Abstract

We present an angular-scattering optical method that is capable of measuring the mean size of scatterers in static ensembles within a field of view less than 20 μm in diameter. Using interferometry, the method overcomes the inability of intensity-based models to tolerate the large speckle grains associated with such small illumination areas. By first estimating each scatterer’s location, the method can model between-scatterer interference as well as traditional single-particle Mie scattering. Direct angular-domain measurements provide finer angular resolution than digitally transformed image-plane recordings. This increases sensitivity to size-dependent scattering features, enabling more robust size estimates. The sensitivity of these angular-scattering measurements to various sizes of polystyrene beads is demonstrated. Interferometry also allows recovery of the full complex scattered field, including a size-dependent phase profile in the angular-scattering pattern.

© 2013 Optical Society of America

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2013

2012

2010

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

2009

2008

W. Choi, C.-C. Yu, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 33, 1596 (2008).
[CrossRef]

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

2007

2005

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, Opt. Lett. 30, 3305 (2005).
[CrossRef]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

2003

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

1998

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

1985

G. Gouesbet, G. Grehan, and B. Maheu, J. Opt. 16, 83 (1985).
[CrossRef]

Alexandrov, S. A.

Alfano, R. R.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Alimova, A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Andersson, C.

Badizadegan, K.

Bansil, R.

Berger, A. J.

Bhaduri, B.

Bigelow, C. E.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

Bigio, I.

Boppart, M.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Boppart, S. A.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Boustany, N. N.

Calkins, D. J.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

Chalut, K. J.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Chen, S.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Choi, W.

Cipolloni, P. B.

Dasari, R.

Dasari, R. R.

Ding, H.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Eick, A. A.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

Fang, H.

Fang-Yen, C.

Feld, M. S.

Finan, J. D.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Foster, T. H.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

Freedman, S. D.

Freyer, J. P.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Giacomelli, M. G.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Gillette, M. U.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, C. Dainty, ed. (Springer-Verlag, 1984).

Gouesbet, G.

G. Gouesbet, G. Grehan, and B. Maheu, J. Opt. 16, 83 (1985).
[CrossRef]

Grehan, G.

G. Gouesbet, G. Grehan, and B. Maheu, J. Opt. 16, 83 (1985).
[CrossRef]

Guilak, F.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Hanlon, E. B.

Hielscher, A. H.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

Hillman, T. R.

Itzkan, I.

Johnson, T. M.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

Katz, A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Keates, S. E.

Kimerer, L. M.

Leong, K. W.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Liu, J.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Maheu, B.

G. Gouesbet, G. Grehan, and B. Maheu, J. Opt. 16, 83 (1985).
[CrossRef]

McCormick, S. A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Millet, L. J.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Modell, M. D.

Mourant, J. R.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

Nguyen, F.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Park, Y.

Perelman, L. T.

Popescu, G.

B. Bhaduri, K. Tangella, and G. Popescu, Biomed. Opt. Express 4, 1434 (2013).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Qiu, L.

Rabin, B.

Rosen, R. B.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Rudolph, E.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Salahuddin, S.

Sampson, D. D.

Savage, H. E.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Shah, M. K.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Sierra, H.

Smith, Z. J.

Tangella, K.

Turner, B. S.

Vitkin, E.

Wang, Z.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

Wax, A.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

Wilson, J. D.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

Xu, M.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

Yaqoob, Z.

Yu, C.-C.

Zaman, M. M.

Zheng, J.-Y.

Appl. Opt.

Biomed. Opt. Express

Biophys. J.

K. J. Chalut, S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong, and A. Wax, Biophys. J. 94, 4948 (2008).
[CrossRef]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, Biophys. J. 88, 2929 (2005).
[CrossRef]

Cancer Cytopathol.

J. R. Mourant, A. H. Hielscher, A. A. Eick, T. M. Johnson, and J. P. Freyer, Cancer Cytopathol. 84, 366 (1998).

IEEE J. Sel. Top. Quantum Electron.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, IEEE J. Sel. Top. Quantum Electron. 9, 277 (2003).
[CrossRef]

J. Comput. Theor. Nanosci.

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, J. Comput. Theor. Nanosci. 7, 1 (2010).

J. Opt.

G. Gouesbet, G. Grehan, and B. Maheu, J. Opt. 16, 83 (1985).
[CrossRef]

Opt. Express

Opt. Lett.

Other

J. W. Goodman, in Laser Speckle and Related Phenomena, C. Dainty, ed. (Springer-Verlag, 1984).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

Noninterferometric scattering intensity from (a) a single squamous murine cancer cell and (b) eight 1 μm beads. In both figures, the smooth scattering distribution predicted by Mie theory is obscured by speckle. The speckle grain size agrees with the predicted value of about 2°.

Fig. 2.
Fig. 2.

Diagram of the angular-scattering interferometer. L, laser; CL, condenser lens; S, sample; MO, microscope objective; DC, DC block. Lens combinations L1-L2 and L3-L4 each form a 4-F relay system.

Fig. 3.
Fig. 3.

Representative sequence of calculating an angle-resolved scattergram of intensity. (a) Angular-domain scattering interferogram of a 1.00±.03μm polystyrene bead after reference beam subtraction. (b) Spatial Fourier transform of (a), corresponding to the distribution of the field in the object plane. The tilt of the reference beam has separated the heterodyned scattering signal (upper left) from other terms. (c) Filtered scattergram obtained by inverse Fourier transforming only the heterodyned signal.

Fig. 4.
Fig. 4.

(a) Fourier transform of interferogram from eight 1.00±.03μm diameter beads. Examples of well-isolated scatterers are circled in white. Examples of scatterers with overlapping scattering content are circled in magenta. (b) Corresponding microscope image of the eight beads. Overlaid dots represent the locations extracted from interferometric scattering data in (a). (c) Intensity scattergram after Hilbert filtering and coherent addition of scatterers. (d) Corresponding best fit of 1.006 μm using forward model including speckle.

Fig. 5.
Fig. 5.

(a) and (c) Angular-scattering phase profile extracted from polystyrene beads measuring 1.00±.03μm and 2.00±.02μm, respectively. (b) and (d) Theoretical phase profiles are shown for comparison. All profiles report absolute phase, with no free scale parameter.

Tables (1)

Tables Icon

Table 1. Results of Angular-Scattering Measurements of Polystyrene Beads Compared to the Manufacturer-Specified Size Distribution

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