Abstract

A new optical device to measure forward scattered light in a range of 3° to 20° has been developed and tested. The scattered light is focused on a plane where its axial position is proportional to the scattered angle θ. A motorized iris diaphragm located at this plane selects the scattered light between 0° and a variable angle θ. This light is collected by an integrating sphere and converted into an electrical signal by an APD. The device was tested with suspensions of polystyrene microspheres of 3 different sizes. The obtained results are in good agreement with the Mie theory.

© 2007 Optical Society of America

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References

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  1. M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
    [CrossRef] [PubMed]
  2. S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).
  3. J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).
  4. I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
    [CrossRef]
  5. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
    [CrossRef]
  6. D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
    [CrossRef] [PubMed]
  7. D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
    [CrossRef]
  8. J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
    [CrossRef]
  9. A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).
  10. S. A. Prahl, "Optical PropertyMeasurements using the Inverse Adding-Doubling Program," (1999), Oregon Medical Laser Center.
  11. S. A. Prahl, "Mie Scattering Calculators," (2006) http://www.omlc.ogi.edu/calc/mie calc.html.
  12. D. Barnett, "Matlab Mie Functions," (1997) http://www.lboro.ac.uk/departments/el/research/photonics/matmie/mfiles.html.

2006 (1)

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

2005 (1)

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

2004 (2)

I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
[CrossRef]

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

2003 (1)

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

1998 (2)

J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
[CrossRef]

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

1995 (1)

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

1987 (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).

Alter, C. A.

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).

Amis, E. J.

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

Bargo, P. R.

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

Beers, K. L.

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

Chachisvilis, M.

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

Cope, M.

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

Cunningham, A.

I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
[CrossRef]

Diver, J.

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

Eick, A. A.

Essenpreis, M.

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

Freyer, J. P.

Guerra, R.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

Hagen, N.

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

Hammer, M.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

Hebden, J. C.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

Hielscher, A. H.

Jacques, S. L.

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).

Johnson, T. M.

Kohl, M.

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

Laufer, J.

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

MacCallum, I.

I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
[CrossRef]

Marchand, P.

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

McKee, D.

I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
[CrossRef]

Mourant, J. R.

Müller, G.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

Norman, A. I.

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

Passos, D.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

Pinto, P. N.

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

Prahl, S. A.

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).

Ramella-Roman, J. C.

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

Roggan, A.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

Schweitzer, D.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

Shen, D.

Simpso, R.

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

Watson, D.

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

Zhang, W.

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

Appl. Opt. (2)

J. Laufer, R. Simpso, M. Kohl, M. Essenpreis, and M. Cope, "Effect of temperature on the optical properties of ex vivo human dermis and subdermis," Appl. Opt. 43, 2479-2489 (1998).

J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
[CrossRef]

Biomed. Opt. (1)

D. Passos, J. C. Hebden, P. N. Pinto, and R. Guerra, "Tissue phantom for optical diagnostics based on a suspension of microspheres with a fractal size distribution," J. Biomed. Opt. 10, 1-11 (2005).
[CrossRef]

Biophys. J. (1)

D. Watson, N. Hagen, J. Diver, P. Marchand, and M. Chachisvilis, "Elastic Light Scattering from Single Cells: Orientational Dynamics in Optical Trap," Biophys. J. 87, 1298-1306 (2004).
[CrossRef] [PubMed]

Colloid Interface Sci. (1)

A. I. Norman,W. Zhang, K. L. Beers, and E. J. Amis, "Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions," J. Colloid Interface Sci. 2, 1-9 (2006).

IEEE J. Quantum Electron (1)

J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Evaluation of spherical particle sizes with an Asymmetric Illumination Microscope," IEEE J. Quantum Electron 9, 301-306 (2003).
[CrossRef]

Lasers Life Sci. (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe Laser Light Scattering by Human Dermis," Lasers Life Sci. 1, 309-334 (1987).

Opt. A, Pure Appl. Opt. (1)

I. MacCallum, A. Cunningham, and D. McKee, "The measurement and modelling of light scattering by phytoplankton cells at narrow forward angles," Opt. A, Pure Appl. Opt. 6, 698-702 (2004).
[CrossRef]

Phys. Med. Biol. (1)

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, "Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation," Phys. Med. Biol. 40, 963-978 (1995).
[CrossRef] [PubMed]

Other (3)

S. A. Prahl, "Optical PropertyMeasurements using the Inverse Adding-Doubling Program," (1999), Oregon Medical Laser Center.

S. A. Prahl, "Mie Scattering Calculators," (2006) http://www.omlc.ogi.edu/calc/mie calc.html.

D. Barnett, "Matlab Mie Functions," (1997) http://www.lboro.ac.uk/departments/el/research/photonics/matmie/mfiles.html.

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Figures (9)

Fig. 1.
Fig. 1.

Goniometric measurements: The sample is located at the origin of the coordinate system and dΩ represents the small solid angle defined by the detector.

Fig. 2.
Fig. 2.

Non goniometric measurements: The scattered light is collected and measured for a large solid angle defined by θ0 and θ max .

Fig. 3.
Fig. 3.

Experimental setup to measure small angle scattering. Light scattered at an angle θ1 is blocked by the iris, whereas light scattered at θ2 is collected (θ1 > θ2).

Fig. 4.
Fig. 4.

Proposed setup: The scattered light is measured for a small solid angle defined by θ i (ri )

Fig. 5.
Fig. 5.

Normalized intensity versus angle of light scattered by polystyrene microspheres (d 1 = 1.03μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, d = 1.03μm and unpolarized light

Fig. 6.
Fig. 6.

Normalized intensity versus angle of light scattered by polystyrene microspheres (d 2 = 2.54μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, d = 2.54μm and unpolarized light

Fig. 7.
Fig. 7.

Normalized intensity versus angle of light scattered by polystyrene microspheres (d 3 = 5.66μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.5864, r = 5.66μm and unpolarized light

Fig. 8.
Fig. 8.

Reproducibility of the measurements with the proposed device. Normalized intensity from 10 measurements versus angle of light scattered by polystyrene micro-spheres ( d = 1.03 μm C = 5.9856 10 5 1 μl , d = 2.54 μm C = 1.1052 10 5 1 μl , d = 5.66 μm C = 2.4561 10 4 1 μl , , from top)

Fig. 9.
Fig. 9.

Results goniometer λ=532nm: Normalized intensity, dashed line with errorbars, versus angle of light scattered by polystyrene microspheres (d = 2.54μm) compared with Mie simulation (continuous line). Parameters for Mie: n = 1.594, d = 2.54μm and parallel polarized light

Tables (1)

Tables Icon

Table 1. Measuring ranges of the scattering angle θ and φ of described systems (1-defined by fiber; 2-defined by detector area; 3-defined by rotating aperture; 4-defined by NA of objective)

Equations (4)

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I∝ θ 0 θ max φ = 0 φ = 360° L ( θ , φ ) dA cos θ d θ d φ
I * ( θ i ( r i ) ) = C θ 0 θ i ( r i ) φ = 0 φ = 360° [ L ( θ , φ ) dA cos θ + D ( θ ) ] d θ d φ
I ( θ i ) = d dS i I * ( θ i ( r i ) )
c = 4 πd 2 5 lQ s

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