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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle I(\theta )=I_0(\frac{2J_1(ka\sin {\theta})}{ka\sin{\theta}})^2=I_0(\frac{2J_1(r)}{r})^2}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \sin{\theta}=\frac{1.22\lambda }{D}}
so far that's all i know. the second equation is the location of the first minimum which could set the smear. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle r=\sqrt{x^2+y^2}} . 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle I_0} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle I_0} )

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