# User:Pranav Rathi/Notebook/OT/2010/11/11/Small Bead Power Spectrum & DOG

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## Power Spectrum

I have done power spectrum analysis for small bead (.5 um) first. I used more than four different beads, (4 different sets one for each); last set contains more than 1 bead. I am discussing parameters, process and the results.

### Parameters

I used AOM input voltage of 1.45 volts which corresponds to 50mW of laser power before the objective. I used low gain (step #3) on the QPD controller. All other parameters can be seen in the first few slides below. To see the slides clearly click on “view on slide share” in the lower right corner.

### Process & Results

I collected each set of data over a z-range of few microns. I started at the point where the trapped bead looks whitish (z=0), and went up into the sample in variable steps. The range of each step is labeled as “z=”. Each line of collected data in particular set has a z value, written before it. All four sets can be seen in the last 4 slides. The stiffness is calculated from the corner frequency in the data sheet. Data sheet also shows the z-piezo voltage and corresponding z-length into the sample away from the lower surface.

 View/Edit Spreadsheet

The raw data can be extracted from this link:[1]

#### Set1-bead1

Started at the surface (z=0) and went up in .1um increments (At z-piezo .1um belongs to 20mVolts) up to 1.2 um into the sample. Average stiffness is 11.76pN.

#### Set2-bead2

Started at the surface (z=0) and went up in .2um increments (At z-piezo .1um belongs to 20mVolts) up to 2 um into the sample. Average stiffness is 12pN, and its better above .8 um.

#### Set3-bead3

Started at the surface (z=0) and went up in .5um increments (At z-piezo .1um belongs to 20mVolts) up to 15 um into the sample. Last three steps are of 5 um each. Average stiffness is 12.54pN, and it is better above 1 um.

#### Set4-bead4

Started at the surface (z=0) and went up in 1um increments (At z-piezo .1um belongs to 20mVolts/ 25 um belongs to 5 volts) up to 25 um into the sample. Average stiffness is 15.35pN, and it is better above 1 um and it somewhat remains same from 1 to 19 um. The straight horizontal line on the plot is average stiffness over 25 um range.

### Conclusion

SJK 00:28, 12 November 2010 (EST)
00:28, 12 November 2010 (EST)
This page rocks!!! I agree I think we can unzip. Here are some comments from me: (1) the 1100bp-374 nm does not get converted to force. Rather how far we can go in the trap does. And actually, once you know stiffness you can calculate the max force by looking at the max deflection in the DOG signal--can explain better tomorrow. (2) I like this water objective! It's not actually that the stiffness is lower near the surface. With the water immersion, I think the stiffness stays the same, since aberrations are the same. Rather, the viscous drag force increases near the surface -- you can see this correction formula in the Svoboda and Block paper that you have. OK, Great work on this!

The stiffness is certainly better above 1 um from the surface which was expected. The overall stiffness is somewhat low at 1 W. The maximum power we can get before the objective is 1.4 W, which will give us 21pN/100nm. This information is enough to estimate the force.