Abstract

We present a new approach to obtain superresolved images in digital holography by means of synthetic aperture generation using common-path interferometry and off-axis illumination in optical imaging systems. The paper includes two parts. First, we present a simple approach to double the resolution of an optical system using tilted illumination onto the object and an optical element in the image plane to produce the holographic recording. Then we present a novel approach consisting of attaching a diffraction grating in parallel together with the object in the input plane and using off-axis illumination provided by a Vertical Cavity Surface Emitting Lasers (VCSEL) array to allow us achieving a major improvement in the optical resolution limit with an extremely low penalty in the complexity of the resulting system. Experimental investigation based on commercial microscope objectives is presented.

© 2006 Optical Society of America

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  1. D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, London, 2003).
  2. M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
    [CrossRef] [PubMed]
  3. Z. Zalevsky and D. Mendlovic, Optical Super Resolution, (Springer 2002).
  4. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," Prog. Opt.,  40, 271-341 (1999).
    [CrossRef]
  5. G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am A. 45, 497-501 (1955).
    [CrossRef]
  6. G. Toraldo di Francia, "Degrees of freedom of an image," J. Opt. Soc. Am. 59, 799-804 (1969).
    [CrossRef] [PubMed]
  7. I. J. Cox and J. R. Sheppard, "Information capacity and resolution in an optical system," J. Opt. Soc. Am. A 3, 1152-1158 (1986).
    [CrossRef]
  8. P. H. Van Cittert, "Zum einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien," Z. Physik 69, 298-308 (1931).
    [CrossRef]
  9. R. W. Gerchberg, "Superresolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
    [CrossRef]
  10. W. Lukosz, "Optical sytems with resolving powers exceeding the classical limits II," J. Opt. Soc. Am 57, 932-941 (1967).
    [CrossRef]
  11. M. A. Grimm and A. W. Lohmann, "Superresolution image for one-dimensional object," J. Opt. Soc. Am. 56, 1151-1156 (1966).
    [CrossRef]
  12. A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. Garcia-Martinez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
    [CrossRef]
  13. M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
    [CrossRef] [PubMed]
  14. M. Françon, "Amélioration the résolution d’optique," Il Nuovo CimentoSuppl. 9, 283-290 (1952).
    [CrossRef]
  15. A. W. Lohmann and D. P. Paris, "Superresolution for nonbirefringent objects," Appl. Opt. 3, 1037-1043 (1964).
    [CrossRef]
  16. A. Zlotnik, Z. Zalevsky, and E. Marom, "Superresolution with nonorthogonal polarization coding," Appl. Opt. 44, 3705-3715 (2005).
    [CrossRef] [PubMed]
  17. A. I. Kartashev, "Optical system with enhanced resolving power," Opt. Spectra. 9, 204-206 (1960).
  18. 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]
  19. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Single step superresolution by interferometric imaging," Opt. Express 12, 2589-2596 (2004).
    [CrossRef] [PubMed]
  20. X. Chen and S. R. J. Brueck, "Imaging interferometric lithography: approaching the resolution limits of optics," Opt. Lett. 24, 124-126 (1999).
    [CrossRef]
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    [CrossRef]
  23. P. C. Sun and E. N. Leith, "Superresolution by spatial-temporal encoding methods," Appl. Opt. 31, 4857- 4862 (1992).
    [CrossRef] [PubMed]
  24. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
    [CrossRef] [PubMed]
  25. H. Kadono, N. Takai, and T. Asakura, "New common-path phase shifting interferometer using a polarization technique," Appl. Opt. 26, 898-904 (1987).
    [CrossRef] [PubMed]
  26. Ch. S. Anderson, "Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances," Appl. Opt. 34, 7474-7485 (1995).
    [CrossRef] [PubMed]
  27. J. Glückstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001).
    [CrossRef]
  28. C. G. Teviño-Palacios, M. D. Iturbe-Castillo, D. Sánchez-de-la-Llave, R. Ramos-García, and L. I. Olivos- Pérez, "Nonlinear common-path interferometer: an image processor," Appl. Opt. 42, 5091-5095 (2003).
    [CrossRef]
  29. V. Arrizón and D. Sánchez-de-la-Llave, "Common-path interferometry with one-dimensional periodic filters," Opt. Lett. 29, 141-143 (2004).
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

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

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

2002 (1)

2001 (1)

1999 (4)

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

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," Prog. Opt.,  40, 271-341 (1999).
[CrossRef]

M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

X. Chen and S. R. J. Brueck, "Imaging interferometric lithography: approaching the resolution limits of optics," Opt. Lett. 24, 124-126 (1999).
[CrossRef]

1995 (1)

1992 (1)

1987 (2)

1986 (1)

1974 (1)

R. W. Gerchberg, "Superresolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

1969 (1)

1967 (1)

W. Lukosz, "Optical sytems with resolving powers exceeding the classical limits II," J. Opt. Soc. Am 57, 932-941 (1967).
[CrossRef]

1966 (1)

1964 (1)

1960 (1)

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

1955 (1)

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am A. 45, 497-501 (1955).
[CrossRef]

1952 (1)

M. Françon, "Amélioration the résolution d’optique," Il Nuovo CimentoSuppl. 9, 283-290 (1952).
[CrossRef]

1931 (1)

P. H. Van Cittert, "Zum einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien," Z. Physik 69, 298-308 (1931).
[CrossRef]

Agard, A.

M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Anderson, Ch. S.

Angell, D.

Arrizón, V.

Asakura, T.

Brueck, S. R. J.

Chen, X.

Cox, I. J.

Françon, M.

M. Françon, "Amélioration the résolution d’optique," Il Nuovo CimentoSuppl. 9, 283-290 (1952).
[CrossRef]

Garcia, J.

García, J.

Garcia-Martinez, P.

García-Martínez, P.

Gerchberg, R. W.

R. W. Gerchberg, "Superresolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

Glückstad, J.

Grimm, M. A.

Gustafsson, M. G. L.

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Kadono, H.

Kartashev, A. I.

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

Konforti, N.

Kuei, C.-P.

Kuznetsova, Y.

Leith, E. N.

Lohmann, A. W.

Lukosz, W.

W. Lukosz, "Optical sytems with resolving powers exceeding the classical limits II," J. Opt. Soc. Am 57, 932-941 (1967).
[CrossRef]

Marom, E.

Mendlovic, D.

Mico, V.

Mogensen, P. C.

Paris, D. P.

Sánchez-de-la-Llave, D.

Schwarz, C. J.

Sedat, W.

M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Shemer, A.

Sheppard, J. R.

Sun, P. C.

Takai, N.

Toraldo di Francia, G.

G. Toraldo di Francia, "Degrees of freedom of an image," J. Opt. Soc. Am. 59, 799-804 (1969).
[CrossRef] [PubMed]

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am A. 45, 497-501 (1955).
[CrossRef]

Van Cittert, P. H.

P. H. Van Cittert, "Zum einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien," Z. Physik 69, 298-308 (1931).
[CrossRef]

Zalevsky, Z.

Zlotnik, A.

Appl. Opt. (9)

A. W. Lohmann and D. P. Paris, "Superresolution for nonbirefringent objects," Appl. Opt. 3, 1037-1043 (1964).
[CrossRef]

H. Kadono, N. Takai, and T. Asakura, "New common-path phase shifting interferometer using a polarization technique," Appl. Opt. 26, 898-904 (1987).
[CrossRef] [PubMed]

Ch. S. Anderson, "Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances," Appl. Opt. 34, 7474-7485 (1995).
[CrossRef] [PubMed]

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

J. Glückstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001).
[CrossRef]

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]

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

Il Nuovo Cimento (1)

M. Françon, "Amélioration the résolution d’optique," Il Nuovo CimentoSuppl. 9, 283-290 (1952).
[CrossRef]

J. Microsc. (1)

M. G. L. Gustafsson, A. Agard, and W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am (1)

W. Lukosz, "Optical sytems with resolving powers exceeding the classical limits II," J. Opt. Soc. Am 57, 932-941 (1967).
[CrossRef]

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

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am A. 45, 497-501 (1955).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

R. W. Gerchberg, "Superresolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Spectra. (1)

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

Proc. Natl. Acad. Sci. USA (1)

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef] [PubMed]

Prog. Opt. (1)

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," Prog. Opt.,  40, 271-341 (1999).
[CrossRef]

Z. Physik (1)

P. H. Van Cittert, "Zum einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien," Z. Physik 69, 298-308 (1931).
[CrossRef]

Other (3)

D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, London, 2003).

Z. Zalevsky and D. Mendlovic, Optical Super Resolution, (Springer 2002).

C. G. Teviño-Palacios, M. D. Iturbe-Castillo, D. Sánchez-de-la-Llave, R. Ramos-García, and L. I. Olivos- Pérez, "Nonlinear common-path interferometer: an image processor," Appl. Opt. 42, 5091-5095 (2003).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Optical setup of the common-path interferometry approach used for superresolution.

Fig. 2.
Fig. 2.

Schematic sketch of the interferometric recording between the object image (horizontal grated rectangle) and the reference beam (uniform gray color rectangle).

Fig. 3.
Fig. 3.

Low resolution images: (a) USAF test imaged with the NIKON objective microscope (0.1NA), and (b) High resolution USAF test imaged with the MITUTOYO infinity corrected objective microscope (0.14NA).

Fig. 4.
Fig. 4.

Superresolved images using the presented approach to double the resolution: (a) USAF test and (b) High resolution USAF test.

Fig. 5.
Fig. 5.

Optical setup of the superresolution by common-path interferometry approach experimentally used.

Fig. 6.
Fig. 6.

(a) Recorded hologram for the on-axis illumination case, and (b) Fourier transformation of the intensity distribution presented in (a).

Fig. 7.
Fig. 7.

Results comparison: (a) superresolved image with the presented approach, and (b) its Fourier transformation (the SA).

Equations (13)

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U input plane ( k , l ) VCSEL ( x , y ) = [ f ( x , y ) + m , n = N + N e j 2 π ν 0 ( mx + ny ) ] exp { j 2 π ( v k x + v l y ) }
U Fourier plane ( k , l ) VCSEL ( u , v ) = [ f ˜ ( u , v k , ν + v l ) + δ ( u + v k + m v 0 , ν + v l + n v 0 ) ] circ ( ρ Δ v )
v k = 2 k Δ v and v l = 2 l Δ v
v k + m v 0 = 0 v 0 = 2 Δ v , if m = k
v l + n v 0 = 0 v 0 = 2 Δ v , if n = l
U Fourier plane ( k , l ) VCSEL ( u , v ) = f ˜ ( u + 2 k Δ v , ν + 2 l Δ v ) circ ( ρ Δ v ) + δ ( u , v )
U Output plane ( k , l ) VCSEL ( x , y ) = [ f ( x , y ) exp { j 2 π 2 Δ v ( x + y ) } ] disk ( Δ v r ) + A m , n
I output plane ( k , l ) VCSEL ( x , y ) = [ f ( x , y ) exp { j 2 π 2 Δ v ( x + y ) } ] disk ( Δ v r ) + A m , n exp { j 2 π v I x } 2
T ˜ 2 ( k , l ) ( u , v ) = [ f ˜ ( u + 2 k Δ v , ν + 2 l Δ v ) circ ( ρ Δ v ) ] * [ f ˜ ( u + 2 k Δ v , ν + 2 l Δ v ) circ ( ρ Δ v ) ]
T ˜ 3 ( k , l ) ( u , v ) = ( A m , n ) * [ f ˜ ( u + 2 k Δ v , ν + 2 l Δ v ) circ ( ρ Δ v ) ] δ ( u + v I , ν )
U rec ( u , v ) = [ k , l = N + N ( A k , l ) * f ˜ ( u + k 2 Δ v , ν + l 2 Δ v ) circ ( ρ Δ v ) ] =
= f ˜ ( u , v ) [ k , l = N + N ( A k , l ) * circ ( ρ Δ v ) δ ( u + k 2 Δ v , ν + l 2 Δ v ) ]
SA ( u , v ) = k , l = N + N ( A k , l ) * circ ( ρ Δ v ) δ ( u + k 2 Δ v , ν + l 2 Δ v )

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