Abstract

For 15 years, lensless microscopes have been constructed based on the use of holography, a digital CCD detector, and a computer for image reconstruction by use of, e.g., Fourier transformation. Thus, no lens is involved and therefore the conventional resolution limit of half the wavelength no longer applies. Instead of being limited by the wavelength, the resolution is in this case limited by how exact one can measure the phases of the light. It is remarkable that the interference-limited resolution is approximately 0.01λ, whereas the diffraction-limited resolution is only of the order of 0.5λ. It is my hope that by combining these two techniques it will be possible to increase the magnification in optical systems by at least an order of magnitude. The calculations also indicate that information does not necessarily decrease with distance.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. T. Poon, "Scanning holography, and two-dimensional image processing by acousto-optic, two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2007 (2)

J. Price, P. R. Bingham, and C. E. Thomas, Jr., "Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain," Appl. Opt. 46, 827-833 (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, 993-999 (2007).
[CrossRef] [PubMed]

2006 (2)

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

2002 (1)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

2001 (1)

V. Kebbel, H. J. Hartmann, and W. Jüptner, "Application of digital holographic microscopy for inspection of micro-optical components," Proc. SPIE 4398, 189-198 (2001).
[CrossRef]

2000 (1)

1985 (1)

T. Poon, "Scanning holography, and two-dimensional image processing by acousto-optic, two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).
[CrossRef]

1972 (2)

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, "Reconstruction of a hologram with computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

N. Abramson, "The holo-diagram VI: Practical device in coherent optics," Appl. Opt. 11, 2562-2571 (1972).
[CrossRef] [PubMed]

1967 (1)

J. Goodman and R. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Abramson, N.

N. Abramson, "The holo-diagram VI: Practical device in coherent optics," Appl. Opt. 11, 2562-2571 (1972).
[CrossRef] [PubMed]

Awatsuji, Y.

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Bingham, P. R.

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Brooker, G.

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, 993-999 (2007).
[CrossRef] [PubMed]

Collot, L.

Fuji, A.

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Goodman, J.

J. Goodman and R. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Gross, M.

Hartmann, H. J.

V. Kebbel, H. J. Hartmann, and W. Jüptner, "Application of digital holographic microscopy for inspection of micro-optical components," Proc. SPIE 4398, 189-198 (2001).
[CrossRef]

Indebetouw, G.

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, 993-999 (2007).
[CrossRef] [PubMed]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2004).

Jüptner, W.

V. Kebbel, H. J. Hartmann, and W. Jüptner, "Application of digital holographic microscopy for inspection of micro-optical components," Proc. SPIE 4398, 189-198 (2001).
[CrossRef]

Kebbel, V.

V. Kebbel, H. J. Hartmann, and W. Jüptner, "Application of digital holographic microscopy for inspection of micro-optical components," Proc. SPIE 4398, 189-198 (2001).
[CrossRef]

Kronrod, M.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, "Reconstruction of a hologram with computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Kubota, T.

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Lawrence, R.

J. Goodman and R. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Le Clerc, F.

Liu, C.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Liu, Z.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Merzlyakov, N.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, "Reconstruction of a hologram with computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Poon, T.

T. Poon, "Scanning holography, and two-dimensional image processing by acousto-optic, two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).
[CrossRef]

Price, J.

Rosen, J.

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, 993-999 (2007).
[CrossRef] [PubMed]

Sasada, M.

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2004).

Tada, Y.

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, 993-999 (2007).
[CrossRef] [PubMed]

Thomas, C. E.

Wang, Y.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Yaroslavskii, L.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, "Reconstruction of a hologram with computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Zhu, J.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Appl. Opt. (4)

N. Abramson, "The holo-diagram VI: Practical device in coherent optics," Appl. Opt. 11, 2562-2571 (1972).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, A. Fuji, and T. Kubota, "Scheme to improve the reconstructed image in parallel quasi-phase-shifting holography," Appl. Opt. 45, 968-974 (2006).
[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, 993-999 (2007).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

J. Goodman and R. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

T. Poon, "Scanning holography, and two-dimensional image processing by acousto-optic, two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

V. Kebbel, H. J. Hartmann, and W. Jüptner, "Application of digital holographic microscopy for inspection of micro-optical components," Proc. SPIE 4398, 189-198 (2001).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, "Reconstruction of a hologram with computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Other (1)

U. Schnars and W. Jueptner, Digital Holography (Springer, 2004).

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Figures (7)

Fig. 1
Fig. 1

The phase angles are divided by six, resulting in each fringe being transformed into six virtual fringes, thus producing a resolving power that is six times higher.

Fig. 2
Fig. 2

The holodiagram is based on two sets of concentric equidistant circles centered on A and B, the intersection of which produces one set of ellipses and one set of hyperbolas.

Fig. 3
Fig. 3

Two rhombs of Fig. 2 are enlarged for calculation of the diagonals.

Fig. 4
Fig. 4

Two point sources are just resolvable by an optical system when their distance apart is such that the central maximum of the diffraction pattern of one source coincides with the first minimum of the diffraction pattern of the other source. (a) Resolved diffraction pattern of two point sources. (b) Just resolvable point sources.

Fig. 5
Fig. 5

Diffraction-limited resolution D R also represents the separation of the interference fringes caused by two laser beams intersecting at 2α. Thus, the Young´s fringes caused by the two laser beams AC and BC will have the same separation D R as the diffraction-limited resolution of a lens.

Fig. 6
Fig. 6

The phases on the spherical wavefront are found by interference with a collimated reference, producing a set of circles. As the phase angle moves in the direction V, the radii of the circles decreases.

Fig. 7
Fig. 7

(a) Intersections of the spherical wavefront produce more circular interference fringes as the separation from the source increases. (b) If the size of the large interference pattern of (a) is decreased, a pattern representing a higher resolving power is formed.

Equations (7)

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

I R = 0.5 λ / cos α ,
D R = 0.5 λ / sin α .
D R = k λ f / D .
D R = 0.5 λ / sin α = 0.5 λ R / r ,
h = R ( 1 cos α ) = 2 R sin 2 α / 2 ,
n = R ( 1 cos α ) / λ .
D R = 0.5 λ / m sin α .

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