and scalar wave propagation are provided. They allow us to determine geometrical tolerance values as well as refractive index homogeneity and nonflatness of MH working surfaces, which provide proper beam guiding. Finally the demonstrative measurement performed with a model of the sensor is presented.

© 2010 Optical Society of America

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References

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  1. J. Dally and W. Riley, “Strain gauges,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 2.
  2. F. Yu and S. Yin, Fiber Optic Sensors (Marcel Dekker, 2002).
    [CrossRef]
  3. T. Kreis, “Digital holography and holographic interferometry,” Machine Graphics Vis. 8, 611–624 (1999).
  4. T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).
  5. W. Ranson, M. Sutton, and W. Peters, “Holographic and laser speckle interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 8.
  6. D. Post, “Moire interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 7.
  7. L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
    [CrossRef]
  8. D. Post, B. Han, and P. Ifju, High Sensitivity Moire Interferometry (Springer-Verlag, 1994).
    [CrossRef]
  9. K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).
  10. R. Czarnek, “High sensitivity moire interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).
    [CrossRef]
  11. J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
    [CrossRef]
  12. B. Han, “Microscopic moiré interferometry,” in Handbook of Moiré Measurement (Institute of Physics, 2004).
  13. L. Salbut, “Waveguide grating (moiré) microinterferometer for in-plane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
    [CrossRef]
  14. J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.
  15. R. Krajewski, “Development of concept and technology chain of miniaturized interferometer for tomographic investigations of 3D refractive index distribution in optical fibers,” Ph.D.dissertation, Institute of Micromechanics and Photonics, Faculty of Mechatronics (Warsaw University of Technology, 2010).
  16. M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
    [CrossRef]
  17. S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.
  18. N. Lindlein and H. Herzig, “Design and modeling of a miniature system containing micro-optics,” Proc. SPIE 4437, 1–13 (2001)
    [CrossRef]
  19. T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Express 17, 13758–13767 (2009).
    [CrossRef] [PubMed]
  20. J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
    [CrossRef]
  21. http://www.veeco.com/.
  22. D. Bone, H. Bachor, and R. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

2005 (1)

L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
[CrossRef]

2002 (1)

L. Salbut, “Waveguide grating (moiré) microinterferometer for in-plane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

2001 (1)

N. Lindlein and H. Herzig, “Design and modeling of a miniature system containing micro-optics,” Proc. SPIE 4437, 1–13 (2001)
[CrossRef]

1999 (1)

T. Kreis, “Digital holography and holographic interferometry,” Machine Graphics Vis. 8, 611–624 (1999).

1998 (1)

M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

1990 (1)

R. Czarnek, “High sensitivity moire interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).
[CrossRef]

1986 (1)

1976 (1)

J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Bacher, W.

M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Bachor, H.

Bargiel, S.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Bone, D.

Callet, D.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Czarnek, R.

R. Czarnek, “High sensitivity moire interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).
[CrossRef]

Dally, J.

J. Dally and W. Riley, “Strain gauges,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 2.

Dymny, G.

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

Dziuban, P.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Fleck, J.

J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Frank, S.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Freit, M.

J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Gorecki, C.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Guttmann, M.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Han, B.

D. Post, B. Han, and P. Ifju, High Sensitivity Moire Interferometry (Springer-Verlag, 1994).
[CrossRef]

B. Han, “Microscopic moiré interferometry,” in Handbook of Moiré Measurement (Institute of Physics, 2004).

Heckele, M.

M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Herzig, H.

N. Lindlein and H. Herzig, “Design and modeling of a miniature system containing micro-optics,” Proc. SPIE 4437, 1–13 (2001)
[CrossRef]

Ifju, P.

D. Post, B. Han, and P. Ifju, High Sensitivity Moire Interferometry (Springer-Verlag, 1994).
[CrossRef]

Jourlin, Y.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Jozwik, M.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Keranen, K.

J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.

Kozacki, T.

Krajewski, R.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

R. Krajewski, “Development of concept and technology chain of miniaturized interferometer for tomographic investigations of 3D refractive index distribution in optical fibers,” Ph.D.dissertation, Institute of Micromechanics and Photonics, Faculty of Mechatronics (Warsaw University of Technology, 2010).

Kreis, T.

T. Kreis, “Digital holography and holographic interferometry,” Machine Graphics Vis. 8, 611–624 (1999).

T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

Krezel, J.

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
[CrossRef]

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.

Kujawinska, M.

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
[CrossRef]

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.

Laszczyk, K.

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Lindlein, N.

N. Lindlein and H. Herzig, “Design and modeling of a miniature system containing micro-optics,” Proc. SPIE 4437, 1–13 (2001)
[CrossRef]

Morris, J.

J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Mueller, K.

M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Peters, W.

W. Ranson, M. Sutton, and W. Peters, “Holographic and laser speckle interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 8.

Post, D.

D. Post, “Moire interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 7.

D. Post, B. Han, and P. Ifju, High Sensitivity Moire Interferometry (Springer-Verlag, 1994).
[CrossRef]

Ranson, W.

W. Ranson, M. Sutton, and W. Peters, “Holographic and laser speckle interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 8.

Reynaud, S.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Riley, W.

J. Dally and W. Riley, “Strain gauges,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 2.

Salbut, L.

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
[CrossRef]

L. Salbut, “Waveguide grating (moiré) microinterferometer for in-plane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.

Sandeman, R.

Sutton, M.

W. Ranson, M. Sutton, and W. Peters, “Holographic and laser speckle interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 8.

Tonchev, S.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Wissmann, M.

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

Yin, S.

F. Yu and S. Yin, Fiber Optic Sensors (Marcel Dekker, 2002).
[CrossRef]

Yu, F.

F. Yu and S. Yin, Fiber Optic Sensors (Marcel Dekker, 2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

J. Fleck, J. Morris, and M. Freit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Machine Graphics Vis. (1)

T. Kreis, “Digital holography and holographic interferometry,” Machine Graphics Vis. 8, 611–624 (1999).

Microsyst. Technol. (1)

M. Heckele, W. Bacher, and K. Mueller, “Hot embossing—The molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Opt. Eng. (1)

L. Salbut, “Waveguide grating (moiré) microinterferometer for in-plane displacement/strain field investigation,” Opt. Eng. 41, 626–631 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

R. Czarnek, “High sensitivity moire interferometry with compact achromatic interferometer,” Opt. Lasers Eng. 13, 99–115 (1990).
[CrossRef]

Proc. SPIE (3)

J. Krezel, M. Kujawinska, G. Dymny, and L. Salbut, “Design and testing of low-cost full-field, integrated optical extensometer,” Proc. SPIE 7003, 70030X (2008).
[CrossRef]

N. Lindlein and H. Herzig, “Design and modeling of a miniature system containing micro-optics,” Proc. SPIE 4437, 1–13 (2001)
[CrossRef]

L. Salbut, M. Kujawinska, and J. Krezel, “Laser waveguide microinterferometer integrated with MEMS platforms,” Proc. SPIE 5958, 59580M (2005).
[CrossRef]

Sens. Actuators A, Phys. (1)

K. Laszczyk, S. Bargiel, C. Gorecki, J. Krezel, P. Dziuban, M. Kujawinska, D. Callet, and S. Frank, “A two directional electrostatic comb-drive X–Y microstage for MOEMS applications,” Sens. Actuators A, Phys. 163, 255–265 (2010).

Other (11)

S. Tonchev, Y. Jourlin, S. Reynaud, M. Guttmann, M. Wissmann, R. Krajewski, and M. Jozwik, “Photolithography of variable depth gratings on a polymer substrate for the mastering of 3D diffractive optical elements,” 14th Microoptics Conference, Brussels, Belgium, 25–27 September 2008.

B. Han, “Microscopic moiré interferometry,” in Handbook of Moiré Measurement (Institute of Physics, 2004).

J. Krezel, M. Kujawinska, L. Salbut, and K. Keranen, “The studies of the illumination/detection module in integrated microinterferometric extensometer,” in Recent Advances in Mechatronics (Springer Verlag, 2007), pp. 637–642.

R. Krajewski, “Development of concept and technology chain of miniaturized interferometer for tomographic investigations of 3D refractive index distribution in optical fibers,” Ph.D.dissertation, Institute of Micromechanics and Photonics, Faculty of Mechatronics (Warsaw University of Technology, 2010).

D. Post, B. Han, and P. Ifju, High Sensitivity Moire Interferometry (Springer-Verlag, 1994).
[CrossRef]

J. Dally and W. Riley, “Strain gauges,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 2.

F. Yu and S. Yin, Fiber Optic Sensors (Marcel Dekker, 2002).
[CrossRef]

T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2005).

W. Ranson, M. Sutton, and W. Peters, “Holographic and laser speckle interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 8.

D. Post, “Moire interferometry,” in Handbook of Experimental Mechanics (Prentice-Hall, 1987), Chap. 7.

http://www.veeco.com/.

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Figures (11)

Fig. 1
Fig. 1

Grating interferometry: (a) the principle, (b) setup according to Czarnek’s concept [10], and (c) setup according to the modified Czarnek’s concept [11]. OG, reflective object grating; L, imaging lens; F, physical load of the measured object; Σ A i Σ B , mutually coherent beams with flat wavefronts; Σ A i Σ B , conjugated object beam carrying information on the object state; M, mirror; A, input beam; B, two conjugated output beams; RDG, reference diffraction grating; ODG, object diffraction grating.

Fig. 2
Fig. 2

General concept of the integrated grating interferometer.

Fig. 3
Fig. 3

Measurement head geometry: (a) monolithic version of Czarnek’s interferometer (MCI) and (b) modified monolithic version of Czarnek’s interferometer (MMCI). RDG, reference diffraction grating; ODG, object diffraction grating; RL, reflective layer.

Fig. 4
Fig. 4

PMMA master fabrication.

Fig. 5
Fig. 5

Replication technology chain.

Fig. 6
Fig. 6

Geometrical tolerances of master: (a) linear and angular tolerances and (b) tolerances of reference grating’s period and angular orientation.

Fig. 7
Fig. 7

Investigation of the local shape of the MH facets’ influence on beam propagation: (a) chosen profile along the x axis and (b) numerically modeled cases of surface local shape (F0—F6). A, MH input beam; RDG, reference diffraction grating; ODG, object diffraction grating; B, conjugated output beams.

Fig. 8
Fig. 8

Analysis of the influence of refractive index distribution on beam propagation diagram.

Fig. 9
Fig. 9

Refractive index distribution: (a) the MH orientation, (b) qualitative stress distribution (FEM), (c) analytical Gaussian elements, and (d) analytical model of refractive index distribution. MH, measurement head replica; A, MH input beam; B, two conjugated output beams.

Fig. 10
Fig. 10

Influence of inhomogeneous refractive index distribution on the output phase difference: (a) map of 2D refractive index distribution along the propagation path and (b) phase difference of interfering output beams. A, input beam; B, two output beam; RF, reflective layer; RGD, reference diffraction grating; ODG, object diffraction grating.

Fig. 11
Fig. 11

Results of u ( x , y ) displacement measurements: (a) contour map of systematic error of the sensor and (b) displacement contour map of the aluminum sample. A, B, and C, local defects increasing the systematic error.

Tables (1)

Tables Icon

Table 1 Acceptable Surface Defects (Nonflatness)

Equations (2)

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

I ( x , y ) = ( Σ A + Σ B ) ( Σ A + Σ B ) * = 2 ( 1 + cos ( ( 4 π u ( x , y ) ) / d ) ) ,
δ n ( x , y , z ) = a * exp ( d 2 / b 2 ) ,

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