Abstract

Synthetic aperture methods are commonly-used techniques for providing images with super-resolution qualities. We propose an improved design of the system, coined “synthetic aperture with Fresnel elements”. The super-resolution capabilities of the proposed scheme are analyzed and experimentally demonstrated.

© 2014 Optical Society of America

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References

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  1. E. Abbe, “Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv. Microskopische Anat. 9(1), 413–418 (1873).
    [CrossRef]
  2. A. A. Michelson, “On the application of interference methods to astronomical measurements,” Proc. Natl. Acad. Sci. U.S.A. 6(8), 474–475 (1920).
    [CrossRef] [PubMed]
  3. P. R. Lawson, Selected Paper on Long Baseline Stellar Interferometry, (SPIE Press Book, 1997).
  4. M. E. Testorf and M. A. Fiddy, “Superresolution imaging-revisited,” Adv. Imaging Electron Phys. 163, 165–218 (2010).
    [CrossRef]
  5. S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, “Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing,” Appl. Opt. 44(35), 7621–7629 (2005).
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  6. V. Micó, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution with multiple off-axis holograms,” J. Opt. Soc. Am. A 23(12), 3162–3170 (2006).
    [CrossRef] [PubMed]
  7. L. Granero, V. Micó, Z. Zalevsky, and J. García, “Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information,” Appl. Opt. 49(5), 845–857 (2010).
    [CrossRef] [PubMed]
  8. L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16(1), 161–169 (2008).
    [CrossRef] [PubMed]
  9. K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
    [CrossRef]
  10. G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, “Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms,” Appl. Opt. 46(6), 993–1000 (2007).
    [CrossRef] [PubMed]
  11. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007).
    [CrossRef] [PubMed]
  12. J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics 2(3), 190–195 (2008).
    [CrossRef]
  13. P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express 19(16), 15603–15620 (2011).
    [CrossRef] [PubMed]
  14. J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19(27), 26249–26268 (2011).
    [CrossRef] [PubMed]
  15. B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20(8), 9109–9121 (2012).
    [CrossRef] [PubMed]
  16. B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express 18(2), 962–972 (2010).
    [CrossRef] [PubMed]
  17. B. Katz and J. Rosen, “Could SAFE concept be applied for designing a new synthetic aperture telescope?” Opt. Express 19(6), 4924–4936 (2011).
    [CrossRef] [PubMed]
  18. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19(6), 5047–5062 (2011).
    [CrossRef] [PubMed]
  19. J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (Roberts and Company Publishers, 2005).
  20. X. Lai, S. Zeng, X. Lv, J. Yuan, and L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38(11), 1896–1898 (2013).
    [CrossRef] [PubMed]

2013 (2)

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

X. Lai, S. Zeng, X. Lv, J. Yuan, and L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38(11), 1896–1898 (2013).
[CrossRef] [PubMed]

2012 (1)

2011 (4)

2010 (3)

2008 (2)

L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16(1), 161–169 (2008).
[CrossRef] [PubMed]

J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

2007 (2)

2006 (1)

2005 (1)

1920 (1)

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Proc. Natl. Acad. Sci. U.S.A. 6(8), 474–475 (1920).
[CrossRef] [PubMed]

1873 (1)

E. Abbe, “Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv. Microskopische Anat. 9(1), 413–418 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv. Microskopische Anat. 9(1), 413–418 (1873).
[CrossRef]

Beck, S. M.

Bouchal, P.

Bouchal, Z.

Brooker, G.

Buck, J. R.

Buell, W. F.

Chmelík, R.

Dickinson, R. P.

Fiddy, M. A.

M. E. Testorf and M. A. Fiddy, “Superresolution imaging-revisited,” Adv. Imaging Electron Phys. 163, 165–218 (2010).
[CrossRef]

Fu, L.

Gao, P.

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

García, J.

García-Martínez, P.

Granero, L.

Guo, R.

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

Indebetouw, G.

Javidi, B.

Ji, K.

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

Kapitán, J.

Katz, B.

Kelner, R.

Kozlowski, D. A.

Lai, X.

Lv, X.

Marechal, N. J.

Martínez-León, L.

Menke, N.

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

Michelson, A. A.

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Proc. Natl. Acad. Sci. U.S.A. 6(8), 474–475 (1920).
[CrossRef] [PubMed]

Micó, V.

Min, J.

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

Rosen, J.

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20(8), 9109–9121 (2012).
[CrossRef] [PubMed]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19(27), 26249–26268 (2011).
[CrossRef] [PubMed]

B. Katz and J. Rosen, “Could SAFE concept be applied for designing a new synthetic aperture telescope?” Opt. Express 19(6), 4924–4936 (2011).
[CrossRef] [PubMed]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19(6), 5047–5062 (2011).
[CrossRef] [PubMed]

B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express 18(2), 962–972 (2010).
[CrossRef] [PubMed]

J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007).
[CrossRef] [PubMed]

G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, “Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms,” Appl. Opt. 46(6), 993–1000 (2007).
[CrossRef] [PubMed]

Siegel, N.

Tada, Y.

Testorf, M. E.

M. E. Testorf and M. A. Fiddy, “Superresolution imaging-revisited,” Adv. Imaging Electron Phys. 163, 165–218 (2010).
[CrossRef]

Wang, V.

Wright, T. J.

Yuan, J.

Zalevsky, Z.

Zeng, S.

Adv. Imaging Electron Phys. (1)

M. E. Testorf and M. A. Fiddy, “Superresolution imaging-revisited,” Adv. Imaging Electron Phys. 163, 165–218 (2010).
[CrossRef]

Appl. Opt. (3)

Archiv. Microskopische Anat. (1)

E. Abbe, “Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv. Microskopische Anat. 9(1), 413–418 (1873).
[CrossRef]

J. Mod. Opt. (1)

K. Ji, P. Gao, J. Min, R. Guo, and N. Menke, “A synthetic aperture telescope based on a pair of gratings,” J. Mod. Opt. 60(15), 1229–1233 (2013).
[CrossRef]

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

Nat. Photonics (1)

J. Rosen and G. Brooker, “Non-Scanning Motionless Fluorescence Three-Dimensional Holographic Microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. U.S.A. (1)

A. A. Michelson, “On the application of interference methods to astronomical measurements,” Proc. Natl. Acad. Sci. U.S.A. 6(8), 474–475 (1920).
[CrossRef] [PubMed]

Other (2)

P. R. Lawson, Selected Paper on Long Baseline Stellar Interferometry, (SPIE Press Book, 1997).

J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (Roberts and Company Publishers, 2005).

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Figures (6)

Fig. 1
Fig. 1

Schematic configurations of the dual lens SAFE concept: L1 and L2, lenses; P1 and P2, polarizers; SLM, SLM1 and SLM2, spatial light modulators; CCD, charged couple device. These elements create (a) a continuous central holographic element by implementing a dual lens FINCH method, fSLM is the focal length of the diffractive lens displayed on the SLM and fL2 is the focal length of the glass lens L2, (b) a marginal holographic element, where SLM1 and SLM2 are shifted in two symmetrical viewpoints in front of the collimation lens L1; two diffractive lenses with focal lengths f1 and f2 are displayed on SLM1 and SLM2, respectively and (c) similar to (b), but the diffractive lenses f1 and f2 are switched. DE, DH are the synthetic aperture and the total digital hologram width, respectively. The symbols oe-22-17-20551-i001 and oe-22-17-20551-i002 represent polarization directions, perpendicular and 45° with respect to the plane of the page, respectively.

Fig. 2
Fig. 2

(a) In the case of m = n = 0, the central mask consists of diffractive lens with a focal length of fSLM. (b) In the case of m = -n = 1, two masks consisting of two diffractive lenses with focal lengths of f1 and f2 are shifted from the center by a distance of (Ax,-Ay) and (-Ax, Ay), respectively. (c) In the case of m = -n = −1, two masks consisting of two diffractive lenses with focal lengths of f2 and f1 are shifted from the center by a distance of (-Ax, Ay) and (Ax, -Ay), respectively.

Fig. 3
Fig. 3

Experimental setups: L1 and L2, lenses; P1 and P2, polarizers; SLM, spatial light modulator; CCD, charged couple device; BS, beam splitter. (a) Configuration for the central holographic element, (b) configuration for the marginal holographic elements, (c) configuration of a conventional imaging system with aperture of 360 × 360 pixels, (d) configuration of dual lens FINCH with aperture of 1080 × 1080 pixels.

Fig. 4
Fig. 4

Experimental results obtained by recording object points with the three systems mentioned in the text: (a) the mask displayed on the SLM in the first dual lens FINCH system (360 × 360 pixels); (b), (c) the corresponding Fresnel hologram magnitude and phase, respectively; (d) the reconstructed image corresponding to hologram (b), (c); (e), (f) the intensity cross-section of (d) along the horizontal and vertical directions, respectively; (g) the nine masks displayed on the SLM with dual lens SAFE; (h), (i) the corresponding Fresnel hologram magnitude and phase, respectively; (j) the reconstructed image corresponding to hologram (h), (i); (k), (l) the intensity cross-section of (j) along the horizontal and vertical directions, respectively; (m) the mask displayed on the SLM in the second dual lens FINCH system (1080 × 1080 pixels); (n), (o) the corresponding Fresnel hologram magnitude and phase, respectively; (p) the reconstructed image corresponding to hologram (n), (o); (q), (r) the intensity cross-section of (p) along the horizontal and vertical directions, respectively. The dashed red lines, depicted in (d), (j) and (p), indicate the cross-section paths used in (e), (f), in (k), (l) and in (q), (r).

Fig. 5
Fig. 5

Experimental results obtained by recording a section of an RC (18 cycle/mm) via the four systems compared in the text: (a) the image obtained by the conventional imaging system; (b), (c) the intensity cross-section of (a) along the horizontal and vertical directions, respectively; (d) the reconstructed image corresponding to the hologram produced by the 360 × 360 FINCH system; (e), (f) the intensity cross-section of (d) along the horizontal and vertical directions, respectively; (g) the reconstructed image corresponding to the hologram produced by dual lens SAFE; (h), (i) the intensity cross-section of (g) along the horizontal and vertical directions, respectively; (j) the reconstructed image corresponding to the hologram produced by the 1080 × 1080 FINCH system; (k), (l) the intensity cross-section of (j) along the horizontal and vertical directions, respectively. The dashed red lines, which are depicted in (a), (d), (g) and (j), indicate the path of the cross-sections used in (b), (c), (e), (f), (h), (i), (k) and (l).

Fig. 6
Fig. 6

Experimental results obtained by recording one dimensional equally-spaced parallel bars (18 cycle/mm) by the five systems described in the text: (a) four masks of (270 × 1080 pixels) displayed on the SLM for dual lens T-SAFE; (b) the reconstructed image of dual lens T-SAFE; (c) the intensity cross-section of (b) along the horizontal direction; (d) four masks of (270 × 1080 pixels) displayed on the SLM for T-SAFE with plane and spherical waves; (e) the reconstructed image of T-SAFE with plane and spherical waves; (f) the intensity cross-section of (e) along the horizontal direction; (g) three masks of (360 × 1080 pixels) displayed on the SLM for dual lens SAFE; (h) the reconstructed image of dual lens SAFE; (i) the intensity cross-section of (h) along the horizontal direction; (j) three masks of (360 × 1080 pixels) displayed on the SLM for SAFE with plane and spherical waves; (k) the reconstructed image of SAFE with plane and spherical waves; (l) the intensity cross-section of (k) along the horizontal direction; (m) the mask of (1080 × 1080 pixels) displayed on the SLM for dual lens FINCH; (n) the reconstructed image of dual lens FINCH; (o) the intensity cross-section of (n) along the horizontal direction;

Equations (11)

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z h = 2 f 1 f 2 f 1 + f 2 .
P mn ( x,y;θ )= C 1 Q( 1 f 1 )rect( x A x m A x , y A y n A y   )+ C 2 Q( 1 f 2 )exp( iθ )rect( x+ A x m A x , y+ A y n A y   ),
rect( x α , y β ){ 1         ( | x |,| y | )( α/2,β/2 ) 0                 otherwise                .
I( r ¯ 0 ; r ¯ s )= m= 1M 2 M1 2 n= 1N 2 N1 2 | I s C( r ¯ s )L( - r ¯ s )Q( 1 f 0 )Q( - 1 f 0 )*Q( 1 d ) × P mn ( x,y;θ )*Q( 1 z h ) | 2 ,
I( r ¯ 0 ; r ¯ s )=( C 3 + C 4 ( r ¯ s )Q( 1 z r )L( r ¯ r )exp( jθ )+ C 4 * ( r ¯ s )Q( 1 z r )L( r ¯ r )exp( jθ ) )× m= 1M 2 M1 2 n= 1N 2 N1 2 rect( x A x m A x , y A y n A y   ),
z r =± ( z h f 1 )( f 2 z h ) f 2 f 1 .
r ¯ r =( x r , y r )=( x s z h f 0 , y s z h f 0 ).
Δ 0 = λ 2 M T N A out = λ| z r | M T D H ,
D H = D E ( f 2 z h ) f 2 .
Δ 0 =λ/4N A in
H( r ¯ 0 )= I s ( r ¯ s )I( r ¯ 0 ; r ¯ s ).

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