Airy Disc Smear
I used this equation from yesterday
[math]\displaystyle{ \nu =2\pi \frac{NA}{\lambda}r_0 }[/math]
I changed the wavlength into pixels so i can work in that unit. I used the factor Andy gave me yesterday. Anyway using pixels the prefactor came out to be 2.71 1/pixels. This gave me a pretty nice looking Airy Function. So I think i am on the right path.
Now i need to figure out the max intensity. Which i think will be just fitting it by eye. I can't think of a better way to do this because it can change oftenfrom bleaching, so it won't be mathematical like this smear was. I am pretty happy with this
This is with a prefactor of 2.71/pixel. It looks pretty nice.
So I can get started on trying to fit this intensity or i can start by throwing random fluorescent dots onto a rectangle that will symbolize the MT. Hey Koch, i can't remember how we decided to split up the microtubule can you chuck a comment here to refresh my memory? Thanks^{SJK 15:53, 15 November 2009 (EST)} 15:53, 15 November 2009 (EST) I think what we were thinking is to first approximate the MT as a 1D contour (ignore the 20 nm width). Then we were thinking approximate it as 13 protofilaments on top of each other. This would give one dimer every 8 nm / 13. You could then distribute the fluorophores (aka emitters) randomly along the line by stepping through each site and rolling dice and setting them with a likelihood equal to the % labeling that Andy uses. This would then generate your map of emitters. (We were pretty sure, though, that this would not produce anything as splotchy as we see in real life, which would imply that real MTs have some kind of cooperativity in polymerizing nonlabeled versus labeled.) How you generate an image from these coordinates was another issue. A kind of first thing to do would be to give each emitter a PSF that you defined above (looks very cool, BTW!) with a random amplitude, but no randomness in terms of pixel intensity within the PSF. In reality, the actual PSF will have photon noise (each photon arriving randomly set by the probability density function determined by the PSF. But that may be overkill, since you'd have to simulate thousands of photons per image.
There should be a good way to figure out this maximum intensity for the dots. I can make this monte carlo algorithm and then see how many of them overlap and then fit that to the image adjusting the intensity at the end. That sounds like the best idea.
The basic idea is that i break up the rectangle that is approximating the microtubule into x subsections. Then run through those subsections and roll the dice for each one. If it is lower than the concentration percentage i put a dot there if not i move on. I am not sure how thick the rectangle will be. I have the feeling that it will be more like a line. I am not sure how wide a microtubule is but if it is less than 180 nm (that is basically what makes up 1 pixel) it can be a line.
