Abstract

An interferometry based method to achieve resolution beyond the diffraction barrier is proposed. Object is illuminated with different tilted beams, generated by using a Spatial Light Modulator (SLM). In addition, some constant phases are also assigned to each tilted beam with the SLM display. Then, the object is simultaneously illuminated with all tilted beams, producing an on-axis interferometry scheme. An interferogram at the image plane is formed for each set of constant phases added to the tilted beams. Using proper selection of constant phases for each of the interferograms, the synthetic aperture can be calculated. During the post processing, we take the Fourier transforms of the each image and the portions of the spectrum are spatially shifted and combined to obtain synthesized spectrum whose inverse Fourier transform gives high resolution image.

© 2013 OSA

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References

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    [CrossRef] [PubMed]

2013

A. Hussain, J. L. Martínez, and J. Campos, “Holographic superresolution using spatial light modulator,” JEOS-Rapid Publ.8, 13007 (2013).

2012

A. Hussain and A. A. Mudassar, “Holography based super resolution,” Opt. Commun.285(9), 2303–2310 (2012).
[CrossRef]

2011

2010

2009

2008

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A, Pure Appl. Opt.10(2), 025304 (2008).
[CrossRef]

V. Mico, Z. Zalevsky, and J. García, “Common-path phases shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun.281(17), 4273–4281 (2008).
[CrossRef]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express16(4), 2555–2569 (2008).
[CrossRef] [PubMed]

V. Mico, O. Limon, A. Gur, Z. Zalevsky, and J. García, “Transverse resolution improvement using rotating-grating time-multiplexing approach,” J. Opt. Soc. Am. A25(5), 1115–1129 (2008).
[CrossRef] [PubMed]

A. Neumann, Y. Kuznetsova, and S. R. J. Brueck, “Structured illumination for the extension of imaging interferometric microscopy,” Opt. Express16(10), 6785–6793 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, “Super-resolution in digital holography by a two-dimensional dynamic phase grating,” Opt. Express16(21), 17107–17118 (2008).
[CrossRef] [PubMed]

2006

2004

2002

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

2000

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
[CrossRef] [PubMed]

1973

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

1971

1967

1966

1952

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3suppl.), 426–438 (1952).
[CrossRef]

Alexandrov, S. A.

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A, Pure Appl. Opt.10(2), 025304 (2008).
[CrossRef]

Bo, F.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Boppart, S. A.

Brueck, S. R. J.

Calabuig, A.

Campos, J.

Carney, P. S.

De Nicola, S.

Estapé, M.

Fernández, E.

Ferraro, P.

Ferreira, C.

Finizio, A.

Francia, G. T.

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3suppl.), 426–438 (1952).
[CrossRef]

Garcia, J.

García, J.

García-Martínez, P.

Greenaway, A. H.

Grilli, S.

Gur, A.

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(2), 82–87 (2000).
[CrossRef] [PubMed]

Harvey, A. R.

Hussain, A.

A. Hussain, J. L. Martínez, and J. Campos, “Holographic superresolution using spatial light modulator,” JEOS-Rapid Publ.8, 13007 (2013).

A. Hussain and A. A. Mudassar, “Holography based super resolution,” Opt. Commun.285(9), 2303–2310 (2012).
[CrossRef]

A. A. Mudassar and A. Hussain, “Super-resolution of active spatial frequency heterodyning using holographic approach,” Appl. Opt.49(17), 3434–3441 (2010).
[CrossRef] [PubMed]

Iemmi, C.

Jones, J. D. C.

Kuznetsova, Y.

Limon, O.

Liu, Ch.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Liu, Z.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Lizana, A.

Lukosz, W.

Lukoz, W.

Marks, D. L.

Márquez, A.

Martín, N.

Martínez, J. L.

A. Hussain, J. L. Martínez, and J. Campos, “Holographic superresolution using spatial light modulator,” JEOS-Rapid Publ.8, 13007 (2013).

Masato, K.

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

Merola, F.

Mico, V.

Micó, V.

Mitsuhiro, U.

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

Moreno, I.

Mudassar, A.

Mudassar, A. A.

Neumann, A.

Paturzo, M.

Ralston, T. S.

Sampson, D. D.

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A, Pure Appl. Opt.10(2), 025304 (2008).
[CrossRef]

Sato, T.

Takuso, S.

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

Ueda, M.

Wang, Y.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Yzuel, M. J.

Zalevsky, Z.

Zhu, J.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett.81(17), 3143–3146 (2002).
[CrossRef]

Chin. Opt. Lett.

J. Microsc.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
[CrossRef] [PubMed]

J. Mod. Opt.

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

J. Opt. A, Pure Appl. Opt.

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A, Pure Appl. Opt.10(2), 025304 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

JEOS-Rapid Publ.

A. Hussain, J. L. Martínez, and J. Campos, “Holographic superresolution using spatial light modulator,” JEOS-Rapid Publ.8, 13007 (2013).

Nuovo Cim.

G. T. Francia, “Super-gain antennas and optical resolving power,” Nuovo Cim.9(S3suppl.), 426–438 (1952).
[CrossRef]

Opt. Commun.

A. Hussain and A. A. Mudassar, “Holography based super resolution,” Opt. Commun.285(9), 2303–2310 (2012).
[CrossRef]

V. Mico, Z. Zalevsky, and J. García, “Common-path phases shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun.281(17), 4273–4281 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. Taylor, Theory and applications of Numerical analysis (Academic Press, 1974).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental optical system for structure illumination using Spatial light modulator for on-axis interferometry. (b) Equivalent and simplified sketch in transmission showing the expanded beams.

Fig. 2
Fig. 2

(a) Example of an object Fourier spectrum; (b) Summation of different parts of the object spectrum displaced to this original position; (c) Summation of different parts of the object spectrum centered at the origin.

Fig. 3
Fig. 3

Different spectra reconstruction obtained after solving the linear equation system composed of 7th correlation terms.

Fig. 4
Fig. 4

(a) Reconstructed spectrum; (b) Single illumination spectrum.

Fig. 5
Fig. 5

Simulated results. a) Original image; b) low resolution image obtained with the system; c) higher resolution image obtained by applying the proposed method.

Fig. 6
Fig. 6

Experimental results: (a) Low resolution image obtained with the system,(c) higher resolution image obtained by applying the proposed method.

Tables (1)

Tables Icon

Table 1 Set of constant phases used to separate the shifted terms

Equations (16)

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I(x)= | O( x )h( x ) | 2 ,
I ˜ (u)=[ ( O ˜ (u).H(u) )( O ˜ (u).H(u) ) ],
I ˜ 0 (u)=[ ( e i δ 0 O ˜ (u u 0 ).H(u) )( e i δ 0 O ˜ (u u 0 ).H(u) ) ].
I ˜ t (u)=[ p=1 n ( e i δ p O ˜ (u u p )H(u) ) k=1 n ( e i δ k O ˜ (u u k )H(u) ) ],
I ˜ t (u)=[ p=1 n k=1 n e i( δ p δ k ) [ ( O ˜ (u u p )H(u) )( O ˜ (u u k )H(u) ) ] ].
δ 1 δ 2 = δ a , δ 1 δ 3 = δ b , δ 2 δ 3 = δ c ,
u 2 =0, u 1 = u 0 , u 3 = u 0 .
I ˜ t (u)={ [ O ˜ (u+ u 0 )H(u) O ˜ (u+ u 0 )H(u) ]+ e i δ a [ O ˜ (u+ u 0 )H(u) O ˜ (u)H(u) ]+ e i δ b [ O ˜ (u+ u 0 )H(u) O ˜ (u u 0 )H(u) ]+ e i δ a [ O ˜ (u)H(u) O ˜ (u+ u 0 )H(u) ] +[ O ˜ (u)H(u) O ˜ (u)H(u) ]+ e i δ c [ O ˜ (u)H(u) O ˜ (u u 0 )H(u) ] + e i δ b [ O ˜ (u u 0 )H(u) O ˜ (u+ u 0 )H(u) ]+ e i δ c [ O ˜ (u u 0 )H(u) O ˜ (u)H(u) ] +[ O ˜ (u u 0 )H(u) O ˜ (u u 0 )H(u) ] }.
I ˜ t (u)= C 0 + C 1 e i δ a + C 2 e i δ b + C 3 e i δ a + C 4 e i δ c + C 5 e i δ b + C 6 e i δ c ,
C 0 =[ O ˜ (u+ u 0 )H(u) O ˜ (u+ u 0 )H(u) ]+[ O ˜ (u)H(u) O ˜ (u)H(u) ]+ +[ O ˜ (u u 0 )H(u) O ˜ (u u 0 )H(u) ]; C 1 =[ O ˜ (u+ u 0 )H(u) O ˜ (u)H(u) ]; C 2 =[ O ˜ (u+ u 0 )H(u) O ˜ (u u 0 )H(u) ]; C 3 =[ O ˜ (u)H(u) O ˜ (u+ u 0 )H(u) ]; C 4 =[ O ˜ (u)H(u) O ˜ (u u 0 )H(u) ]; C 5 =[ O ˜ (u u 0 )H(u) O ˜ (u+ u 0 )H(u) ]; C 6 =[ O ˜ (u u 0 )H(u) O ˜ (u)H(u) ];
[ I 1 I 2 I 3 I 4 I 5 I 6 I 7 ] A = [ 1 1 1 1 1 1 1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 i i -i 1 -i 1 1 -i 1 i i 1 -i 1 -1 i -1 -i -i i ] M [ C 0 C 1 C 2 C 3 C 4 C 5 C 6 ] X ,
A=MX, X=A M 1 .
A( x )B( x )=C( x ), A( x+s )B( x+r )=C( x+sr ),
I ˜ (u)= C 0 (u)+ C 1 (u u 0 )+ C 2 (u2 u 0 )+ C 3 (u+ u 0 )+ C 4 (u u 0 )+ + C 5 (u+2 u 0 )+ C 6 (u+ u 0 ).
I ˜ (u)=( O ˜ ( u ) H ( u ) )*( O ˜ ( u ) H ( u ) ).
I t (x)= | O( x ) h ( x ) | 2 .

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