## Characterizing and tracking single colloidal particles with video holographic microscopy

Optics Express, Vol. 15, Issue 26, pp. 18275-18282 (2007)

http://dx.doi.org/10.1364/OE.15.018275

Acrobat PDF (392 KB)

### 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

## 1. Introduction

*in situ*.

1. 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]

2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express **15**, 1505–1512 (2007) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-4-1505. [CrossRef] [PubMed]

4. P.W. Barber and S. C. Hill, *Light Scattering by Particles: Computational Methods* (World Scientific, New Jersey, 1990). [CrossRef]

5. A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. **30**, 3974–3983 (1991). [CrossRef] [PubMed]

6. 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]

7. 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]

9. K. Sasaki, M. Koshio, H. Misawa, N. Kitamura, and H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett. **16**, 1463–1465 (1991). [CrossRef] [PubMed]

10. D. G. Grier, “A revolution in optical manipulation,” Nature **424**, 810–816 (2003). [CrossRef] [PubMed]

## 2. Video holographic microscopy

*µ*m) replacing the conventional incandescent illuminator and condenser. As indicated schematically in Fig. 1, light scattered by a particle propagates to the microscope’s focal plane, where it interferes with the undiffracted portion of the beam. The resulting interference pattern is magnified [1

1. 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]

*µ*m

^{2}field of view. Images are recorded as uncompressed digital video at 30 frames per second using a commercial digital video recorder (Pioneer 520HS).

*r*, its radius,

_{p}*a*, and its index of refraction,

*n*. We assume that the incident field,

_{p}*E*

_{0}(

*r*)=

*u*

_{0}(

*ρ*) exp(

*ikz*)

*̂*, is uniformly polarized in the

*̂*direction and varies slowly enough over the size of the particle to be treated as a plane wave propagating along the

*ẑ*direction. Its amplitude

*u*

_{0}(

*ρ*) at position

*ρ*=(

*x,y*) in the plane

*z*=

*z*of the particle is thus the same as its amplitude in the focal plane,

_{p}*z*=0. The wave propagates along the

*ẑ*direction with wave number

*k*=2

*πn*, where

_{m}/λ*λ*is the light’s wavelength in vacuum and

*n*is the refractive index of the medium. For pure water at 25°C,

_{m}*n*=1.3326 at λ=0.632

_{m}*µ*m.

## 3. Fitting to Lorenz-Mie theory

*r*scatters a portion of the incident field into a highly structured outgoing wave,

_{p}*E*(

_{s}*r*)=

*α*exp(-

*ikz*)

_{p}*u*(

_{o}*r*)

_{p}*f*(

_{s}*r-r*), where

_{p}*α*≈1 accounts for variations in the illumination, and where

*f*(

_{s}*r*) is the Lorenz-Mie scattering function [3, 4

4. P.W. Barber and S. C. Hill, *Light Scattering by Particles: Computational Methods* (World Scientific, New Jersey, 1990). [CrossRef]

*a, n*,

_{p}*n*and λ. The scattered field generally covers a large enough area at the focal plane that the interference pattern,

_{m}*u*

_{0}(

*ρ*)|

^{2}. The resulting distortions have been characterized [12

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

*I*(

*ρ*) [5

5. A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. **30**, 3974–3983 (1991). [CrossRef] [PubMed]

6. 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]

7. 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]

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

13. Y.-K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. **32**, 811–813 (2007). [CrossRef] [PubMed]

*u*

_{0}(

*ρ*)|

^{2}can be measured in an empty field of view, and the in-line hologram can be normalized to obtain the undistorted image

23. P. E. Gill and W. Muray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. **15**, 977–992 (1978). [CrossRef]

*χ*

^{2}deviates for all of the fits we report are of order unity, so that the calculated uncertainties in the fit parameters accurately reflect their precision [21, 23

23. P. E. Gill and W. Muray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. **15**, 977–992 (1978). [CrossRef]

24. J. E. Dennis and R. B. Schnabel, *Numerical Methods for Unconstrained Optimization and Nonlinear Equations* (SIAM, Philadelphia, 1996). [CrossRef]

1. 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]

2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express **15**, 1505–1512 (2007) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-4-1505. [CrossRef] [PubMed]

13. Y.-K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. **32**, 811–813 (2007). [CrossRef] [PubMed]

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

26. 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,” Microscopy Research and Technique **44**, 378–386 (1999). [CrossRef] [PubMed]

27. 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]

## 4. Tracking and characterizing colloidal spheres

*B*(

*ρ*), for a polystyrene sulfate sphere dispersed in water at height

*z*=22.7 µm above the focal plane. This sphere was obtained from a commercial sample with a nominal diameter of 2

_{p}*a*=1.48±0.03 µm (Bangs Labs, Lot PS04N/6064). The camera’s electronic shutter was set for an exposure time of 0.25 msec to minimize blurring due to Brownian motion [28

28. 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]

*B*(

*ρ*) faithfully reproduces not just the position of the interference fringes, but also their magnitudes. The quality of the fit may be judged from the azimuthal average; the solid curve is an angular average about the center of

*B*(

*ρ*), the dashed curves indicate the standard deviations of the average, and the discrete points are obtained from the fit.

*a*=0.73±0.01

*µ*m, falls in the sample’s specified range, which reflected a lower bound of 0.69±0.07

*µ*m obtained with a Beckman Z2 Coulter Counter and an upper bound of 0.76±0.08

*µ*m obtained by analytical centrifugation. Agreement between the quoted and measured particle size suggests that the present measurement’s accuracy is comparable to its precision. In that case, both precision and accuracy surpass results previously obtained [6

6. 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]

*I*(

*ρ*). The trajectory-averaged value for the refractive index,

*n*=1.55±0.03, also is consistent with the properties of polystyrene colloid inferred from light scattering measurements on bulk dispersions [29

_{p}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]

30. 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]

*n*≈1.3

_{p}*n*are difficult to trap. Holographic characterization, by contrast, requires only a single holographic snapshot rather than an extensive time series, does not require optical trapping, and so does not require separate calibration of the trap, and is effective over a wider range of particle sizes and refractive indexes.

_{m}*µ*m diameter TiO

_{2}sphere at

*z*=7

_{p}*µ*m above the focal plane. This sample was synthesized from titanium tetraethoxide and was heat-treated to increase its density [31

31. S. Eiden-Assmann, J. Widoniak, and G. Maret, “Synthesis and characterization of porous and nonporous mondisperse colloidal TiO_{2} particles,” Chem. Mater. **16**, 6–11 (2004). [CrossRef]

*n*=1.515) eliminates these artifacts, but introduces spherical aberration for the lens we used, which must be corrected [32

_{m}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]

*µ*m and refractive index of 2.01±0.05 are consistent with results obtained by electron microscopy and bulk light scattering, respectively. This result is noteworthy because no other single-particle characterization method works for such high refractive indexes.

*µ*m silica sphere (Bangs Labs, Lot SS05N/4364) dispersed in water at

*z*=38.8 µm above the focal plane. The fit refractive index,

_{p}*n*=1.434±0.001, is appropriate for porous silica and the diameter,

_{p}*a*=4.51±0.01µmagrees with the 4.82±0.59 µm value obtained for this sample with a Beckman Z2 Coulter Counter.

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

**45**, 3893–3901 (2006). [CrossRef] [PubMed]

2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express **15**, 1505–1512 (2007) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-4-1505. [CrossRef] [PubMed]

25. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. **179**, 298–310 (1996). [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]

*µ*m, which contrasts with the ±3

*µ*m useful depth of focus using conventional illumination [33

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

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]

*µ*m above the focal plane with an optical tweezer, and then released and allowed to sediment. The images in Fig. 3(a) and (c) show the particle near the beginning of its trajectory and near the end. Fits to Eq. (3) are shown in Figs. 3(b) and (d).

*z*(

*t*), Fig. 3(f), displays fluctuations about a uniform sedimentation speed,

*v*=1.021±0.005

*µ*m/s. This provides an estimate for the particle’s density through

*ρ*=

_{p}*ρ*+9

_{m}*ηv*/(2

*a*

^{2}

*g*), where

*ρ*=0.997

_{m}*g*/cm

^{3}is the density of water and

*η*=0.0105 P is its viscosity at

*T*=21°C, and where

*g*=9.8m/s

^{2}is the acceleration due to gravity. The fit value for the particle’s radius, at

*a*=0.729±0.012µm, remained constant as the particle settled. This value is consistent with the manufacturer’s specified radius of 0.76±0.04 µm, measured with a Beckman Z2 Coulter Counter. Accordingly, we obtain ρ

*p*=1.92±0.02 g/cm

^{3}, which is a few percent smaller than the manufacturer’s rating for the sample. However, the fit value for the refractive index,

*n*=1.430±0.007, also is 1.5% below the rated value, suggesting that the particle is indeed less dense than specified.

_{p}*r*2

_{j}(

*τ*)=〈(

*r*(

_{j}*t*+

*τ*)-

*r*(

_{j}*t*))

^{2}〉, of the components of the particle’s position provide additional consistency checks. As the data in Fig. 3(g) show, fluctuations in the trajectory’s individual Cartesian components agree with each other, and all three display linear Einstein-Smoluchowsky scaling, Δ

*r*

^{2}

_{j}(

*τ*)=2

*Dτ*, with a diffusion coefficient

*D*=0.33±0.03

*µ*m

^{2}/s. This is consistent with the anticipated Stokes-Einstein value,

*D*

_{0}=

*k*/(6

_{B}T*πηa*)=0.30±0.02

*µ*m

^{2}/s, where

*k*is Boltzmann’s constant. Using the methods of Ref. [28

_{B}28. 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]

*r*

^{2}

_{j}(

*t*) to be consistent with no worse than 1 nm accuracy for in-plane positions and 10 nm for axial positions throughout the trajectory. The optical characterization of the particle’s properties thus is consistent with the particle’s measured dynamics.

## 5. Conclusions

*µ*m. Unlike model-based analytical methods, fitting to the exact Lorenz-Mie scattering theory is robust and reliable over a far wider range of particle sizes, provided that care is taken to maintain numerical stability in calculating

*f*(

_{s}*r*) [3, 19

19. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. **19**, 1505–1509 (1980). [CrossRef] [PubMed]

20. H. Du, “Mie-scattering calculation,” Appl. Opt. **43**, 1951–1956 (2004). [CrossRef] [PubMed]

*m*=0.1 to over 10, and with large imaginary refractive indexes. In all cases, the instrumental magnification and field of view must be selected to fit the sample.

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) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5475. [CrossRef] [PubMed]

38. Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express **13**, 5434–5439 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-14-5434. [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]

## Acknowledgments

## References and links

1. | J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. |

2. | S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express |

3. | C. F. Bohren and D. R. Huffman, |

4. | P.W. Barber and S. C. Hill, |

5. | A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. |

6. | L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, “Direct extraction of the mean particle size from a digital hologram,” Appl. Opt. |

7. | 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. |

8. | R. Xu, |

9. | K. Sasaki, M. Koshio, H. Misawa, N. Kitamura, and H. Masuhara, “Pattern formation and flow control of fine particles by laser-scanning micromanipulation,” Opt. Lett. |

10. | D. G. Grier, “A revolution in optical manipulation,” Nature |

11. | M. I. Mishchenko, L. D. Travis, and A. A. Lais, |

12. | Y. Pu and H. Meng, “Intrinsic aberrations due to Mie scattering in particle holography,” J. Opt. Soc. Am. A |

13. | Y.-K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. |

14. | B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E: Sci. Instru. |

15. | S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. |

16. | 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 |

17. | J. A. Guerrero-Viramontes, D. Moreno-Hernández, 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. |

18. | S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. |

19. | W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. |

20. | H. Du, “Mie-scattering calculation,” Appl. Opt. |

21. | J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “User Guide for MINPACK-1,” Tech. Rep. ANL-80-74, Argonne National Laboratory, Argonne, IL (1980). |

22. | J. J. Moré, “The Levenberg-Marquardt Algorithm: Implementation and Theory,” in |

23. | P. E. Gill and W. Muray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal. |

24. | J. E. Dennis and R. B. Schnabel, |

25. | J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. |

26. | 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,” Microscopy Research and Technique |

27. | 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. | T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E |

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. |

30. | 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. |

31. | S. Eiden-Assmann, J. Widoniak, and G. Maret, “Synthesis and characterization of porous and nonporous mondisperse colloidal TiO |

32. | Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, “Performance of optical traps with geometric aberrations,” Appl. Opt. |

33. | C. Gosse and V. Croquette, “Magnetic tweezers: Micromanipulation and force measurement at the molecular level,” Biophys. J. |

34. | F. Gittes and C. F. Schmidt, “Signals and noise in micromechanical measurements,” Methods in Cell Biology |

35. | M. A. Brown and E. J. Staples, “Measurement of absolute particle-surface separation using total internal reflection microscopy and radiation pressure forces,” Langmuir |

36. | D. C. Prieve and N. A. Frej, “Total internal reflection microscopy: A quantitative tool for the measurement of colloidal forces,” Langmuir |

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 |

38. | Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express |

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. |

**OCIS Codes**

(090.1760) Holography : Computer holography

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(180.6900) Microscopy : Three-dimensional microscopy

**ToC Category:**

Microscopy

**History**

Original Manuscript: October 12, 2007

Revised Manuscript: December 9, 2007

Manuscript Accepted: December 17, 2007

Published: December 20, 2007

**Virtual Issues**

Vol. 3, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Sang-Hyuk Lee, Yohai Roichman, Gi-Ra Yi, Shin-Hyun Kim, Seung-Man Yang, Alfons van Blaaderen, Peter van Oostrum, and David G. Grier, "Characterizing and tracking single colloidal particles with video holographic microscopy," Opt. Express **15**, 18275-18282 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18275

Sort: Year | Journal | Reset

### References

- 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]
- S.-H. Lee and D. G. Grier, "Holographic microscopy of holographically trapped three-dimensional structures," Opt. Express 15, 1505-1512 (2007). [CrossRef] [PubMed]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).
- P.W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, New Jersey, 1990). [CrossRef]
- A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microspheres," Appl. Opt. 30, 3974-3983 (1991). [CrossRef] [PubMed]
- 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]
- 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]
- R. Xu, Particle Characterization: Light Scattering Methods (Springer, New York, 2002).
- K. Sasaki, M. Koshio, H. Misawa, N. Kitamura, and H. Masuhara, "Pattern formation and flow control of fine particles by laser-scanning micromanipulation," Opt. Lett. 16, 1463-1465 (1991). [CrossRef] [PubMed]
- D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003). [CrossRef] [PubMed]
- M. I. Mishchenko, L. D. Travis, and A. A. Lais, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, New York, 2002).
- Y. Pu and H. Meng, "Intrinsic aberrations due to Mie scattering in particle holography," J. Opt. Soc. Am. A 20, 1920-1932 (2003). [CrossRef]
- Y.-K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Fresnel particle tracing in three dimensions using diffraction phase microscopy," Opt. Lett. 32, 811-813 (2007). [CrossRef] [PubMed]
- B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E: Sci. Instru. 7, 781-788 (1974). [CrossRef]
- 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. 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]
- 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]
- 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]
- W. J. Wiscombe, "Improved Mie scattering algorithms," Appl. Opt. 19, 1505-1509 (1980). [CrossRef] [PubMed]
- H. Du, "Mie-scattering calculation," Appl. Opt. 43, 1951-1956 (2004). [CrossRef] [PubMed]
- J. J. More, B. S. Garbow, and K. E. Hillstrom, "User Guide for MINPACK-1," Tech. Rep. ANL-80-74, Argonne National Laboratory, Argonne, IL (1980).
- J. J. More, "The Levenberg-Marquardt Algorithm: Implementation and Theory," in Numerical Analysis, G. A. Watson, ed., (Springer-Verlag, Berlin, 1977).
- 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]
- J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (SIAM, Philadelphia, 1996). [CrossRef]
- J. C. Crocker and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298-310 (1996). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Gosse and V. Croquette, "Magnetic tweezers: Micromanipulation and force measurement at the molecular level," Biophys. J. 82, 3314-3329 (2002). [CrossRef] [PubMed]
- F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," Methods in Cell Biology 55, 129-156 (1998). [CrossRef]
- 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]
- 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]
- Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005). [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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.