Abstract

Three-wavelength digital holography is applied to obtain surface height measurements over several microns of range, while simultaneously maintaining the low noise precision of the single wavelength phase measurement. The precision is preserved by the use of intermediate synthetic wavelength steps generated from the three wavelengths and the use of hierarchical optical phase unwrapping. As the complex wave-front of each wavelength can be captured simultaneously in one digital image, real-time performance is achievable.

© 2008 Optical Society of America

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  1. U. Schnars and W. P. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-81 (1994).
    [CrossRef] [PubMed]
  2. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  3. E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999).
    [CrossRef]
  4. K. W. Tobin, P. R Bingham, and J. R Price, "Optical Spatial Heterodyned Interferometry and Inspection of Micro-Electro-Mechanical Systems," Proc. SPIE 6356, 63560G (2007).
    [CrossRef]
  5. C. Mann, L. Yu, C. M. Lo, and M. Kim, "High-resolution quantitative phase-contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (2005).
    [CrossRef] [PubMed]
  6. P. Ferraro, G. Coppola, S. De Nicola, A. Finizio, and G. Pierattini, "Digital holographic microscope with automatic focus tracking by detecting sample displacement in real time," Opt. Lett. 28, 1257-1259 (2003).
    [CrossRef] [PubMed]
  7. C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).
  8. J. M. Huntley and H. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
    [CrossRef] [PubMed]
  9. J. Gass, A. Dakoff, and M. K. Kim, "Phase imaging without 2?? ambiguity by multiple-wavelength digital holography," Opt. Lett. 28, 1141-1143 (2003).
    [CrossRef] [PubMed]
  10. A. Wada, M. Kato, and Y. Ishii, "Multiple-wavelength digital holographic interferometry using tunable laser diodes," Appl. Opt. 47, 2053-2060 (2008).
    [CrossRef] [PubMed]
  11. Y.-Y. Cheng and J. C. Wyant, "Multiple-wavelength phase-shifting interferometry," Appl. Opt. 24, 804-807 (1985).
    [CrossRef] [PubMed]
  12. U. Skudayski and W. P. Jüptner, "Synthetic wavelength interferometry for the extension of the dynamic range," Proc. SPIE 1508, 68-72 (1991).
    [CrossRef]
  13. R. Dandliker, R. Thalmann, and D. Prongue, "Two-wavelength laser interferometry using superheterodyne detection," Opt. Lett. 13, 339-341 (1988).
    [CrossRef] [PubMed]
  14. C. Polhemus, "Two-wavelength interferometry," Appl. Opt. 12, 2071-2074 (1973).
    [CrossRef] [PubMed]
  15. Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
    [CrossRef]
  16. N. Warnasooriya and M. K. Kim, "LED-based multi-wavelength phase imaging interference microscopy," Opt. Express 15, 9239-9247 (2007).
    [CrossRef] [PubMed]
  17. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, "Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition," Opt. Express 15, 7231-7242 (2007).
    [CrossRef] [PubMed]
  18. P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, "Quantitative Phase Microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography," Opt. Express 15, 14591-14600 (2007).
    [CrossRef] [PubMed]
  19. W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
    [CrossRef]
  20. C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
    [CrossRef]
  21. W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
    [CrossRef]
  22. U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).
  23. D.  Parshall and M. K.  Kim, "Digital holographic microscopy with dual wavelength phase unwrapping," Appl. Opt.  45, 451-459 (2006).
    [CrossRef] [PubMed]
  24. P. de Groot and S. Kishner, "Synthetic wavelength stabilization for two-color laser-diode interferometry," Appl. Opt. 30, 4026-4033 (1991).
    [CrossRef] [PubMed]

2008 (1)

2007 (4)

2006 (1)

2005 (1)

2003 (2)

2002 (1)

C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).

2000 (1)

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

1999 (1)

1996 (3)

W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
[CrossRef]

W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
[CrossRef]

1994 (1)

1993 (1)

1991 (2)

U. Skudayski and W. P. Jüptner, "Synthetic wavelength interferometry for the extension of the dynamic range," Proc. SPIE 1508, 68-72 (1991).
[CrossRef]

P. de Groot and S. Kishner, "Synthetic wavelength stabilization for two-color laser-diode interferometry," Appl. Opt. 30, 4026-4033 (1991).
[CrossRef] [PubMed]

1988 (1)

1985 (1)

1973 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Andra, P.

W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
[CrossRef]

Andrä, P.

W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Bevilacqua, F.

Bingham, P. R

K. W. Tobin, P. R Bingham, and J. R Price, "Optical Spatial Heterodyned Interferometry and Inspection of Micro-Electro-Mechanical Systems," Proc. SPIE 6356, 63560G (2007).
[CrossRef]

Cai, L.

C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).

Charrière, F.

Cheng, Y.-Y.

Colomb, T.

Coppola, G.

Cuche, E.

Dakoff, A.

Dandliker, R.

de Groot, P.

De Nicola, S.

Depeursinge, C.

Emery, Y.

Ferraro, P.

Finizio, A.

Gass, J.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Grilli, S.

Huntley, J. M.

Ishii, Y.

Jüptner, W. P.

U. Schnars and W. P. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-81 (1994).
[CrossRef] [PubMed]

U. Skudayski and W. P. Jüptner, "Synthetic wavelength interferometry for the extension of the dynamic range," Proc. SPIE 1508, 68-72 (1991).
[CrossRef]

Kato, M.

Kim, M.

Kim, M. K.

Kishner, S.

Kühn, J.

Laporta, P.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Lo, C. F.

C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).

Lo, C. M.

Mann, C.

Marquet, P.

Miccio, L.

Montfort, F.

Nadeborn, W.

W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
[CrossRef]

W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Osellame, R.

Osten, W.

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
[CrossRef]

Parshall, D.

Paturzo, M.

Pedrini, G.

Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
[CrossRef]

Peng, X.

C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).

Pierattini, G.

Polhemus, C.

Price, J. R

K. W. Tobin, P. R Bingham, and J. R Price, "Optical Spatial Heterodyned Interferometry and Inspection of Micro-Electro-Mechanical Systems," Proc. SPIE 6356, 63560G (2007).
[CrossRef]

Prongue, D.

Saldner, H.

Schnars, U.

Seebacher, S.

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

Skudayski, U.

U. Skudayski and W. P. Jüptner, "Synthetic wavelength interferometry for the extension of the dynamic range," Proc. SPIE 1508, 68-72 (1991).
[CrossRef]

Thalmann, R.

Tiziani, H.

Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
[CrossRef]

Tobin, K. W.

K. W. Tobin, P. R Bingham, and J. R Price, "Optical Spatial Heterodyned Interferometry and Inspection of Micro-Electro-Mechanical Systems," Proc. SPIE 6356, 63560G (2007).
[CrossRef]

Wada, A.

Wagner, C.

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

Warnasooriya, N.

Wyant, J. C.

Yu, L.

Zou, Y.

Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Opt. Eng. (2)

Y. Zou, G. Pedrini, and H. Tiziani, "Surface contouring in a video frame by changing the wavelength of a diode laser," Opt. Eng. 35, 1074-1079 (1996).
[CrossRef]

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

Opt. Express (4)

Opt. Laser Eng. (1)

W. Nadeborn, P. Andra, and W. Osten "A Robust Procedure for Absolute Phase Measurement," Opt. Laser Eng. 24, 245-260 (1996).
[CrossRef]

Opt. Lett. (4)

Optik (1)

C. F. Lo, X. Peng, and L. Cai, "Surface normal guided method for two-dimensional phase unwrapping," Optik 113, 439-447 (2002).

Proc. SPIE (3)

U. Skudayski and W. P. Jüptner, "Synthetic wavelength interferometry for the extension of the dynamic range," Proc. SPIE 1508, 68-72 (1991).
[CrossRef]

K. W. Tobin, P. R Bingham, and J. R Price, "Optical Spatial Heterodyned Interferometry and Inspection of Micro-Electro-Mechanical Systems," Proc. SPIE 6356, 63560G (2007).
[CrossRef]

W. Osten, W. Nadeborn, and P. Andrä, "General hierarchical approach in absolute phase measurement," Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Other (1)

U. Schnars and W. Jüptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Supplementary Material (1)

» Media 1: MOV (81 KB)     

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Figures (8)

Fig.1.
Fig.1.

Three-wavelength digital hologram (a), and corresponding Fourier spectrum (b).

Fig. 2.
Fig. 2.

Flow-chart representation of the process of hierarchical optical phase unwrapping.

Fig. 3.
Fig. 3.

Simulation of two-wavelength digital holography. (a) Actual height profile of object with a maximum height of h=9.0µm, (b) surface profile plot for z′1 derived from φ1 where λ1=633nm, z′2 derived from φ2 where λ2=612nm, and the corresponding two-wavelength unambiguous surface profile z12 with synthetic wavelength Λ12=18.45µm, derived from the single wavelength profiles z′1 and z′2. (c) 2π ambiguity correction of z′1 using the two-wavelength surface profile z12. (d) Final ambiguity corrected surface height prfile, z1.

Fig. 4.
Fig. 4.

Simulation of three-wavelength digital holography using the same theoretical object as in Fig. 3(a). (a) single-wavelength surface profile z′3 derived from φ3 where λ3=532nm, twowavelength surface profile z′23 derived from φ23 with synthetic wavelength of Λ23=4.07µm, two-wavelength surface profile z′13 derived from φ13 with synthetic wavelength of Λ13=3.33µm and the unambiguous two-wavelength surface profile z13–23 with synthetic wavelength Λ12=18.45µm derived from z′23 and z′13, (b) ambiguity correction of the intermediate synthetic wavelength profile z′13 using z13–23, (c) ambiguity corrected profile, z13, (d) second step ambiguity correction using the phase data from the intermediate profile z13 to correct for the ambiguities in the single-wavelength phase data z′3. e) Final ambiguity corrected surface height profile z3.

Fig. 5.
Fig. 5.

Apparatus for three-wavelength digital holography. λ/2: half-wave plate, PBS: polarizing beamsplitter, λ/4: quarter-wave plate, M.O: microscope objective.

Fig. 6.
Fig. 6.

Three-wavelength digital holography of a USAF 1951 gold-on-chrome resolution target. Structures possess heights of 6.6µm. (a) three-wavelength digital hologram, (b) single-wavelength phase image with λ1=633nm, (c) single-wavelength phase image with λ2=612nm, (d) single-wavelength phase image with λ3=532nm, (e) two-wavelength phase image with synthetic wavelength Λ12=18.45µm, (f) two-wavelength phase image with synthetic wavelength Λ13=3.33µm, (g) final ambiguity-corrected phase image, h) 2π ambiguity correction of the intermediate synthetic wavelength profile z′13 using z13–23, i) ambiguity corrected profile z13, j) second step 2π ambiguity correction of single wavelength profile z′3 using z13, k) final ambiguity corrected surface height profile z3, and l) surface height 3-D rendering of g).

Fig. 7.
Fig. 7.

Three-wavelength digital holography of an infra-red, micro-cantilever device with dimensions of 100µm×88µm. (a) SEM image, (b) amplitude reconstruction, (c) single-wavelength phase image with λ1=633nm, (d) single-wavelength phase image with λ2=612nm, (e) single-wavelength phase image with λ3=532nm, (f) two-wavelength phase image with synthetic wavelength Λ12=18.45µm, (g) three-wavelength final phase image with synthetic wavelength Λ12=18.45µm, and (h) 3D rendering of highlighted area in (g).

Fig. 8.
Fig. 8.

Three-wavelength quantitative phase movie of the shape deflection exhibited by an infra-red sensing micro-cantilever. (Fig_8_Can.mov, 81KB)

Equations (7)

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

Λ 12 = λ 1 λ 2 λ 1 λ 2
Λ n + 1 ( 1 4 ε n + 1 ) Λ n ε n
E ( x , y , z ) = 1 { filter [ { U ( x 0 , y 0 , 0 ) } ] exp [ i z 2 π ( 1 λ ) 2 ( f x ) 2 ( f y ) 2 ] }
z n = θ n 4 π λ n
Δ z = z n z n + x
N = floor ( 2 Δ z Λ n + x + 0.5 )
z n + x = z n + x + Λ n + x 2 N

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