Abstract

We have designed miniaturized, simple, and robust cameras composed of a single diffractive optical element (DOE) that generates a continuously self-imaging (CSI) beam. Two different DOEs are explored: the J0 Bessel transmittance, characterized by a continuous optical transfer function (OTF) and the CSI grating (CSIG), characterized by a sparse OTF. In this Letter, we will analyze the properties of both DOEs in terms of radiometric performances. We will demonstrate that the noise robustness is enhanced for a CSIG, thanks to the sparsity of its OTF. A camera using this DOE has been made and experimental images are presented to illustrate the noise robustness.

© 2012 Optical Society of America

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References

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2011 (3)

2009 (2)

2008 (1)

2007 (2)

2005 (1)

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

2001 (2)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

N. Guérineau, B. Harchaoui, J. Primot, and K. Heggarty, Opt. Lett. 26, 411 (2001).
[CrossRef]

1997 (1)

1987 (1)

1985 (1)

J. Durnin, J. Opt. Soc. Am. A 2, 110 (1985).

1967 (1)

1958 (1)

J. Dyson, Proc. R. Soc. Lond. A 248, 93 (1958).
[CrossRef]

1954 (1)

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Castro, A.

Cigna, J.-C.

Cottrell, D. M.

Craven, J. M.

Davis, J. A.

de Bougrenet, J.-L.

de la Barrière, F.

Druart, G.

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. Opt. Soc. Am. A 2, 110 (1985).

Dyson, J.

J. Dyson, Proc. R. Soc. Lond. A 248, 93 (1958).
[CrossRef]

Fendler, M.

Ferrec, Y.

Frauel, Y.

Guérineau, N.

Guo, C.-S.

Haïdar, R.

Harchaoui, B.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Heggarty, K.

Javidi, B.

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Kattnig, A.

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Kolodziejczyk, A.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Lanzl, T.

Lu, L.-L.

Maier, Max

Makowski, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

McLeod, J. H.

Mikula, G.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Montgomery, W. D.

Niggl, L.

Piponnier, M.

Primot, J.

Prokopowicz, C.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Rommeluère, S.

Sauer, H.

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Sypek, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Taboury, J.

Wang, H.-T.

Wei, G.-X.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Nature (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef]

Opt. Eng. (1)

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, Opt. Eng. 44, 058001 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Proc. R. Soc. Lond. A (1)

J. Dyson, Proc. R. Soc. Lond. A 248, 93 (1958).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the FT of the transmittance for (a) a J 0 object and (b) a CSIG of parameter η 2 = 325 ( N = 24 ). Both DOEs have the same ρ 0 .

Fig. 2.
Fig. 2.

Illustration of the intensity pattern for the (a)  J 0 object and (b) for the CSIG of parameter η 2 = 325 . The spatial spectrum of the (c)  J 0 object and (d) the CSIG are also represented. Both DOEs have the same f c .

Fig. 3.
Fig. 3.

Illustration of the radial profile of the spatial spectra I ˜ for the CSIG and the J 0 object. A white noise of variance V = 0.0225 is considered. We get SNR CSIG = 11.85 and SNR J 0 = 0.17 .

Fig. 4.
Fig. 4.

Illustration of a rose-shaped object [panel (a)] imaged by a CSIG. An experimental noiseless image obtained with a long exposure time is shown in (b), and (d) is the reconstructed image of (b). (c) shows a noisy image obtained with a shorter exposure time, and (e) is the reconstructed image of (c).

Equations (10)

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I prop ( x , y , z ) = I 0 | t device ( x , y ) | 2 .
T J 0 ( ρ ) = 1 2 π ρ 0 ϵ ring ( ρ ρ 0 ) ,
T CSIG ( f x , f y ) = 1 N ϵ 2 ring ( ρ ρ 0 ) × Ш 1 / a 0 ( f x , f y ) ,
p k 2 a 0 2 + q k 2 a 0 2 = η 2 a 0 2 = ρ 0 2 ,
t device ( 0 , 0 ) = R 2 T device ( f x , f y ) d f x d f y = 1.
R 2 I ˜ device ( f x , f y ) d f x d f y = I device ( 0 , 0 ) = I 0 .
A J 0 = 2 I 0 ϵ 2 ( 2 π ρ 0 ϵ ) 2 = 2 I 0 ( 2 π ρ 0 ) 2 ,
A CSIG = 2 I 0 ϵ 2 ( N ϵ 2 ) 2 = 2 I 0 ( N ϵ ) 2 .
m = V a ,
SNR = A device m .

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