User:TheLarry/Notebook/Larrys Notebook/2010/02/24

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Simulating Images

Normalizing Image

It seems like a monte carlo integration method is doable but pretty difficult to pull off. So I am gonna back away from that and do the integration using while loops and all.

I think i have the correct set up but the answer i get is off by .03. I don't know if i am doing something wrong and getting lucky or it can be that much different. I'll put below an image of the back panel.

The 2-d array that comes in is the z values. So the function i am using here is z = x + y. The graph goes from [0,1). So I should get an answer of 1 from this formula (i did it by hand). So for a step size of .1 I get 1.000 as an answer, but for a step size of .01 i get .97. Not sure why yet.
The 2-d array that comes in is the z values. So the function i am using here is z = x + y. The graph goes from [0,1). So I should get an answer of 1 from this formula (i did it by hand). So for a step size of .1 I get 1.000 as an answer, but for a step size of .01 i get .97. Not sure why yet.

I think the disparity is from including the last point or not. It must be an artifact of a double being slightly higher than 1 because if i say stop if x or y gets greater than or equal to 1.01 instead of just 1 (with a step size of .01) i get an answer of 1 which is what i was looking for. Strange I haven't seen this before though. Maybe doing a second dimension exasperates the problem. I am not sure but i'll have to come back to this and double check it later.

here is the airy discs that i had the image for yesterday on the left and the normalized version on the right. It is mighty small.
here is the airy discs that i had the image for yesterday on the left and the normalized version on the right. It is mighty small.

i don't trust this yet, but there has to be a normalized airy disk equation out there. so if i can find it i can double check my normalization. it is also possibly my normalized airy disk is so small because my intensity is so high. 125 as can be seen on the left may be a tad unreasonable and something like 1 may better. Same with the prefactor for the airy disk. I chose something so i can see it but it might be a lot higher.

Questions

Hey kocher,
I have a question in the mind map part: two random numbers per photon. I might have more questions. Can i get a meeting time sometime?
also i was thinking about the kinesin meeting: should i have two posters: one for kinesin model and one for tracking. if so i should spend half the time making kinesin better. just thinking. Can we get a meeting?

Steve Koch 22:34, 25 February 2010 (EST): Yeah, let's talk tomorrow.
Steve Koch 12:15, 27 February 2010 (EST): I edited part of the mindmap to let you know what I was thinking about random numbers. What you're doing now is creating a summed PDF for all of the emitters in the sample plane, which is a different way but should also work if you can figure out how to generate the random positions for 2-D PDF.
As for poster, I think you should only do one poster. I think it worked fine. I don't even know whether there'd be two sessions.
Although if there are definitely two sessions, I guess we can think about it.


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