User:TheLarry/Notebook/Larrys Notebook/2009/11/13

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Gaussian Point Spread Function

So my point spread function will be approximated as a Gaussian. It can be an Airy Disc but i still don't know how to make a 3-d airy disc, so for now I'll use a Gaussian.

After today's group meeting Koch helped me out with some troublesome parts of this simulation

  1. To find the spread for the Gaussian, I can just look at a picture of the quantum dot and match the spread for that
  2. To find the amplitude best just fit as best as i can by eye
  3. For the placement of the fluorescent dots I can split up the microtubule into x number of spots (Koch can you write down how to split this up again, i forgot), then roll the dice for each spit giving it a 17% chance that the dot will be at that location. 17% is the percentage of concentration in the solution.

Right now i have the Gaussian spread to be about .09 which looks pretty good but i am unhappy with this procedure there must be a more precise way to do this. I just don't know how, and every where i look this part seems glazed over

Airy Disco

On the bright side i got my 3-d Airy Disc going. Hooray for me. Now i can use this instead of the Gaussian for my point spread function. That is good news.

Airy Disc mother-fuckers

This opens up the question now of how do i deal with the smear. before i didn't know what i was doing but was confident i know what sigma of the Gaussian is. Now I have this Airy Disc and I am not 100% confident i know what to change to match experimental conditions. Here i'll write down what i do know:
[math]\displaystyle{ I(\theta )=I_0(\frac{2J_1(ka\sin {\theta})}{ka\sin{\theta}})^2=I_0(\frac{2J_1(r)}{r})^2 }[/math]
[math]\displaystyle{ \sin{\theta}=\frac{1.22\lambda }{D} }[/math]
so far that's all i know. the second equation is the location of the first minimum which could set the smear. [math]\displaystyle{ \lambda }[/math] is set -- probably the emission wavelength. And D is the aperture size. I am not sure what that is for the microscope. But that is a number that isn't changed as well. So possibly this can be adjusted. Also when they replace the argument for the Bessel function with r that is [math]\displaystyle{ r=\sqrt{x^2+y^2} }[/math]. or so i think. So if i'm lucky and usually i am not in these cases there might not be any more fucking around outside of the [math]\displaystyle{ I_0 }[/math] and that was something i was gonna have to fuck around with in the end anyways. Also i am not confident in my understanding of k or a. k is the wave number, and a is the radius of the aperture

Oh so i don't forget Andy said there are probably some software packages that figures out the PSF already. That might be worth looking into if this starts to drive me crazy. But i feel right now that i am on the right path.

I'll fight it but i probably have to read a book or a chapter or something to get this right.

OK I'll read Born/Wolf chapter on Airy Discs. Chapter 8. Hopefully that gives me some background to play with this function. I am keeping my fingers crossed that the wavelength and aperture size is all i really need to match the images from the microscope. It could be -- i wanna believe (also [math]\displaystyle{ I_0 }[/math])

Also if any one knows this aperture size please feel free to put it here