Abstract

Model-based image processing techniques have been proposed as a way to increase the resolution of optical microscopes. Here a model based on the microscope’s point-spread function is analyzed, and the resolution limits achieved with a proposed goodness-of-fit criterion are quantified. Several experiments were performed to evaluate the possibilities and limitations of this method: (a) experiments with an ideal (diffraction-limited) microscope, (b) experiments with simulated dots and a real microscope, and (c) experiments with real dots acquired with a real microscope. The results show that a threefold increase over classical resolution (e.g., Rayleigh) is possible. These results can be affected by model misspecifications, whereas model corruption, as seen in the effect of Poisson noise, seems to be unimportant. This research can be considered to be preliminary with the final goal being the accurate measurement of various cytogenetic properties, such as gene distributions, in labeled preparations.

© 2000 Optical Society of America

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References

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  1. S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
    [CrossRef]
  2. A. Van den Bos, “Ultimate resolution: a mathematical framework,” Ultramicroscopy 47, 298–306 (1992).
    [CrossRef]
  3. A. J. den Dekker, A. Van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
    [CrossRef]
  4. H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
    [CrossRef] [PubMed]
  5. H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
    [CrossRef]
  6. C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).
  7. L. J. van Vliet, P. W. Verbeek, “Better geometric measurements based on photometric information,” in Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, S. Okamura, T. Nemoto, S. Fujimura, K. Watanabe, eds. (IEEE, New York, 1994), pp. 1357–1360.
  8. A. J. den Dekker, “Model-based resolution,” Ph.D. dissertation in Applied Physics (Delft University of Technology, Delft, The Netherlands, 1997).
  9. W. F. Maddams, “The scope and limitations of curve fitting,” Appl. Spectrosc. 34, 245–267 (1980).
    [CrossRef]
  10. A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).
  11. H. Netten, “Automated image analysis of FISH-stained cell nuclei,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1997).
  12. P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
    [CrossRef] [PubMed]

1998 (1)

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

1997 (2)

A. J. den Dekker, A. Van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

1996 (1)

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

1995 (1)

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

1992 (2)

A. Van den Bos, “Ultimate resolution: a mathematical framework,” Ultramicroscopy 47, 298–306 (1992).
[CrossRef]

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

1980 (1)

Cremer, C.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

Cremer, T.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

del Pozo, F.

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

den Dekker, A. J.

A. J. den Dekker, A. Van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

A. J. den Dekker, “Model-based resolution,” Ph.D. dissertation in Applied Physics (Delft University of Technology, Delft, The Netherlands, 1997).

Dietzel, S.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

Eils, R.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

Ellenberger, S.

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

García-Sagredo, J. M.

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

Klein, A.

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

Maddams, W. F.

Münkel, C.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

Nederlof, P. M.

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

Netten, H.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

H. Netten, “Automated image analysis of FISH-stained cell nuclei,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1997).

Ortiz de Solórzano, C.

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

Raap, A. K.

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

Santos, A.

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

Sloos, W. C. R.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

Tanke, H. J.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

Vallcorba, I.

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

Van den Bos, A.

A. J. den Dekker, A. Van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

A. Van den Bos, “Ultimate resolution: a mathematical framework,” Ultramicroscopy 47, 298–306 (1992).
[CrossRef]

van den Doel, R.

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

van der Flier, S.

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

van Vliet, L. J.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

L. J. van Vliet, P. W. Verbeek, “Better geometric measurements based on photometric information,” in Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, S. Okamura, T. Nemoto, S. Fujimura, K. Watanabe, eds. (IEEE, New York, 1994), pp. 1357–1360.

Verbeek, P. W.

L. J. van Vliet, P. W. Verbeek, “Better geometric measurements based on photometric information,” in Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, S. Okamura, T. Nemoto, S. Fujimura, K. Watanabe, eds. (IEEE, New York, 1994), pp. 1357–1360.

Vrolijk, H.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

Weilandt, E.

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

Young, I. T.

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

Appl. Spectrosc. (1)

Bioimaging (2)

S. Dietzel, E. Weilandt, R. Eils, C. Münkel, C. Cremer, T. Cremer, “Three-dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography,” Bioimaging 3, 121–133 (1995).
[CrossRef]

H. Netten, L. J. van Vliet, H. Vrolijk, W. C. R. Sloos, H. J. Tanke, I. T. Young, “Fluorescent dot counting in interphase cell nuclei,” Bioimaging 4, 93–106 (1996).
[CrossRef]

Cytometry (3)

C. Ortiz de Solórzano, A. Santos, I. Vallcorba, J. M. García-Sagredo, F. del Pozo, ”Automated FISH spot counting in interphase nuclei: statistical validation and data correction,” Cytometry 31, 93–99 (1998).

H. Netten, I. T. Young, L. J. van Vliet, H. J. Tanke, H. Vrolijk, W. C. R. Sloos, “FISH and chips: automation of fluorescent dot counting in interphase cell nuclei,” Cytometry 28, 1–10 (1997).
[CrossRef] [PubMed]

P. M. Nederlof, S. van der Flier, A. K. Raap, H. J. Tanke, “Quantification of inter- and intra-nuclear variation of fluorescence in situ hybridization signals,” Cytometry 13, 831–838 (1992).
[CrossRef] [PubMed]

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

Ultramicroscopy (1)

A. Van den Bos, “Ultimate resolution: a mathematical framework,” Ultramicroscopy 47, 298–306 (1992).
[CrossRef]

Other (4)

L. J. van Vliet, P. W. Verbeek, “Better geometric measurements based on photometric information,” in Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, S. Okamura, T. Nemoto, S. Fujimura, K. Watanabe, eds. (IEEE, New York, 1994), pp. 1357–1360.

A. J. den Dekker, “Model-based resolution,” Ph.D. dissertation in Applied Physics (Delft University of Technology, Delft, The Netherlands, 1997).

A. Klein, R. van den Doel, I. T. Young, S. Ellenberger, L. J. van Vliet, “Quantitative evaluation and comparison of light microscopes,” in Optical Investigation of Cells In Vitro and In Vivo, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3260, 162–173 (1998).

H. Netten, “Automated image analysis of FISH-stained cell nuclei,” Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1997).

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Figures (5)

Fig. 1
Fig. 1

Bessel-based (above) and Gaussian-based (below) models. Solid curve, models; dotted curve, Zeiss Axioskop microscope PSF. The fitting was performed as described in the text.

Fig. 2
Fig. 2

Results of the two-dot model fit in the ideal case. The simulated image is from an ideal diffraction-limited microscope with consideration of Poisson noise. Left-hand side, results of all fits obtained; right-hand side, discarding cases in which ξ < 0.1. Note the different vertical scales.

Fig. 3
Fig. 3

Results of the experiments with simulated dots with the Bessel model for the Zeiss microscope parameters and including Poisson noise. Left-hand side, discarding cases in which ξ < 0.1; right-hand side, discarding cases in which ξ < 0.4. Distances in pixels are in interpolated space. Note the different vertical scales.

Fig. 4
Fig. 4

Results of the experiments with simulated dots with the Gaussian model for the Zeiss microscope parameters and including Poisson noise. Left-hand side, discarding cases in which ξ < 0.1; right-hand side, discarding cases in which ξ < 0.4. Distances in pixels are in interpolated space. Note the different vertical scales.

Fig. 5
Fig. 5

Simulated dots without noise. Error in the distance estimation and the peak ratio estimation for three values of the true peak ratio γ = 0.7 (top), γ = 0.6 (middle), and γ = 0.5 (bottom).

Tables (5)

Tables Icon

Table 1 Ideal Case: Diffraction-Limited Microscope with Two Infinitesimally Small Objectsa

Tables Icon

Table 2 Experiment with Two Overlapping Simulated Dots and Gaussian and Bessel Models (Adjusted to the Zeiss Axioskop Microscope)a

Tables Icon

Table 3 FWHM of the Acquired Dots Used in the Experiments, with and without Cubic Interpolation

Tables Icon

Table 4 Results with a Single (Acquired) Dot with and without Interpolation: Estimated Distance, Peak Ratios, and Goodness-of-Fit Criterion for Two-Dot Model Fitting

Tables Icon

Table 5 Results with Two (Replicated) Dotsa

Equations (13)

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

gx, y/α, β=α1hx-βx1, y-βy1+α2hx-βx2, y-βy2,
gx, y/α, β, γ=α0γhx-βx1, y-βy1+1-γhx-βx2, y-βy2,
hx=p1J1p2x-p3x-p32,
hx=p1 exp-p2x-p32.
d=x-t22+y-t321/2,  model1=t1J1p2dd2
d1=x-t22+y-t321/2,  d2=x-t42+y-t521/2,  dot1=J1p2d1d12,  dot2=J1p2d2d22,  model2=t1t6 dot1+1-t6dot2.
model1=t1 exp-p2x-t22exp-p2x-t32
dot1=exp-p2x-t22exp-p2y-t32,  dot2=exp-p2x-t42exp-p2y-t52,  model2=t1t6 dot1+1-t6dot2,
one dot,  err1=x,y=1Nimage_datax, y-model1x, y2,two dot,  err2=x,y=1Nimage_datax, y-model2x, y2,
mse=1N2  err2,
ξ=mse2-mse1mse2,
PSFr=constant2 J1arr2,
r=0.2898a=0.289813.614 μm-1=0.021 μm,

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