# User:TheLarry/Notebook/Larrys Notebook/2009/11/14

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## Airy Disc

This is what Nikon had to say:
$\displaystyle{ r=\frac{1.22\lambda}{2(NA)} }$
the radius to the first zero is a function of the numerical aperture. This is what i was looking for or something like this. Yesterday there was the nice formula linking sin(theta) to the first minimum but this one is a bit easier for me to think about. Also this means there is a shit load more information out there about what i am trying to do. So i gotta find that and learn it. Note: This 2 in the denominator is from the assumption that the condensor and the objective have the same numerical aperture. If not it looks like you just add them together. without the 2.

I should still read that Born/Wolf chapter, but it might be more helpful to read something on resolution in microscopy or something like that that talks about Airy Discs in more detail than the Nikon page.

So using the above equation and $\displaystyle{ \lambda=330 }$ and NA as 1.4 i get an r = 143.7 nm. So i can try to fit the Airy Disc i am playing with to have a minimum there. Maybe?(Steve Koch 15:53, 14 November 2009 (EST): I think you're using the wrong wavelength. It should be for rhodamine emission which is like 600-ish)

TheLarry 15:54, 14 November 2009 (EST): Thanks--I thought Andy told me Rhoadmine was 300 something but i must have heard wrong.

I need to know the nm/pixel factor so i can think about this right. Andy figured that out i gotta ask him before he leaves. Unless he is reading this then can you put it in here. Right now i have something like 32 pixels to the first minimum. I can adjust that. I am curious if this is the way to handle this. It sounds right to me (You should be able to back this number out from Andy's poster, since he converted that into nm)

I think this is the right way to go about this. I just have to do some reading to make it clearer in my head. The wolf/born is a good place to start. So I'll go home and read a bit of that chapter. This Airy Disc stuff is assuming there is no aberrations which may be a good enough approximation I am not sure yet. Just making note of it.

The wolf/born is very complicated and probably a very good source if i wanted to be extremely thorough. But since E&M was my weakest field i decided to look for other sources. I came across Handbook of Optics and they had something interesting to say. The argument of the first Bessel function is written below:
$\displaystyle{ \nu =2\pi \frac{NA}{M\lambda}r_i }$
$\displaystyle{ \nu =2\pi \frac{NA}{\lambda}r_0 }$
I am not clear on which one to use. They define the r's differently but they take this then find the equation for the first minimum that i have above. Anyway this might be what i am looking for. I gotta read more

## Pixels

Andy Maloney 18:51, 14 November 2009 (EST): So there are 184.5 nm/pixel.