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Non-Parametric Analysis of Positional data of a Micro-Nano Sphere Trapped by Optical Tweezers

Mousavi Kolkasaraei, Mahdiyeh | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47660 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Reihani, Nader; Rahimi Tabar, Mohammad Reza
  7. Abstract:
  8. Optical tweezers consist of a tightly focused laser beam. A particle with refractive index greater than that of the surrounding medium can be trapped at the focus of the laser. The trapped object experiences a three-dimensional Hookean restoring force towards the focus. Nano (micron)-sized spheres can produce forces in the range of few pico-newton to few nano-newton. This range covers a large number of the forces, which contribute in biological processes; therefore, optical tweezers are very often used for micromanipulation of biological tissues. In a typical micromanipulation experiment it is crucial to perform proper positional calibration prior to use. There are several calibrate methods among which power spectrum method is known as the most reliable one. For the first time ever, in this thesis we apply a new method to analyze the positional data of a spherical particle trapped in optical tweezers. The equation of motion for the trapped object, results in a stochastic differential equation. This equation consists of deterministic and stochastic parts, which respectively represent the drift and the diffusion coefficients of the Langevin equation-describing particle’s dynamics. In our method drift and diffusion coefficients are obtained by calculation of the first and second coefficients of Kramers-Moyal expansion, respectively. In this thesis we have shown that the slope of the drift coefficient, which is equivalent to the trap stiffness, will increase linearly with the power of laser. In fact, this is one of the hallmarks of optical trap and agrees well with other calibration methods. Calculation of the second coefficient of K-M expansion revealed that the diffusion coefficient is a function of the particle’s position in trap. One explanation for this behavior could be that beside temperature there should be another randomness source
  9. Keywords:
  10. Optical Tweezer ; Brownian motion ; Stochastic Process ; Kramers-Moyal Coefficient ;

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