Abstract

The effect of optical superresolution on speckle correlations is studied. Simulations reveal that using a lateral superresolution pupil filter more than twice the out of plane correlation length of the clear pupil can be achieved. This means that the measurement range in speckle correlation measurements doubles. To verify the correlation length an experiment is performed using a liquid crystal (LCD) spatial light modulator as a programmable superresolution filter. The results corroborate the simulation.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. L. Leushacke and M. Keichner, �??Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures,�?? J. Opt. Soc. Am. A 7, 828-832 (1990).
    [CrossRef]
  2. Q. B. Li and F. P. Chiang, �??Three-dimensional dimension of laser speckle,�?? Appl. Opt. 31, 6287-6291(1992).
    [CrossRef] [PubMed]
  3. S. A. Ledesma, J. Campos, J. C. Escalera, and M. J. Yzuel, "Symmetry properties with pupil phase-filters," Opt. Express 12, 2548-2559 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2548">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2548</a>.
    [CrossRef] [PubMed]
  4. B.R.Frieden, "Longitudinal image formation," J. Opt. Soc. Am. 56, 1495-1501 (1966).
    [CrossRef]
  5. S. Yuan, A. Devor, D.A. Boas and A.K. Dunn, �??Determination of optimal exposure time for imaging of blood flow changes with laser speckle contrast imaging,�?? Appl. Opt. 44, 1823-1830(2005).
    [CrossRef] [PubMed]
  6. D. M. de Juana, V.F. Canales, P.J. Valle and M.P. Cagigal, �??Focusing properties of annular binary phase filters,�?? Opt. Comm. 229, 71-77(2004).
    [CrossRef]
  7. X. Deng, L. Liu, G. Wang, Z. Xu, �??Superresolution phase-only filters in confocal scanning imaging system,�?? Optik 111, (503-507) 2000.
  8. V.F. Canales, D. M. de Juana and M. P. Cagigal, �??Superresolution in compensated telescopes,�?? Opt. Lett. 29, 1-3 (2004).
    [CrossRef]
  9. H. Wang, Z. Chen and F. Gan, �??Phase-shifting apodizer for next-generation digital versatile disk,�?? Opt. Eng. 40, 991-994 (2001).
    [CrossRef]
  10. J.W. Goodman, Introduction to Fourier optics, 2nd Ed (McGraw-Hill, New York, 1996).
  11. P. N. Gundu, E. Hack, and P. Rastogi, "High efficient superresolution combination filter with twin LCD spatial light modulators," Opt. Express 13, 2835-2842 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2835">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2835</a>.
    [CrossRef] [PubMed]
  12. P.N. Gundu, E. Hack and P. Rastogi, �??�??Apodized superresolution�?? �?? concept and simulations,�?? Opt. Commun. 249, 101-107 (2005).
    [CrossRef]
  13. J.L. Pezzaniti and R.A. Chipaman, �??Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,�?? Opt. Lett. 18, 1567-1569 (1993).
    [CrossRef] [PubMed]
  14. J.A. Davis, I. Moreno, and P. Tsai, �??Polarization eigenstates for twisted-nematic liquid crystal displays,�?? Appl. Opt. 37, 937-945 (1998).
    [CrossRef]
  15. I. Moreno, J.A. Davis, K.G. D�??Nelly, and D.B. Allison, �??Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,�?? Opt. Eng. 37, 3048-3052 (1998).
    [CrossRef]
  16. E. Hack, P.N. Gundu and P. Rastogi, �??Adaptive correction to the speckle correlation fringes by using a twisted-nematic liquid-crystal display,�?? Appl. Opt. 44, 2772-2781 (2005)
    [CrossRef] [PubMed]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

L. Leushacke and M. Keichner, �??Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures,�?? J. Opt. Soc. Am. A 7, 828-832 (1990).
[CrossRef]

Opt. Comm.

D. M. de Juana, V.F. Canales, P.J. Valle and M.P. Cagigal, �??Focusing properties of annular binary phase filters,�?? Opt. Comm. 229, 71-77(2004).
[CrossRef]

Opt. Commun.

P.N. Gundu, E. Hack and P. Rastogi, �??�??Apodized superresolution�?? �?? concept and simulations,�?? Opt. Commun. 249, 101-107 (2005).
[CrossRef]

Opt. Eng.

I. Moreno, J.A. Davis, K.G. D�??Nelly, and D.B. Allison, �??Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,�?? Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

H. Wang, Z. Chen and F. Gan, �??Phase-shifting apodizer for next-generation digital versatile disk,�?? Opt. Eng. 40, 991-994 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

X. Deng, L. Liu, G. Wang, Z. Xu, �??Superresolution phase-only filters in confocal scanning imaging system,�?? Optik 111, (503-507) 2000.

Other

J.W. Goodman, Introduction to Fourier optics, 2nd Ed (McGraw-Hill, New York, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

PSFs along axial direction for various pupil functions.

Fig. 2.
Fig. 2.

Variation of speckle intensity correlation coefficient with defocus for various pupil functions.

Fig. 3.
Fig. 3.

(a), (b), (c) and (d) are the DSPI fringes at locations 0 mm, 0.04 mm, 0.08 mm and 0.1 mm from focus respectively. (e), (f), (g) and (h) are typical line intensity profiles of (a), (b), (c) and (d), respectively.

Fig. 4.
Fig. 4.

(a), (b), (c), (d), (e) and (f) are the DSPI fringes obtained using an amplitude filter with G = 81% at locations 0 mm, 0.04 mm, 0.08 mm, 0.12 mm, 0.16 mm and 0.18 mm from focus, respectively. (g–l) are line intensity profiles of (a–f), respectively.

Fig. 5.
Fig. 5.

Setup for measuring speckle correlations.

Fig. 6.
Fig. 6.

Variation of speckle correlation with defocus using setup shown in Fig. 5

Tables (1)

Tables Icon

Table 1. Coefficients b 2n for continuous filters with various G values.

Equations (6)

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

U i ( x , y ) = ξ η U o ( ξ , η ) h ( x ξ , y η ) dξdη
h ( x , y , z ) = K exp ( ikz ) z u v P ( u , v ) exp [ i k 2 ( 1 f 1 z ) ( u 2 + v 2 ) ] exp [ i k f ( xu + yu ) ] dudv
U o ( ξ , η ) = a ( ξ , η ) exp [ i ϕ ( ξ , η ) ]
P ( ρ ) = n = 0 k b 2 n ρ 2 n
U ( ζ ) = 2 0 1 P ( ρ ) exp ( i u ρ 2 2 ) ρ d ρ
r = m n ( I f ( m , n ) I f ) ( I def ( m , n ) I def ) m n ( I f ( m , n ) I f ) 2 m n ( I def ( m , n ) I def ) 2

Metrics