Optical Tweezers – Measuring the Stiffness of an Optical Trap
Experimental Setup:
Data Collection and Analysis:
By the equipartition theorem, each degree of freedom has energy kBT/2. So for an optical
trap in one dimension:
1
1
k BT  k x 2
2
2
where:
k B  Boltzmann constant = 1.38 x10 23 J/K
T  Temperature of medium = 300K
k  One-dimensional spring constant
x  Relative displacement from average location
Relative X or Y / micron
Relative X and Y as functions of time, 10-degree
filter
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
Relative X
Relative Y
0
10
20
30
40
Time / second
k x = 0.91 pN / um
k y = 8.70 pN / um
At the 10-degree setting of the gradient filter, there appears to be a large level of
anisotropy in the spring constant of the trap, with ky about an order of magnitude greater
than kx. This is visually apparent from the graph above, in which the bead’s y-position
remains much closer to its average value than does the bead’s x-position.
Relative X or Y / micron
Relative X and Y as functions of time, 170-degree
filter
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
Relative X
Relative Y
0
10
20
30
40
50
Time / second
k x = 1.23 pN / um
k y = 1.67 pN / um
At the 170-degree setting of the gradient filter, there appears to be much less anisotropy
in the trap’s spring constant than at the 10-degree setting. This is also clear from the
graph, as the variation in relative x-position and relative y-position are more comparable.