THORLABS EDU-OT3, User Manual

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Portable Optical Tweezers Kit Chapter 6: Experiments
Page 70
MTN024417-D02
In order to eliminate statistically possible deviations of individual particles, it is
recommended to once again determine the mean value over
𝑀𝑀
various particles. We
recommend doing this for at least
5
particles.
〈𝑟𝑟
2
〉 ( 𝑡𝑡
𝑛𝑛
) =
1
𝑀𝑀 �
1
𝑛𝑛 � 𝑟𝑟
2
( 𝑡𝑡
𝑖𝑖
)
𝑛𝑛
𝑖𝑖=1
(31)
The obtained values for average displacement, 〈𝑟𝑟
2
〉 (
𝑡𝑡
𝑛𝑛
) , are now plotted with respect to
time. Figure 53 shows an example of mean squared displacement over time for three
different sizes of polystyrene beads. Here, each straight line is the mean value of several
particles of the same sample. It is recommended to perform a linear fit through the resulting
curves in order to obtain the slope,
𝑚𝑚
, of the straight lines.
Scaling of the camera image
: To accurately determine the movement of the particles, the
real, physical dimensions need to be known. There are two options:
(i) use a microscopic ruler to determine how many pixels correspond to a micrometer.
Standard test/resolution targets such as the USAF pattern or the NBS 1952 pattern can
be found on our website.
(ii) you can calculate the theoretical dimensions. For that, it is important to note that the
objective magnification always depends on the tube lens. The objective used in this setup
is made by Zeiss and is labeled as a “63x” objective. However, Zeiss’ standard for tube
lenses is a focal length of 165 mm while our system’s tube lens has a 100 mm focal length.
To obtain the “effective objective magnification”, you multiply the design magnification with
the actual tube lens focal length and divide by the design tube lens focal length. That
means that the effective magnification in our system is
63 𝑥𝑥 ⋅ 100 mm/165 mm = 38.2 𝑥𝑥
.
The sample area is then retrieved by dividing the camera sensor dimensions by the system
magnification. The CS165CU camera’s CMOS sensor has an imaging area of 4.968 mm
x 3.726 mm. Thus, the imaged sample area is
4.968 mm
38.2 𝑥𝑥
×
3.726 mm
38.2 𝑥𝑥
= 130 µm × 98 µm
Exercise
What differences do you expect between the Brownian motion of the 3 µm and 1 µm
spheres and why?
Solution
The slope of the lines in Figure 53 decreases with increasing diameter of the beads,
meaning that larger beads move less. This result can be easily explained through
Brownian motion. The 1 µm spheres can be more easily sent into motion by impact with
the water molecules than larger spheres. Therefore, a 1 µm bead travels more in a certain
time interval than a larger bead.