Difference between revisions of "ThorLabs OTKB optical trapping kit"

Revision as of 14:58, 8 July 2010

Thorlabs optical trapping kit

OTKB construction

Modifications to ThorLabs suggested layout

The main modifications to the ThorLabs suggested layout were to make the trap more modular. This allows for the trap to be more easily adjustable and alignable. Thus, any lens tube that was used in the original design for the purpose of enclosing the beam was replaced with a smaller lens tube and a plastic cover. This allows for the trap to be easily taken apart. Also, the beam expander segment was simplified by just having 4 ER8 rods connecting the KCB1 attached to the fiberport and the C6W cube holding the first dichroic. Then, the lens tube holding the first achromatic doublet lens (part number AC254-060-B) was attached to a CP02 that was positioned on the ER8 rods between the two aforementioned components. This way, the lens can easily be adjusted by sliding the CP02 along the ER8 rods instead of worrying about screwing and unscrewing lens tubes and couplers. Another adjustment that was made to the trap was to remove the SM1Z cage translator and instead, we used a CP02 attached to the 4 ER03 rods (section 4.3 number 8) to hold the objective. This makes the alignment procedure much easier because the objective can be moved up and down along the ER03 rods to align and collimate the beam. Another change that was made was the replacement of the sample holder. Because the old sample holder had a very precisely measured indent for a slide, it was impossible to mount a slide with an over extending coverslip on it (which are the type of slides that we are making). In addition, this sample holder would not necessarily fit every different brand of slide. Finally, adding a new and more flexible sample holder allows for the slide to be moved left and right by hand as well as the stage, which gives unlimited movement over the span of the slide.

Alignment procedure

Comparison of OTKB and 20.309 optical trap operating characteristics

Position calibration

	ThorLabs OTKB	20.309
X position	TBD
Y position	TBD

COMMENT: "X Axis" and "Y Axis" are not a good titles for a plots.

Methodology

Figure 1: A sample calibration curve

Figure 2: The linear portion of a calibration curve fit to a line

COMMENT: "Sample Trial" is not a good title for a plot.

1. 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.
2. 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.)
3. Using QPD Alignment Tester, adjust the QPD position until the voltage output on both axes is near zero.
4. Save an image of the trapped bead.
5. Find a stuck bead.
6. Adjust the focus so that the stuck bead looks similar to the saved image of the free trapped bead.
7. 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?
8. 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.
9. Repeat 5 times on 5 different stuck beads.
10. Use the same procedure on the other axis
11. Repeat the entire process at 5 power levels
12. 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

1. Picomotor step size assumed to be 30nm. Using actual step size would increase accuracy of the position calibration.
2. 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