Optical Tweezers Trap Force Measurement¶

May 15th, 2014
Brian Perrett, Kyle Eichenberger, Samuel Estrella
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:
    reader = csv.reader(f)
    for row in reader:
        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]:

Optical Tweezers Trap Force Measurement¶

May 15th, 2014 Brian Perrett, Kyle Eichenberger, Samuel Estrella Advanced Projects Lab

May 15th, 2014
Brian Perrett, Kyle Eichenberger, Samuel Estrella
Advanced Projects Lab