Difference between revisions of "Optical trap"

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==Summary of calibration methods==
 
==Summary of calibration methods==
  
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<table>
+
<table class="wikitable" align="center">
 +
<caption style="font-size:16pt">Effect of Systematic Errors on Measured Value of <math>\alpha</math></caption>
 
  <tr>
 
  <tr>
−
   <th scope="col">Method</th>
+
   <th scope="col" rowspan="2">Method</th>
−
   <th scope="col">Equation</th>
+
   <th scope="col" rowspan="2">Equation</th>
−
   <th scope="col">Equation</th>
+
   <th scope="col">QPD Responsivit</th>
−
   <th scope="col">Equation</th>
+
   <th scope="col">Stage Responsivity</th>
 +
  <th scope="col">Solvent Viscosity</th>
 +
  <th scope="col">Particle Diameter</th>
 +
  <th scope="col">Temperature</th>
 +
  <th scope="col" rowspan="2">Technical Noise</th>
 +
</tr>
 +
 
 +
<tr>
 +
  <th scope="col"><math>R_{QPD}</math></th>
 +
  <th scope="col"><math>R_{stage}</math></th>
 +
  <th scope="col"><math>\eta</math></th>
 +
  <th scope="col"><math>d</math></th>
 +
  <th scope="col"><math>T</math></th>
 
  </tr>
 
  </tr>
 +
 
  <tr>
 
  <tr>
 +
  <th scope="row">Equipartition</th>
 +
  <td><math>\frac{K_B T}{\langle R_{QPD} V_{qpd} \rangle ^ 2}</math></td>
 +
  <td>inverse square</td>
 +
  <td>none</td>
 +
  <td>none</td>
 +
  <td>none</td>
 +
  <td>linear and indirect (viscosity change)</td>
 +
  <td>systematic decrease</td>
 +
</tr>
  
 
  <tr>
 
  <tr>
 +
  <th scope="row">PSD</th>
 
   <td>
 
   <td>
 
   <math>
 
   <math>
−
     \alpha = \frac{K_B T}{\langle R V_qpd \rangle ^ 2}
+
     \left. {6 \pi^2 \eta d \, f_0} \right.
 
   </math>
 
   </math>
 
   </td>
 
   </td>
 +
  <td><math>\frac{K_B T}{\langle R_{QPD} V_{qpd} \rangle ^ 2}</math></td>
 +
  <td>none</td>
 +
  <td>none</td>
 +
  <td>linear</td>
 +
  <td>linear</td>
 +
  <td>indirect (viscosity change)</td>
 +
  <td>very small</td>
 
  </tr>
 
  </tr>
  
 
  <tr>
 
  <tr>
−
   <td>
+
   <th scope="row">Stokes</th>
 +
  <td>
 
   <math>
 
   <math>
−
     \alpha = 2 \pi  \Beta f_0
+
     \langle \frac{3 \pi \eta d \, R_{stage} \, ^{d V_{stage}} / _{dt}} {R V_{qpd}} \rangle
 
   </math>
 
   </math>
 
   </td>
 
   </td>
 +
  <td>inverse</td>
 +
  <td>linear</td>
 +
  <td>linear</td>
 +
  <td>linear</td>
 +
  <td>indirect (viscosity change)</td>
 +
  <td>none</td>
 
  </tr>
 
  </tr>
−
 
−
<td>
 
−
  <tr>
 
−
  <math>
 
−
    \alpha = \langle \frac{3 \pi \eta d v}{R V_qpd} \rangle
 
−
  </math>
 
−
  </tr>
 
−
</td>
 
  
 
</table>
 
</table>

Revision as of 16:00, 2 August 2012

MIT Bioinstrumentation Teaching Lab

ImageBar 774.jpg

Laser tweezers based on the ThorLabs OTKB optical trap kit.

Introduction

Optical tweezers can exert measurable forces on micron-scale dielectric particles. This capability offers a unique and valuable tool for manipulating and measuring cell components at the single molecule level. For example, optical traps have been used extensively to investigate the mechanical properties of biological polymers and the force generation mechanisms of molecular motors. In many studies, optical tweezers apply force to functionalized microspheres, which act as convenient handles attached to molecules of interest.

To make quantitative force measurements, the instrument records the displacement of a trapped microsphere over time. For small displacements, the exerted force is very nearly proportional to displacement, so the trap can be modeled as a linear spring. Accurate force and position measurements depend on careful calibration of the position detector responsivity, G, and the trap stiffness α, also called the spring constant. The stiffness is a function of trapping laser power, bead size, bead composition, and optical properties of the sample.

This page has tips for setting up and aligning an optical trap. It discusses three methods for obtaining the spring constant and two methods for measuring α.

Overview of the instrument

Summary of calibration methods

Effect of Systematic Errors on Measured Value of $ \alpha $
Method Equation QPD Responsivit Stage Responsivity Solvent Viscosity Particle Diameter Temperature Technical Noise
$ R_{QPD} $ $ R_{stage} $ $ \eta $ $ d $ $ T $
Equipartition $ \frac{K_B T}{\langle R_{QPD} V_{qpd} \rangle ^ 2} $ inverse square none none none linear and indirect (viscosity change) systematic decrease
PSD 
  $      \left. {6 \pi^2 \eta d \, f_0} \right.     $
$ \frac{K_B T}{\langle R_{QPD} V_{qpd} \rangle ^ 2} $ none none linear linear indirect (viscosity change) very small
Stokes 
  $      \langle \frac{3 \pi \eta d \, R_{stage}  \, ^{d V_{stage}} / _{dt}} {R V_{qpd}} \rangle     $
inverse linear linear linear indirect (viscosity change) none

Setup and alignment

Remove the optics

Collimating and adjusting the fiber port

Initial laser alignment

Beam expander coarse adjustment

Condenser adjustment

Connecting the piezo stage

Fine adjusting the beam expander

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OTKB software

Starting the software

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Calibration

Measuring R by scanning a stuck bead

PSD method

Equipartition method

Stokes method

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