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Experiment B-
Optical Tweezers
This is a new experiment developed recently for the Light Laboratory. The primary goal of this lab is to understand the principles of optical trapping, familiarize with various optical components, acquire skills in using the optical imaging software and understand the basic techniques of image data analysis.
For this lab, we will follow the procedures reported by Adam Dally. His report is attached with this handout. You should read the report as well as the references mentioned in the report before coming to the lab to save your time during the lab period.
Our aim is to prepare a sample of 1 or 5 micron polystyrene beads on a glass slide and then “trap” or “capture” the beads with the laser. Once they are trapped, several measurements will be taken using the imaging software. Also you will observe the position variance of the trapped beads with respect to changes in the laser power. Laser power can be varied using the neutral density filter. From these measurements and equipartition theorem, you will determine the trap spring constant of the beads.
Lab report: Include in your report, write down your measurement and data analysis techniques along with your complete data. Discuss how you would improve the measurements and analysis.
Design of Optical Tweezers for Undergraduate Lab
Adam Dally (REU Program at UIUC, Summer 2005) (Department of Physics, University of Minnesota)
ABSTRACT I describe the setup and testing of an optical tweezers for use in the University of Illinois undergraduate light lab. This setup was built large with materials at hand and freeware software making it very inexpensive and still effective.
I. Background and Introduction In 1970 Arthur Ashkin at Bell Labs developed a way to move small latex spheres with laser light.^1 This is what became known as optical tweezers. Optical tweezers are useful in many scientific experiments especially biology.
The setup of an optical tweezers can be a complicated and elaborate undertaking. Many commercially available optical tweezers cost thousands of dollars.^2 The purpose of this experiment is to make a very simple, cheap, and still effective optical tweezers for use in an undergraduate laboratory at UIUC.
The tweezers work by creating a force gradient on the trapped particle. The force is from the radiation pressure of the focused laser. The equation for radiation pressure is U P c
As the light enters the sphere the difference of the index of refraction from the sphere and the solution it is in causes the light to change the angle of refraction by Snell’s Law. The more intense light at the focus has greater recoil toward the center of the trap after refraction as seen is Figure 1. Snell’s law is
n 1 sin θ 1 = n 2 sin θ 2 n 1 sin θ 1 = n 2 sin θ 2 (2).
Figure 1: Shows how the force gradient is created in an optical tweezers. The size of the arrow is corresponding to the magnitude of the beam.
II. Method The components and setup of the tweezers was undertaken with the equipment available. Using the materials at hand saved time and money. The tweezers setup is diagramed in Figure 2.
Figure 2: Setup diagram of the optical tweezers.
Point Grey Research FlyCap software. The camera is a grayscale 640 x 480 firewire camera.
Aligning the laser into the trap is nontrivial. Small adjustments of the mirror are necessary to get the laser right down the barrel of the microscope. The laser needs to fill the back aperture of the objective lens. In this case the beam appears to do that. If a larger beam is necessary a lens can be added in the beam path to expand the spot size. The slide also needs to be adjusted by way of moving the translation stage to have the laser focus in the zone of the microspheres.
FlyCap can get images or many frames of video. 100 frames for the video give a good number of data points for analysis. An example frame from a video is shown in figure 3. One picture of the stage area without the microsphere should be taken for the image analysis, this is the background frame. The background needs to be saves as a Portable Pixel Map (.ppm) file as seen (inverted) in Figure 4.
Figure 3: Frame from the video of the trapped microsphere.
The video from FlyCap is in a compressed AVI format. The videos need to be decompressed for the analysis program. To decompress the files the freeware program Virtual Dub by Avery Lee^3 was
used. The video is now ready for image analysis.
The image analysis is done by the freeware program ImageJ from the National Institutes of Health by Wayne Rasband.^4 The background frame is opened with ImageJ. Then the image is inverted by the Edit/Invert function. This looks like a negative of the picture as seen in Figure 4.
Figure 4: The invert background frame. Next the Process/Image Calculator is used to add the negative of the background to all of the video frames. The resultant video should have a few light grey areas and the dark microsphere as in Figure 5.
Figure 5: An example image of the negative added video frames. The threshold is then changed to binary using Process/Binary/Threshold. The resultant video is a black microsphere on a white background as shown in figure 6.
Figure 6: The black microsphere on a white background. It is now ready for "Tracking”. It doesn’t look like much, and that is the point really.
The Plugin/Tracker plugin is used to find the center of the microsphere in all of the frames of the video. This is printed in a window titled “Results” with counts, file number, an X1, Y1, X2, Y2, and a distance value for each of the frames. The X1 and Y1 values are the only important numbers here. X2 and Y2 values are redundant if the video is clear of any other microspheres or other garbage getting in the video. If there is other stuff in the video it needs to be cropped using Image/Crop in a safe region.
This list of coordinates can be analyzed using the equipartition theorem,^2
k (^) x x kB T 2
kx is the spring constant for the x-axis, x is the deviation from the mean value of x, kB is Boltzmann’s constant, and T is temperature. This same analysis holds for the y values as well.
The width of a pixel from the camera must be converted to meters in the video. Since the microspheres are uniform and of a known diameter they can be used to scale the image. The pixel values can then be converted into a meter value by a direct linear conversion.
By adjusting the ND filter value, the percent power of the laser is reduced. This allows repeated measurements for different power levels. These measurements can be compared to the measured spring constant values. The spring constant should be proportional to the laser power.
III. Results and Discussion The measurement of the spring constant for the trap is relatively straight forward. Getting values that make sense require very close attention to detail and a careful method.
Spr i ng Cons t a nt
0 0 E+0 0
0 0 E- 0 8
0 0 E- 0 7
5 0 E- 0 7
0 0 E- 0 7
5 0 E- 0 7
0 0 E- 0 7
0 2 0 4 0 6 0 8 0 10 0 P e r c e n t P o w e r ( u n i t l e s s )
X Y
Figure 7: Shows the spring constant as a percentage of the laser power for both the X and Y directions. The Y value is an outlier in this data which could be from the large errors in that measurement. The difference between the X and Y directions is from the beam shape of the diode laser which is elliptical. Pixel Scatter
0
50
100
150
200
250
0 50 100 150 200 250 X Pixels
Y Pixels
100% 90% 80%
Figure 8: Shows the spread of pixel in the trap for different percentages of power.
