Abstract

The use of camera imaging enables trap calibration for multiple particles simultaneously. For stiff traps, however, blur from image integration time affects the detected particle positions significantly. In this paper we use power spectral analysis to calibrate stiff optical traps, taking the effects of blur, aliasing and position detection error into account, as put forward by Wong and Halvorsen [Opt. Express 14, 12517 (2006)]. We find agreement with simultaneously obtained photodiode data and the expected relation of corner frequency fc with laser power, up to fc = 3.6 kHz for a Nyquist frequency of 1.25 kHz. Spectral analysis enables easy identification of the contribution of noise. We demonstrate the utility of our approach with simultaneous calibration of multiple holographic optical traps.

© 2010 OSA

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References

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  1. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [CrossRef]
  2. W. P. Wong and K. Halvorsen, “The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur,” Opt. Express 14(25), 12517–12531 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-12517 .
    [CrossRef] [PubMed]
  3. A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20987 .
    [CrossRef] [PubMed]
  4. A. van der Horst, B. P. B. Downing, and N. R. Forde, “Position and intensity modulations in holographic optical traps created by a Liquid Crystal Spatial Light Modulator,” in Optical Trapping Applications, Vol. 1 of 2009 OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMB3. http://www.opticsinfobase.org/oe/abstract.cfm?URI=OTA-2009-OMB3
  5. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
    [CrossRef]
  6. O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
    [CrossRef] [PubMed]
  7. E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
    [CrossRef]
  8. E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
    [CrossRef] [PubMed]
  9. H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
    [CrossRef] [PubMed]
  10. A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
    [CrossRef]

2010

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

2008

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20987 .
[CrossRef] [PubMed]

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

2006

2005

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

2004

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef]

2003

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[CrossRef] [PubMed]

Arias-Gonzalez, J. R.

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

Blab, G. A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef]

Bustamante, C.

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

Downing, B. P. B.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

Farré, A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

Forde, N. R.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20987 .
[CrossRef] [PubMed]

Gittes, F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[CrossRef] [PubMed]

Gutsche, C.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

Halvorsen, K.

Kapitein, L. C.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

Keyser, U. F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

Kremer, F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

Mao, H.

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef]

Otto, O.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

Peterman, E. J. G.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[CrossRef] [PubMed]

Schmidt, C. F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[CrossRef] [PubMed]

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

Smith, S. B.

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

Tinoco, I.

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

van der Horst, A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20987 .
[CrossRef] [PubMed]

van Dijk, M. A.

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

Wong, W. P.

Biophys. J.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[CrossRef] [PubMed]

H. Mao, J. R. Arias-Gonzalez, S. B. Smith, I. Tinoco, and C. Bustamante, “Temperature control methods in a laser tweezers system,” Biophys. J. 89(2), 1308–1316 (2005).
[CrossRef] [PubMed]

J. Biophoton.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224-233 (2010).
[CrossRef]

Opt. Express

Rev. Sci. Instrum.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[CrossRef]

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79(2), 023710 (2008).
[CrossRef] [PubMed]

E. J. G. Peterman, M. A. van Dijk, L. C. Kapitein, and C. F. Schmidt, “Extending the bandwidth of optical-tweezers interferometry,” Rev. Sci. Instrum. 74(7), 3246–3249 (2003).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[CrossRef]

Other

A. van der Horst, B. P. B. Downing, and N. R. Forde, “Position and intensity modulations in holographic optical traps created by a Liquid Crystal Spatial Light Modulator,” in Optical Trapping Applications, Vol. 1 of 2009 OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMB3. http://www.opticsinfobase.org/oe/abstract.cfm?URI=OTA-2009-OMB3

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Figures (5)

Fig. 1
Fig. 1

Theoretical power spectra with fNyq = 1250Hz and W = 0.4ms for fc = 0.2 × fNyq (a), 0.8 × fNyq (b) and 2 × fNyq (c), showing the effects of aliasing and blur. Plotted: pure Lorentzian (Eq. (1); black solid), aliased Lorentzian (black dashed), blurred (Eq. (2); solid red) and blurred aliased spectrum (Eq. (3); dash-dotted red). In blue, the blurred aliased spectra are plotted for the same fNyq and fc , but for W = 0.1ms.

Fig. 2
Fig. 2

(a) Simplified schematic of the setup. (b) Camera power spectrum (average over 15 spectra; fNyq = 1250Hz) for a stuck particle. The median noise power from 400 to 600Hz is taken as the noise level: 7.2 × 10−4 nm2/Hz in x (shown) and 14.5 × 10−4 nm2/Hz in y (not shown).

Fig. 3
Fig. 3

(a and b) Measured power spectra in x with fits (red lines) for three laser powers for (a) PSD (fit: Eq. (5)) and (b) camera (Eq. (4)). In the power spectra shown in (b), before removal of noise, mechanical noise peaks can be seen. In (c) a camera spectrum in y for 105 mW is shown, fit with Eq. (5) (blue line; fc = 583 Hz) and with Eq. (4) (red; fc = 774 Hz).

Fig. 4
Fig. 4

(a) Fit results for fc as a function of laser power in x (solid symbols) and y (open), for camera and PSD. Also shown are the results for pure Lorentzian fits to the camera data (Eq. (1)). (b) Expanded view of the low laser power region. Lines are linear fits forced through zero to camera results up to 53 mW (x: solid; y: dashed).

Fig. 5
Fig. 5

(a) Power spectrum of camera y positions for a 2.10-μm-diameter particle in a HOT trap (711 mW). Deleted noise peak at 300 Hz is due to SLM pixel addressing [4]. Inset: camera image. Scale bar is 3 μm. (b) fc in x and y as a function of laser power for both 2.10 μm and 3.17 μm particles. Lines are linear fits forced through zero (x: solid; y: dashed).

Equations (5)

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S x x ( f ) = k B T 2 γ   ​ π 2 ( f c 2 + f 2 ) ,
S b l u r ( f ) = S x x ( f ) ×   ​ ( sin ( W π f ) W π f ) 2 .
S a l i a s ( f )     = n = S ( f + 2 n f N y q ) .
S m e a s ( f )     = n = S b l u r ( f + 2 n f N y q ) +     ε 2 2 f N y q .
S P S D ( f )     =     β ×     k B T γ   ​ π 2 ( f c 2 + f 2 ) ,

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