Abstract

Several recently developed particle-tracking and imaging methods have achieved three-dimensional sensitivity through the introduction of angled micromirrors into the observation volume of an optical microscope. We model the imaging response of such devices and show how the direct and reflected images of a fluorescent particle are affected. In particle-tracking applications, asymmetric image degradation manifests itself as systematic tracking errors. Based on our results, we identify strategies for reducing systematic errors to the 10nm level in practical applications.

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    [CrossRef] [PubMed]
  2. M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
    [CrossRef] [PubMed]
  3. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
    [CrossRef] [PubMed]
  4. J. Crocker and D. Grier, J. Colloid Interface Sci. 179, 298 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (5)

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
[CrossRef] [PubMed]

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, Opt. Express 17, 13071 (2009).
[CrossRef] [PubMed]

S. B. Oh and G. Barbastathis, Appl. Opt. 48, 5881 (2009).
[CrossRef] [PubMed]

2008 (3)

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

S. Choi and J.-K. Park, Appl. Phys. Lett. 93, 191909 (2008).
[CrossRef]

S. Pavani and R. Piestun, Opt. Express 16, 22048 (2008).
[CrossRef] [PubMed]

2007 (1)

S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007).
[CrossRef] [PubMed]

2006 (1)

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

2003 (3)

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

M. Speidel, A. Jonáš, and E.-L. Florin, Opt. Lett. 28, 69(2003).
[CrossRef] [PubMed]

1999 (2)

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

S. Lindek, J. Swoger, and E. Stelzer, J. Mod. Opt. 46, 843 (1999).

1996 (1)

J. Crocker and D. Grier, J. Colloid Interface Sci. 179, 298 (1996).
[CrossRef]

1995 (1)

1994 (1)

H. Kao and A. Verkman, Biophys. J. 67, 1291 (1994).
[CrossRef] [PubMed]

1991 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Amato-Grill, J.

Ashmore, J.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Bancaud, A.

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Barbastathis, G.

Baumberg, J.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Berglund, A. J.

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

Booker, G.

Bystricky, K.

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Carmichael, P.

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

Cheong, F. C.

Choi, S.

S. Choi and J.-K. Park, Appl. Phys. Lett. 93, 191909 (2008).
[CrossRef]

Cochello, J. A.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Cooper, J.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Crocker, J.

J. Crocker and D. Grier, J. Colloid Interface Sci. 179, 298 (1996).
[CrossRef]

Curtis, E.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Dahan, M.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Dixon, L.

Dreyfus, R.

Dufresne, E. R.

S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007).
[CrossRef] [PubMed]

Eriksson, S.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Florin, E.-L.

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

Germain, V.

S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007).
[CrossRef] [PubMed]

Ges, I. A.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Gibson, S.

Gollasch, C.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Goodman, Y. E.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

Grier, D.

J. Crocker and D. Grier, J. Colloid Interface Sci. 179, 298 (1996).
[CrossRef]

Grier, D. G.

Ha, T.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

Hajjoul, H.

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Hinds, E.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Janetopoulos, C.

K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
[CrossRef] [PubMed]

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Jonáš, A.

Kao, H.

H. Kao and A. Verkman, Biophys. J. 67, 1291 (1994).
[CrossRef] [PubMed]

Karpova, T.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Kocanova, S.

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Kraft, M.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Laczik, Z.

Lanni, F.

Lassadi, I.

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Levi, S.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Liddle, J. A.

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

Lindek, S.

S. Lindek, J. Swoger, and E. Stelzer, J. Mod. Opt. 46, 843 (1999).

Luccardini, C.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Markov, D. A.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

McClelland, J. J.

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

McMahon, M. D.

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

McNally, J. G.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Moktadir, Z.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Oh, S. B.

Park, J.-K.

S. Choi and J.-K. Park, Appl. Phys. Lett. 93, 191909 (2008).
[CrossRef]

Pavani, S.

Piestun, R.

Prakash, G.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Ramirez-Martinez, F.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Reiserer, R. S.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Riveau, B.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Rostaing, P.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Sainis, S. K.

S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007).
[CrossRef] [PubMed]

Seale, K.

K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
[CrossRef] [PubMed]

Seale, K. T.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Selvin, P. R.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

Speidel, M.

Stelzer, E.

S. Lindek, J. Swoger, and E. Stelzer, J. Mod. Opt. 46, 843 (1999).

Sun, B.

Swoger, J.

S. Lindek, J. Swoger, and E. Stelzer, J. Mod. Opt. 46, 843 (1999).

Török, P.

Triller, A.

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

Trupke, M.

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Varga, P.

Verkman, A.

H. Kao and A. Verkman, Biophys. J. 67, 1291 (1994).
[CrossRef] [PubMed]

Wikswo, J.

K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
[CrossRef] [PubMed]

Wikswo, J. P.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Wright, C.

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

Xiao, K.

Yildiz, A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

ACS Nano (2)

M. D. McMahon, A. J. Berglund, P. Carmichael, J. J. McClelland, and J. A. Liddle, ACS Nano 3, 609 (2009).
[CrossRef] [PubMed]

K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. Choi and J.-K. Park, Appl. Phys. Lett. 93, 191909 (2008).
[CrossRef]

M. Trupke, F. Ramirez-Martinez, E. Curtis, J. Ashmore, S. Eriksson, E. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. Prakash, and J. Baumberg, Appl. Phys. Lett. 88, 071116(2006).
[CrossRef]

Biophys. J. (1)

H. Kao and A. Verkman, Biophys. J. 67, 1291 (1994).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (1)

J. Crocker and D. Grier, J. Colloid Interface Sci. 179, 298 (1996).
[CrossRef]

J. Microsc. (1)

K. T. Seale, R. S. Reiserer, D. A. Markov, I. A. Ges, C. Wright, C. Janetopoulos, and J. P. Wikswo, J. Microsc. 232, 1 (2008).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

S. Lindek, J. Swoger, and E. Stelzer, J. Mod. Opt. 46, 843 (1999).

J. Opt. Soc. Am. A (2)

Lab Chip (1)

H. Hajjoul, S. Kocanova, I. Lassadi, K. Bystricky, and A. Bancaud, Lab Chip 9, 3054 (2009).
[CrossRef] [PubMed]

Methods (1)

J. G. McNally, T. Karpova, J. Cooper, and J. A. Cochello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. K. Sainis, V. Germain, and E. R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007).
[CrossRef] [PubMed]

Proc. R. Soc. London (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Science (2)

M. Dahan, S. Levi, C. Luccardini, P. Rostaing, B. Riveau, and A. Triller, Science 302, 442 (2003).
[CrossRef] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goodman, and P. R. Selvin, Science 300, 2061 (2003).
[CrossRef] [PubMed]

Other (1)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (3)

Fig. 1
Fig. 1

Geometry of the model. The ray along direction u ^ reflects off the micromirror at t r and eventually reaches the BFP. No ray leaving along u ^ reaches the BFP, because the reflection point t r lies outside the finite extent of the mirror ( t r · z ^ > z 1 ).

Fig. 2
Fig. 2

Observed and calculated images of a particle in a PMW. (a) Measured image of a 190 nm diameter fluorescent microparticle in a PMW ( θ = 35 ° , imaged with NA 0.95 / 40 × air objective), showing the direct image and four reflected images. (b) x z cross section of the geometry used for calculations (c),(d). The collected light cone is asymmetrically truncated by the mirror on the left and by the NA on the right. The particle and mirror positions are estimated from analysis of a, while unknown experimental parameters such as the position of the focal plane (dashed line) are chosen by hand. (c) Calculated images as described in the text, modified to account for truncation by the four triangular PMW faces. (d) Perfect images, which would arise if microscope aberrations were present but there were no truncation of rays by the mirror. Other parameters: specimen index n s = 1.47 (a 4:1 glycerine–water mixture), cover glass ( n g = 1.5 ), 2 π / k = 550 nm . To represent a spherical aberration correction collar on the objective, the calculations use an index-matched immersion medium n i = 1.5 . The contrast is enhanced equally in (a), (c), and (d) to aid in viewing the weaker reflections. Scale bar, 5 μm .

Fig. 3
Fig. 3

Contour plots showing the regions where absolute tracking errors are below 10 nm (lighter region, yellow online) and below 250 nm (darker region, red online) for various scenarios. For each plot, the NA, mirror angle θ, and mirror depth z 1 z 2 are shown at the top. The reflected image of a particle is calculated at each position, and the center of mass of the brightest 95% of the reflection is determined; the 3D position is reconstructed using this value as the reflected position, and the resulting tracking error is recorded. Scale bar, 5 μm . Insets, calculated reflection at the point indicated by the arrow (scale bar 1 μm ). Other parameters: n s = 1.33 , n g = 1.5 , n i = 1.5 , 2 π / k = 550 nm .

Equations (1)

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I r ( x , y ) = | S r d ξ d η A r e i k W p r ( ρ ) i ( k / f ) [ ( x M p r · x ^ ) ξ + ( y M p r · y ^ ) η ] | 2 ,

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