ThorLabs OTKB optical trapping kit
OTKB construction
Modifications to ThorLabs suggested layout
Below are a list of modifications that were made to the ThorLabs suggested layout: 1. Instead of connecting the fiberport to the KCB1 via a lens tube, we instead directly connected it using 4 ER05 rods. The small gap between the fiberport and the KCB1 was covered using electrical tape
2. The beam expander section was changed to be simpler. The KCB1 attached to the fiberport was directly connected to a CP02T with 4 ER05 rods, a SM1L03 lens tube, and an SM1T2 lens tube coupler. This CP02T was then connected to the C6W holding the first dichroic with 3 ER8 rods. In between the CP02T and the C6W, two CP02s were mounted on CPB1 bases: the closest one to the KCB1 was attached to an SM1L05 lens tube that holds the first achromatic doublet lens (part number AC254-060-B) and the other is connected to two lens tubes used to enclose the beam (specific sizes will be given when we enclose the beam).
3. The section connecting the C6W to the second KCB1 (the one leading to the objective) was changed. Now, a SM1L03 lens tube connected to a SM1L10 lens tube was screwed into the KCB1. The SM1L05, that holds the second achromatic doublet (part number AC-254-150-B), attached to the C6W, was connected to these combined lens tubes via a 1 inch piece of plastic tubing.
4. The vertical segment was changed. The top of the KCB1 that leads to the objective (the end opposite that mentioned in the previous step) now has a SM1L05 lens tube connected to a SM1L03 lens tube threaded into it. In addition, the SM1Z that originally held the objective was replaced by a CP02. This CP02 was mounted on the ER3 rods that were attached to the KCB1.
5. The sample holder was changed
6. The height of the stage was lowered. Now, the TBB0606 translating breadboard is directly connected to the breadboard on which the trap is assembled via 4 P2 cylinders.
Alignment procedure
Comparison of OTKB and 20.309 optical trap operating characteristics
Position calibration
| ThorLabs OTKB | 20.309 | |
|---|---|---|
| X position | TBD | 
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| Y position | TBD | 
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COMMENT: "X Axis" and "Y Axis" are not a good titles for a plots.
Methodology
COMMENT: "Sample Trial" is not a good title for a plot.
- Prepare a sample cell per section 3.5 of the Optical Trapping Lab Manualand load it with stuck and suspended silica microspheres as per section 4.1.1.
- Trap a suspended microsphere and adjust the focus to place it near the middle vertically of the sample cell. (Crash the trapped bead into the coverslip and then raise it abaout half of the height of the cell, which is about 100 microns.)
- Using QPD Alignment Tester, adjust the QPD position until the voltage output on both axes is near zero.
- Save an image of the trapped bead.
- Find a stuck bead.
- Adjust the focus so that the stuck bead looks similar to the saved image of the free trapped bead.
- Center the bead as per section 4.1.2. and run the Position Calibration VI. In the data file, the first row gives displacement from the starting position (in nm) and the second row gives the QPD signal (in V). WHAT ABOUT THE THIRD ROW?
- Fit a line to the approximately linear portion of the graph where the bead passes through the center of the trap. The slope of the line is the position sensitivity in V/nm.
- Repeat 5 times on 5 different stuck beads.
- Use the same procedure on the other axis
- Repeat the entire process at 5 power levels
- Compute the average sensitivity and standard deviation at each power level. Fit a line and plot to facilitate interpolation.
Materials
- 1μm silica microspheres, BangsLabs SS03N/4669
- 25x75mm glass slide
- 22x40mm #0 coverslip
- 1M NaCl
Comments
- Picomotor step size assumed to be 30nm. Using actual step size would increase accuracy of the position calibration.
- Estimated sensitivity is affected by focus.
Trap stiffness
The force calibrations determine the stiffness of the trap. The stiffness of the trap characterizes the forces exerted by it. Three different methods were used in order to determine the stiffness of each trap: Equipartition, noise PSD roll-off, and Stokes drag.
Methodology
Equipartition
For small displacements from the center of the trap, the trap is considered to be like a spring. The Equipartition method of calculating trap stiffness centers around relating the variance in a trapped object's position due to thermally induced position fluctuations. From the Equipartition Theorem, every degree of freedom in a harmonic potential will contain $ \frac{1}{2} k_B T $ of energy, where $ k_B $ is Boltzmann's constant and T is the absolute temperature. Since the trap acts as a spring, we can equate this energy to the potential energy stored in the 'spring': $ \frac{1}{2} \alpha \left \langle \Delta x^2 \right \rangle $, where $ \alpha $ is the trap stiffness and $ \left \langle \Delta x^2 \right \rangle $ is the variance in position. Solving for $ \alpha $, we get: $ \alpha = \frac{k_B T}{\left \langle \Delta x^2 \right \rangle} $. Assuming these experiments are being run at room temperature, this equation simplifies to: $ \alpha = \frac{4.1124*10^-21}{\left \langle \Delta x^2 \right \rangle} $. Thus, in order to solve for the trap stiffness, the variance in position is the only thing that needs to be calculated. However, since this variance is measured in volts, position calibrations will be required in order to convert the voltage signal into a position in meters (note: since the calibration values from the previous section were in V/nm, you will need to convert these into V/m in order to solve for $ \alpha $). The next section will explain the procedure used to perform this force calibration.
Procedure
1. Using the methods discussed in the Position Calibration procedure, make a slide and load a 1:50,000 dilution of 10% wt stock beads (1 μm silica, Bangs, SS03N/4669) in its channel.
2. Load the slide onto the microscope and trap a bead. Raise the bead to the middle of the slide and move it away from any obstructions. Open the QPD Alignment Tester VI and make sure that the voltage signal is centered at 0 (if it is not, adjust the screws on the QPD so that the signal rests at 0)
3. Open the WriteXYTraceToFile VI. Select which channel you would like to sample from (for this experiment, dev1/ai0 corresponded to the X-axis and dev1/ai1 corresponded to the Y-axis). Enter the Sampling rate in Hz and the sampling time in seconds (for this experiment, 64000 and 3 were used respectively). Start the VI. While the VI is running, carefully watch the IC capture of the slide to make sure that neither the bead leaves the trap nor something else becomes trapped. If either of these things happen, you should discard the data for that trial.
4. Save the data, and load them into an analysis software (Matlab was used for this experiment). Using this software, calculate the variance of the data. The answer given will be in Volts. In order to convert this to meters, divide by your calibration factor squared (NOTE: THE CALIBRATION FACTOR NEEDS TO BE IN V/M AND NOT V/NM AS YOU MEASURED IT!). Finally, using the equation stated in the introduction to this method, calculate your trap stiffness. This answer will be in Newtons per Meter. Since trap stiffnesses are usually measured in picoNewtons per nanoMeter, multiply your result by 1000 to get the right magnitude for those units.
5. As with the position calibration, make sure you run multiple trials for each axis and power level and average the results (depending on the variance of your results, you may wish to take the median of all trials instead of the mean).
6. For each axis and power level, plot the trap stiffness versus the power level. Fit these data to a line. If this calibration and the position calibration were done carefully, the linear fit should be quite accurate.
Possible Sources of Error
1. This calibration requires extremely accurate position calibrations in order to yield accurate data
2. This calibration is very sensitive to noise.
Results
Equipartition
| ThorLabs OTKB | 20.309 | |
|---|---|---|
| X and Y axes | TBD | 
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