Abstract

We use digital holographic microscopy and Mie scattering theory to simultaneously characterize and track individual colloidal particles. Each holographic snapshot provides enough information to measure a colloidal sphere’s radius and refractive index to within 1%, and simultaneously to measure its three-dimensional position with nanometer in-plane precision and 10 nanometer axial resolution.

© 2007 Optical Society of America

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  29. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  32. Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt. 45, 3425-3429 (2005).
    [CrossRef]
  33. C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002).
    [CrossRef] [PubMed]
  34. F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998).
    [CrossRef]
  35. M. A. Brown and E. J. Staples, "Measurement of absolute particle-surface separation using total internal reflection microscopy and radiation pressure forces," Langmuir 6, 1260-1265 (1990).
    [CrossRef]
  36. D. C. Prieve and N. A. Frej, "Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces," Langmuir 6, 396-403 (1990).
    [CrossRef]
  37. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12, 5475-5480 (2004).
    [CrossRef] [PubMed]
  38. Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
    [CrossRef] [PubMed]
  39. A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
    [CrossRef]

2007 (2)

2006 (5)

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of the mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

J. Sheng, E. Malkiel, and J. Katz, "Digital holographic microscope for measuring three-dimensional particle distributions and motions," Appl. Opt. 45, 3893-3901 (2006).
[CrossRef] [PubMed]

J. A. Guerrero-Viramontes, D. Moreno-Hernandez, F. Mendoza-Santoyo, and M. Funes-Gallanzi, "3D particle positioning from CCD images using the generalized Lorenz-Mie and Huygens-Fresnel theories," Meas. Sci. Technol. 17, 2328-2334 (2006).
[CrossRef]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

2005 (5)

T. Savin and P. S. Doyle, "Role of finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 041,106 (2005).
[CrossRef]

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt. 45, 3425-3429 (2005).
[CrossRef]

Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, "Spatially resolved Fourier holographic light scattering angular spectroscopy," Opt. Lett. 30, 3305-3307 (2005).
[CrossRef]

2004 (4)

H. Du, "Mie-scattering calculation," Appl. Opt. 43, 1951-1956 (2004).
[CrossRef] [PubMed]

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12, 5475-5480 (2004).
[CrossRef] [PubMed]

S. Soontaranon, J. Widjaja, and T. Asakura, "Improved holographic particle sizing by using absolute values of the wavelet transform," Opt. Commun. 240, 253-260 (2004).
[CrossRef]

S. Eiden-Assmann, J. Widoniak, and G. Maret, "Synthesis and characterization of porous and nonporous mondisperse colloidal TiO2 particles," Chem. Mater. 16, 6-11 (2004).
[CrossRef]

2003 (4)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

M. Speidel, A. Jonáš, and E.-L. Florin, "Three-dimensional tracking of fluorescent nanoparticles with subnaometer precision by use of off-focus imaging," Opt. Lett. 28, 69-71 (2003).
[CrossRef] [PubMed]

Y. Pu and H. Meng, "Intrinsic aberrations due to Mie scattering in particle holography," J. Opt. Soc. Am. A 20, 1920-1932 (2003).
[CrossRef]

2002 (1)

C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

1998 (1)

F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998).
[CrossRef]

1996 (1)

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

1991 (2)

1990 (2)

M. A. Brown and E. J. Staples, "Measurement of absolute particle-surface separation using total internal reflection microscopy and radiation pressure forces," Langmuir 6, 1260-1265 (1990).
[CrossRef]

D. C. Prieve and N. A. Frej, "Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces," Langmuir 6, 396-403 (1990).
[CrossRef]

1980 (1)

1978 (1)

P. E. Gill and W. Muray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. (Soc. Ind. Appl. Math.) Numer. Anal. 15, 977-992 (1978).
[CrossRef]

1974 (1)

B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E: Sci. Instru. 7, 781-788 (1974).
[CrossRef]

Alexandrov, S. A.

Allano, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Allen, T. M.

Asakura, T.

S. Soontaranon, J. Widjaja, and T. Asakura, "Improved holographic particle sizing by using absolute values of the wavelet transform," Opt. Commun. 240, 253-260 (2004).
[CrossRef]

Badizadegan, K.

Battersby, B. J.

A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Brown, M. A.

M. A. Brown and E. J. Staples, "Measurement of absolute particle-surface separation using total internal reflection microscopy and radiation pressure forces," Langmuir 6, 1260-1265 (1990).
[CrossRef]

Cen, K. F.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Cooper, J.

Courtial, J.

Crocker, J. C.

J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

Croquette, V.

C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002).
[CrossRef] [PubMed]

Dasari, R. R.

Davis, E. J.

Denis, L.

Doyle, P. S.

T. Savin and P. S. Doyle, "Role of finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 041,106 (2005).
[CrossRef]

Du, H.

Ducottet, C.

Eiden-Assmann, S.

S. Eiden-Assmann, J. Widoniak, and G. Maret, "Synthesis and characterization of porous and nonporous mondisperse colloidal TiO2 particles," Chem. Mater. 16, 6-11 (2004).
[CrossRef]

Feld, M. S.

Florin, E. L.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Florin, E.-L.

Fournel, T.

Fournier, C.

Frej, N. A.

D. C. Prieve and N. A. Frej, "Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces," Langmuir 6, 396-403 (1990).
[CrossRef]

Funes-Gallanzi, M.

J. A. Guerrero-Viramontes, D. Moreno-Hernandez, F. Mendoza-Santoyo, and M. Funes-Gallanzi, "3D particle positioning from CCD images using the generalized Lorenz-Mie and Huygens-Fresnel theories," Meas. Sci. Technol. 17, 2328-2334 (2006).
[CrossRef]

D. Moreno, F. M. Santoyo, J. A. Guerrero, and M. Funes-Gallanzi, "Particle positioning from charge-coupled device images by the generalized Lorenz-Mie theory and comparison with experiment," Appl. Opt. 39, 5117-5124 (2000).
[CrossRef]

Gardel, E.

Gill, P. E.

P. E. Gill and W. Muray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. (Soc. Ind. Appl. Math.) Numer. Anal. 15, 977-992 (1978).
[CrossRef]

Gittes, F.

F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998).
[CrossRef]

Gosse, C.

C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002).
[CrossRef] [PubMed]

Grier, D. G.

Guerrero, J. A.

Guerrero-Viramontes, J. A.

J. A. Guerrero-Viramontes, D. Moreno-Hernandez, F. Mendoza-Santoyo, and M. Funes-Gallanzi, "3D particle positioning from CCD images using the generalized Lorenz-Mie and Huygens-Fresnel theories," Meas. Sci. Technol. 17, 2328-2334 (2006).
[CrossRef]

Heckenberg, N. R.

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Hillman, T. R.

Horber, J. K. H.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Jeulin, D.

Johnston, A. P. R.

A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

Jonáš, A.

Jordan, P.

Katz, J.

Kitamura, N.

Knöner, G.

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Koshio, M.

Laczik, Z. J.

Lambert, L. K.

A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

Lawrie, G. A.

A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

Lebrun, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Lee, S.-H.

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Malek, M.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Malkiel, E.

Maret, G.

S. Eiden-Assmann, J. Widoniak, and G. Maret, "Synthesis and characterization of porous and nonporous mondisperse colloidal TiO2 particles," Chem. Mater. 16, 6-11 (2004).
[CrossRef]

Masuhara, H.

Mendoza-Santoyo, F.

J. A. Guerrero-Viramontes, D. Moreno-Hernandez, F. Mendoza-Santoyo, and M. Funes-Gallanzi, "3D particle positioning from CCD images using the generalized Lorenz-Mie and Huygens-Fresnel theories," Meas. Sci. Technol. 17, 2328-2334 (2006).
[CrossRef]

Meng, H.

Misawa, H.

Moreno, D.

Moreno-Hernandez, D.

J. A. Guerrero-Viramontes, D. Moreno-Hernandez, F. Mendoza-Santoyo, and M. Funes-Gallanzi, "3D particle positioning from CCD images using the generalized Lorenz-Mie and Huygens-Fresnel theories," Meas. Sci. Technol. 17, 2328-2334 (2006).
[CrossRef]

Muray, W.

P. E. Gill and W. Muray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. (Soc. Ind. Appl. Math.) Numer. Anal. 15, 977-992 (1978).
[CrossRef]

Nieminen, T. A.

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Padgett, M.

Park, Y.-K.

Parkin, S.

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Patte-Rouland, B.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

Popescu, G.

Pralle, A.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Prieve, D. C.

D. C. Prieve and N. A. Frej, "Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces," Langmuir 6, 396-403 (1990).
[CrossRef]

Prummer, M.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Pu, S. L.

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[CrossRef]

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G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

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Santoyo, F. M.

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T. Savin and P. S. Doyle, "Role of finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 041,106 (2005).
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F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998).
[CrossRef]

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Sinclair, G.

Soontaranon, S.

S. Soontaranon, J. Widjaja, and T. Asakura, "Improved holographic particle sizing by using absolute values of the wavelet transform," Opt. Commun. 240, 253-260 (2004).
[CrossRef]

Souyri, A.

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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S. Eiden-Assmann, J. Widoniak, and G. Maret, "Synthesis and characterization of porous and nonporous mondisperse colloidal TiO2 particles," Chem. Mater. 16, 6-11 (2004).
[CrossRef]

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X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

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X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
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Appl. Opt. (7)

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C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002).
[CrossRef] [PubMed]

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A. P. R. Johnston, B. J. Battersby, G. A. Lawrie, L. K. Lambert, and M. Trau, "A mechanism for forming large fluorescent organo-silica particles: Potential supports for combinatorial synthesis," Chem. Mater. 18, 6163-6169 (2006).
[CrossRef]

S. Eiden-Assmann, J. Widoniak, and G. Maret, "Synthesis and characterization of porous and nonporous mondisperse colloidal TiO2 particles," Chem. Mater. 16, 6-11 (2004).
[CrossRef]

Exp. Fluids (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, "Particle field characterization by digital in-line holography: 3D location and sizing," Exp. Fluids 39, 1-9 (2005).
[CrossRef]

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J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996).
[CrossRef]

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

J. Phys. E: Sci. Instru. (1)

B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E: Sci. Instru. 7, 781-788 (1974).
[CrossRef]

Langmuir (2)

M. A. Brown and E. J. Staples, "Measurement of absolute particle-surface separation using total internal reflection microscopy and radiation pressure forces," Langmuir 6, 1260-1265 (1990).
[CrossRef]

D. C. Prieve and N. A. Frej, "Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces," Langmuir 6, 396-403 (1990).
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F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998).
[CrossRef]

Microsc. Res. Tech. (1)

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
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[CrossRef]

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[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Med. Biol. (1)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and H. Xin-Hua, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Phys. Rev. E (1)

T. Savin and P. S. Doyle, "Role of finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 041,106 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the index of refraction of single microparticles," Phys. Rev. Lett. 97, 157402 (2006).
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Supplementary Material (1)

» Media 1: MPG (7650 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Principle of holographic microscopy. A colloidal particle scatters a portion Es (r) of an initially collimated laser beam E 0(r). The scattered beam, here represented by 5 calculated iso-amplitude surfaces, interferes with the unscattered portion of the beam in the focal plane of a microscope objective, thereby forming an in-line hologram, I(ρ).

Fig. 2.
Fig. 2.

Fitting to normalized holograms. (a) Normalized hologram B(ρ), numerical fit to Eq. (3), and azimuthally averaged radial profile B(ρ) for a 1.43 µm diameter polystyrene sphere in water at zp =22.7 µm. All scale bars indicate 10 µm. Curves in the radial profile are obtained from experimental data, discrete points were obtained from the fit. (b) Data for a 1.45 µm diameter TiO2 sphere dispersed in immersion oil (nm =1.515) at zp =7.0 µm (c) Data for a 4.5 µm diameter SiO2 sphere in water at zp =38.8 µm.

Fig. 3.
Fig. 3.

Holographic tracking of a sedimenting colloidal silica sphere. (a) and (c) DHM images of the sphere at the beginning and end of its trajectory, respectively. The scale bar indicates 5 µm. (b) and (d) Fits to Eq. (3). (e) Three-dimensional trajectory with starting point (circle) and end point (square) labeled. (f) z(t), showing thermal fluctuations about uniform sedimentation. Inset: The fit refractive index is independent of position. (g) Mean-square positional fluctuations display Einstein-Smoluchowsky scaling in x, y and z. [Media 1]

Equations (3)

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I ( ρ ) = E s ( r ) + E 0 ( r ) 2 z = 0 ,
B ( ρ ) I ( ρ ) u 0 ( ρ ) 2 = 1 + 2 { E s ( r ) · E 0 * ( r ) } u 0 ( ρ ) 2 + E s ( r ) 2 u 0 ( ρ ) 2 ,
B ( ρ ) 1 + 2 α { f s ( r r p ) · ε ̂ e i k z p } + α 2 f s ( r r p ) 2 .

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