Abstract

We have measured the overall transmittance of a laser beam through an oil immersion objective as a function of the transverse size of the laser beam, using the dual-objective method. Our results show that the objective transmittance is not uniform and that its dependence on the radial beam's position can be modeled by a Gaussian function. This property affects the intensity distribution pattern in the sample region and should be taken into account in theoretical descriptions of optical tweezers. Moreover, one must consider this position dependence to determine the local laser power delivered at the sample region by the dual-objective method, especially when the beam overfills the objective's back entrance. If the transmittance is assumed to be uniform, the local power is overestimated.

© 2006 Optical Society of America

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  1. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
    [CrossRef] [PubMed]
  2. K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  3. A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
    [CrossRef]
  4. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358-379 (1959).
    [CrossRef]
  5. C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
    [CrossRef]
  6. D. Ganic, X. Gan, and M. Gu, "Exact radiation trapping force calculation based on vectorial diffraction theory," Opt. Express 12, 2670-2675 (2004).
    [CrossRef] [PubMed]
  7. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).
  8. H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
    [CrossRef]
  9. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]
  10. N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
    [CrossRef]
  11. If the refractive index of sample chamber nS is smaller than the numerical aperture NA, then the rays at a distance p > ≥ Rc = nSRobj/NA from the axis are eliminated by total internal reflection. This is the case for water samples (nS = 1.33) with objectives of 1.4 NA. In this case we could substitute Rc for Robj throughout this section. However, the effect of this replacement is negligible because of the transmittance decay for large radial distances. For instance, Eq. (9) would yield, with Rc instead of Robj, an output power smaller by only 2%.

2004 (2)

2003 (1)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

2002 (1)

N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
[CrossRef]

1997 (1)

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1991 (1)

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

1987 (1)

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Block, S. M.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Gan, X.

Ganic, D.

Gu, M.

Kitamura, N.

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

Koshioka, M.

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

Masuhara, H.

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

Mazolli, A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Mesquita, O. N.

N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Misawa, H.

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

Neto, P. A. Maia

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Nussenzveig, H. M.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Rocha, M. S.

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Sasak, K.

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

Török, P.

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

Viana, N. B.

N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
[CrossRef]

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Appl. Phys. Lett. (1)

N. B. Viana, O. N. Mesquita, and A. Mazolli, "In situ measurement of laser power at the focus of a high numerical aperture objective using a microbolometer," Appl. Phys. Lett. 81, 1765-1767 (2002).
[CrossRef]

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

J. App. Phys. (1)

H. Misawa, M. Koshioka, K. Sasak, N. Kitamura, and H. Masuhara, "3-Dimensional optical trapping and laser ablation of a single polymer latex particle in water," J. App. Phys. 70, 3829-3836 (1991).
[CrossRef]

J. Microsc. (1)

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

Opt. Express (1)

Proc. R. Soc. London Ser. A (2)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. R. Soc. London Ser. A 459, 3021-3041 (2003).
[CrossRef]

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358-379 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Science (1)

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef] [PubMed]

Other (2)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Absolute calibration of optical tweezers," Appl. Phys. Lett. 88, 131110 (2006).

If the refractive index of sample chamber nS is smaller than the numerical aperture NA, then the rays at a distance p > ≥ Rc = nSRobj/NA from the axis are eliminated by total internal reflection. This is the case for water samples (nS = 1.33) with objectives of 1.4 NA. In this case we could substitute Rc for Robj throughout this section. However, the effect of this replacement is negligible because of the transmittance decay for large radial distances. For instance, Eq. (9) would yield, with Rc instead of Robj, an output power smaller by only 2%.

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Figures (8)

Fig. 1
Fig. 1

Schematic representation of the dual-objective method.

Fig. 2
Fig. 2

Power transmitted by diaphragm PE as a function of its radius R for the diode laser beam.

Fig. 3
Fig. 3

Same conventions as for Fig. 2, for the Nd:YAG laser beam.

Fig. 4
Fig. 4

Power emerging from the dual-objective system as a function of radius R of the diaphragm, for the diode laser beam. Dashed curve, best fit when a uniform objective transmittance is assumed; solid curve, best fit with a nonuniform transmittance.

Fig. 5
Fig. 5

Same conventions as for Fig. 4, for the Nd:YAG laser beam.

Fig. 6
Fig. 6

Relative discrepancy Δ as a function of σ for R obj = 3.5 mm and ξ = 2.2 mm.

Fig. 7
Fig. 7

Asymptotic value Δover for large σ (overfilling) as a function of ξ.

Fig. 8
Fig. 8

Stiffness of transverse trap (divided by the local power) as a function of bead radius, for the diode laser beam, calculated by the MDSA theory. Dotted curve, transmittance assumed to be uniform; solid curve; measured transmittance function used.

Tables (2)

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Table 1 Parameters that Characterize the Gaussian Transmittance Function Given by Eq. (5) for Two Wavelengths a

Tables Icon

Table 2 Index of Symbols

Equations (17)

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P E = 0 R P t σ 2 exp ( ρ 2 2 σ 2 ) ρ d ρ .
P E ( R ) = A ( R , σ ) P t ,
A ( R , σ ) = 1 exp ( R 2 2 σ 2 )
P out = T 2 A ( R , σ ) P t .
T ( ρ ) = T A exp ( ρ 2 2 ξ 2 )
P out = 0 R T ( ρ ) 2 P t σ 2 exp ( ρ 2 2 σ 2 ) ρ d ρ .
P out = T A     2 ξ 2 2 σ 2 + ξ 2 A ( R , σ ξ 2 σ 2 + ξ 2 ) P t ,
P out = T 2 A ( R obj , σ ) P t ,
T 2 = 1 σ 2 A ( R obj , σ ) 0 R obj T ( ρ ) 2 exp ( ρ 2 2 σ 2 ) ρ d ρ .
P L rms = T 2 A ( R obj , σ ) P t .
P L = T A ( R obj , σ ) P t ,
T = 1 σ 2 A ( R obj , σ ) 0 R obj T ( ρ ) exp ( ρ 2 2 σ 2 ) ρ d ρ .
Δ = P L rms P L P L = T 2 T 1.
1 σ eff 2 = 1 σ 2 + 1 ξ 2 .
Δ = σ 2 + ξ 2 ξ 2 σ 2 + ξ 2 { A ( R obj , σ ) A [ R obj , ( σ ξ / 2 σ 2 + ξ 2 ) ] } 1 / 2 A ( R obj , σ eff ) 1.
Δ over = R obj 2 ξ { 1 exp [ ( R obj 2 / ξ 2 ) ] } 1 / 2 1 exp [ ( R obj 2 / 2 ξ 2 ) ] 1 ,
Δ = ( σ σ eff ) 2 A ( R obj , σ ) A ( R obj , σ eff ) 1.

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