Abstract

This paper describes a technique of super-resolution that is based on holographic imaging in which three holograms corresponding to one orientation of the fringes are recorded. To recover the two-dimensional object spatial frequency, we take four orientations of the fringes with 45° steps. For each orientation of the fringes, the hologram recording scheme will remain the same. The orientation of the reference beam is fixed throughout the measurements. Once the three holograms are recorded for each orientation of the fringes with a fixed amplitude of the reference beam, an algorithm is applied for each orientation. The algorithm processes the three holograms to construct a synthesized spectrum in a particular orientation; taking the inverse Fourier transform of this synthesized spectrum will give the synthesized image in that particular orientation. Different synthesized spectra are combined to obtain an overall synthesized spectrum and a super-resolved image is formed.

© 2010 Optical Society of America

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References

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2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232–7236(2000).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef] [PubMed]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “Super resolution optical system with two fixed generalized Damman gratings,” Appl. Opt. 39, 5318–5325 (2000).
[CrossRef]

1997

1996

1992

1991

1987

1973

U. Mitsuhiro, S. Takuso, and K. Masato, “Superresolution by multiple super-position of image holograms having different carrier frequencies,” J. Mod. Opt. 20, 403–410 (1973).
[CrossRef]

Angell, D.

Barton, J. S.

Bokor, J.

Brooker, G.

Campos, J.

Collot, L.

De Nicola, S.

Ferraro, P.

Finizio, A.

Fixler, D.

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232–7236(2000).
[CrossRef] [PubMed]

Garcia, J.

García, J.

García-Martinez, P.

Goldberg, K. A.

Gougeon, S.

Granero, L.

Greenaway, A. H.

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. Jones, “Band pass active aperture synthesis using spatial frequency heterodyning,” J. Phys.: Conf. Ser. 15, 290–295 (2005).
[CrossRef]

Grilli, S.

Gross, M.

Guo, B. J.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef] [PubMed]

Harvey, A. R.

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. Jones, “Band pass active aperture synthesis using spatial frequency heterodyning,” J. Phys.: Conf. Ser. 15, 290–295 (2005).
[CrossRef]

Iemmi, C.

Indebetouw, G.

Jones, J.

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. Jones, “Band pass active aperture synthesis using spatial frequency heterodyning,” J. Phys.: Conf. Ser. 15, 290–295 (2005).
[CrossRef]

Jones, J. D. C.

Kato, J.

Kemper, B.

Kiryushev, I.

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232–7236(2000).
[CrossRef] [PubMed]

Komforti, N.

Kuei, C.-P.

Le Clerc, F.

Leith, E. N.

Leval, J.

Liu, H.

Marom, E.

Martinez, P. Garcia

Masato, K.

U. Mitsuhiro, S. Takuso, and K. Masato, “Superresolution by multiple super-position of image holograms having different carrier frequencies,” J. Mod. Opt. 20, 403–410 (1973).
[CrossRef]

McBride, R.

Medecki, H.

Mendlovic, D.

Merola, F.

Mico, V.

Micó, V.

Mitsuhiro, U.

U. Mitsuhiro, S. Takuso, and K. Masato, “Superresolution by multiple super-position of image holograms having different carrier frequencies,” J. Mod. Opt. 20, 403–410 (1973).
[CrossRef]

Mizuno, J.

Moore, A. J.

Moreno, A.

Mounier, D.

Mudassar, A.

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. Jones, “Band pass active aperture synthesis using spatial frequency heterodyning,” J. Phys.: Conf. Ser. 15, 290–295 (2005).
[CrossRef]

Ohta, S.

Paturzo, M.

Picart, P.

Rosen, J.

Sabo, E.

Stemmer, A.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232–7236(2000).
[CrossRef] [PubMed]

Sun, P. C.

Tada, Y.

Takuso, S.

U. Mitsuhiro, S. Takuso, and K. Masato, “Superresolution by multiple super-position of image holograms having different carrier frequencies,” J. Mod. Opt. 20, 403–410 (1973).
[CrossRef]

Tamaguchi, I.

Tejnil, E.

von Bally, G.

Yamaguchi, I.

Yuan, C.

Zalevsky, Z.

Zhai, H.

Zhong, T.

Zhuang, S. L.

Zlotnik, A.

Appl. Opt.

J. Microsc.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[CrossRef] [PubMed]

J. Mod. Opt.

U. Mitsuhiro, S. Takuso, and K. Masato, “Superresolution by multiple super-position of image holograms having different carrier frequencies,” J. Mod. Opt. 20, 403–410 (1973).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys.: Conf. Ser.

A. Mudassar, A. R. Harvey, A. H. Greenaway, and J. Jones, “Band pass active aperture synthesis using spatial frequency heterodyning,” J. Phys.: Conf. Ser. 15, 290–295 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci. U.S.A.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232–7236(2000).
[CrossRef] [PubMed]

Other

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

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Figures (9)

Fig. 1
Fig. 1

Conventional optical system for recording hologram of the object transparencies.

Fig. 2
Fig. 2

(a) One-dimensional view of rect function of a typical optical system. (b) One-dimensional view of sinc function, i.e., PSF of the conventional system.

Fig. 3
Fig. 3

(a) Extended transfer function (rect) of the super-resolved optical system (b) PSF (sinc) of the super-resolved optical system.

Fig. 4
Fig. 4

Recorded images and their spectra in three measurements: (a) input object; (b) hologram recorded in measurement 1; (c) hologram in measurement 2; (d) hologram in measurement 3; (e) spectrum of the input object; (f), (g), (h) spectra of (b), (c), and (d), respectively.

Fig. 5
Fig. 5

Selection of desired spectra from measurements: (a) selected spectrum from Fig. 4f, (b) selected spectrum from Fig. 4g, (c) selected spectrum from Fig. 4h.

Fig. 6
Fig. 6

Spectrum synthesis: (a) synthesized spectrum along one dimension; (b) synthesized spectrum in two dimensions obtained by combining spectra obtained with different orientations of the fringes.

Fig. 7
Fig. 7

Comparison of spectra and images of conventional, band-limited, and super-resolved optical systems: (a), (b), and (c) are the spectra obtained with conventional optical, band-limited, and super-resolved optical systems and the corresponding images are shown in (d), (e), and (f), respectively.

Fig. 8
Fig. 8

Flow chart of the super-resolution of active spatial frequency heterodyning using holographic approach.

Fig. 9
Fig. 9

Proposed experimental setup for recording three measurements.

Equations (23)

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G b ( f x , f y ) = G ( f x , f y ) rect ( f x ) rect ( f y ) .
S b ( x , y ) = | g b ( x , y ) + R | 2 R = A exp ( 2 i π x sin θ ) ,
S b ( x , y ) = { g b ( x , y ) + R } { g * b ( x , y ) + R * } , S b ( x , y ) = I b ( x , y ) + g b ( x , y ) R * + g * b ( x , y ) R + | R | 2 ,
g c ( x , y ) = g ( x , y ) Cos ( 2 π . f . x ) .
G c ( f x , f y ) = [ G ( f x , f y ) { 1 2 δ ( f x + f , f y + f ) + 1 2 δ ( f x f , f y f ) } ] .
G b c ( f x , f y ) = G c ( f x , f y ) rect ( f x ) rect ( f y ) .
S b c ( x , y ) = | g b c ( x , y ) + R | 2 ,
S b c ( x , y ) = I b c ( x , y ) + | R | 2 + g b c ( x , y ) R * + g * b c ( x , y ) R ,
g s ( x , y ) = g ( x , y ) Sin ( 2 π . f . x ) .
G s ( f x , f y ) = [ G ( f x , f y ) ( i 2 δ ( f x + f , f y + f ) i 2 δ ( f x f , f y f ) ) ] .
G b s ( f x , f y ) = G s ( f x , f y ) rect ( f x ) rect ( f y ) .
S b s ( x , y ) = | g b s ( x , y ) + R | 2 , S b s ( x , y ) = I b s ( x , y ) + | R | 2 + g b s ( x , y ) R * + g * b s ( x , y ) R ,
S b ( f x , f y ) = G ( f x , f y ) rect ( f x ) rect ( f y ) ,
S b c ( f x , f y ) = { 1 2 G ( f x + f , f y + f ) + 1 2 G ( f x f , f y f ) } rect ( f x ) rect ( f y ) ,
S b s ( f x , f y ) = { i 2 G ( f x + f , f y + f ) i 2 G ( f x f , f y f ) } rect ( f x ) rect ( f y ) .
USB = S b c ( f x , f y ) i S b s ( f x , f y ) = G ( f x + f , f y + f ) rect ( f x ) rect ( f y ) ,
LSB = S b c ( f x , f y ) + i S b s ( f x , f y ) = G ( f x f , f y f ) rect ( f x ) rect ( f y ) .
= 1 2 [ G ( f x + 2 f , f y + 2 f ) rect ( f x + f ) rect ( f y + f ) ] + 1 2 [ G ( f x , f y ) rect ( f x f ) rect ( f y f ) ] + [ G ( f x + f , f y + f ) rect ( f x ) rect ( f y ) ] ,
= 1 2 [ G ( f x , f y ) rect ( f x + f ) rect ( f y + f ) ] + 1 2 [ G ( f x 2 f , f y 2 f ) rect ( f x f ) rect ( f y f ) ] + [ G ( f x + f , f y + f ) rect ( f x ) rect ( f y ) ] .
G E ( f x , f y ) = [ G ( f x , f y ) rect ( f x f ) rect ( f y f ) + [ G ( f x , f y ) rect ( f x ) rect ( f y ) ] + [ G ( f x , f y ) rect ( f x + f ) rect ( f y + f ) ] .
G E ( f x , f y ) = G ( f x , f y ) [ rect E ( f x ) rect E ( f y ) ] ,
[ rect E ( f x ) rect E ( f y ) ] = [ rect ( f x f ) rect ( f y f ) + [ rect ( f x ) rect ( f y ) ] + [ rect ( f x + f ) rect ( f y + f ) ] .
g e ( x , y ) = g ( x , y ) Sinc e ( x ) Sinc e ( y ) .

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