Portable Optical Tweezers Kit
Chapter 6: Experiments
Rev B, February 15, 2022
Page 69
Brownian Motion
Use the sample with the 3 µm polystyrene spheres. You must first switch the laser off so
that you can observe only Brownian motion. For evaluation, a video sequence with a
duration of 2 minutes or more must be recorded. During this period, about
5
particles,
which do not touch each other, should be in the image. A similar video should be recorded
with the 1 µm spheres. The videos must be evaluated with the aid of image analysis
software, whih provides the x and y position of a particle over time. A program that makes
evaluation possible and is offered for free is “Viana”, available at
Note: Before taking the video sequence, make sure that the beads do not show a drift in
any direction, which can be caused by an air bubble. Allow the sample to settle for a
minute. If necessary, prepare another sample. Sometimes, collecting shorter video
sequences with more particles is helpful.
We recommend evaluating the data obtained with the aid of a table calculation program
and to show the results in a graph. First, the mean squared displacement
𝑟𝑟
2
(
𝑡𝑡
𝑖𝑖
)
of the
beads must be determined. This can be calculated with the positions
�𝑥𝑥
𝑖𝑖
(
𝑡𝑡
𝑖𝑖
),
𝑦𝑦
𝑖𝑖
(
𝑡𝑡
𝑖𝑖
)
�
of the
particles at different times
𝑡𝑡
𝑖𝑖
, which must be taken from the video:
𝑟𝑟
2
(
𝑡𝑡
𝑖𝑖
) =
�𝑥𝑥
(
𝑡𝑡
𝑖𝑖
)
− 𝑥𝑥
(0)
�
2
+
�𝑦𝑦
(
𝑡𝑡
𝑖𝑖
)
− 𝑦𝑦
(0)
�
2
(29)
The time mean value
〈𝑟𝑟
2
〉
𝑡𝑡𝑖𝑖𝑚𝑚𝑔𝑔
at time
𝑡𝑡
𝑛𝑛
results from the averaging of all measured values
𝑟𝑟
2
(
𝑡𝑡
1
), … ,
𝑟𝑟
2
(
𝑡𝑡
𝑛𝑛
)
at the measurement times:
〈𝑟𝑟
2
〉
𝑡𝑡𝑖𝑖𝑚𝑚𝑔𝑔
(
𝑡𝑡
𝑛𝑛
) =
1
𝑛𝑛 � 𝑟𝑟
2
(
𝑡𝑡
𝑖𝑖
)
𝑛𝑛
𝑖𝑖=1
(30)
Summary of Contents for EDU-OT3
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