Abstract

In this Letter, we propose a method to perform 3D imaging with a simple and robust imaging system only composed of a continuously self-imaging grating (CSIG) and a matrix detector. With a CSIG, the intensity pattern generated by an object source is periodic and propagation invariant, apart from a dilatation factor that depends on the distance of the object. We demonstrate, theoretically and experimentally, how to exploit this property to analyze a scene in three dimensions. Such an imaging system can be used, for example, for tomographic applications.

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  1. C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).
  2. N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
    [CrossRef]
  3. B. Laude-Boulesteix, A. De Martino, B. Drevillon, and L. Schwartz, Appl. Opt. 43, 2824 (2004).
    [CrossRef]
  4. G. Anna, H. Sauer, F. Goudail, and D. Dolfi, Appl. Opt. 51, 5302 (2012).
    [CrossRef]
  5. R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, Opt. Rev. 14, 347 (2007).
    [CrossRef]
  6. Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).
  7. S. McEldowney, “Use of wavefront coding to create a depth image,” U.S. patent application20110310226 (December22, 2011).
  8. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).
  9. A. Koschan, M. Pollefeys, and M. Abidi, 3D Imaging for Safety and Security, Computational Imaging and Vision (Springer, 2007), Vol. 35.
  10. P. J. Besl, Mach. Vis. Appl. 1, 127 (1988).
    [CrossRef]
  11. N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 26, 411 (2001).
    [CrossRef]
  12. W. D. Montgomery, J. Opt. Soc. Am. 57, 772 (1967).
    [CrossRef]
  13. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  14. D. Joyeux and Y. Cohen-Sabban, Appl. Opt. 21, 625 (1982).
    [CrossRef]
  15. M. Piponnier, R. Horisaki, G. Druart, N. Guérineau, A. Kattnig, and J. Primot, Opt. Lett. 37, 3492 (2012).
    [CrossRef]
  16. R. Horisaki, M. Piponnier, G. Druart, N. Guérineau, J. Primot, F. Goudail, J. Taboury, and J. Tanida, Appl. Opt. 52, 3802 (2013).
    [CrossRef]

2013

2012

2011

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

2009

C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).

2008

Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).

2007

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, Opt. Rev. 14, 347 (2007).
[CrossRef]

2006

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

2004

2001

1988

P. J. Besl, Mach. Vis. Appl. 1, 127 (1988).
[CrossRef]

1987

1982

1967

Abidi, M.

A. Koschan, M. Pollefeys, and M. Abidi, 3D Imaging for Safety and Security, Computational Imaging and Vision (Springer, 2007), Vol. 35.

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Anna, G.

Bando, Y.

Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).

Besl, P. J.

P. J. Besl, Mach. Vis. Appl. 1, 127 (1988).
[CrossRef]

Chambon, M.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Chen, B.-Y.

Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).

Cohen-Sabban, Y.

De Martino, A.

Dolfi, D.

Drevillon, B.

Druart, G.

Durnin, J.

Fendler, M.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Ferrec, Y.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Gillard, F.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Goudail, F.

Guérineau, N.

Haïdar, R.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Harchaoui, B.

Heggarty, K.

Horisaki, R.

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Irie, S.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, Opt. Rev. 14, 347 (2007).
[CrossRef]

Joyeux, D.

Kattnig, A.

Koschan, A.

A. Koschan, M. Pollefeys, and M. Abidi, 3D Imaging for Safety and Security, Computational Imaging and Vision (Springer, 2007), Vol. 35.

Laude-Boulesteix, B.

Levoy, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Lin, S.

C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).

McEldowney, S.

S. McEldowney, “Use of wavefront coding to create a depth image,” U.S. patent application20110310226 (December22, 2011).

Montgomery, W. D.

Nayar, S.

C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Nishita, T.

Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).

Ogura, Y.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, Opt. Rev. 14, 347 (2007).
[CrossRef]

Piponnier, M.

Pollefeys, M.

A. Koschan, M. Pollefeys, and M. Abidi, 3D Imaging for Safety and Security, Computational Imaging and Vision (Springer, 2007), Vol. 35.

Primot, J.

Rommeluère, S.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Sauer, H.

Schwartz, L.

Taboury, J.

R. Horisaki, M. Piponnier, G. Druart, N. Guérineau, J. Primot, F. Goudail, J. Taboury, and J. Tanida, Appl. Opt. 52, 3802 (2013).
[CrossRef]

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Tanida, J.

Vincent, G.

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Zhou, C.

C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).

ACM Trans. Graph.

Y. Bando, B.-Y. Chen, and T. Nishita, ACM Trans. Graph. 27, 134 (2008).

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, ACM Trans. Graph. 25, 924 (2006).

Appl. Opt.

IEEE

C. Zhou, S. Lin, and S. Nayar, IEEE 978, 325 (2009).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Mach. Vis. Appl.

P. J. Besl, Mach. Vis. Appl. 1, 127 (1988).
[CrossRef]

Opt. Lett.

Opt. Rev.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, Opt. Rev. 14, 347 (2007).
[CrossRef]

Proc. SPIE

N. Guérineau, G. Druart, F. Gillard, Y. Ferrec, M. Chambon, S. Rommeluère, G. Vincent, R. Haïdar, J. Taboury, and M. Fendler, Proc. SPIE 8012, 801229 (2011).
[CrossRef]

Other

A. Koschan, M. Pollefeys, and M. Abidi, 3D Imaging for Safety and Security, Computational Imaging and Vision (Springer, 2007), Vol. 35.

S. McEldowney, “Use of wavefront coding to create a depth image,” U.S. patent application20110310226 (December22, 2011).

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of (a)  T , (b)  I ref , and (c)  I ˜ ref for a CSIG of parameter η 2 = 325 that diffracts N = 24 orders. For I ref , only an elementary pattern of size a 0 × a 0 is represented.

Fig. 2.
Fig. 2.

Illustration of separated spectra generated by two point sources at the distances d 1 = (light gray dots) and d 2 = 710 mm (dark gray dots) from the CSIG.

Fig. 3.
Fig. 3.

(a) Scheme of the setup used to image two point sources at different distances from the CSIG. (b) Experimental image (in reversed contrast) obtained with this setup.

Fig. 4.
Fig. 4.

Illustration of the correlation between the experimental spectrum and the reference spectrum contracted by a factor of C varying in the range [0.5, 1].

Fig. 5.
Fig. 5.

(a) Scheme of the setup used to image two extended objects at different distances of the CSIG. (b) Experimental image (in reversed contrast) obtained with this setup.

Fig. 6.
Fig. 6.

Illustration of the reconstructed objects (in reversed contrast) located at a distance (a)  d 1 = 493 mm and (b)  d 2 = 1004 mm .

Equations (11)

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

T ( f x , f y ) = k = 1 N c k δ ( f x p k a 0 , f y q k a 0 ) ,
p k 2 a 0 2 + q k 2 a 0 2 = ρ 0 2 = η 2 a 0 2 ,
I ref ( x , y ) = I 0 | t ( x , y ) | 2 .
I ˜ ref ( f x , f y ) = I 0 [ T T ] ( f x , f y ) ,
I ( x , y ) = 1 Δ 2 I ref ( x Δ , y Δ ) ,
Δ = 1 + F d ,
I ˜ ( f x , f y ) = C I ˜ ref ( f x C , f y C ) ,
C = 1 Δ = d d + F .
I ( x , y ) = i = 1 n I i Δ i 2 I ref I 0 ( x Δ i , y Δ i ) .
I ˜ ( f x , f y ) = i = 1 n I i C i I ˜ ref I 0 ( f x C i , f y C i ) .
cor ( C ) = R 2 I ˜ ( f x , f y ) × I ˜ ref ( f x C , f y C ) d f x d f y .

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