Abstract

Goniometry and optical scatter imaging have been used for optical determination of particle size based upon optical scattering. Polystyrene microspheres in suspension serve as a standard for system validation purposes. The design and calibration of a digital Fourier holographic microscope (DFHM) are reported. Of crucial importance is the appropriate scaling of scattering angle space in the conjugate Fourier plane. A detailed description of this calibration process is described. Spatial filtering of the acquired digital hologram to use photons scattered within a restricted angular range produces an image. A pair of images, one using photons narrowly scattered within 8 − 15° (LNA), and one using photons broadly scattered within 8 − 39° (HNA), are produced. An image based on the ratio of these two images, OSIR = HNA/LNA, following Boustany et al. (2002), yields a 2D Optical Scatter Image (OSI) whose contrast is based on the angular dependence of photon scattering and is sensitive to the microsphere size, especially in the 0.5−1.0µm range. Goniometric results are also given for polystyrene microspheres in suspension as additional proof of principle for particle sizing via the DFHM.

© 2016 Optical Society of America

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References

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  1. L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
    [Crossref] [PubMed]
  2. J. Lichtman and J. Conchello, “Fluorescence microscopy,” Nat. Meth. 2, 910–919 (2005).
    [Crossref]
  3. B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
    [Crossref] [PubMed]
  4. B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
    [Crossref]
  5. H. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  6. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).
  7. N. Boustany, S. Kuo, and N. Thakor, “Optical scatter imaging: subcellular morphometry in situ with fourier filtering,” Opt. Lett. 26, 1063–1065 (2001).
    [Crossref]
  8. N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
    [Crossref]
  9. N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
    [Crossref] [PubMed]
  10. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005).
  11. P. Picart and J. Li, Digital Holography (John Wiley and Sons, Inc., 2012).
  12. M. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications, in Springer Series in Optical Sciences (Springer, 2011).
    [Crossref]
  13. S. Alexandrov, T. Hillman, and D. Sampson, “Spatially resolved fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
    [Crossref]
  14. S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
    [Crossref]
  15. T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
    [Crossref]
  16. K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
    [Crossref]
  17. P. Prasad, Introduction to Biophotonics (John Wiley and Sons, Inc., 2003).
    [Crossref]
  18. V. Rossi, “Digital fourier holographic microscopy and potential applications towards the design of photodynamic therapy of osteosarcoma,” Ph.D. Dissertation, Oregon State University, Department of Physics, 301 Weniger Hall, Corvallis, OR 97331 (2015).
  19. S. Prahl and OMLC, “Mie scattering calculator,” (2012).
  20. D. Nolte, “Bioanalysis: advanced materials, methods, and devices,” Optical Interferrometry for Biology and Medicine (Springer, 2012).
    [Crossref]
  21. J. Mertz, Introduction to Optical Microscopy (Roberts and Company, 2010).
  22. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  23. D. Voelz, “Computational Fourier Optics: a Matlab Tutorial,” Tutorial Texts in Optical Engineering (SPIE Press, 2011).
  24. R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2007).

2009 (1)

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[Crossref]

2006 (2)

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

2005 (3)

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

S. Alexandrov, T. Hillman, and D. Sampson, “Spatially resolved fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[Crossref]

J. Lichtman and J. Conchello, “Fluorescence microscopy,” Nat. Meth. 2, 910–919 (2005).
[Crossref]

2004 (1)

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

2002 (1)

N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
[Crossref]

2001 (2)

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

N. Boustany, S. Kuo, and N. Thakor, “Optical scatter imaging: subcellular morphometry in situ with fourier filtering,” Opt. Lett. 26, 1063–1065 (2001).
[Crossref]

Adams, S.

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

Alexandrov, S.

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

S. Alexandrov, T. Hillman, and D. Sampson, “Spatially resolved fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[Crossref]

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

Bartko, A.

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

Bates, M.

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[Crossref]

Blazkiewicz, P.

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

Boustany, N.

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
[Crossref]

N. Boustany, S. Kuo, and N. Thakor, “Optical scatter imaging: subcellular morphometry in situ with fourier filtering,” Opt. Lett. 26, 1063–1065 (2001).
[Crossref]

Conchello, J.

J. Lichtman and J. Conchello, “Fluorescence microscopy,” Nat. Meth. 2, 910–919 (2005).
[Crossref]

Dickson, R.

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

Drezek, R.

N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
[Crossref]

Ellisman, M.

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

Giepmans, B.

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

Gonzalez, R.

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2007).

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005).

Gutzler, T.

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Hillman, T.

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

S. Alexandrov, T. Hillman, and D. Sampson, “Spatially resolved fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[Crossref]

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

Huang, B.

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[Crossref]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

Joiner, W.

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

Kim, M.

M. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications, in Springer Series in Optical Sciences (Springer, 2011).
[Crossref]

Kuo, S.

Li, J.

P. Picart and J. Li, Digital Holography (John Wiley and Sons, Inc., 2012).

Lichtman, J.

J. Lichtman and J. Conchello, “Fluorescence microscopy,” Nat. Meth. 2, 910–919 (2005).
[Crossref]

Meredith, P.

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

Mertz, J.

J. Mertz, Introduction to Optical Microscopy (Roberts and Company, 2010).

Nolte, D.

D. Nolte, “Bioanalysis: advanced materials, methods, and devices,” Optical Interferrometry for Biology and Medicine (Springer, 2012).
[Crossref]

Oyler, G.

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

Peyser, L.

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

Pfister, B.

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

Picart, P.

P. Picart and J. Li, Digital Holography (John Wiley and Sons, Inc., 2012).

Prahl, S.

S. Prahl and OMLC, “Mie scattering calculator,” (2012).

Prasad, P.

P. Prasad, Introduction to Biophotonics (John Wiley and Sons, Inc., 2003).
[Crossref]

Rossi, V.

V. Rossi, “Digital fourier holographic microscopy and potential applications towards the design of photodynamic therapy of osteosarcoma,” Ph.D. Dissertation, Oregon State University, Department of Physics, 301 Weniger Hall, Corvallis, OR 97331 (2015).

Same, M.

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

Sampson, D.

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

S. Alexandrov, T. Hillman, and D. Sampson, “Spatially resolved fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[Crossref]

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

Seet, K.

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

Thakor, N.

N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
[Crossref]

N. Boustany, S. Kuo, and N. Thakor, “Optical scatter imaging: subcellular morphometry in situ with fourier filtering,” Opt. Lett. 26, 1063–1065 (2001).
[Crossref]

Tsai, Y.

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

Tsien, R.

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

van de Hulst, H.

H. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Vinson, A.

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

Voelz, D.

D. Voelz, “Computational Fourier Optics: a Matlab Tutorial,” Tutorial Texts in Optical Engineering (SPIE Press, 2011).

Woods, R.

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2007).

Zhuang, X.

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[Crossref]

Zvyagin, A.

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

Annu. Rev. Biochem. (1)

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[Crossref]

Biophys. J. (2)

N. Boustany, R. Drezek, and N. Thakor, “Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging,” Biophys. J. 83, 1697–1700 (2002).
[Crossref]

N. Boustany, Y. Tsai, B. Pfister, W. Joiner, and G. Oyler, “BCL − xL – dependent light scattering by apoptotic cells,” Biophys. J. 87, 4163–4171 (2004).
[Crossref] [PubMed]

J. Phys. D: Appl. Phys. (1)

K. Seet, P. Blazkiewicz, P. Meredith, and A. Zvyagin, “Optical scatter imaging using digital fourier microscopy,” J. Phys. D: Appl. Phys. 38, 3590–3598 (2005).
[Crossref]

Nat. Meth. (1)

J. Lichtman and J. Conchello, “Fluorescence microscopy,” Nat. Meth. 2, 910–919 (2005).
[Crossref]

Opt. Exp. (1)

T. Hillman, S. Alexandrov, T. Gutzler, and D. Sampson, “Microscopic particle discrimination using spatially-resolved fourier-holographic light scattering angular spectroscopy,” Opt. Exp. 14, 11088–11102 (2006).
[Crossref]

Opt. Lett. (2)

Science (2)

L. Peyser, A. Vinson, A. Bartko, and R. Dickson, “Photoactivated fluorescence from individual silver nanoclusters,” Science 291, 103–106 (2001).
[Crossref] [PubMed]

B. Giepmans, S. Adams, M. Ellisman, and R. Tsien, “The fluorescent toolbox for assessing protein location and function,” Science 312, 217–224 (2006).
[Crossref] [PubMed]

Other (14)

H. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005).

P. Picart and J. Li, Digital Holography (John Wiley and Sons, Inc., 2012).

M. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications, in Springer Series in Optical Sciences (Springer, 2011).
[Crossref]

S. Alexandrov, T. Hillman, T. Gutzler, M. Same, and D. Sampson, “Particle sizing with spatially-resolved fourier-holographic light scattering angular spectroscopy,” in Multimodal Biomedical Imaging, F. Azar and D. Metaxas, eds. (SPIE, 2006).
[Crossref]

P. Prasad, Introduction to Biophotonics (John Wiley and Sons, Inc., 2003).
[Crossref]

V. Rossi, “Digital fourier holographic microscopy and potential applications towards the design of photodynamic therapy of osteosarcoma,” Ph.D. Dissertation, Oregon State University, Department of Physics, 301 Weniger Hall, Corvallis, OR 97331 (2015).

S. Prahl and OMLC, “Mie scattering calculator,” (2012).

D. Nolte, “Bioanalysis: advanced materials, methods, and devices,” Optical Interferrometry for Biology and Medicine (Springer, 2012).
[Crossref]

J. Mertz, Introduction to Optical Microscopy (Roberts and Company, 2010).

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

D. Voelz, “Computational Fourier Optics: a Matlab Tutorial,” Tutorial Texts in Optical Engineering (SPIE Press, 2011).

R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2007).

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Figures (7)

Fig. 1
Fig. 1 A schematic of the Digital Fourier Holographic Microscope with elements: telescoping system (T), cube beam splitters (BS), variable neutral density filters (ND), electronic shutters (SH), microscope objective (O), lenses (L1, L2, L3), and mirrors (M). Planes of importance are also indicated: sample plane (S), Fourier plane (F) and conjugate Fourier plane (F′). Cameras CCD1 and CCD2 are used to capture the optical Fourier transform and image of the sample, respectively. The incident beam is indicated by a dashed (green) outline. Light scattered by the sample is indicated by a solid (red) outline. Light unscattered (or directly transmitted) by the sample, as well as the reference beam are indicated by a continuation of the dashed (green) outline.
Fig. 2
Fig. 2 A diagram of the media-glass-immersion oil geometry and its refraction effects. While diffraction occurs initially through the mounting media, θm is used in place of the more generic θmed variable to indicate discrete angles of constructive interference due to the diffraction grating. The diffracted rays are then tracked through the glass coverslip (θg) and and immersion oil (θoil) via Snell’s Law prior to collection by the objective lens.
Fig. 3
Fig. 3 Scattered light is projected to the conjugate Fourier plane, such that the scattering angle, θ, is projected along what would be the radial direction of the CCD in polar coordinates.
Fig. 4
Fig. 4 Goniometric results for polystyrene microspheres embedded in Aqua-Poly/Mount. The solid (black) line represents the scattering function predicted via Mie theory. The (green) circles represent experimental data upon normalization in order to account for intensity variations based upon the random number of particles in the field of view for a given measurement.
Fig. 5
Fig. 5 The holographic reconstruction process is depicted visually. A smoothing window is used prior to every Fourier and inverse Fourier transform in order to eliminate high frequency noise as a result of what would otherwise be hard edges within the images. Note the separation of the twin images from the central DC component upon taking the first inverse Fourier transform. In isolating a single twin image for analysis, the cropped field of view is again passed through a smoothing window in order to eliminate any remnant of the DC signal (red arrows). Also note that the final Fourier transform depicted is missing the bright, central max that was initially present. This is because the spatial heterodyne filtering used to isolate the twin images thereby removed the central DC signal.
Fig. 6
Fig. 6 a) and b) The LNA and HNA masks used for spatial filtering, respectively. c) and d) The corresponding LNA and HNA images that result from the inverse Fourier transform after spatial filtering with a) and b) respectively. e) An image of the reconstructed hologram of 2.90µm polystyrene microspheres. f) The corresponding Optical Scatter Image.
Fig. 7
Fig. 7 Polystyrene microspheres from 0.36 to 2.90µm in diameter were suspended in the manufacturer’s mounting media and imaged with the DFHM. The collected scattering function is then spatially filtered and analyzed via optical scatter imaging using angles θblock = 8°, θmin = 15° and θmax = 39°. The expected OSIR was determined for each particle size based upon an application of Mie theory to a simulated model of the DFHM OSIR system, as indicated by (blue) circles and solid curve with error bars. The average and standard deviation of the mean for the OSIR were determined from ten simulated trials. Experimental results using the DFHM for OSI are displayed as (red) diamonds.

Equations (23)

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

I H = I f + I r + 2 f r c o s ϕ ,
ϕ = ϕ r ϕ f .
( k x , k y ) = 2 f ( k x , k y ) r ( k x , k y ) cos ϕ ( k x , k y ) ,
I f ( I H I r ) 2 2 ( I H + I r ) ,
( k x , k y ) I H I r ( I H I r ) 2 2 ( I H + I r ) .
θ o i l = sin 1 ( n m e d n o i l sin θ m e d ) ,
θ m = sin 1 ( m λ d n m e d ) ,
P ( θ ) = 0 2 π F ( θ , φ ) θ d φ ,
E ( x , y , z = 0 ) = 1 [ ( k k , k y , z = 0 ) ] ,
E ( ρ , z ) = i k 2 π E ( ρ o , 0 ) e i k R R cos θ d 2 ρ o ,
H ( ρ , z ) = i k 2 π e i k R R cos θ .
R z [ 1 + ( ρ ρ o ) 2 2 z 2 ] z + ( ρ ρ o ) 2 2 z .
E ( x , y , z ) = i k 2 π z e i k z e i k ( x 2 + y 2 ) 2 z × [ E ( ξ , η , 0 ) e i k ( ξ 2 + η 2 ) 2 z ] e i k z ( x ξ + y η ) d ξ d η .
H ( x , y , z ) = i k 2 π z e i k z e i k ( x 2 + y 2 ) 2 z .
E ( x , y , z ) = [ H ( x , y , z ) E ( ξ , η , 0 ) ] .
[ H ( x , y , z ) E ( ξ , η , 0 ) ] = ( k , z ) ( k , 0 ) ,
( k , z ) = [ H ( x , y , z ) ]
( k , 0 ) = [ E ( ξ , η , 0 ) ] .
[ E ( x , y , z ) ] = ( k , z ) ( k , 0 ) ,
E ( x , y , z ) = 1 [ ( k , z ) ( k , 0 ) ] ,
( k , z ) = e i k z e i π λ z ( k x 2 + k y 2 ) .
E ( x , y , z ) = 1 [ e i k z e i π λ z ( k x 2 + k y 2 ) ( k , 0 ) ] .
O S I ( x , y , z ) = | E H N A ( x , y , z ) | 2 | E L N A ( x , y , z ) | 2 .

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