Abstract

We present two approaches that use the environmental conditions in order to exceed the classical Abbe's limit of resolution of an aperture-limited imaging system. At first we use water drops in order to improve the resolving capabilities of an imaging system using a time-multiplexing approach. The limit for the resolution improvement capabilities is equal to the size of the rain drops. The rain drops falling close to the imaged object act as a sparse and random high-resolution mask attached to it. By applying proper image processing, the center of each falling drop is located, and the parameters of the encoding grating are extracted from the captured set of images. The decoding is done digitally by applying the same mask and time averaging. In many cases urban environment includes periodic or other high-resolution objects such as fences. Actually urban environment includes many objects of this type since from an engineering point of view they are considered appealing. Those objects follow well known standards, and therefore their structure can be a priori known even without being fully capable of imaging them. We show experimentally how we use such objects in order to superresolve the contour of moving targets passing in front of them.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2006

2005

2004

2002

2001

Z. Zalevsky, E. Leith, and K. Mills, "Optical implementation of code division multiplexing for super resolution. Part I. Spectroscopic method," Opt. Commun. 195, 93-100 (2001).
[CrossRef]

Z. Zalevsky, E. Leith, and K. Mills, "Optical implementation of code division multiplexing for super resolution. Part II. Temporal method," Opt. Commun. 195, 101-106 (2001).
[CrossRef]

K. D. Mills, L. Deslaurier, D. S. Dilworth, S. M. Grannell, B. G. Hoover, B. D. Athey, and E. N. Leith, "Investigation of ultrafast time gating by spatial filtering," Appl. Opt. 40, 2282-2289 (2001).
[CrossRef]

1999

1997

1996

1992

1982

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).
[CrossRef]

1967

1966

1963

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18 (1963).

1960

A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).

1952

M. Francon, "Amélioration de résolution d'optique," Nuovo Cimento Suppl. 9, 283-290 (1952).

Appl. Opt.

D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, "Two dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 6687-6691 (1997).
[CrossRef]

D. Mendlovic, J. Garcia, Z. Zalevsky, E. Marom, D. Mas, C. Ferreira, and A. W. Lohmann, "Wavelength multiplexing system for a single mode image transmission," Appl. Opt. 36, 8474-8480 (1997).
[CrossRef]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. G. Martinez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
[CrossRef]

K. D. Mills, L. Deslaurier, D. S. Dilworth, S. M. Grannell, B. G. Hoover, B. D. Athey, and E. N. Leith, "Investigation of ultrafast time gating by spatial filtering," Appl. Opt. 40, 2282-2289 (2001).
[CrossRef]

K. Mills, Z. Zalevsky, and E. N. Leith, "Holographic generalized first-arriving light approach for resolving images viewed through a scattering medium," Appl. Opt. 41, 2116-2121 (2002).
[CrossRef] [PubMed]

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, "Time multiplexing superresolution based on interference grating projection," Appl. Opt. 41, 7397-7404 (2002).
[CrossRef] [PubMed]

P. C. Sun and E. N. Leith, "Superresolution by spatial-temporal encoding methods," Appl. Opt. 31, 4857-4862 (1992).
[CrossRef] [PubMed]

A. Zlotnik, Z. Zalevsky, and E. Marom, "Superresolution with nonorthogonal polarization coding," Appl. Opt. 44, 3705-3715 (2005).
[CrossRef] [PubMed]

W.-C. Chien, D. S. Dilworth, E. Liu, and E. N. Leith, "Synthetic-aperture chirp confocal imaging," Appl. Opt. 45, 501-510 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nuovo Cimento Suppl.

M. Francon, "Amélioration de résolution d'optique," Nuovo Cimento Suppl. 9, 283-290 (1952).

Opt. Commun.

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Super resolution optical systems using fixed gratings," Opt. Commun. 163, 79-85 (1999).
[CrossRef]

Z. Zalevsky, E. Leith, and K. Mills, "Optical implementation of code division multiplexing for super resolution. Part I. Spectroscopic method," Opt. Commun. 195, 93-100 (2001).
[CrossRef]

Z. Zalevsky, E. Leith, and K. Mills, "Optical implementation of code division multiplexing for super resolution. Part II. Temporal method," Opt. Commun. 195, 101-106 (2001).
[CrossRef]

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).

Z. Phys.

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18 (1963).

Other

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer-Verlag, 2003).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, E.Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 271-341.

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Figures (2)

Fig. 1
Fig. 1

Experimental results:(a) the low-resolution images; (b) the high-resolution target we used for the experiment; (c) the obtained reconstruction after averaging over more than 100 frames.

Fig. 2
Fig. 2

(Color online) (a) High-resolution urban environment; (b) part of the sequence of low-resolution images containing moving target; (c) the superresolved moving target.

Equations (16)

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

I ( x , t ) = s ( x ) g ( x , t ) p ( x x ) d x .
d ( x , t ) = [ I ( x , t ) I ( x , t ) I m ] K ,
g ( x , t ) d ( x , t ) d t δ ( x x ) + κ ,
r ( x ) = I ( x , t ) d ( x , t ) d t = s ( x ) g ( x , t ) p ( x x ) × d ( x , t ) d x d t .
r ( x ) = s ( x ) p ( x x ) [ g ( x , t ) d ( x , t ) d t ] d x = s ( x ) p ( x x ) δ ( x x ) d x + κ s ( x ) p ( x x ) d x = s ( x ) p ( 0 ) + κ · LRI ,
s 1 ( x ) = { 1 s ( x ) > 0 0 s ( x ) = 0 .
t ( x , t ) = [ 1 s 1 ( x v t ) ] [ n A n   exp ( 2 π i n x μ 0 ) ] + s ( x v t ) ,
I ( x , t ) = t ( x , t ) p ( x x ) d x ′ .
I ( x , t ) = n A n exp ( 2 π i n x μ 0 ) p ( x x ) d x n A n s 1 ( x v t ) exp ( 2 π i n x μ 0 ) p ( x x ) d x + s ( x v t ) p ( x x ) d x ′ .
R ( x ) = n A n I ( x + v t , t ) exp [ 2 π i n ( x + v t ) μ 0 ] d t ,
R ( x ) = n m A n A m exp [ 2 π i n ( x + v t ) μ 0 ] × { exp [ 2 π i m ( x + v t ) μ 0 ] p ( x x ) d x } d t n m A n A m exp [ 2 π i n ( x + v t ) μ 0 ] × { s 1 ( x ) exp [ 2 π i m ( x + v t ) μ 0 ] p ( x x ) d x } d t + n A n exp [ 2 π i n ( x + v t ) μ 0 ] × [ s ( x ) p ( x x ) d x ] d t .
exp ( 2 π i n v μ 0 t ) exp ( 2 π i m v μ 0 t ) d t = δ ( n m ) ,
exp ( 2 π i n v μ 0 t ) d t = δ ( n ) ,
n δ ( x n μ 0 ) n A n   exp ( 2 π i n x μ 0 ) n A n A n   exp ( 2 π i n x μ 0 ) .
R ( x ) = p ( 0 ) s 1 ( x ) n δ ( x x n μ 0 ) p ( x x ) d x + A 0 s ( x ) p ( x x ) d x ″ .
R ( x ) = p ( 0 ) s 1 ( x ) δ ( x x ) p ( x x ) d x + A 0 s ( x ) p ( x x ) d x = p ( 0 ) + A 0 s ( x ) p ( x x ) d x s 1 ( x ) ,

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