Abstract

We present parallel processing implementation for rapid extraction of the quantitative phase maps from off-axis holograms on the Graphics Processing Unit (GPU) of the computer using computer unified device architecture (CUDA) programming. To obtain efficient implementation, we parallelized both the wrapped phase map extraction algorithm and the two-dimensional phase unwrapping algorithm. In contrast to previous implementations, we utilized unweighted least squares phase unwrapping algorithm that better suits parallelism. We compared the proposed algorithm run times on the CPU and the GPU of the computer for various sizes of off-axis holograms. Using the GPU implementation, we extracted the unwrapped phase maps from the recorded off-axis holograms at 35 frames per second (fps) for 4 mega pixel holograms, and at 129 fps for 1 mega pixel holograms, which presents the fastest processing framerates obtained so far, to the best of our knowledge. We then used common-path off-axis interferometric imaging to quantitatively capture the phase maps of a micro-organism with rapid flagellum movements.

© 2016 Optical Society of America

Full Article  |  PDF Article

Corrections

16 February 2016: Corrections were made to the body text.


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References

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2015 (2)

2014 (1)

2013 (3)

2012 (4)

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Y. Jang, J. Jang, and Y. Park, “Dynamic spectroscopic phase microscopy for quantifying hemoglobin concentration and dynamic membrane fluctuation in red blood cells,” Opt. Express 20(9), 9673–9681 (2012).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Generalized cell morphological parameters based on interferometric phase microscopy and their application to cell life cycle characterization,” Biomed. Opt. Express 3(8), 1757–1773 (2012).
[Crossref] [PubMed]

2011 (5)

2009 (1)

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

2008 (1)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

2007 (1)

B. Kemper, P. Langehanenberg, and G. von Bally, “Digital holographic microscopy: A new method for surface analysis and marker-free dynamic life cell imaging,” Optik Photonik 2(2), 41–44 (2007).
[Crossref]

Arbabi, A.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Balla, A.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16(11), 116017 (2011).
[Crossref] [PubMed]

Barbul, A.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Coppola, S.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Depeursinge, C.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Ding, H.

Do, M.

Doronin, A.

Edwards, C.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

Emery, Y.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Ferraro, P.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Gawad, S.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Gilboa, B.

Girshovitz, P.

Giugliano, M.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Goddard, L. L.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

Grilli, S.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Habaza, M.

Heuschkel, M.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Jang, J.

Jang, Y.

Kemper, B.

B. Kemper, P. Langehanenberg, and G. von Bally, “Digital holographic microscopy: A new method for surface analysis and marker-free dynamic life cell imaging,” Optik Photonik 2(2), 41–44 (2007).
[Crossref]

Kim, K.

Kim, K. S.

Korenstein, R.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Langehanenberg, P.

B. Kemper, P. Langehanenberg, and G. von Bally, “Digital holographic microscopy: A new method for surface analysis and marker-free dynamic life cell imaging,” Optik Photonik 2(2), 41–44 (2007).
[Crossref]

Magistretti, P. J.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Markram, H.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Marquet, P.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Meglinski, I.

Merola, F.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Miccio, L.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Mir, M.

Morgan, H.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Park, H.

Park, Y.

Patel, S.

Paturzo, M.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Pham, H.

Popescu, G.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16(11), 116017 (2011).
[Crossref] [PubMed]

H. Pham, H. Ding, N. Sobh, M. Do, S. Patel, and G. Popescu, “Off-axis quantitative phase imaging processing using CUDA: toward real-time applications,” Biomed. Opt. Express 2(7), 1781–1793 (2011).
[Crossref] [PubMed]

M. Mir, K. Tangella, and G. Popescu, “Blood testing at the single cell level using quantitative phase and amplitude microscopy,” Biomed. Opt. Express 2(12), 3259–3266 (2011).
[Crossref] [PubMed]

Rappaz, B.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Renaud, P.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Roichman, Y.

Schnakenberg, U.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Shaked, N. T.

Sobh, N.

Tangella, K.

Vespini, V.

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

von Bally, G.

B. Kemper, P. Langehanenberg, and G. von Bally, “Digital holographic microscopy: A new method for surface analysis and marker-free dynamic life cell imaging,” Optik Photonik 2(2), 41–44 (2007).
[Crossref]

Wang, Z.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16(11), 116017 (2011).
[Crossref] [PubMed]

Wessling, B.

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

Ye, J. C.

Zhou, R.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

3D Res. (1)

S. Grilli, V. Vespini, F. Merola, P. Ferraro, L. Miccio, M. Paturzo, and S. Coppola, “Exploring the capabilities of digital holography as tool for testing optical microstructures,” 3D Res. 2, 1007 (2011).

Biomed. Opt. Express (4)

Cytometry A (1)

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73(10), 895–903 (2008).
[Crossref] [PubMed]

Front. Neuroeng. (1)

S. Gawad, M. Giugliano, M. Heuschkel, B. Wessling, H. Markram, U. Schnakenberg, P. Renaud, and H. Morgan, “Substrate arrays of iridium oxide microelectrodes for in vitro neuronal interfacing,” Front. Neuroeng. 2, 1 (2009).
[PubMed]

J. Biomed. Opt. (1)

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16(11), 116017 (2011).
[Crossref] [PubMed]

Light Sci. Appl. (2)

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 1(9), e30 (2012).
[Crossref]

C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Optically monitoring and controlling nanoscale topography during semiconductor etching,” Light Sci. Appl. 30, e130 (2012).

Nano Lett. (1)

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13(8), 3716–3721 (2013).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Optik Photonik (1)

B. Kemper, P. Langehanenberg, and G. von Bally, “Digital holographic microscopy: A new method for surface analysis and marker-free dynamic life cell imaging,” Optik Photonik 2(2), 41–44 (2007).
[Crossref]

Other (5)

L. Waller, CalOptrics: Compuational Optical Imaging Open Source Library for CUDA, UC Berkeley (2014). https://github.com/Waller-Lab/CalOptrics

P. A. Karasev, D. P. Campbell, and M. A. Richards, “Obtaining a 35x speedup in 2d phase unwrapping using commodity graphics processors,” in 2007 IEEE Radar Conference (IEEE, 2007), pp. 574–578.

P. Mistry, S. Braganza, D. Kaeli, and M. Leeser, “Accelerating phase unwrapping and affine transformations for optical quadrature microscopy using CUDA,” in 2nd Workshop on General Purpose Processing on Graphics Processing Units (ACM, Washington, D.C., 2009), pp. 28–37.
[Crossref]

D. C. Ghihlia and M. D. Pritt, Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

University of Oslo, “Implementation of the DFT and the DCT,” in MAT-INF2360: Applications of Linear Algebra (2012). http://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v12/fft.pdf

Supplementary Material (1)

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» Visualization 1: MP4 (1399 KB)      Visualization 1

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Figures (6)

Fig. 1
Fig. 1 Digital process for the extraction of the phase map from an off-axis image hologram.
Fig. 2
Fig. 2 The DCT-based UWLS 2-D phase unwrapping algorithm.
Fig. 3
Fig. 3 The off-axis imaging interferometer used for the hologram acquisition. HeNe – Helium-Neon laser; AOTF – Acousto-optical tunable filter; L1-L5 – lenses; P1,P2 – Pinholes; M – Mirror; FM – Flip mirror, for light source selection, MO – Microscope objective; RR – Retro-reflector; CMOS – Digital camera.
Fig. 4
Fig. 4 Evaluation of the reconstruction quality. (a) Off-axis image hologram of a 1951 USAF phase test target. (b-d) The unwrapped phase maps reconstructed from the hologram on: (b) the CPU (Matlab) using the Goldstein's phase unwrapping algorithm, (c) the CPU (Matlab) using the UWLS algorithm, and (d) the GPU (CUDA) using the DCT-based UWLS phase unwrapping algorithm. (e) Cross section across group 8 as indicated by the black lines marked on Figs. 4(b-d).
Fig. 5
Fig. 5 Comparison of the framerates on the CPU (C + + ) and the GPU of the entire reconstruction process of the proposed implementation, for various hologram sizes.
Fig. 6
Fig. 6 Quantitative phase map of a micro-organism in water, as processed on the GPU using the proposed algorithm. Video of the rapid flagellum dynamics in 129 actual fps is shown in Visualization 1 (MP4, 1.4MB).

Tables (1)

Tables Icon

Table 1 Comparison of the calculation times (in ms) on the CPU (C++) and the GPU (CUDA) of the various stages of the proposed implementation for various hologram sizes.

Equations (9)

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

H= | E s + E r | 2 = | E s | 2 + | E r | 2 + E s * E r + E s E r * = | E s | 2 + | E r | 2 +2| E s || E r |cos( φ k m sin( θ ) ),
ψ ( m , n ) = φ ( m , n ) + 2 π q ( m , n ) ,
φ ( r ) = φ ( r 0 ) + c φ d r ,
J = | φ x ψ x | 2 + | φ y ψ y | 2 d x d y ,
x ( φ x ψ x ) + y ( φ y ψ y ) = 0 ,
φ x x + φ y y = ψ x x + ψ y y ,
2 φ = ρ ,
[ 2 cos ( π m M ) + 2 cos ( π n N ) 4 ] D C T { φ ( m , n ) } = D C T { ρ ( m , n ) } ,
φ ( m , n ) = I D C T { D C T { ρ ( m , n ) } / [ 2 cos ( π m M ) + 2 cos ( π n N ) 4 ] } ,

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