Abstract

We demonstrate imaging of complex amplitude objects through digital holography with phase-structured illumination and bucket detection. The object is sampled with a set of micro-structured phase patterns implemented onto a liquid-crystal spatial light modulator while a bucket detector sequentially records the irradiance fluctuations corresponding to the interference between object and reference beams. Our reconstruction algorithm retrieves the unknown phase information from the full set of photocurrent measurements. Interestingly, the sampling functions can be codified onto the reference beam, so they can be nonlocal with respect to the object. Finally, we show that the system is well-fitted for transmission of the object information through scattering media.

© 2017 Optical Society of America

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2016 (6)

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

N. Huynh, E. Zhang, M. Betcke, S. Arridge, P. Beard, and B. Cox, “Single-pixel optical camera for video rate ultrasonic imaging,” Optica 3(1), 26–29 (2016).
[Crossref]

M. J. Purcell, M. Kumar, S. C. Rand, and V. Lakshminarayanan, “Holographic imaging through a scattering medium by diffuser-aided statistical averaging,” J. Opt. Soc. Am. A 33(7), 1291–1297 (2016).
[Crossref] [PubMed]

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

A. C. S. Chan, K. K. Tsia, and E. Y. Lam, “Subsampled scanning holographic imaging (SuSHI) for fast, non-adaptive recording of three-dimensional objects,” Optica 3(8), 911–917 (2016).
[Crossref]

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

2015 (4)

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

Y.-K. Xu, W. T. Liu, E. F. Zhang, Q. Li, H. Y. Dai, and P. X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
[Crossref] [PubMed]

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (6)

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, “Compressive holography with a single-pixel detector,” Opt. Lett. 38(14), 2524–2527 (2013).
[Crossref] [PubMed]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

2012 (6)

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

G. Rousseau and A. Blouin, “Hadamard multiplexing in laser ultrasonics,” Opt. Express 20(23), 25798–25816 (2012).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “When holography meets coherent diffraction imaging,” Opt. Express 20(27), 28871–28892 (2012).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

2010 (5)

2009 (4)

2008 (3)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251–348 (2008).
[Crossref]

2006 (2)

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2002 (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

1997 (1)

1969 (1)

W. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Andrés, P.

Andrews, H. C.

W. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Angelini, E.

Araiza-E, M.

Arce, G. R.

Arridge, S.

Atlan, M.

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Beard, P.

Betcke, M.

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Blouin, A.

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Brady, D. J.

Brambilla, E.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251–348 (2008).
[Crossref]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Candes, E.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Chahid, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Chan, A. C. S.

Chen, P. X.

Choi, K.

Clemente, P.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22(14), 16945–16955 (2014).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, “Compressive holography with a single-pixel detector,” Opt. Lett. 38(14), 2524–2527 (2013).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

Climent, V.

Cox, B.

Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Dai, H. Y.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Durán, V.

Edgar, M. P.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Fernández-Alonso, M.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

Ferri, F.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Fink, H.-W.

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Gatti, A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251–348 (2008).
[Crossref]

Gibson, G. M.

Horisaki, R.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Howell, J. C.

Howland, G. A.

Hunt, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Huynh, N.

Imbe, M.

Irles, E.

Javidi, B.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Kane, J.

W. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Katz, O.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kelly,

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Kim, T.

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

Kim, Y. S.

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

Krishna, S.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Kumar, M.

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Lakshminarayanan, V.

Lam, E. Y.

Lancis, J.

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22(14), 16945–16955 (2014).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, “Compressive holography with a single-pixel detector,” Opt. Lett. 38(14), 2524–2527 (2013).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

L. Martínez-León, M. Araiza-E, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, “Single-shot digital holography by use of the fractional Talbot effect,” Opt. Express 17(15), 12900–12909 (2009).
[Crossref] [PubMed]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Latychevskaia, T.

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Li, Q.

Lim, S.

Lipworth, G.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Liu, J.-P.

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

Liu, W. T.

Longchamp, J.-N.

Lugiato, L. A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, and L. A. Lugiato, “Quantum imaging,” Prog. Opt. 51, 251–348 (2008).
[Crossref]

Lum, D. J.

Magatti, D.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Marim, M. M.

Marks, D. L.

Martínez-León, L.

Mirza, I. O.

Mitchell, K. J.

Molteni, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref] [PubMed]

Montoya, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Mousavi, H. S.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Naik, D. N.

Nomura, T.

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[Crossref] [PubMed]

Olivo-Marin, J.-C.

Osten, W.

Padgett, M. J.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Padilla, W. J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Pedrini, G.

Poon, T.-C.

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

T.-C. Poon, “Optical scanning holography: a review of recent progress,” J. Opt. Soc. Korea 13(4), 406–415 (2009).
[Crossref]

Prather, D. W.

Pratt, W.

W. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Purcell, M. J.

Radwell, N.

Rand, S. C.

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Rodríguez, A. D.

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

Romberg, J.

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Rousseau, G.

Salvador-Balaguer, E.

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Shrekenhamer, D.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Singh, A. K.

Sleasman, T.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Smith, D. R.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Soldevila, F.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22(14), 16945–16955 (2014).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 109(26), E1679–E1687 (2012).
[Crossref] [PubMed]

Sun, B.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Tajahuerce, E.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

F. Soldevila, E. Salvador-Balaguer, P. Clemente, E. Tajahuerce, and J. Lancis, “High-resolution adaptive imaging with a single photodiode,” Sci. Rep. 5, 14300 (2015).
[Crossref] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
[Crossref] [PubMed]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22(14), 16945–16955 (2014).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, “Compressive holography with a single-pixel detector,” Opt. Lett. 38(14), 2524–2527 (2013).
[Crossref] [PubMed]

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging,” Opt. Lett. 37(5), 824–826 (2012).
[Crossref] [PubMed]

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

L. Martínez-León, M. Araiza-E, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, “Single-shot digital holography by use of the fractional Talbot effect,” Opt. Express 17(15), 12900–12909 (2009).
[Crossref] [PubMed]

Takeda, M.

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Tao, T.

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Ting Sun, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Torres-Company, V.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

Tsang, P. W. M.

P. W. M. Tsang, T.-C. Poon, J.-P. Liu, T. Kim, and Y. S. Kim, “Low complexity compression and speed enhancement for optical scanning holography,” Sci. Rep. 6, 34724 (2016).
[Crossref] [PubMed]

Tsia, K. K.

Uribe-Patarroyo, N.

F. Soldevila, P. Clemente, E. Tajahuerce, N. Uribe-Patarroyo, P. Andrés, and J. Lancis, “Computational imaging with a balanced detector,” Sci. Rep. 6, 29181 (2016).
[Crossref] [PubMed]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

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E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Ware, M. R.

Watts, C. M.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref] [PubMed]

Welsh, S. S.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

Wu, Y.

Xu, Y.-K.

Yamaguchi, I.

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Ye, P.

Zhang, E.

Zhang, E. F.

Zhang, T.

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Appl. Phys. B (1)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B 113(4), 551–558 (2013).
[Crossref]

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

IEEE Signal Process. Mag. (2)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

IEEE Trans. Inf. Theory (2)

E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[Crossref]

J. Opt. (1)

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17(2), 025705 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (1)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Nat. Methods (1)

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7(8), 603–614 (2010).
[Crossref] [PubMed]

Nat. Photonics (3)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Opt. Express (10)

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20), 23822–23837 (2013).
[Crossref] [PubMed]

E. Tajahuerce, V. Durán, P. Clemente, E. Irles, F. Soldevila, P. Andrés, and J. Lancis, “Image transmission through dynamic scattering media by single-pixel photodetection,” Opt. Express 22(14), 16945–16955 (2014).
[Crossref] [PubMed]

V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23(11), 14424–14433 (2015).
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T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “When holography meets coherent diffraction imaging,” Opt. Express 20(27), 28871–28892 (2012).
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L. Martínez-León, M. Araiza-E, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, “Single-shot digital holography by use of the fractional Talbot effect,” Opt. Express 17(15), 12900–12909 (2009).
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Y.-K. Xu, W. T. Liu, E. F. Zhang, Q. Li, H. Y. Dai, and P. X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
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Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (CSM),” Opt. Express 18(24), 24565–24578 (2010).
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A. K. Singh, D. N. Naik, G. Pedrini, M. Takeda, and W. Osten, “Looking through a diffuser and around an opaque surface: a holographic approach,” Opt. Express 22(7), 7694–7701 (2014).
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G. Rousseau and A. Blouin, “Hadamard multiplexing in laser ultrasonics,” Opt. Express 20(23), 25798–25816 (2012).
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Opt. Lasers Eng. (1)

A. D. Rodríguez, P. Clemente, E. Tajahuerce, and J. Lancis, “Dual-mode optical microscope based on single-pixel imaging,” Opt. Lasers Eng. 82, 87–94 (2016).
[Crossref]

Opt. Lett. (5)

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Phys. Rev. A (2)

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[Crossref]

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, “Single-pixel digital ghost holography,” Phys. Rev. A 86, 041803 (2012).

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M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
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[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

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Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
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G. Popescu, Quantitative phase imaging of cells and tissues (Mc Graw-Hill, 2011).

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Figures (6)

Fig. 1
Fig. 1 Hadamard masks for a 2 × 2 dimension.
Fig. 2
Fig. 2 Experimental set-up.
Fig. 3
Fig. 3 Conventional direct imaging (left) and single-pixel hologram reconstruction (right) of an amplitude object.
Fig. 4
Fig. 4 64 × 64 pixel original image (left) and single-pixel hologram reconstruction (right) of a phase object displayed onto the SLM.
Fig. 5
Fig. 5 Experimental set-up for phase imaging through a diffuser.
Fig. 6
Fig. 6 Conventional direct imaging (left) and single-pixel hologram reconstruction (right) of an amplitude object, through a diffuser.

Equations (6)

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I i | t( r ) m i ( r ) | 2 d 2 r .
| t( r ) | 2 = i I i m i ( r ).
I i,φ | t( r ) m i ( r )+ e jφ R( r ) | 2 d 2 r .
y i = 1 4| R | [ ( I i,0 I i,π )+j( I i,3π/2 I i,π/2 ) ],
t( r )= i y i m i ( r ).
I i,φ | t( r )+ e jφ m i ( r )R( r ) | 2 d 2 r ,

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