Abstract

Pattern recognition methods can be used in the context of digital holography to perform the task of object detection, classification, and position extraction directly from the hologram rather than from the reconstructed optical field. These approaches may exploit the differences between the holographic signatures of objects coming from distinct object classes and/or different depth positions. Direct matching of diffraction patterns, however, becomes computationally intractable with increasing variability of objects due to the very high dimensionality of the dictionary of all reference diffraction patterns. We show that most of the diffraction pattern variability can be captured in a lower dimensional space. Good performance for object recognition and localization is demonstrated at a reduced computational cost using a low-dimensional dictionary. The principle of the method is illustrated on a digit recognition problem and on a video of experimental holograms of particles.

© 2013 Optical Society of America

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References

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2013

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

A. Bourquard, N. Pavillon, E. Bostan, C. Depeursinge, and M. Unser, “A practical inverse-problem approach to digital holographic reconstruction,” Opt. Express 21, 3417–3433 (2013).
[CrossRef]

2011

2010

2009

2008

J. Coupland and J. Lobera, “Optical tomography and digital holography,” Meas. Sci. Technol. 19, 070101 (2008).
[CrossRef]

2007

2006

2004

K. D. Hinsch and S. F. Herrmann, “Holographic particle image velocimetry,” Meas. Sci. Technol. 15, R61 (2004).
[CrossRef]

J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
[CrossRef]

2000

1999

T. Kim and T.-C. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

1974

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Allier, C. P.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

C. P. Allier, G. Hiernard, V. Poher, and J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomed. Opt. Express 1, 762–770 (2010).
[CrossRef]

Angelini, E.

Atlan, M.

Bostan, E.

Bourquard, A.

Brady, D. J.

Catalano, P. N.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Cheong, F. C.

Choi, K.

Coskun, A. F.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Coupland, J.

J. Coupland and J. Lobera, “Optical tomography and digital holography,” Meas. Sci. Technol. 19, 070101 (2008).
[CrossRef]

Demirci, U.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Denis, L.

Depeursinge, C.

Dinten, J. M.

Fournel, T.

Fournier, C.

Fung, J.

Garcia-Sucerquia, J.

Goepfert, C.

Greenbaum, A.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Grier, D. G.

Gurkan, U. A.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Hahn, J.

Hennequin, Y.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Herrmann, S. F.

K. D. Hinsch and S. F. Herrmann, “Holographic particle image velocimetry,” Meas. Sci. Technol. 15, R61 (2004).
[CrossRef]

Hiernard, G.

Hinsch, K. D.

K. D. Hinsch and S. F. Herrmann, “Holographic particle image velocimetry,” Meas. Sci. Technol. 15, R61 (2004).
[CrossRef]

Horisaki, R.

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Katz, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42, 531–555 (2010).
[CrossRef]

Kayaalp, E.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Kaz, D. M.

Keles, H. O.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Khimji, I.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Kim, S. H.

Kim, T.

T. Kim and T.-C. Poon, “Three-dimensional matching by use of phase-only holographic information and the Wigner distribution,” J. Opt. Soc. Am. A 17, 2520–2528 (2000).
[CrossRef]

T. Kim and T.-C. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Klages, P.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods, 1st ed. (Wiley-VCH, 2005).

Kreuzer, H. J.

Krishnatreya, B. J.

Lam, E. Y.

Larsen, R. M.

R. M. Larsen, Lanczos Bidiagonalization with Partial Reorthogonalization (Aarhus University, 1998).

Lee, S. H.

Lim, S.

Lobera, J.

J. Coupland and J. Lobera, “Optical tomography and digital holography,” Meas. Sci. Technol. 19, 070101 (2008).
[CrossRef]

Lorenz, D.

Luo, W.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Manoharan, V. N.

Marim, M. M.

Marks, D. L.

Martin, K. E.

McGorty, R.

McLeod, E.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Mudanyali, O.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Olivo-Marin, J.-C.

Ozcan, A.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Pavillon, N.

Perry, R. W.

Poher, V.

Poon, T.-C.

T. Kim and T.-C. Poon, “Three-dimensional matching by use of phase-only holographic information and the Wigner distribution,” J. Opt. Soc. Am. A 17, 2520–2528 (2000).
[CrossRef]

T. Kim and T.-C. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Rivenson, Y.

Roichman, Y.

Royer, H.

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Safaee, H.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Schulz, T. J.

Sheng, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42, 531–555 (2010).
[CrossRef]

Simon, H. D.

H. D. Simon and H. Zha, “Low rank matrix approximation using the lanczos bidiagonalization process with applications,” SIAM J. Sci. Comput 21, 2257–2274 (2000).
[CrossRef]

Soulez, F.

Stern, A.

Tajahuerce, E.

Thiébaut, E.

Thiébaut, É.

Trede, D.

Tropp, J. A.

J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
[CrossRef]

Unser, M.

van Blaaderen, A.

van Oostrum, P.

Xu, W.

Yang, S. M.

Yi, G. R.

Zha, H.

H. D. Simon and H. Zha, “Low rank matrix approximation using the lanczos bidiagonalization process with applications,” SIAM J. Sci. Comput 21, 2257–2274 (2000).
[CrossRef]

Zhang, X.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A 27, 1630–1637 (2010).
[CrossRef]

Annu. Rev. Fluid Mech.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42, 531–555 (2010).
[CrossRef]

Appl. Opt.

Biomed. Opt. Express

IEEE Trans. Inf. Theory

J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
[CrossRef]

J. Display Technol.

J. Opt. Soc. Am. A

Lab Chip

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, and U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab Chip 11, 2535–2540 (2011).
[CrossRef]

Meas. Sci. Technol.

J. Coupland and J. Lobera, “Optical tomography and digital holography,” Meas. Sci. Technol. 19, 070101 (2008).
[CrossRef]

K. D. Hinsch and S. F. Herrmann, “Holographic particle image velocimetry,” Meas. Sci. Technol. 15, R61 (2004).
[CrossRef]

Nat. Photonics

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[CrossRef]

Nouv. Rev. Opt.

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Opt. Eng.

T. Kim and T.-C. Poon, “Extraction of 3-D location of matched 3-D object using power fringe-adjusted filtering and Wigner analysis,” Opt. Eng. 38, 2176–2183 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

SIAM J. Sci. Comput

H. D. Simon and H. Zha, “Low rank matrix approximation using the lanczos bidiagonalization process with applications,” SIAM J. Sci. Comput 21, 2257–2274 (2000).
[CrossRef]

Other

R. M. Larsen, Lanczos Bidiagonalization with Partial Reorthogonalization (Aarhus University, 1998).

“FFTW,” http://www.fftw.org/ . [Online; accessed 23-November-2012].

“OpenMP,” http://openmp.org/wp/ . [Online; accessed 23-November-2012].

“PROPACK,” http://soi.stanford.edu/~rmunk/PROPACK/ . [Online; accessed 23-November-2012].

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods, 1st ed. (Wiley-VCH, 2005).

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Figures (8)

Fig. 1.
Fig. 1.

Illustration of a digit recognition task from a digital hologram: (a) a simulation of a 400×400-pixels hologram of digits located at different distances (pixel size, 20 μm; fill-factor, 0.7; laser wavelength, 0.532 μm; depth range, [0.550.85]m) and (b) Fresnel reconstruction of the volume displaying both in-focus and out-of-focus images of the digits, which makes digit recognition from the reconstructed volume a difficult task. Direct recognition of the diffraction patterns using the approach described in the paper avoids dealing with these numerous image artifacts.

Fig. 2.
Fig. 2.

Identification of the best-matching pattern in the dictionary: (a) by correlation with each element of the dictionary, straightforward but costly; or (b) by linear combination of the correlation with few diffraction-pattern modes, much faster. Computation of correlation maps is denoted using the symbol “*.”

Fig. 3.
Fig. 3.

First 100 singular values of the dictionary in descending order. The dictionary of digits (in green) contains 300 centered patterns for digits placed at different depth positions with the application parameters in Subsection 4.A. The dictionary of spherical particles (in red) consists of the diffraction models for spherical objects changing depth and radius with the application parameters in Subsection 4.B. The Fresnel dictionary (in blue) corresponds to Fresnel functions with changing depth values. The dictionary of rotated digits (in mustard) contains 900 centered patterns [10(digits)×90(angle samples)]. In the case of spherical objects, five first modes can approximate the dictionary accurately. The vanishing rate of the singular values of the Fresnel dictionary is very low, which implies that it is not possible to deduce an accurate low-rank approximation of Fresnel dictionary.

Fig. 4.
Fig. 4.

Digit recognition from a digital hologram: (a) the hologram of digits and (b) the residuals after cleaning all the signatures from the hologram.

Fig. 5.
Fig. 5.

Study of the error rate on object recognition for the toy problem of holograms of digits (see Subsection 4.A). (a) shows the error rates of object recognition for a “2” placed at 0.17 m from the sensor. The curves show the error rate for different approximation ranks and different noise levels, (b) illustrates one hologram of a “2” degraded by white Gaussian noise with σ=0.01, (c) plots the error rates representing the discriminating power of approximated dictionaries for a fixed level of noise resulting in a SNR 3, and (d) illustrates one of the holograms of Subsection 4.A for object “2” placed at 0.17 m from the sensor.

Fig. 6.
Fig. 6.

Study of the robustness of our method to the orientation factor (see Subsection 4.A). (a) shows an object “2” rotated counterclockwise on the object plane by 210.5 deg, (b) illustrates one of the simulated holograms for object “2” placed at depth of 0.75 m. This hologram is degraded by white and Gaussian noise with σ=0.31, and (c) shows the error rates of object recognition and orientation estimation for this object.

Fig. 7.
Fig. 7.

With an increased number of modes, the approximation of the dictionary improves and matching a reference diffraction pattern against the approximated dictionary produces a sharper correlation peak leading to more accurate 3D location. Plotted curves represent the mean square difference between diffraction patterns, i.e., the opposite of their correlation. Reddest curves correspond to the most accurate approximations of the dictionary (using up to 50 modes). The pattern of the dictionary minimizing the mean square difference is in best match with the reference diffraction pattern and gives the 3D location and diameter of the detected particle.

Fig. 8.
Fig. 8.

(a) Experimental hologram of droplets from LMFA Lyon used in Subsection 4.C and (b) same experimental hologram cleaned from the in-field particles using the five first modes. The magnitude of the residuals is high due to the signature of the out-of-field particles placed close to the borders.

Equations (6)

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

d=Mα+ϵ,
argmaxjmjtWr,
Ci=1kuisivit,
cji=1kuiβi,j,withβi,j=si·vj,i.
cjtWri=1kβi,jκi,withκi=uitWr.
argmaxjmjtWrmjtWmj,

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