Abstract

We use optical Gabor-like filtering implemented with a digital micromirror device to achieve nanoscale sensitivity to changes in the size of finite and periodic objects imaged at low resolution. The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal. Using this optimum filter period as a measure of object size, we show sensitivity to a 7.5 nm change in the period of a chirped phase mask with period around 1µm. We also show 30nm sensitivity to change in the size of polystyrene spheres with diameters around 500nm. Unlike digital post-processing our optical processing method retains its sensitivity when implemented at low magnification in undersampled images. Furthermore, the optimum Gabor filter period found experimentally is linearly related to sphere diameter over the range 0.46µm-1µm and does not rely on a predictive scatter model such as Mie theory. The technique may have applications in high throughput optical analysis of subcellular morphology to study organelle function in living cells.

© 2009 OSA

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References

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  1. Z. Pincus and J. A. Theriot, “Comparison of quantitative methods for cell-shape analysis,” J. Microsc. 227(2), 140–156 (2007).
    [CrossRef]
  2. J. Angulo and S. Matou, “Application of mathematical morphology to the quantification of in vitro endothelial cell organization into tubular-like structures,” Cell Mol Biol (Noisy-le-grand) 53(2), 22–35 (2007).
  3. A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15(25), 17334–17342 (2007).
    [CrossRef]
  4. J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2242–2244 (2005).
  5. Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
  6. H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).
  7. J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
    [CrossRef]
  8. J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
    [CrossRef]
  9. L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).
  10. R. M. Pasternack, Z. Qian, J.-Y. Zheng, D. N. Metaxas, E. White, and N. N. Boustany, “Measurement of subcellular texture by optical Gabor-like filtering with a digital micromirror device,” Opt. Lett. 33(19), 2209–2211 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. N. N. Boustany, S. C. Kuo, and N. V. Thakor, “Optical scatter imaging: subcellular morphometry in situ with Fourier filtering,” Opt. Lett. 26(14), 1063–1065 (2001).
    [CrossRef]

2008 (1)

2007 (3)

Z. Pincus and J. A. Theriot, “Comparison of quantitative methods for cell-shape analysis,” J. Microsc. 227(2), 140–156 (2007).
[CrossRef]

J. Angulo and S. Matou, “Application of mathematical morphology to the quantification of in vitro endothelial cell organization into tubular-like structures,” Cell Mol Biol (Noisy-le-grand) 53(2), 22–35 (2007).

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15(25), 17334–17342 (2007).
[CrossRef]

2005 (3)

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2242–2244 (2005).

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).

2003 (2)

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

2002 (1)

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

2001 (1)

1992 (1)

R. Mehtrotra, K. R. Namuduri, and N. Ranganathan, “Gabor filter-based edge detection,” Pattern Recognit. 25(12), 1479–1494 (1992).
[CrossRef]

1989 (1)

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).

1985 (1)

Aida, T.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Angulo, J.

J. Angulo and S. Matou, “Application of mathematical morphology to the quantification of in vitro endothelial cell organization into tubular-like structures,” Cell Mol Biol (Noisy-le-grand) 53(2), 22–35 (2007).

Backman, V.

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15(25), 17334–17342 (2007).
[CrossRef]

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Bigelow, C. E.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

Bigio, I. J.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Boustany, N. N.

Calkins, D. J.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

Carpenter, S.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Chen, K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Cipolloni, P. B.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Daugman, J. G.

Fang, H.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Fogel, I.

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).

Foster, T. H.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2242–2244 (2005).

Freedman, S. D.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Freyer, J. P.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Goldberg, M. J.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Guerra, A.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Hanlon, E. B.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Heifetz, A.

Itzkan, I.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Johnson, T. M.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Kim, Y. L.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Kimerer, L. M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Kong, S.-C.

Kromin, A. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Kuo, S. C.

Liu, Y.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Matou, S.

J. Angulo and S. Matou, “Application of mathematical morphology to the quantification of in vitro endothelial cell organization into tubular-like structures,” Cell Mol Biol (Noisy-le-grand) 53(2), 22–35 (2007).

Mehtrotra, R.

R. Mehtrotra, K. R. Namuduri, and N. Ranganathan, “Gabor filter-based edge detection,” Pattern Recognit. 25(12), 1479–1494 (1992).
[CrossRef]

Metaxas, D. N.

Mourant, J. R.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

Namuduri, K. R.

R. Mehtrotra, K. R. Namuduri, and N. Ranganathan, “Gabor filter-based edge detection,” Pattern Recognit. 25(12), 1479–1494 (1992).
[CrossRef]

Ollero, M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Pasternack, R. M.

Perelman, L. T.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Pincus, Z.

Z. Pincus and J. A. Theriot, “Comparison of quantitative methods for cell-shape analysis,” J. Microsc. 227(2), 140–156 (2007).
[CrossRef]

Qian, Z.

Ranganathan, N.

R. Mehtrotra, K. R. Namuduri, and N. Ranganathan, “Gabor filter-based edge detection,” Pattern Recognit. 25(12), 1479–1494 (1992).
[CrossRef]

Roy, H. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

Sagi, D.

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).

Simpson, J. J.

Taflove, A.

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15(25), 17334–17342 (2007).
[CrossRef]

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).

Thakor, N. V.

Theriot, J. A.

Z. Pincus and J. A. Theriot, “Comparison of quantitative methods for cell-shape analysis,” J. Microsc. 227(2), 140–156 (2007).
[CrossRef]

Vitkin, E.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Wali, R. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

White, E.

Wilson, J. D.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2242–2244 (2005).

Xu, L.

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).

Zaman, M. M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

Zheng, J.-Y.

Biol. Cybern. (1)

I. Fogel and D. Sagi, “Gabor filters as texture discriminator,” Biol. Cybern. 61(2), 103–113 (1989).

Biophys. J. (1)

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys. J. 88(4), 2929–2938 (2005).
[CrossRef]

Cell Mol Biol (Noisy-le-grand) (1)

J. Angulo and S. Matou, “Application of mathematical morphology to the quantification of in vitro endothelial cell organization into tubular-like structures,” Cell Mol Biol (Noisy-le-grand) 53(2), 22–35 (2007).

IEEE J. Sel. Top. Quantum Electron. (3)

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and its Alteration in Early Precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003).

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light scatter properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11(4), 759–765 (2005).

J. Biomed. Opt. (1)

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7(3), 378–387 (2002).
[CrossRef]

J. Microsc. (1)

Z. Pincus and J. A. Theriot, “Comparison of quantitative methods for cell-shape analysis,” J. Microsc. 227(2), 140–156 (2007).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Pattern Recognit. (1)

R. Mehtrotra, K. R. Namuduri, and N. Ranganathan, “Gabor filter-based edge detection,” Pattern Recognit. 25(12), 1479–1494 (1992).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of DMD implementation of Gabor filter. (a): Ideal Gabor Filter in k-space. (b): DMD approximation formed by overlay of binary concentric discs. (c): Overlapping profile views of (a) and (b).

Fig. 2.
Fig. 2.

Illustration of DMD implementation of Gabor filter bank and subsequent processing shown here for a phase mask data set. (a): Gabor-like filter bank applied to optical object transform in k-space. (b): Resultant stack of Gabor-like filtered images. (c): Representative fit of filter response as a function of Gabor filter frequency at one pixel of the image stack. Squares represent data points, the solid line represents the fit, and the dashed line represents the residual. (d): Morphometric-encoded image generated from fit for all pixels in the image. The colorscale indicates the Gaussian mean resulting from the pixel response fit and thus gives at each pixel the optimum Gabor filter frequency, 1/Smax, giving maximum response.

Fig. 3.
Fig. 3.

Representative phase mask images. (a) Bright field taken at 0.080µm/pixel, (b): Bright field taken at 0.205µm/pixel (c): Gabor-filtered image filtered at mask frequency, showing the edge of the condenser field stop and taken at 0.275µm/pixel. Optically filtered images were used for optical processing. Bright field images were used for digital post-processing (Section 3.2).

Fig. 4.
Fig. 4.

Optical and digital Gabor filtering of phase masks. (a): Top to bottom: Color-coded images encoding measured phase mask frequency pixel-by pixel from optical Gabor-like filtering at locations 1 mm, 3mm and 5mm from arbitrary starting point xo=0 on chirped phase mask. Darkened regions of each image are excluded from analysis (b): Measured chirp as a function of displacement along the chirped (black diamonds) and unchirped (gray squares) phase masks imaged at 0.275 µm/pixel using Gabor-like optical filtering. Data are mean+/- standard deviation of the pixel values included in the processed regions of interest (ROI) (e.g. highlighted regions within the color encoded images in panel (a). (c): Measured chirp as a function of displacement along the chirped phase mask imaged in bright field at 0.205 µm/pixel (black triangles) and 0.080 µm/pixel (gray squares) and digitally post-processed using Gabor digital filtering. Data are mean +/- standard deviation of the mask periods measured at the pixels included in the processed ROI’s within the bright field images The analyzed ROIs were pixel rows 80-446 and columns 65-446 for optical processing (highlighted areas in (a)), and pixel rows 75-448 and columns 75-448 for digital post-processing.

Fig. 5.
Fig. 5.

Optical processing of 0.465 µm (top row) and 0.494 µm (bottom row) polystyrene microspheres at low magnification (0.275 µm/pixel). (a): Representative dark field (DF) image of 0.465µm spheres in polyacrylamide gel. (b): Differential Interference Contrast (DIC) image. (c): Representative Gabor-filtered image. (d): Optically processed image encoding optimum Gabor period Smax giving maximal filter response. (e): Processed image encoding Smax gated to DF intensity image from Panel (a). (f)-(j): Same representation for 0.494 µm spheres in polyacrylamide gel as (a)-(e), respectively. For Panels (d)-(e) and (i)-(j), color hue encodes filter period Smax at which the filter response is maximized and intensity encodes relative fit amplitude.

Fig. 6.
Fig. 6.

Measurement of sphere size derived from optical Gabor-like processing. (a): Representative Gaussian fit to the filter response curve as a function of Gabor filter period at one pixel for (left to right) 0.465 µm, 0.494 µm, 0.548 µm, 0.771 µm, 0.989 µm and 1.053 µm sphere diameters. Fits are generated in the frequency domain before the abscissa is converted to Period. The fitted Gaussian mean gives the optimum period Smax that maximizes the filtered response. (b): Histogram showing the distribution of Gabor filter periods Smax at which local response for each sphere is maximized. Each sphere region is derived from the dark-field-gated responses (e.g. Fig. 5(e)). (c): Linear fit (with intercept fixed at zero) to plot of Smax as a function of sphere diameter. Data are the mean +/- standard deviation values found in Table 1. The coefficient of correlation between Smax and sphere diameter is 0.99.

Fig. 7.
Fig. 7.

Measurement of sphere size based on Smax values derived from digitally post-processed images. (a): Histogram derived from digital Gabor filter bank applied to dark field image. (b): Histogram derived from digital Gabor filter bank aligned to the axis of contrast applied to DIC image. (c): Histogram derived from digital Gabor filter bank misaligned with the axis of contrast applied to DIC image. (d) & (e): Sphere diameter measured using Gaussian second derivative template-matching algorithm for dark field and DIC images, respectively.

Tables (2)

Tables Icon

Table 1. Optical filtering response showing nanoscale sensitivity to spheres with diameter ~500 nm

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Table 2. Digital filtering response to spheres with diameter ~500 nm

Equations (3)

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H ( u , v ) =A1 e2π2σs2[(uUh)2+(vVh)2]
S=1Uh2+Vh2 , and φ =arctan (VhUh)
F=N txtyσ N ( tx , ty , 2 σ )

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