Abstract

We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary bases using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice.

© 2018 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Compressive optical interferometry under structural constraints

Davood Mardani, H. Esat Kondakci, Lane Martin, Ayman F. Abouraddy, and George K. Atia
Opt. Express 26(5) 5225-5239 (2018)

Efficient modal analysis using compressive optical interferometry

Davood Mardani, Ayman F. Abouraddy, and George K. Atia
Opt. Express 23(22) 28449-28458 (2015)

Discrete linear canonical transforms based on dilated Hermite functions

Soo-Chang Pei and Yun-Chiu Lai
J. Opt. Soc. Am. A 28(8) 1695-1708 (2011)

References

  • View by:
  • |
  • |
  • |

  1. M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
    [Crossref]
  2. Z. Wang and Z. Yu, “Spectral analysis based on compressive sensing in nanophotonic structures,” Opt. Express 22, 25608–25614 (2014).
    [Crossref]
  3. L. Martínez-León, P. Clemente, Y. Mori, V. Climent, J. Lancis, and E. Tajahuerce, “Single-pixel digital holography with phase-encoded illumination,” Opt. Express 25, 4975–4984 (2017).
    [Crossref]
  4. P. Clemente, V. Durán, E. Tajahuerce, P. Andrés, V. Climent, and J. Lancis, “Compressive holography with a single-pixel detector,” Opt. Lett. 38, 2524–2527 (2013).
    [Crossref]
  5. A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Generalized optical interferometry for modal analysis in arbitrary degrees of freedom,” Opt. Lett. 37, 2889–2891 (2012).
    [Crossref]
  6. M. E. Brezinski, Optical Coherenece Tomography (Academic, 2006).
  7. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [Crossref]
  8. M. I. Akhlaghi and A. Dogariu, “Compressive correlation imaging with random illumination,” Opt. Lett. 40, 4464–4467 (2015).
    [Crossref]
  9. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
    [Crossref]
  10. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref]
  11. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
    [Crossref]
  12. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
    [Crossref]
  13. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2480 (2012).
    [Crossref]
  14. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
    [Crossref]
  15. Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
    [Crossref]
  16. 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 Process. Mag. 25, 83–91 (2008).
    [Crossref]
  17. D. Mardani, A. F. Abouraddy, and G. K. Atia, “Efficient modal analysis using compressive optical interferometry,” Opt. Express 23, 28449–28458 (2015).
    [Crossref]
  18. D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
    [Crossref]
  19. V. Durán, F. Soldevila, E. Irles, P. Clemente, E. Tajahuerce, P. Andrés, and J. Lancis, “Compressive imaging in scattering media,” Opt. Express 23, 14424–14433 (2015).
    [Crossref]
  20. 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, 16945–16955 (2014).
    [Crossref]
  21. L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
    [Crossref]
  22. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
    [Crossref]
  23. W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
    [Crossref]
  24. G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
    [Crossref]
  25. G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
    [Crossref]
  26. G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
    [Crossref]
  27. J. P. Dumas, M. A. Lodhi, W. U. Bajwa, and M. C. Pierce, “From modeling to hardware: an experimental evaluation of image plane and Fourier plane coded compressive optical imaging,” Opt. Express 25, 29472–29491 (2017).
    [Crossref]
  28. D. Marcos, T. Lasser, A. López, and A. Bourquard, “Compressed imaging by sparse random convolution,” Opt. Express 24, 1269–1290 (2016).
    [Crossref]
  29. E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. 346, 589–592 (2008).
    [Crossref]
  30. E. Hecht, Optics (Addison-Wesley, 2002).
  31. D. Mendlovic, Optical Superresolution (Springer, 2012).
  32. S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
    [Crossref]
  33. D. Mardani, G. K. Atia, and A. F. Abouraddy, “Signal reconstruction from interferometric measurements under sensing constraints,” arXiv:1706.10275 (2017).
  34. M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” J. Math. Phys. 12, 1772–1780 (1971).
    [Crossref]
  35. B. D. Cullity, Introduction to Magnetic Materials (Addison-Wesley, 1972).
  36. S.-C. Pei and J.-J. Ding, “Eigenfunctions of linear canonical transform,” IEEE Trans. Signal Process. 50, 11–26 (2002).
    [Crossref]
  37. E. Candes and T. Tao, “The Dantzig selector: Statistical estimation when p is much larger than n,” Ann. Statist. 35, 2313–2351 (2007).
    [Crossref]
  38. L. B. Almeida, “Product and convolution theorems for the fractional Fourier transform,” IEEE Signal Process. Lett. 4, 15–17 (1997).
    [Crossref]

2018 (1)

2017 (3)

2016 (2)

D. Marcos, T. Lasser, A. López, and A. Bourquard, “Compressed imaging by sparse random convolution,” Opt. Express 24, 1269–1290 (2016).
[Crossref]

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

2015 (4)

2014 (4)

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, 16945–16955 (2014).
[Crossref]

Z. Wang and Z. Yu, “Spectral analysis based on compressive sensing in nanophotonic structures,” Opt. Express 22, 25608–25614 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

2013 (2)

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

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

2012 (3)

2009 (1)

2008 (4)

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[Crossref]

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. 346, 589–592 (2008).
[Crossref]

2007 (1)

E. Candes and T. Tao, “The Dantzig selector: Statistical estimation when p is much larger than n,” Ann. Statist. 35, 2313–2351 (2007).
[Crossref]

2005 (1)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[Crossref]

2004 (1)

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

2003 (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

2002 (1)

S.-C. Pei and J.-J. Ding, “Eigenfunctions of linear canonical transform,” IEEE Trans. Signal Process. 50, 11–26 (2002).
[Crossref]

1997 (1)

L. B. Almeida, “Product and convolution theorems for the fractional Fourier transform,” IEEE Signal Process. Lett. 4, 15–17 (1997).
[Crossref]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

1989 (1)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

1971 (1)

M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” J. Math. Phys. 12, 1772–1780 (1971).
[Crossref]

Abouraddy, A. F.

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

D. Mardani, A. F. Abouraddy, and G. K. Atia, “Efficient modal analysis using compressive optical interferometry,” Opt. Express 23, 28449–28458 (2015).
[Crossref]

A. F. Abouraddy, T. M. Yarnall, and B. E. A. Saleh, “Generalized optical interferometry for modal analysis in arbitrary degrees of freedom,” Opt. Lett. 37, 2889–2891 (2012).
[Crossref]

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[Crossref]

D. Mardani, G. K. Atia, and A. F. Abouraddy, “Signal reconstruction from interferometric measurements under sensing constraints,” arXiv:1706.10275 (2017).

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Akhlaghi, M. I.

Almeida, L. B.

L. B. Almeida, “Product and convolution theorems for the fractional Fourier transform,” IEEE Signal Process. Lett. 4, 15–17 (1997).
[Crossref]

Andrés, P.

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Atia, G. K.

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

D. Mardani, A. F. Abouraddy, and G. K. Atia, “Efficient modal analysis using compressive optical interferometry,” Opt. Express 23, 28449–28458 (2015).
[Crossref]

D. Mardani, G. K. Atia, and A. F. Abouraddy, “Signal reconstruction from interferometric measurements under sensing constraints,” arXiv:1706.10275 (2017).

Bajwa, W. U.

Baney, D. M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Bourquard, A.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Brady, D. J.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Brezinski, M. E.

M. E. Brezinski, Optical Coherenece Tomography (Academic, 2006).

Candes, E.

E. Candes and T. Tao, “The Dantzig selector: Statistical estimation when p is much larger than n,” Ann. Statist. 35, 2313–2351 (2007).
[Crossref]

Candes, E. J.

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. 346, 589–592 (2008).
[Crossref]

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Clemente, P.

Climent, V.

Cullity, B. D.

B. D. Cullity, Introduction to Magnetic Materials (Addison-Wesley, 1972).

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Denis, L.

Ding, J.-J.

S.-C. Pei and J.-J. Ding, “Eigenfunctions of linear canonical transform,” IEEE Trans. Signal Process. 50, 11–26 (2002).
[Crossref]

Dogariu, A.

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Dumas, J. P.

Duparré, M.

Durán, V.

Elad, M.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

Farsiu, S.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

Fink, Y.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[Crossref]

Flamm, D.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Forbes, A.

Fournier, C.

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Ghalmi, S.

Gong, W.

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Han, S.

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 2002).

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

Howell, J. C.

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

Howland, G. A.

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Irles, E.

Jahromi, A. K.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Joannopoulos, J. D.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

Knarr, S. H.

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

Kondakci, H. E.

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Lancis, J.

Larson, W. D.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Lasser, T.

D. Marcos, T. Lasser, A. López, and A. Bourquard, “Compressed imaging by sparse random convolution,” Opt. Express 24, 1269–1290 (2016).
[Crossref]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Lodhi, M. A.

López, A.

Lorenz, D.

Lum, D. J.

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

Malhotra, T.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Marcos, D.

Mardani, D.

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

D. Mardani, A. F. Abouraddy, and G. K. Atia, “Efficient modal analysis using compressive optical interferometry,” Opt. Express 23, 28449–28458 (2015).
[Crossref]

D. Mardani, G. K. Atia, and A. F. Abouraddy, “Signal reconstruction from interferometric measurements under sensing constraints,” arXiv:1706.10275 (2017).

Martin, L.

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Martínez-León, L.

Mendlovic, D.

D. Mendlovic, Optical Superresolution (Springer, 2012).

Milanfar, P.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

Mori, Y.

Moshinsky, M.

M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” J. Math. Phys. 12, 1772–1780 (1971).
[Crossref]

Naidoo, D.

Nazarathy, M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

Newton, S. A.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

Nicholson, J. W.

Pei, S.-C.

S.-C. Pei and J.-J. Ding, “Eigenfunctions of linear canonical transform,” IEEE Trans. Signal Process. 50, 11–26 (2002).
[Crossref]

Pierce, M. C.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Quesne, C.

M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” J. Math. Phys. 12, 1772–1780 (1971).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[Crossref]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Robinson, D.

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

Saleh, B. E. A.

Schneeloch, J.

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

Schulze, C.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Shabahang, S.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Shapira, O.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[Crossref]

Soldevila, F.

Sorin, W. V.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Tajahuerce, E.

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

Tao, T.

E. Candes and T. Tao, “The Dantzig selector: Statistical estimation when p is much larger than n,” Ann. Statist. 35, 2313–2351 (2007).
[Crossref]

Thiébaut, E.

Trede, D.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Vamivakas, A. N.

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Wang, Y.

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

Wang, Z.

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yablon, A. D.

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yang, J.

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yarnall, T. M.

Yin, W.

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

Yu, Z.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Zhang, Y.

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

Ann. Statist. (1)

E. Candes and T. Tao, “The Dantzig selector: Statistical estimation when p is much larger than n,” Ann. Statist. 35, 2313–2351 (2007).
[Crossref]

C. R. Acad. Sci. (1)

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. 346, 589–592 (2008).
[Crossref]

IEEE Signal Process. Lett. (1)

L. B. Almeida, “Product and convolution theorems for the fractional Fourier transform,” IEEE Signal Process. Lett. 4, 15–17 (1997).
[Crossref]

IEEE Signal Process. Mag. (2)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging: an introduction,” IEEE Signal Process. Mag. 31, 105–115 (2014).
[Crossref]

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 Process. Mag. 25, 83–91 (2008).
[Crossref]

IEEE Trans. Signal Process. (1)

S.-C. Pei and J.-J. Ding, “Eigenfunctions of linear canonical transform,” IEEE Trans. Signal Process. 50, 11–26 (2002).
[Crossref]

Int. J. Imaging Syst. Technol. (1)

S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, “Advances and challenges in super-resolution,” Int. J. Imaging Syst. Technol. 14, 47–57 (2004).
[Crossref]

J. Lightwave Technol. (1)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7, 1083–1096 (1989).
[Crossref]

J. Math. Phys. (1)

M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” J. Math. Phys. 12, 1772–1780 (1971).
[Crossref]

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Opt. Express (9)

Z. Wang and Z. Yu, “Spectral analysis based on compressive sensing in nanophotonic structures,” Opt. Express 22, 25608–25614 (2014).
[Crossref]

L. Martínez-León, P. Clemente, Y. Mori, V. Climent, J. Lancis, and E. Tajahuerce, “Single-pixel digital holography with phase-encoded illumination,” Opt. Express 25, 4975–4984 (2017).
[Crossref]

D. Mardani, A. F. Abouraddy, and G. K. Atia, “Efficient modal analysis using compressive optical interferometry,” Opt. Express 23, 28449–28458 (2015).
[Crossref]

D. Mardani, H. E. Kondakci, L. Martin, A. F. Abouraddy, and G. K. Atia, “Compressive optical interferometry under structural constraints,” Opt. Express 26, 5225–5239 (2018).
[Crossref]

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

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, 16945–16955 (2014).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008).
[Crossref]

J. P. Dumas, M. A. Lodhi, W. U. Bajwa, and M. C. Pierce, “From modeling to hardware: an experimental evaluation of image plane and Fourier plane coded compressive optical imaging,” Opt. Express 25, 29472–29491 (2017).
[Crossref]

D. Marcos, T. Lasser, A. López, and A. Bourquard, “Compressed imaging by sparse random convolution,” Opt. Express 24, 1269–1290 (2016).
[Crossref]

Opt. Lett. (5)

Phys. Rev. Lett. (2)

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94, 143902 (2005).
[Crossref]

G. A. Howland, J. Schneeloch, D. J. Lum, and J. C. Howell, “Simultaneous measurement of complementary observables with compressive sensing,” Phys. Rev. Lett. 112, 253602 (2014).
[Crossref]

Phys. Rev. X (1)

G. A. Howland, S. H. Knarr, J. Schneeloch, D. J. Lum, and J. C. Howell, “Compressively characterizing high-dimensional entangled states with complementary, random filtering,” Phys. Rev. X 6, 021018 (2016).
[Crossref]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[Crossref]

Sci. Rep. (2)

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, W. D. Larson, S. Shabahang, A. K. Jahromi, T. Malhotra, A. N. Vamivakas, G. K. Atia, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Science (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

SIAM J. Imaging Sci. (1)

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[Crossref]

Other (5)

M. E. Brezinski, Optical Coherenece Tomography (Academic, 2006).

E. Hecht, Optics (Addison-Wesley, 2002).

D. Mendlovic, Optical Superresolution (Springer, 2012).

B. D. Cullity, Introduction to Magnetic Materials (Addison-Wesley, 1972).

D. Mardani, G. K. Atia, and A. F. Abouraddy, “Signal reconstruction from interferometric measurements under sensing constraints,” arXiv:1706.10275 (2017).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. Schematic of a frFT filter implemented using SLMs that act as quadratic phase operators.
Fig. 2.
Fig. 2. Effect of spatial aperture and pixel size on the quality of the interferograms. (a) SLM size of 16 mm and pixel size of 10 μm. (b) SLM size of 16 mm and pixel size of 5 μm. (c) SLM size of 60 mm and pixel size of 10 μm [21].
Fig. 3.
Fig. 3. Progression of a beam obtained as the superposition of HG 1 , HG 2 , HG 4 modes as it propagates, diffracts, and gets clipped by the SLMs of the frFT filter. The SLM width is w = 5    mm .
Fig. 4.
Fig. 4. Measurement model error in presence of clipping effect.
Fig. 5.
Fig. 5. FT-based modal recovery and considering the clipping effect, reconstruction error versus SLM size.
Fig. 6.
Fig. 6. Comparing reconstruction performance of the CS-based approach with consideration of the clipping terms e o ( w ) and A ¯ to that of the case in which the clipping effect is ignored. (a)  SNR = 20    dB . (b)  SNR = 30    dB . (c) Comparing the reconstruction error of the iterative algorithm to that of the regular CS-based algorithm where the term B x ¯ is ignored, SNR = 30    dB .
Fig. 7.
Fig. 7. Reconstruction of modal coefficients. w = 6    mm , SNR = 30    dB .

Tables (1)

Tables Icon

Algorithm 1 Iterative reconstruction algorithm

Equations (36)

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

I ( τ ) = | ψ ( t ; τ ) + ψ ( t ) | 2 ,
I ( τ ) = 2 + 2 n = 1 N | c n | 2 cos ( n τ ) .
ψ ( x ; α ) = n = 1 N c n e i n α ϕ n ( x ) ,
y = Ax ,
ψ M ( u ) = T M { ψ ( x ) } ( u ) = ψ ( x ) h M ( x , u ) d x ,
h M ( x , u ) = 1 j 2 π b exp ( j 2 b ( a x 2 2 x u + d u 2 ) )
ψ M ( u ) = T M { ψ ( x ) } ( u ) = d exp ( j c d u 2 2 ) ψ ( d u )
ψ M ( u ; w ) = w 2 π | b | e j d 2 b u 2 ( ( ψ M ( u ) e j d 2 b u 2 ) * sinc ( w u 2 π b ) ) ,
ψ M ( u ; w ) = d exp ( i c d 2 u 2 ) ψ ( d u ) Π ( d u w )
ϕ ^ n ( x ; α , w ) = w 1 w 2 | csc α | ( λ l ) 2 [ ( exp ( j π csc α λ l x 2 ) × ( ϕ n ( x ) exp ( j π cot α λ l x 2 ) * sinc ( w 1 x csc α λ l ) ) ) * sinc ( w 2 x λ l ) ] × Π ( x w 3 ) exp ( j π ( csc α + cot α ) λ l x 2 ) .
ψ ( x ; α , w ) = L { n = 1 N c n ϕ n ( x ) } = n = 1 N c n e i n α ϕ ^ n ( x ; α , w ) .
I ( α ; w ) = | ψ ( x ) | 2 + | ψ ( x ; α , w ) | 2 + ψ ( x ) ψ * ( x ; α , w ) + ψ ( x ; α , w ) ψ * ( x ) ,
2 R e { n = 1 N | c n | 2 e i n α + ϕ ^ n ( x ; α , w ) ϕ n * ( x ) d x } + n = 1 N n = 1 n n N c n c n * ( e i n α + ϕ ^ n ( x ; α , w ) ϕ n * ( x ) d x + e i n α + ϕ n ( x ) ϕ ^ n * ( x ; α , w ) d x ) ,
I ( α ; w ) = 1 + e o ( α , w ) + 2 n = 1 N | c n | 2 | g n n ( α ; w ) | cos ( n α + g n n ( α ; w ) ) + n = 1 N n = 1 n 1 N c n c n * ( e i n α g n n ( α ; w ) + e i n α g n n * ( α ; w ) ) .
y = A ¯ x + B x ¯ ,
y = A ¯ x + B x ¯ + z .
y A ¯ x + z ,
minimize x ^ 1 subject to A ¯ T ( A ¯ x ^ y ) η σ ,
T M { ψ ( x ) } ( u ) = ψ M ( u ) = 1 2 π | b | e i d 2 b u 2 [ ( s M ( u ) e i d 2 b u 2 ) * g FT ( u 2 π b ) ] = 1 2 π | b | e i d 2 b u 2 [ ( g M ( u ) e i d 2 b u 2 ) * s FT ( u 2 π b ) ]
T M { ψ ( x ) } ( u ) = d e i c d 2 u 2 s ( d u ) g ( d u )
T M { s ( x ) · g ( x ) } ( u ) = ( s ( x ) · g ( x ) ) × 1 i 2 π b exp ( i 2 b ( a x 2 2 x u + d u 2 ) ) d x .
T M { ψ ( x ) } ( u ) = ψ M ( u ) = ( g ( x ) × 1 i 2 π b exp ( i 2 b ( a x 2 2 x u + d u 2 ) ) × s M ( u ^ ) 1 i 2 π b exp ( i 2 b ( d u ^ 2 2 x u ^ + a x 2 ) ) d u ^ ) d x = exp ( i d 2 b u 2 ) 2 π | b | s M ( u ^ ) exp ( i d 2 b u ^ 2 ) × ( g ( x ) exp ( i 2 π b 2 π x ( u u ^ ) ) d x ) d u ^ .
ψ M ( u ) = exp ( i d 2 b u 2 ) 2 π | b | × s M ( u ^ ) exp ( i d 2 b u ^ 2 ) g FT ( u u ^ 2 π b ) d u ^ = exp ( i d 2 b u 2 ) 2 π | b | [ ( s M ( u ) exp ( i d 2 b u 2 ) ) * g FT ( u 2 π b ) ] .
ψ M ( u ) = e ( i d 2 b u 2 ) 2 π | b | [ ( g M ( u ) e ( i d 2 b u 2 ) ) * s FT ( u 2 π b ) ] ,
T M 2 { T w M 1 { ψ ( x ) } ( u 1 ) } ( u 2 ) = T w M 2 M 1 { ψ ( x ) } ( u 2 ) ,
κ n { ψ ( x ) ; { M L } , { w } } ( u ) = exp ( i ( d L n 2 b L n d L ( n + 1 ) 2 b L ( n + 1 ) ) u 2 ) × [ κ n 1 { ψ ( x ) ; { M L } , { w } } ( u ) * sinc ( w n u 2 π b L n ) ] , n = 2 , 3 , , L ,
κ 1 { ψ ( x ) ; { M L } , { w } } ( u ) = exp ( i ( d L 1 2 b L 1 d L 2 2 b L 2 ) u 2 ) × ( T M L 1 { ψ ( x ) } ( u ) exp ( i d L 1 2 b L 1 u 2 ) * sinc ( w 1 u 2 π b L 1 ) ) ,
ψ o ( u ) = ( = 1 L w 2 π | b L | ) × κ L { ψ ( x ) ; { M L } , { w } } ( u ) , = 1 , 2 , , L ,
ψ o ( u ) = T M L M L 1 M 2 M 1 { ψ ( x ) } ( u ) × Π ( u min { w 1 | d L 1 | , w 2 | d L 2 | , , w L | d L | } ) .
ψ o ( u ) = T w L M L { T w L 1 M L 1 { { T w 1 M 1 { ψ ( x ) } } } } ( u ) = d L d L 1 d 3 d 2 d 1 exp ( i d L d L 1 d 3 d 2 d 1 2 u 2 × ( c L d L 1 d L 2 d 3 d 2 d 1 + c L 1 d L d L 2 d 3 d 2 d 1 + + c 2 d L d L 1 d 3 d 1 + c 1 d L d L 1 d 3 d 2 ) ) × ψ ( d L d L 1 d 3 d 2 d 1 u ) × Π ( u min { w 1 | d L d L 1 d 3 d 2 d 1 | , w 2 | d L d L 1 d 3 d 2 | , , w L | d L | } ) .
M L M L 1 M 1 = [ 1 d L d L 1 d 2 d 1 0 c L d L 1 d 1 + c L 1 d L d L 2 d 1 + + c 1 d L d L 1 d 2 d L d 2 d 1 ] [ a L 1 b L 1 c L 1 d L 1 ] ,
ψ o ( u ) = ( = 1 L 2 w 2 π | b L 2 | ) × κ L 2 { ψ ( x ) ; { M L 2 } , { w } } ( u ) , = 1 , 2 , , L 2 ,
T w 2 M 2 { T w 2 1 M 2 1 { ψ ( x ) } ( v ) } ( u ) = d 2 1 e i c 2 1 d 2 1 2 v 2 × ψ ( d 2 1 v ) Π ( d 2 1 v w 2 1 ) × h M 2 ( v , u ) Π ( v w 2 ) d v = T M 2 1 { ψ ( x ) } ( v ) h M 2 ( v , u ) Π ( v min { w 2 , w 2 1 | d 2 1 | } ) d v = T min { w 2 , w 2 1 | d 2 1 | } M 2 M 2 1 { ψ ( x ) } ( u ) ,
ψ o ( u ) = ( = 1 L 2 w 2 π | b L 2 | ) × κ L 2 { ψ ( x ) ; { M L 2 } , { w } } ( u ) × Π ( d L u w L ) , = 1 , 2 , , L 2 ,
T w 2 M 2 { T w 2 1 M 2 1 { ψ ( x ) } } ( u ) = d 2 exp ( i c 2 d 2 2 u 2 ) × ψ ( x ) h M 2 1 ( x , d 2 u ) Π ( x w 2 1 ) d x × Π ( d 2 u w 2 ) = T w 2 1 M 2 M 2 1 { ψ ( x ) } ( u ) Π ( d 2 u w 2 ) , = 1 , 2 , , L 2 .
ψ o ( u ) = T min { w L 1 , w L 2 | d L 2 | } M L M L 1 { T min { w L 3 , w L 4 | d L 4 | } M L 2 M L 3 { { T w 1 M 2 M 1 { ψ ( x ) } } } } ( u ) × Π ( d L u w L ) .