Abstract

An extremely simple setup for real-time color digital holography using single-mode fibers as light guides and a directional coupler as a beam-splitting device is presented. With the directional coupler we have two object beams and one residual crosstalk used as a reference beam. This facilitates the adjustment and improves robustness. With the use of graphics processing units, real-time hologram reconstruction was possible. Due to adaptation of the optical setup and scaling, zero-order and complex image influence is highly reduced.

© 2013 Optical Society of America

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References

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  1. M. Lee, O. Yaglidere, and A. Ozcan, “Field-portable reflection and transmission microscopy based on lensless holography,” Biomed. Opt. Express 2, 2721–2730 (2011).
    [CrossRef]
  2. L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
    [CrossRef]
  3. A. M. P. P. Leite, “Optical fibre illuminators for holography,” Opt. Commun. 28, 303–308 (1979).
    [CrossRef]
  4. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  5. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
    [CrossRef]
  6. A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
    [CrossRef]
  7. Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. K. Maejima and K. Sato, “One-shot digital holography for real-time recording of moving color 3-D images,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DMA2.
  15. A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
    [CrossRef]
  16. X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
    [CrossRef]

2011 (2)

2010 (3)

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

2009 (3)

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

C. J. Tay, C. Quan, and W. Chen, “Dynamic measurement by digital holographic interferometry based on complex phasor method,” Opt. Laser Technol. 41, 172–180 (2009).
[CrossRef]

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

2008 (2)

2007 (1)

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

2004 (1)

2002 (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

1984 (1)

H. I. Bjelkhagen, “Pulsed fiber holography: a new technique for hologram interferometry,” Opt. Eng. 24, 244645 (1984).
[CrossRef]

1979 (1)

A. M. P. P. Leite, “Optical fibre illuminators for holography,” Opt. Commun. 28, 303–308 (1979).
[CrossRef]

Ahrenberg, L.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Bjelkhagen, H. I.

H. I. Bjelkhagen, “Pulsed fiber holography: a new technique for hologram interferometry,” Opt. Eng. 24, 244645 (1984).
[CrossRef]

Cai, L. Z.

Chen, W.

C. J. Tay, C. Quan, and W. Chen, “Dynamic measurement by digital holographic interferometry based on complex phasor method,” Opt. Laser Technol. 41, 172–180 (2009).
[CrossRef]

Cheng, X. C.

Dong, G. Y.

Ducin, I.

Fajst, A.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

Finke, G.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

Gorocs, Z.

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

Hennelly, B. M.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Jaroszewicz, L. R.

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kakarenko, K.

Kelly, D. P.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

Kiss, M.

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

Kolodziejczyk, A.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

Kozacki, T.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

Kujawinska, M.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

Lee, M.

Leite, A. M. P. P.

A. M. P. P. Leite, “Optical fibre illuminators for holography,” Opt. Commun. 28, 303–308 (1979).
[CrossRef]

Maejima, K.

K. Maejima and K. Sato, “One-shot digital holography for real-time recording of moving color 3-D images,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DMA2.

Makowski, M.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

McDonald, J. B.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Meng, X. F.

Michalkiewicz, A.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

Monaghan, D. S.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

Naughton, T. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Orzo, L.

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

Ozcan, A.

Page, A. J.

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Pan, F.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Pandey, N.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

Quan, C.

C. J. Tay, C. Quan, and W. Chen, “Dynamic measurement by digital holographic interferometry based on complex phasor method,” Opt. Laser Technol. 41, 172–180 (2009).
[CrossRef]

Rong, L.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Sato, K.

K. Maejima and K. Sato, “One-shot digital holography for real-time recording of moving color 3-D images,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DMA2.

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Shen, X. X.

Siemion, A.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

Stasiewicz, K.

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

Sun, W. J.

Suszek, J.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

Sypek, M.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

Tay, C. J.

C. J. Tay, C. Quan, and W. Chen, “Dynamic measurement by digital holographic interferometry based on complex phasor method,” Opt. Laser Technol. 41, 172–180 (2009).
[CrossRef]

Tokes, S.

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

Toth, V.

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

Wang, Y. R.

Wojnowski, D.

M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. 36, 3018–3020 (2011).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

Xiao, W.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Xu, X. F.

Yaglidere, O.

Yamaguchi, I.

Yaroslavsky, L. P.

Zhang, F.

Zhang, H.

Biomed. Opt. Express (1)

Int. J. Digital Multimedia Broadcast. (1)

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, G. Finke, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digital Multimedia Broadcast. 2010, 1 (2010).
[CrossRef]

J. Disp. Technol. (1)

L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, “Using commodity graphics hardware for real-time digital hologram view-reconstruction,” J. Disp. Technol. 5, 111–119 (2009).
[CrossRef]

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Opt. Commun. (1)

A. M. P. P. Leite, “Optical fibre illuminators for holography,” Opt. Commun. 28, 303–308 (1979).
[CrossRef]

Opt. Eng. (2)

H. I. Bjelkhagen, “Pulsed fiber holography: a new technique for hologram interferometry,” Opt. Eng. 24, 244645 (1984).
[CrossRef]

A. Siemion, M. Sypek, M. Makowski, J. Suszek, A. Siemion, D. Wojnowski, and A. Kolodziejczyk, “One-exposure phase-shifting digital holography based on the self-imaging effect,” Opt. Eng. 49, 055802 (2010).
[CrossRef]

Opt. Laser Technol. (1)

C. J. Tay, C. Quan, and W. Chen, “Dynamic measurement by digital holographic interferometry based on complex phasor method,” Opt. Laser Technol. 41, 172–180 (2009).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (4)

Z. Gorocs, M. Kiss, V. Toth, L. Orzo, and S. Tokes, “Multi-color digital holographic microscope (DHM) for biological purposes,” Proc. SPIE 7568, 75681P (2010).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Optical properties of the self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 714123 (2008).
[CrossRef]

A. Michalkiewicz, M. Kujawinska, K. Stasiewicz, and L. R. Jaroszewicz, “Digital holocameras for laboratory and outdoor measurements of engineering objects,” Proc. SPIE 6616, 66162P (2007).
[CrossRef]

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Other (1)

K. Maejima and K. Sato, “One-shot digital holography for real-time recording of moving color 3-D images,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DMA2.

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Figures (8)

Fig. 1.
Fig. 1.

Ideal scheme of the hologram recording setup. Beam marked in blue is reference beam and marked in yellow are object beams. L, lasers; M, half-mirrors; C, collimator; FC, fiber coupler; O, object.

Fig. 2.
Fig. 2.

Reconstruction for 8192 by 8192 resolution with scale factor (a) M=1, (b) M=3, and (c) M=5.

Fig. 3.
Fig. 3.

Reconstruction algorithms for (a) incoherent and (b) coherent variant.

Fig. 4.
Fig. 4.

Photograph of the object.

Fig. 5.
Fig. 5.

Holographic reconstruction of a diffuse color object obtained by (a) monochromatic CCD and (b) CCD with Bayer filter.

Fig. 6.
Fig. 6.

Holographically reconstructed color images for a 4096 by 4096 resolution: (a) no speckle integration and (b) with four-frame integration.

Fig. 7.
Fig. 7.

Photography of object to observe strain.

Fig. 8.
Fig. 8.

Strain observed using (a) 660 nm and (b) 532 nm lasers.

Tables (1)

Tables Icon

Table 1. Computation Time and Frame Rate of Hologram Processing on GPU

Equations (7)

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

h(x,y)=eikziλzexp[ik2z(x2+y2)].
uB(x,y)=eikziλzAuA(x,y)exp(ik2f(x2+y2))×exp{ik2z[(xx)2+(yy)2]}dxdy,
uB(x,y)=eikziλzexp(ik2z(x2+y2))AuA(x,y)×exp(ik2(1z1f)(x2+y2))exp{ikz[xx+yy]}dxdy,
zM=zM,1z1f=1zM1fM.
uBM(x,y)=eikzMiλzexp(ik2zM(x2+y2))AuA(x,y)×exp(ik2(1zM1fM)(x2+y2))exp{ikzM[xx+yy]}dxdy.
|uBM(x,y)|=M|1iλzAuA(x,y)exp(ik2(1z1f)(x2+y2))×exp(ikz(x(Mx)+y(My)))dxdy|.
Δϕ=Arg{U0(x,y)U1*(x,y)}.

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