Abstract

In this work multiwavelength digital holography is applied to calculate the volume displacement of various topographic surface features. To accurately measure the volume displacement of macroscopic features, long synthetic wavelengths up to several millimeters are generated using tunable IR laser sources. Practical methods of implementation are considered, including geometric effects of both Michelson and Mach–Zehnder recording configurations and error due to wavelength selection.

© 2014 Optical Society of America

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References

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  1. U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2010).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
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2012

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

2011

2008

2007

J. Kuhn, T. Colomb, F. Montfort, F. Charriere, Y. Emery, E. Cuche, P. Marquet, and C. Despeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007).
[CrossRef]

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans. Image Process. 16, 698–709 (2007).
[CrossRef]

1991

J. Dirckx and W. Decraemer, “Deformation measurements of the human tympanic membrane under static pressure using automated moire topography,” Proc. SPIE 1429, 34–38 (1991).
[CrossRef]

1979

S. Xenofos and C. Jones, “Theoretical aspects and practical applications of Moire topography,” Phys. Med. Biol. 24, 250–261 (1979).
[CrossRef]

Abdelsalam, D.

Banerjee, P.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Barbosa, E.

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Bingham, P.

Bioucas-Dias, J.

J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans. Image Process. 16, 698–709 (2007).
[CrossRef]

Charriere, F.

Colomb, T.

Cuche, E.

Dapore, B.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Decraemer, W.

J. Dirckx and W. Decraemer, “Deformation measurements of the human tympanic membrane under static pressure using automated moire topography,” Proc. SPIE 1429, 34–38 (1991).
[CrossRef]

Despeursinge, C.

Dirckx, J.

J. Dirckx and W. Decraemer, “Deformation measurements of the human tympanic membrane under static pressure using automated moire topography,” Proc. SPIE 1429, 34–38 (1991).
[CrossRef]

Emery, Y.

Fujigaki, M.

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

Gesualdi, M.

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Haus, J.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Jones, C.

S. Xenofos and C. Jones, “Theoretical aspects and practical applications of Moire topography,” Phys. Med. Biol. 24, 250–261 (1979).
[CrossRef]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2010).

Kawagishi, N.

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

Kim, D.

Kreis, T.

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

Kuhn, J.

Lima, E.

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Magnusson, R.

Mann, C.

Marquet, P.

Matui, T.

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

McManamon, P.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Miller, N.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Montfort, F.

Morimoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

Muramatsu, M.

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Nehmetallah, G.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Paquit, V.

Powers, P.

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2010).

Tobin, K.

Valadao, G.

J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans. Image Process. 16, 698–709 (2007).
[CrossRef]

Xenofos, S.

S. Xenofos and C. Jones, “Theoretical aspects and practical applications of Moire topography,” Phys. Med. Biol. 24, 250–261 (1979).
[CrossRef]

Appl. Opt.

IEEE Trans. Image Process.

J. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Trans. Image Process. 16, 698–709 (2007).
[CrossRef]

Opt. Eng.

E. Barbosa, E. Lima, M. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Y. Morimoto, T. Matui, M. Fujigaki, and N. Kawagishi, “Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry,” Opt. Eng. 46, 025603 (2007).
[CrossRef]

Opt. Express

Phys. Med. Biol.

S. Xenofos and C. Jones, “Theoretical aspects and practical applications of Moire topography,” Phys. Med. Biol. 24, 250–261 (1979).
[CrossRef]

Proc. SPIE

J. Haus, B. Dapore, N. Miller, P. Banerjee, G. Nehmetallah, P. Powers, and P. McManamon, “Instantaneously captured images using multiwavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

J. Dirckx and W. Decraemer, “Deformation measurements of the human tympanic membrane under static pressure using automated moire topography,” Proc. SPIE 1429, 34–38 (1991).
[CrossRef]

Other

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2010).

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

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

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Figures (6)

Fig. 1.
Fig. 1.

Synthetic wavelength as a function of the variable wavelength λ1, with λ2=766nm.

Fig. 2.
Fig. 2.

Length of phase accumulation in relation to object height, htrue, and incident angle.

Fig. 3.
Fig. 3.

Percent error in Λ as a function of (a) λ1 and (b) Λ, for the measured values of σλ1=±0.0085nm and σλ2=±0.0092nm.

Fig. 4.
Fig. 4.

Illustration of holographic volume calculation. (a) The unwrapped phase surface (e.g., an asymmetric Gaussian surface) with the region of integration bounding the area of interest, (b) the reference volume, which is then subtracted from the volume found in (a) to yield the volume of the Gaussian cap only, (c) contour map of the tilted surface, and (d) contour map determined from (c) after numerical flattening, i.e., reducing the average “bias” incline to zero.

Fig. 5.
Fig. 5.

Modified Michelson configuration (a) allowing for object illumination at normal incidence with a tilted reference wave and Mach–Zehnder configuration (b) with 45° object illumination angle.

Fig. 6.
Fig. 6.

Illustration of the MDH volume calculation process for Λ=1.869mm (color online). (a) Photograph of the dent in an aluminum test surface, (b) one of the reconstructed holograms, (c) the wrapped 2D phase map after phase subtraction, (d) the unwrapped 2D phase map via PUMA algorithm, (e) distance-scaled 3D topographic map, (f) contour map illustrating topography, (g) 3D topographic map including the reference surface (red circular area), and (h) the reference volume without topographic map.

Equations (7)

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

φλ1,2(ξ,η)=arctanImΓ1,2(ξ,η)ReΓ1,2(ξ,η),
Δφ={φλ1φλ2ifφλ1φλ2,φλ1φλ2+2πifφλ1<φλ2.
Λ=λ1·λ2|λ1λ2|.
htrue=Λ·Δφ·cosθ4π.
σΛ2=(Λλ1)2σλ12+(Λλ2)2σλ22,
σΛ=Λ2(σλ1λ12)2+(σλ2λ22)2.
Volume=|AϕΛdA±AρdS|,

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