Abstract

The usage of two static gratings for obtaining super-resolved imaging dates back to the work by Bachl and Lukosz in 1967. However, in their approach a severe reduction in the field of view was the necessary condition for improving the resolution. We present an approach based on two static gratings without sacrificing the field of view. The key idea for not paying with the field of view is to use white light illumination to average the ghost images obtained outside the region of interest since the positions of those images are wavelength dependent. Moreover, large magnification is achieved by using a commercial microscope objective instead of a test system with a unity magnification as presented in previous works. Because of the large magnification, the second grating has a low spatial period. This allows us to create an intermediate image and use a second imaging lens with low resolution capability while still obtaining an imaging quality as good as that provided by the first imaging lens. This is an important improvement in comparison with the original super-resolving method with two fixed gratings.

© 2008 Optical Society of America

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References

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  1. G. Toraldo di Francia, “Resolving power and information,” J. Opt. Soc. Am. 45, 497-501 (1955).
    [CrossRef]
  2. G. Toraldo di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799-804 (1969).
    [CrossRef] [PubMed]
  3. J. Cox and J. R. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3, 1152-1158(1986).
    [CrossRef]
  4. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “About the space bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470-473 (1996).
    [CrossRef]
  5. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Understanding super resolution in Wigner space,” J. Opt. Soc. Am. A 17, 2422-2430 (2000).
    [CrossRef]
  6. M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).
  7. W. Lukosz, “Optical systems with resolving powers exceeding the classical limits II,” J. Opt. Soc. Am. 57, 932-941 (1967).
    [CrossRef]
  8. A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. García-Martínez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245-7251(1999).
    [CrossRef]
  9. Z. Zalevsky, J. García, P. García-Martínez, and C. Ferreira, “Spatial information transmission using orthogonal mutual coherence coding,” Opt. Lett. 30, 2837-2839 (2005).
    [CrossRef] [PubMed]
  10. D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, “Two dimensional super resolution optical system for temporally restricted objects,” Appl. Opt. 36, 6687-6691(1997).
    [CrossRef]
  11. A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectrosc. 9, 204-206 (1960).
  12. 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]
  13. M. A. Grimm and A. W. Lohmann, “Superresolution image for one-dimensional object,” J. Opt. Soc. Am. 56, 1151-1156(1966).
    [CrossRef]
  14. Z. Zalevsky, P. García-Martínez, and J. García, “Superresolution using gray level coding,” Opt. Express 14, 5178-5182(2006).
    [CrossRef] [PubMed]
  15. W. Gartner and A. W. Lohmann, “An experiment going beyond Abbe's limit of diffraction,” Z. Phys. 174, 18 (1963).
    [CrossRef]
  16. A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects ,” Appl. Opt. 3, 1037-1043 (1964).
  17. A. Zlotnik, Z. Zalevsky, and E. Marom, “Superresolution with nonorthogonal polarization coding,” Appl. Opt. 44, 3705-3715(2005).
    [CrossRef] [PubMed]
  18. W. Lukosz, “Optical systems with resolving powers exceeding the classical limits,” J. Opt. Soc. Am. 56, 1463-1472 (1966).
    [CrossRef]
  19. A. Bachl and W. Lukosz, “Experiments on superresolution imaging of a reduced object field,” J. Opt. Soc. Am. 57, 163-169(1967).
    [CrossRef]
  20. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using two fixed generalized Dammann gratings,” Appl. Opt. 39, 5318-5325(2000).
    [CrossRef]
  21. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Super resolution optical systems using fixed gratings,” Opt. Commun. 163, 79-85 (1999).
    [CrossRef]
  22. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using there fixed generalized gratings: Experimental results,” J. Opt. Soc. Am. A 18, 514-520 (2001).
    [CrossRef]
  23. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical system with improved resolving power,” in Progress in Optics (Elsevier, 1999), Vol. 60, Chap. 4.
  24. Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer-Verlag, 2003).

2006

2005

2001

2000

1999

1997

1996

1986

1969

1967

1966

1964

A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects ,” Appl. Opt. 3, 1037-1043 (1964).

1963

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

1960

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

1955

1952

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

Bachl, A.

Cox, J.

Dorsch, R. G.

Farkas, D.

Ferreira, C.

Francon, M.

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

Garcia, J.

García, J.

García-Martínez, P.

Gartner, W.

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

Grimm, M. A.

Kartashev, A. I.

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

Kiryuschev, I.

Konforti, N.

Lohmann, A. W.

Lukosz, W.

Marom, E.

Mas, D.

Mendlovic, D.

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using there fixed generalized gratings: Experimental results,” J. Opt. Soc. Am. A 18, 514-520 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using two fixed generalized Dammann gratings,” Appl. Opt. 39, 5318-5325(2000).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Understanding super resolution in Wigner space,” J. Opt. Soc. Am. A 17, 2422-2430 (2000).
[CrossRef]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. García-Martínez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245-7251(1999).
[CrossRef]

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

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

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “About the space bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470-473 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical system with improved resolving power,” in Progress in Optics (Elsevier, 1999), Vol. 60, Chap. 4.

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

Paris, D. P.

A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects ,” Appl. Opt. 3, 1037-1043 (1964).

Sabo, E.

Shemer, A.

Sheppard, J. R.

Toraldo di Francia, G.

Zalevsky, Z.

Z. Zalevsky, P. García-Martínez, and J. García, “Superresolution using gray level coding,” Opt. Express 14, 5178-5182(2006).
[CrossRef] [PubMed]

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

Z. Zalevsky, J. García, P. García-Martínez, and C. Ferreira, “Spatial information transmission using orthogonal mutual coherence coding,” Opt. Lett. 30, 2837-2839 (2005).
[CrossRef] [PubMed]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using there fixed generalized gratings: Experimental results,” J. Opt. Soc. Am. A 18, 514-520 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Super resolution optical system using two fixed generalized Dammann gratings,” Appl. Opt. 39, 5318-5325(2000).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Understanding super resolution in Wigner space,” J. Opt. Soc. Am. A 17, 2422-2430 (2000).
[CrossRef]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. García-Martínez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245-7251(1999).
[CrossRef]

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

D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, “Two dimensional super resolution 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. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “About the space bandwidth product of optical signal and systems,” J. Opt. Soc. Am. A 13, 470-473 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical system with improved resolving power,” in Progress in Optics (Elsevier, 1999), Vol. 60, Chap. 4.

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

Zlotnik, A.

Appl. Opt.

Il Nuovo Cimento Suppl.

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

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

Opt. Express

Opt. Lett.

Opt. Spectrosc.

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

Superresolution for nonbirefringent objects

A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects ,” Appl. Opt. 3, 1037-1043 (1964).

Z. Phys.

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

Other

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical system with improved resolving power,” in Progress in Optics (Elsevier, 1999), Vol. 60, Chap. 4.

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

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Figures (5)

Fig. 1
Fig. 1

Proposed experimental setup.

Fig. 2
Fig. 2

Photograph of the experimental setup in the laboratory.

Fig. 3
Fig. 3

(a) Illumination spectrum of the halogen lamp. (b) Sensitivity response of the three channels (R, G, and B) of the CCD. (c) The combined response of the illumination spectrum and the sensitivity of the CCD (the addition of the three channels’ sensitivities each multiplied by the spectral irradiance of the lamp). (d) The magnitude of the Fourier transform of the combined chart of (c).

Fig. 4
Fig. 4

Experimental results. (a) The full field of view super-resolved image obtained using the presented approach, and (b) the full field of view image with monochromatic illumination (Bachl and Lukosz [19] approach). (c) Cross section of (a) for the purpose of computing the reduction in contrast.

Fig. 5
Fig. 5

Experimental results; the high-resolution region of interest in Fig. 4a. The squares in vertical and horizontal lines mark the resolution limit with and without applying the presented approach, respectively.

Equations (13)

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u 0 ( x , z = 4 F ) = m n A m B n u ˜ 0 ( ν ) rect ( ν + m ν 0 Δ μ / λ 2 F ) · exp [ 2 π i ( x ( m ν 0 + n ν 1 ) + ν ( z 0 λ m ν 0 z 1 λ n ν 1 ) + z 0 λ m 2 ν 0 2 2 z 1 λ n 2 ν 1 2 2 z 1 λ m n ν 0 ν 1 ) ] exp [ 2 π i x ν ] d ν ,
exp [ 2 π i ( x ( m ν 0 + n ν 1 ) + ν ( z 0 λ m ν 0 z 1 λ n ν 1 ) + z 0 λ m 2 ν 0 2 2 z 1 λ n 2 ν 1 2 2 z 1 λ m n ν 0 ν 1 ) ] .
u 0 ( x , z = 4 F ) = m n A m B n u ˜ 0 ( ν ) rect ( ν + m ν 0 Δ μ / λ 2 F ) · exp [ 2 π i ( x ( ν + ν 0 ( m + n ) ) + ν ( z 0 λ ( m + n ) ν 0 ) + z 0 λ ν 0 2 2 ( m + n ) 2 ) ] d ν .
u 0 ( x , z = 4 F ) = u ˜ 0 ( ν ) [ m A m B m rect ( ν + m ν 0 Δ μ / λ 2 F ) ] exp [ 2 π i x ν ] d ν .
x m , n = λ z 0 ν 0 ( m + n ) .
| h ( x , z = 4 F ) | 2 = Δ λ S ( λ ) m n m n A m B n A m * B n * rect ( ν + m ν 0 Δ μ / λ 2 F ) rect ( ν + m ν 0 Δ μ / λ 2 F ) · exp [ 2 π i ( x ( ν + ν 0 ( m + n ) ) + ν ( z 0 λ ( m + n ) ν 0 ) + z 0 λ ν 0 2 2 ( m + n ) 2 ) ] · exp [ 2 π i ( x ( ν + ν 0 ( m + n ) ) + ν ( z 0 λ ( m + n ) ν 0 ) + z 0 λ ν 0 2 2 ( m + n ) 2 ) ] d λ d ν d ν ,
ξ ν ( z 0 ( m + n ) ν 0 ) + z 0 ν 0 2 2 ( m + n ) 2 ν ( z 0 ( m + n ) ν 0 ) z 0 ν 0 2 2 ( m + n ) 2 .
| h ( x , z = 4 F ) | 2 = m n m n A m B n A m * B n * rect ( ν + m ν 0 Δ μ / λ ¯ 2 F ) rect ( ν + m ν 0 Δ μ / λ ¯ 2 F ) · exp [ 2 π i x ( ν + ν 0 ( m + n ) ν ν 0 ( m + n ) ) ] · Δ λ S ( λ ) exp [ 2 π i λ ξ ] d λ d ν d ν ,
Δ λ S ( λ ) exp [ 2 π i λ ξ ] d λ S ( λ ¯ ) Δ λ exp [ 2 π i λ ξ ] d λ = κ δ ( ξ ) ,
| h ( x , z = 4 F ) | 2 = | [ m A m B m rect ( ν + m ν 0 Δ μ / λ ¯ 2 F ) ] exp ( 2 π i x ν ) d ν | 2 .
C = I max I min I max + I min ,
C = I max I min I max + I min + 2 DC ,
DC = Δ λ S ( λ ) u 0 ( x β 1 λ , y β 2 λ ) d λ Δ λ ,

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