Abstract

We present an approach enabling the representation of complex values using intensity only fields. The method can be used for imaging with structured illumination and allows the study of new propagating physical quantities with the classical coherent or incoherent light field playing the role of hidden variable. This approach can further be generalized to encode higher order N-dimensional vectors and ensembles of N orthogonal fields. Different orthogonal, incoherent illumination patterns (Hadamard, sinusoidal, Laguerre-Gauss) have been experimentally tested in a single-pixel detection imaging scheme in order to compare their performances in terms of obtainable resolution. We show experimentally that our encoding technique allows to reduce the required number of illuminations for a given, desired resolution.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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  1. A. R. Hibbs, Confocal Microscopy for Biologists (Springer, 2004).
    [Crossref]
  2. A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2001).
  3. A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
    [Crossref] [PubMed]
  4. S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
    [Crossref]
  5. L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
    [Crossref]
  6. A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
    [Crossref] [PubMed]
  7. H. Rueda, H. Arguello, and G. R. Arce, “DMD-based implementation of patterned optical filter arrays for compressive spectral imaging,” J. Opt. Soc. Am. A 32, 80–89 (2015).
    [Crossref]
  8. G. G. Stokes, “On the perfect blackness of the central spot in Newton’s rings, and on the verification of Fresnel’s formulae for the intensities of reflected and refracted rays,” Cambridge Dublin Math. J. 4, 1–14 (1849).
  9. H. von Helmholtz, Handbuch der physiologischen Optik (Leopold Voss, 1856).
  10. F. Soldevila, E. Irles, V. Duran, P. Clemente, M. Fernàndez-Alonso, E. Tajahuerce, and J. Lancis, “Single-pixel polarimetric imaging spectrometer by compressive sensing,” Appl. Phys. B,  113, 551–558 (2013).
    [Crossref]
  11. Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
    [Crossref]
  12. V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” PNAS 109, E1679–E1687 (2012).
    [Crossref] [PubMed]
  13. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25, 83–91 (2008).
    [Crossref]
  14. F. J. Salgado-Remacha, “Laguerre-Gaussian beam shaping by binary phase plates as illumination sources in micro-optics,” Appl. Opt. 53, 6782–6788 (2014).
    [Crossref] [PubMed]
  15. T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
    [Crossref] [PubMed]
  16. A. C. De Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A,  84, 021803 (2011).
    [Crossref]
  17. J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
    [Crossref]
  18. Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
    [Crossref] [PubMed]
  19. S. Kosmeier, S. Zolotovskaya, A. C. De Luca, A. Riches, C. S. Herrington, K. Dholakia, and M. Mazilu, “Nonredundant Raman imaging using optical eigenmodes,” Optica 1, 257–263 (2014).
    [Crossref]
  20. M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
    [Crossref] [PubMed]
  21. R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, (Springer, 2008).
    [Crossref]
  22. E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
    [Crossref]

2016 (1)

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

2015 (3)

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

H. Rueda, H. Arguello, and G. R. Arce, “DMD-based implementation of patterned optical filter arrays for compressive spectral imaging,” J. Opt. Soc. Am. A 32, 80–89 (2015).
[Crossref]

Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

2014 (4)

2013 (2)

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

L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
[Crossref]

2012 (2)

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

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

2011 (1)

A. C. De Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A,  84, 021803 (2011).
[Crossref]

2008 (1)

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

2006 (1)

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

1993 (1)

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

1849 (1)

G. G. Stokes, “On the perfect blackness of the central spot in Newton’s rings, and on the verification of Fresnel’s formulae for the intensities of reflected and refracted rays,” Cambridge Dublin Math. J. 4, 1–14 (1849).

Arce, G. R.

Arguello, H.

Baraniuk, R. G.

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

Bianchini, P.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

Bobin, J.

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

Candes, E.

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

Chahid, M.

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

Chen, M.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

Cižmár, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Clemente, P.

A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
[Crossref] [PubMed]

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

Coll-Lladó, C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Dahan, M.

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

Dalgarno, H. I. C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Davenport, M. A.

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

De Luca, A. C.

De Tommasi, E.

E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
[Crossref]

Dholakia, K.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

S. Kosmeier, S. Zolotovskaya, A. C. De Luca, A. Riches, C. S. Herrington, K. Dholakia, and M. Mazilu, “Nonredundant Raman imaging using optical eigenmodes,” Optica 1, 257–263 (2014).
[Crossref]

A. C. De Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A,  84, 021803 (2011).
[Crossref]

Diaspro, A.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2001).

Duarte, M. F.

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

Duran, V.

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

Faretta, M.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

Farouki, R. T.

R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, (Springer, 2008).
[Crossref]

Fernàndez-Alonso, M.

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

Ferrier, D. E. K.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Gong, L.

Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Gourlay, J.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

Gunn-Moore, F. J.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Herrington, C. S.

Hibbs, A. R.

A. R. Hibbs, Confocal Microscopy for Biologists (Springer, 2004).
[Crossref]

Irles, E.

A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
[Crossref] [PubMed]

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

Kelly, K. F.

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

Kosmeier, S.

Lancis, J.

A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
[Crossref] [PubMed]

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

Laska, J. N.

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

Lavanga, L.

E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
[Crossref]

Lu, R-D.

Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

Mazilu, M.

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

S. Kosmeier, S. Zolotovskaya, A. C. De Luca, A. Riches, C. S. Herrington, K. Dholakia, and M. Mazilu, “Nonredundant Raman imaging using optical eigenmodes,” Optica 1, 257–263 (2014).
[Crossref]

A. C. De Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A,  84, 021803 (2011).
[Crossref]

E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
[Crossref]

McOwan, P.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[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,” PNAS 109, E1679–E1687 (2012).
[Crossref] [PubMed]

Nelson, M. P.

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

Nylk, J.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Opilik, L.

L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
[Crossref]

Priore, R. J.

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

Ramoino, P.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

Ren, Y.-X.

Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Riches, A.

Rodrìguez, A. D.

Rueda, H.

Salgado-Remacha, F. J.

Schmid, T.

L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
[Crossref]

Soldevila, F.

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

Stewart, S.

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

Stokes, G. G.

G. G. Stokes, “On the perfect blackness of the central spot in Newton’s rings, and on the verification of Fresnel’s formulae for the intensities of reflected and refracted rays,” Cambridge Dublin Math. J. 4, 1–14 (1849).

Studer, V.

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

Sun, T.

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

Tajahuerce, E.

A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
[Crossref] [PubMed]

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

Takhar, D.

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

Treado, P. J.

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

Underwood, I.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

Usai, C.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

Vass, D. G.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

Vettenburg, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Vicidomini, G.

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

von Helmholtz, H.

H. von Helmholtz, Handbuch der physiologischen Optik (Leopold Voss, 1856).

Watson, S.

E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
[Crossref]

Worboys, M.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

Zenobi, R.

L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
[Crossref]

Zhang, Z.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

Zhong, J.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

Zolotovskaya, S.

Ann. Phys. (1)

Y.-X. Ren, R-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Annu. Rev. Anal. Chem. (2)

S. Stewart, R. J. Priore, M. P. Nelson, and P. J. Treado, “Raman imaging,” Annu. Rev. Anal. Chem. 5, 337–360 (2012).
[Crossref]

L. Opilik, T. Schmid, and R. Zenobi, “Modern Raman imaging: vibrational spectroscopy on the micrometer and nanometer scales,” Annu. Rev. Anal. Chem. 6, 379–398 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

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

Biomed Eng Online. (1)

A. Diaspro, P. Bianchini, G. Vicidomini, M. Faretta, P. Ramoino, and C. Usai, “Multi-photon excitation microscopy,” Biomed Eng Online. 5, 36 (2006).
[Crossref] [PubMed]

Cambridge Dublin Math. J. (1)

G. G. Stokes, “On the perfect blackness of the central spot in Newton’s rings, and on the verification of Fresnel’s formulae for the intensities of reflected and refracted rays,” Cambridge Dublin Math. J. 4, 1–14 (1849).

IEEE Signal Proc. Mag. (1)

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

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

Nat. Commun. (1)

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

Nat. Methods (1)

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, D. E. K. Ferrier, T. Čižmár, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an Airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Opt. Lett. (2)

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, and M. Worboys, “Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators,” Opt. Lett. 201745–1747 (1993).
[Crossref]

A. D. Rodrìguez, P. Clemente, E. Irles, E. Tajahuerce, and J. Lancis, “Resolution analysis in computational imaging with patterned illumination and bucket detection,” Opt. Lett. 39, 3888–3891 (2014).
[Crossref] [PubMed]

Optica (1)

Phys. Rev. A (1)

A. C. De Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, “Optical eigenmode imaging,” Phys. Rev. A,  84, 021803 (2011).
[Crossref]

PNAS (1)

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

Sci. Rep. (1)

M. Chen, K. Dholakia, and M. Mazilu, “Is there an optimal basis to maximise optical information transfer,” Sci. Rep. 6, 22821 (2016).
[Crossref] [PubMed]

Other (5)

R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, (Springer, 2008).
[Crossref]

E. De Tommasi, L. Lavanga, S. Watson, and M. Mazilu, “Data underpinning - Encoding complex valued fields using intensity,” University of St. Andrews, St. Andrews, UK, 2016,
[Crossref]

A. R. Hibbs, Confocal Microscopy for Biologists (Springer, 2004).
[Crossref]

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2001).

H. von Helmholtz, Handbuch der physiologischen Optik (Leopold Voss, 1856).

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Figures (7)

Fig. 1
Fig. 1 (a–f) A single element of a sinusoidal pattern can be expressed as the difference of two elements with no negative values. (g) 2-simplex encoding: a complex number z can be represented in the complex plane with components x and y respect to the real and imaginary axis or in a three-dimensional “rgb space” where the components of z can assume only positive values and at least one of them equals zero. (h) 3-simplex encoding: for each pixel P, a set of 3 orthogonal fields can be represented in a 3-dimensional space with real components x,y,z or in a 4-dimensional space with real, positive components r,g,b,c, where at least one of them equals zero.
Fig. 2
Fig. 2 Experimentally retrieved PSFs obtained by making use of 1024 Hadamard probes, 841 sinusoidal probes and 810 LG beams, respectively (a); examples of reconstructions of target 3 for a given cardinality N using respectively: 1024 binary masks generated from Hadamard matrices, 625 sinusoidal probes, and 816 LG beams (b).
Fig. 3
Fig. 3 Full width half maximum (FWHM) of the point spread function (PSF) as a function of the number of probes for different families of structured illumination.
Fig. 4
Fig. 4 Standard deviation (SD) of the intensity histograms (a) and mean squared error (MSE) evaluated along a linear section of the targets (b) as a function of the number of probes for Hadamard (left), sinusoidal (center) and Laguerre-Gauss (right) patterns. Black, red, blue and dark cyan plots refer respectively to Targets 1, 2, 3, and 4 as defined in Fig. 6(c).
Fig. 5
Fig. 5 Mean Squared Error along a linear section in image reconstruction of Target 3 as a function of the number of illuminations and for sinusoidal probes, with (red) and without (black) the application of N-simplex encoding.
Fig. 6
Fig. 6 (a) Tested illumination patterns: binary mask generated by Hadamard matrix; continuous grayscale sinusoidal pattern; 2-simplex encoded Laguerre-Gaussian beam. (b) 2-simplex encoding of a Laguerre-Gauss beam. Every complex value of phase is decomposed in rgb space where every component corresponds to a fundamental color. (c) Extended targets used in image retrieval. (d) Schematic layout of the experimental set-up. PC: personal computer; DLP: digital light projector; PD: photodiode; DAQ: data acquisition board.
Fig. 7
Fig. 7 Simulated PSFs for Hadamard (N=1024), sinusoidal (N=841), LG1 (810) and LG2 (N=820) probes respectively (a); FWHM of PSFs as a function of the number of probes for the different illumination patterns (b).

Equations (11)

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

I r , g , b ( t ) = A ( 1 + cos ( ω t + Δ r , g , b ) )
V ( t ) = I r ( t ) u r + I g ( t ) u g + I b ( t ) u b = 3 A 2 exp ( i ω t )
f r , g , b ( t ) = a ( cos ( ( ω r , g , b + ω / 2 ) t + Δ r , g , b ) + cos ( ( ω r , g , b ω / 2 ) t Δ r , g , b ) ) ,
i r , g , b ( t ) = f r , g , b 2 ( t ) = a 2 ( 1 + cos ( ω t + Δ r , g , b ) ) ( 1 + cos ( 2 ω r , g , b t ) )
ρ ( x , y ) = j t j ( x , y )
M S E = 1 N P j = 1 N P ( x j x ^ j ) 2
I ^ = i a i E i i = 1 , , N
u ( r , ϕ , z ) = C l p w ( z ) ( r 2 w ( z ) ) | l | e r 2 w 2 ( z ) L p | l | ( 2 r 2 w 2 ( z ) ) e i k r 2 2 R ( z ) e i l ϕ e [ i ( 2 p + | l | + 1 ) ξ ( z ) ]
L p l ( x ) = x l e x p ! d p d x p e x e l + p
p = 0 , , N ; l = p , , p
n = 2 p + | l | n = 0 , , N ;

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