# Optical Tweezers Trap Force Measurement¶

#### May 15th, 2014 </br> Brian Perrett, Kyle Eichenberger, Samuel Estrella </br> Advanced Projects Lab¶

 Microsphere Size $2.56\mu m$ Beam Strength $4.6mW$ Measurements Per Second $200$ $\Delta t$ between measurements $.005s$

Import Data from .csv file... Add them to arrays.

In [2]:
x_pos = []
y_pos = []

###########################
import csv
with open('C:/Users/Brian/Google Drive/Sophomore/Physics/Advanced Projects Lab 491/2.56 micrometer tracking 5-14-14/2.56 micrometer parsed.csv') as f:
x_pos.append(float(row[0]))
y_pos.append(float(row[1]))
###########################

# convert lists to arrays for simplified calculations
x_pos = array(x_pos)
y_pos = array(y_pos)


Convert from $\mu m$ to $m$

In [3]:
x_pos = x_pos*10**(-6)
y_pos = y_pos*10**(-6)


$\frac {1}{2} k_b T = \frac {1}{2} k <x^2>$

• Using the equipartition Theorem and equating it to the potential energy of the trap, we can solve for k

to compute the variance we must solve...

$variance=\overline{(x_{mean}-x_t)^2}$

In [4]:
x_mean = mean(x_pos)
y_mean = mean(y_pos)

In [5]:
x_var = mean((x_mean - x_pos)**2)
y_var = mean((y_mean - y_pos)**2)

In [6]:
print("The x variation is " + str(x_var))
print("The y variation is " + str(y_var))

The x variation is 6.92133033795e-16
The y variation is 2.57011754526e-15

 x var 6.92133E-16 m y var 2.57012E-15

$\ \frac {k_b T}{<x^2>} = k$

In [7]:
kb = 1.3806488e-23
T = 298

In [8]:
x_strength = (kb*T)/x_var
y_strength = (kb*T)/y_var


Let's convert from standard units to piconewtons per micrometer

In [9]:
x_strength = x_strength*(10**12)/(10**6)
y_strength = y_strength*(10**12)/(10**6)

In [10]:
x_strength # piconewtons/micrometer

Out[10]:
5.9444257434757573
In [11]:
y_strength # piconewtons/micrometer

Out[11]:
1.6008347289755338
direction k
x trap strength $5.94 \frac {pN}{\mu m}$
y trap strength $1.60 \frac {pN}{\mu m}$
In [11]: