# User:Andy Maloney/Notebook/Lab Notebook of Andy Maloney/2009/04/15/Optical tweezers

## Calibration

Okay. I've heard a lot about calibration and people in the lab keep telling me that it's an important thing. They also keep telling me that it is some magical power spectrum that you take the corner frequency for and low and behold you have the trap stiffness.

While all of those words above mean something and I thank the guys for trying to describe to me what calibration means by repeating just those words above, I still do not have a physical grasp of what it means. I'm going to go out on a limb here and try and describe what I think calibration is and why it is necessary to make force measurements. I'm going to have to pictures later.

So a trap in my mind means a little ball at the bottom of a hill. When the ball is at the bottom, there is no force on it making it move to the bottom of the hill. However, when the ball moves up the hill, it feels a force for it to return to the bottom. This is exactly the situation for optical trapping except instead of a gravitational force field, I'm dealing with an electric force field.

So, imagine that you can make the ball traverse the entire force field, i.e. the trap. You can do this by putting the ball in some sort of gooey matrix so it doesn't have Brownian motion. Move it around with stages and measure how the ball deflects the laser light. If the ball stops deflecting light, then you know you are outside of the trap. If you do this in the x and y directions, you can measure the size of your trap. If you know the size of the trap and how much power you are pumping into it, then you know the electric force field at that spot. If you know the field, then you can calculate the potential. If you know the potential, then you can calculate the force exerted on something dependent on where it is in the potential. Ha! But you know where the ball is because you just mapped out where it is with your position detector, i.e. you know how it deflects light.

So, if you know how the ball deflects light, you know where it is in the trap. If you know the size and the power of the trap, you know the potential field. Knowing the potential and where the ball is tells you the force on the ball for it to go to the center of the trap. Thus, you know the force exerted on the ball dependent on how the trap light is deflected on a QPD.

I cannot believe that this has eluded me for so long. Of course, I still do not know what people mean when they talk about power spectra and corner frequencies for measuring the trap stiffness, but at least I understand the physics somewhat more now. I'm assuming that taking power spectra and measuring the corner frequencies is the terminology for mapping out the force field. Now all I need to understand is where those terms come from.

It's so simple!

• Ramalldf 00:54, 25 May 2009 (EDT):Hey Andy, you've probably figured this out by now and probably won't need this, but Zev Bryant referred me to this review which he thought gave a good introduction for calibration of a trap (Box 1). I've been doing some research on this to understand it myself. You'll probably understand this better than I did :).
• Ramalldf 18:39, 1 June 2009 (EDT):Here's an even better review written by Keir Neuman.