Abstract

Recent works have applied diffraction-based wave propagation for compressive imaging applications. In this Letter, we derive the theoretical bounds on the performance of compressive imaging systems based on Fresnel wave propagation, and we show that it is related to the imaging sensor’s physical attributes, illumination wavelength, and working distance.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
    [CrossRef] [PubMed]
  2. M. M. Marim, M. Atlan, E. Angelini, and J.-C. Olivo-Marin, Opt. Lett. 35, 871 (2010).
    [CrossRef] [PubMed]
  3. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, Appl. Opt. 49, E67 (2010).
    [CrossRef] [PubMed]
  4. Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
    [CrossRef]
  5. A. F. Coskun, I. Sencan, T.-W. Su, and A. Ozcan, Opt. Express 18, 10510 (2010).
    [CrossRef] [PubMed]
  6. Y. Rivenson, A. Stern, and J. Rosen, Opt. Express 19, 6109 (2011).
    [CrossRef] [PubMed]
  7. J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, Opt. Express 19, 7289 (2011).
    [CrossRef] [PubMed]
  8. E. Candes and M. Wakin, IEEE Signal Process. Mag. 25 (2), 21 (2008).
    [CrossRef]
  9. E. J. Candès and Y. Plan, “A probabilistic and RIPless theory of compressed sensing,” IEEE Trans. Inf. Theory (to be published).
  10. S. Sotthivirat and J. A. Fessler, J. Opt. Soc. Am. A 21, 737 (2004).
    [CrossRef]
  11. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, Opt. Lett. 34, 3475 (2009).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill, 1996).
  13. T. Kreis, Handbook of Holographic Interferometry, 1st ed. (Wiley-VCH, 2004).
    [CrossRef]
  14. D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
    [CrossRef]
  15. A. Stern and B. Javidi, Opt. Eng. 43, 239 (2004).
    [CrossRef]
  16. D. L. Marks, J. Hahn, R. Horisaki, and D. J. Brady, in IEEE International Conference on Computational Photography (ICCP) 2010 (IEEE, 2010), pp. 1–8.
    [CrossRef]
  17. J. Romberg, SIAM J. Imaging Sci. 2, 1098 (2009).
    [CrossRef]
  18. Y. Rivenson, A. Stern, and B. Javidi, Opt. Express 18, 15094 (2010).
    [CrossRef] [PubMed]
  19. Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
    [CrossRef]
  20. J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
    [CrossRef]
  21. Y. Rivenson and A. Stern, in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWB6.

2011 (2)

2010 (5)

2009 (4)

2008 (1)

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25 (2), 21 (2008).
[CrossRef]

2007 (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

2004 (2)

1999 (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Angelini, E.

Atlan, M.

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Brady, D. J.

Candes, E.

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25 (2), 21 (2008).
[CrossRef]

Candès, E. J.

E. J. Candès and Y. Plan, “A probabilistic and RIPless theory of compressed sensing,” IEEE Trans. Inf. Theory (to be published).

Choi, K.

Coskun, A. F.

Cull, C. F.

Denis, L.

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Fessler, J. A.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Fournier, C.

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill, 1996).

Hahn, J.

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, Opt. Express 19, 7289 (2011).
[CrossRef] [PubMed]

D. L. Marks, J. Hahn, R. Horisaki, and D. J. Brady, in IEEE International Conference on Computational Photography (ICCP) 2010 (IEEE, 2010), pp. 1–8.
[CrossRef]

Horisaki, R.

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, Opt. Express 19, 7289 (2011).
[CrossRef] [PubMed]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
[CrossRef] [PubMed]

D. L. Marks, J. Hahn, R. Horisaki, and D. J. Brady, in IEEE International Conference on Computational Photography (ICCP) 2010 (IEEE, 2010), pp. 1–8.
[CrossRef]

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, Opt. Express 18, 15094 (2010).
[CrossRef] [PubMed]

A. Stern and B. Javidi, Opt. Eng. 43, 239 (2004).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry, 1st ed. (Wiley-VCH, 2004).
[CrossRef]

Lim, S.

Lorenz, D.

Mait, J. N.

Marim, M. M.

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Marks, D. L.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
[CrossRef] [PubMed]

D. L. Marks, J. Hahn, R. Horisaki, and D. J. Brady, in IEEE International Conference on Computational Photography (ICCP) 2010 (IEEE, 2010), pp. 1–8.
[CrossRef]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Mattheiss, M.

Olivo-Marin, J.-C.

Ozcan, A.

Plan, Y.

E. J. Candès and Y. Plan, “A probabilistic and RIPless theory of compressed sensing,” IEEE Trans. Inf. Theory (to be published).

Rivenson, Y.

Y. Rivenson, A. Stern, and J. Rosen, Opt. Express 19, 6109 (2011).
[CrossRef] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, Opt. Express 18, 15094 (2010).
[CrossRef] [PubMed]

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

Y. Rivenson and A. Stern, in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWB6.

Romberg, J.

J. Romberg, SIAM J. Imaging Sci. 2, 1098 (2009).
[CrossRef]

Rosen, J.

Sencan, I.

Sotthivirat, S.

Stern, A.

Y. Rivenson, A. Stern, and J. Rosen, Opt. Express 19, 6109 (2011).
[CrossRef] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, Opt. Express 18, 15094 (2010).
[CrossRef] [PubMed]

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

A. Stern and B. Javidi, Opt. Eng. 43, 239 (2004).
[CrossRef]

Y. Rivenson and A. Stern, in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWB6.

Su, T.-W.

Thiébaut, E.

Trede, D.

Wakin, M.

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25 (2), 21 (2008).
[CrossRef]

Wikner, D. A.

Appl. Opt. (1)

IEEE Signal Process. Lett. (1)

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

IEEE Signal Process. Mag. (1)

E. Candes and M. Wakin, IEEE Signal Process. Mag. 25 (2), 21 (2008).
[CrossRef]

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

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

Opt. Commun. (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, Opt. Commun. 164, 233 (1999).
[CrossRef]

Opt. Eng. (1)

A. Stern and B. Javidi, Opt. Eng. 43, 239 (2004).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

SIAM J. Imaging Sci. (1)

J. Romberg, SIAM J. Imaging Sci. 2, 1098 (2009).
[CrossRef]

Other (5)

D. L. Marks, J. Hahn, R. Horisaki, and D. J. Brady, in IEEE International Conference on Computational Photography (ICCP) 2010 (IEEE, 2010), pp. 1–8.
[CrossRef]

E. J. Candès and Y. Plan, “A probabilistic and RIPless theory of compressed sensing,” IEEE Trans. Inf. Theory (to be published).

J. W. Goodman, Introduction to Fourier Optics(McGraw-Hill, 1996).

T. Kreis, Handbook of Holographic Interferometry, 1st ed. (Wiley-VCH, 2004).
[CrossRef]

Y. Rivenson and A. Stern, in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWB6.

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 (2)

Fig. 1
Fig. 1

Numerical near-field evaluation of the Fresnel 1D PSF.

Fig. 2
Fig. 2

Simulation results showing the compressive sampling ratio required for reconstruction of the resolution target (inset) as a function of the working distance.

Equations (13)

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

u ( ξ ) = u i n * exp { j π λ z x 2 } = exp { j π λ z ξ 2 } u i n ( x ) exp { j π λ z x 2 } exp { j 2 π λ z ξ x } d x ,
m C μ s log n ,
u ( r Δ x z ) = exp { j π r 2 Δ x z 2 λ z } F [ u ( q Δ x 0 ) exp { j π q 2 Δ x 0 2 λ z } ] ,
z z 0 = n Δ x 0 2 / λ .
u z = Q Δ x z , z FQ Δ x 0 , z u = Φ F F u ,
m C s log n .
u z ( r Δ x z ) = F 1 exp { j π λ z n 2 Δ x 0 2 m 2 } F { u ( l Δ x 0 ) } ,
u z = F 1 Q ˜ Δ x 0 , z Fu = Φ N F u ,
Φ N F = [ ϕ ( 1 ) ϕ ( n ) ϕ ( 2 ) ϕ ( 2 ) ϕ ( 1 ) ϕ ( n ) ϕ ( 2 ) ϕ ( 1 ) ] ,
μ 1 D = n max r | ϕ ( r ) | 2 n Δ x 0 2 λ z .
μ 2 D = μ 1 D 2 n 2 ( max r | ϕ ( r ) | 2 ) 2 N ( Δ x 0 2 λ z ) 2 = N F 2 N ,
m C N F 2 s N log N = C N F 2 ρ s log N ,
μ 2 D ( z 0 ) = N ( Δ x 0 2 λ z 0 ) 2 = N · ( Δ x 0 2 λ ( n Δ x 0 2 / λ ) ) 2 = 1 ,

Metrics