Abstract

Structured illumination microscopy applied to in-vivo retinal imaging has the potential to provide a low-cost and powerful diagnostic tool for retinal disease. In this paper the key parameters that affect performance in structured illumination ophthalmoscopy are studied theoretically. These include the number of images that need to be acquired in order to generate a sectioned image, which is affected by the non-stationary nature of the retina during acquisition, the choice of spatial frequency of the illuminating sinusoid, the effect of typical ocular aberrations on axial resolution and the nature of the sinusoidal pattern produced by the illumination system. The results indicate that structured illumination ophthalmoscopy can be a robust technique for achieving axial sectioning in retinal imaging without the need for complex optical systems.

© 2012 OSA

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References

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  1. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
    [CrossRef]
  2. D. Karadaglić, “Image formation in conventional brightfield reflection microscopes with optical sectioning via structured illumination,” Micron39, 302–310 (2008).
    [CrossRef]
  3. D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron39, 808–818 (2008).
    [CrossRef]
  4. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proceedings of the National Academy of Science102(37), 13,081–13,086 (2005).
    [CrossRef]
  5. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
    [CrossRef] [PubMed]
  6. S. Gruppetta and S. Chetty, “Theoretical study of multispectral structured illumination for depth resolved imaging of non-stationary objects: focus on retinal imaging,” Biomedical Optics Express2(2), 255–263 (2011).
    [CrossRef] [PubMed]
  7. S. Gruppetta, “Optical Imaging System,” WO Patent WO/2012/059564, PCT/EP2011/069375 (2011).
  8. D. Karadaglić, “Wide-field Optical Sectioning Microscopy using Structured Illumination,” Ph.D. thesis, University of Oxford (2004).
  9. N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
    [CrossRef]
  10. T. Wilson and C. Sheppard, eds., Theory and Practice of Scanning Optical Microscopy (Academic Press, 1984).
  11. S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A26(2), 413–424 (2009).
    [CrossRef]
  12. S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
    [CrossRef] [PubMed]
  13. G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge University Press, 2011).
  14. L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, 1999).

2012 (1)

N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
[CrossRef]

2011 (1)

S. Gruppetta and S. Chetty, “Theoretical study of multispectral structured illumination for depth resolved imaging of non-stationary objects: focus on retinal imaging,” Biomedical Optics Express2(2), 255–263 (2011).
[CrossRef] [PubMed]

2010 (1)

S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
[CrossRef] [PubMed]

2009 (2)

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A26(2), 413–424 (2009).
[CrossRef]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

2008 (2)

D. Karadaglić, “Image formation in conventional brightfield reflection microscopes with optical sectioning via structured illumination,” Micron39, 302–310 (2008).
[CrossRef]

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron39, 808–818 (2008).
[CrossRef]

2005 (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proceedings of the National Academy of Science102(37), 13,081–13,086 (2005).
[CrossRef]

2002 (1)

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
[CrossRef]

1997 (1)

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, 1999).

Bradley, A.

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
[CrossRef]

Chetty, S.

S. Gruppetta and S. Chetty, “Theoretical study of multispectral structured illumination for depth resolved imaging of non-stationary objects: focus on retinal imaging,” Biomedical Optics Express2(2), 255–263 (2011).
[CrossRef] [PubMed]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Fienup, J.

S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
[CrossRef] [PubMed]

Fienup, J. R.

Gao, L.

N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
[CrossRef]

Gbur, G. J.

G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge University Press, 2011).

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Gruppetta, S.

S. Gruppetta and S. Chetty, “Theoretical study of multispectral structured illumination for depth resolved imaging of non-stationary objects: focus on retinal imaging,” Biomedical Optics Express2(2), 255–263 (2011).
[CrossRef] [PubMed]

S. Gruppetta, “Optical Imaging System,” WO Patent WO/2012/059564, PCT/EP2011/069375 (2011).

Gustafsson, M. G. L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proceedings of the National Academy of Science102(37), 13,081–13,086 (2005).
[CrossRef]

Hagan, N.

N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
[CrossRef]

Hong, X.

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
[CrossRef]

Juskaitis, R.

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
[CrossRef]

Karadaglic, D.

D. Karadaglić, “Image formation in conventional brightfield reflection microscopes with optical sectioning via structured illumination,” Micron39, 302–310 (2008).
[CrossRef]

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron39, 808–818 (2008).
[CrossRef]

D. Karadaglić, “Wide-field Optical Sectioning Microscopy using Structured Illumination,” Ph.D. thesis, University of Oxford (2004).

Kner, P.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Neil, M. A. A.

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
[CrossRef]

Shroff, S.

S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
[CrossRef] [PubMed]

Shroff, S. A.

Thibos, L. N.

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
[CrossRef]

Tkaczyk, T. S.

N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
[CrossRef]

Williams, D.

S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
[CrossRef] [PubMed]

Williams, D. R.

Wilson, T.

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron39, 808–818 (2008).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
[CrossRef]

Winoto, L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, 1999).

Biomedical Optics Express (1)

S. Gruppetta and S. Chetty, “Theoretical study of multispectral structured illumination for depth resolved imaging of non-stationary objects: focus on retinal imaging,” Biomedical Optics Express2(2), 255–263 (2011).
[CrossRef] [PubMed]

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

JOSA A (1)

S. Shroff, J. Fienup, and D. Williams, “Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results,” JOSA A27(8), 1770–1782 (2010).
[CrossRef] [PubMed]

Micron (2)

D. Karadaglić, “Image formation in conventional brightfield reflection microscopes with optical sectioning via structured illumination,” Micron39, 302–310 (2008).
[CrossRef]

D. Karadaglić and T. Wilson, “Image formation in structured illumination wide-field fluorescence microscopy,” Micron39, 808–818 (2008).
[CrossRef]

Nature Methods (1)

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nature Methods6, 339–342 (2009).
[CrossRef] [PubMed]

Ophthal. Physiol. Opt. (1)

L. N. Thibos, A. Bradley, and X. Hong, “A statistical model of the aberration structure of normal, well-corrected eyes,” Ophthal. Physiol. Opt.22, 427–433 (2002).
[CrossRef]

Optics Express (1)

N. Hagan, L. Gao, and T. S. Tkaczyk, “Quantitative sectioning and noise analysis for structured illumination microscopy,” Optics Express20(1), 403–413 (2012).
[CrossRef]

Optics Letters (1)

M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Optics Letters22(24), 1905–1907 (1997).
[CrossRef]

Proceedings of the National Academy of Science (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proceedings of the National Academy of Science102(37), 13,081–13,086 (2005).
[CrossRef]

Other (5)

T. Wilson and C. Sheppard, eds., Theory and Practice of Scanning Optical Microscopy (Academic Press, 1984).

S. Gruppetta, “Optical Imaging System,” WO Patent WO/2012/059564, PCT/EP2011/069375 (2011).

D. Karadaglić, “Wide-field Optical Sectioning Microscopy using Structured Illumination,” Ph.D. thesis, University of Oxford (2004).

M. Born and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, 1999).

G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge University Press, 2011).

Supplementary Material (1)

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Figures (8)

Fig. 1
Fig. 1

Plot of median condition number κ(A) (blue line) for sets of 100 matrices with N random phases, N = 3, 4,...,9. The dotted green lines indicate the 25th and 75th centiles (75th centile for N = 3 is 22.9) and the dashed black line indicates the floor for this plot given by the ideal case κ(A) = 1.

Fig. 2
Fig. 2

Comparison of the integrated intensity curves for the conventional imaging system (green), the Scanning Laser Ophthalmoscope (SLO, dotted), and the SIO (red and blue). The blue plot represents the theoretical performance of the SIO as given by the Stokseth approximation [2] while the red plot represents the simulation results.

Fig. 3
Fig. 3

Modulation transfer function at various normalised units of defocus. ( Media 1) The red dot represents the optimum frequency ν = 1.

Fig. 4
Fig. 4

A plot of the FWHM of the integrated intensity curves as a function of spatial frequency ν. The FWHM is a measure of axial resolution.

Fig. 5
Fig. 5

Distribution of Zernike coefficients for 100 virtual eyes. Data point shows the mean coefficient while error bars represent 2 standard deviations. Both single- and double-index notations are used to label Zernike terms.

Fig. 6
Fig. 6

Integrated intensity plots corresponding to aberrated wavefronts (dashed lines) and the unaberrated case (solid blue line). The three plots shown for the aberrated cases correspond to those which yield the 5th, 50th and 95th percentile FWHM. Therefore 90% of all aberrated wavefronts generated would produce integrated intensity curves that fall within the limits shown.

Fig. 7
Fig. 7

Experimentally determined modulation change with defocus in the SIO prototype using the modified Fizeau fringe projection illumination technique [6].

Fig. 8
Fig. 8

Integrated intensity plot for constant modulation (μ = 1, blue) and for the variable modulation in Fig. 7 (red).

Equations (9)

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I illumination ( t o , w o ) = 1 + μ cos ( ν t o + ϕ ) ,
I ( t i , w i ) = I 0 ( t i , w i ) + μ 2 e i ϕ I ν ( t i , w i ) + μ 2 e i ϕ I ν ( t i , w i ) ,
I 0 ( t i , w i ) = ρ ( t o , w o ) | h ( t i + t o , w i + w o ) | 2 d t o d w o ,
I ν ( t i , w i ) = e i ν t o ρ ( t o , w o ) | h ( t i + t o , w i + w o ) | 2 d t o d w o ,
I ν ( t i , w i ) = e i ν t o ρ ( t o , w o ) | h ( t i + t o , w i + w o ) | 2 d t o d w o ,
b = Ax ,
b = [ I 1 I 2 I N ] N × 1 ,
A = [ 1 μ 2 e i ϕ 1 μ 2 e i ϕ 1 1 μ 2 e i ϕ 2 μ 2 e i ϕ 2 1 μ 2 e i ϕ n μ 2 e i ϕ n ] N × 3 ,
x = [ I 0 I ν I ν ] 3 × 1 .

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