Developing a video tracking method to study interactions between close pairs of optically trapped particles in three dimensions

Allan Raudsepp; Marjorie Griffiths; Andrew J. Sutherland-Smith; Martin A. K. Williams

doi:10.1364/AO.54.009518

Applied Optics
Vol. 54,
Issue 32,
pp. 9518-9527
(2015)
•https://doi.org/10.1364/AO.54.009518

Developing a video tracking method to study interactions between close pairs of optically trapped particles in three dimensions

Allan Raudsepp, Marjorie Griffiths, Andrew J. Sutherland-Smith, and Martin A. K. Williams

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Allan Raudsepp, Marjorie Griffiths, Andrew J. Sutherland-Smith, and Martin A. K. Williams, "Developing a video tracking method to study interactions between close pairs of optically trapped particles in three dimensions," Appl. Opt. 54, 9518-9527 (2015)

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Table of Contents Category
- Optical Tweezers or Optical Manipulation
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: May 21, 2015
- Revised Manuscript: September 28, 2015
- Manuscript Accepted: October 9, 2015
- Published: November 9, 2015
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 11, Iss. 1

Abstract

We develop a video tracking method that utilizes an interpolation-based normalized cross-correlation approach to track the position of microscopic spherical particles in three dimensions. Subnanometer resolution is demonstrated. The method does not assume that the particle’s image is radially symmetric, making it useful for determining the position when particles are close and their images overlap. This is demonstrated in a study of the electrostatic and hydrodynamic interactions between a pair of beads in dual laser tweezers traps.

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	Mean [nm]	Min. [nm]	Max. [nm]	Std. Dev. [nm]
$〈 I 〉 = 20 kcounts$
$σ_{x}$ (measured)	0.67	0.53	0.84	0.071
$σ_{z}$ (measured)	1.2	0.69	1.8	0.29
$σ_{x}$ (simulated)	0.33	0.17	0.69	0.14
$σ_{x}^{'}$ (simulated)	0.67	0.60	0.89	0.076
$σ_{z}$ (simulated)	1.1	0.67	1.6	0.29
$〈 I 〉 = 10 kcounts$
$σ_{x}$ (measured)	0.72	0.58	1.1	0.14
$σ_{z}$ (measured)	1.8	1.1	2.7	0.46
$σ_{x}$ (simulated)	0.51	0.28	1.1	0.19
$σ_{x}^{'}$ (simulated)	0.78	0.64	1.2	0.14
$σ_{z}$ (simulated)	1.6	0.98	2.4	0.43

power $[W]$	$k_{x A}$ $[\frac{pN}{μm}]$	$k_{y A}$ $[\frac{pN}{μm}]$	$k_{z A}$ $[\frac{pN}{μm}]$	$k_{x B}$ $[\frac{pN}{μm}]$	$k_{y B}$ $[\frac{pN}{μm}]$	$k_{z B}$ $[\frac{pN}{μm}]$
1.0	5.8	6.0	1.5	5.3	6.0	1.8
0.7	4.1	4.2	1.2	3.8	4.3	1.3
0.5	2.9	3.0	0.80	2.4	2.8	0.80

	Mean [nm]	Min. [nm]	Max. [nm]	Std. Dev. [nm]
$〈 I 〉 = 20 kcounts$
$σ_{x}$ (measured)	0.67	0.53	0.84	0.071
$σ_{z}$ (measured)	1.2	0.69	1.8	0.29
$σ_{x}$ (simulated)	0.33	0.17	0.69	0.14
$σ_{x}^{'}$ (simulated)	0.67	0.60	0.89	0.076
$σ_{z}$ (simulated)	1.1	0.67	1.6	0.29
$〈 I 〉 = 10 kcounts$
$σ_{x}$ (measured)	0.72	0.58	1.1	0.14
$σ_{z}$ (measured)	1.8	1.1	2.7	0.46
$σ_{x}$ (simulated)	0.51	0.28	1.1	0.19
$σ_{x}^{'}$ (simulated)	0.78	0.64	1.2	0.14
$σ_{z}$ (simulated)	1.6	0.98	2.4	0.43

power $[W]$	$k_{x A}$ $[\frac{pN}{μm}]$	$k_{y A}$ $[\frac{pN}{μm}]$	$k_{z A}$ $[\frac{pN}{μm}]$	$k_{x B}$ $[\frac{pN}{μm}]$	$k_{y B}$ $[\frac{pN}{μm}]$	$k_{z B}$ $[\frac{pN}{μm}]$
1.0	5.8	6.0	1.5	5.3	6.0	1.8
0.7	4.1	4.2	1.2	3.8	4.3	1.3
0.5	2.9	3.0	0.80	2.4	2.8	0.80

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Equations (23)

Applied Optics