Hi Tom.
>Yeah, you "sort of" validated the Virenda >equation. Like the girl who "sort of" took >precautions and is only slightly pregnant.
I've not heard this saying before - quite amusing!
That the Virenda equation might be the expected function for a point image (might be, do your optics meet the conditions that lead to the Virenda equation?) that is different from it being the expected function for your beads.
See the attached. Firstly, the Virendra equations describe fully the (unconvolved psf) when spherical aberration is present. As this is my dominant aberration (albeit small), its a good starting point - much better than what I had before Gaussian or Bessel. So yes it does represent the real psf. But does it represent the convolved psf?
Well correctly or incorrectly, I am using the fact that the Virendra equations have enough freedom to allow an interploation of my convolved psf. As & Ad allow for shape change, and psi allows for size change. So the values actually obtained for As,Ad and psi ar enot necessarily the real values for the psf, but they are values that allows a good fit to my data (again I am using good to mean better than a previous method)
>Your information in your later post here >suggests nowhere near. You list a bead size of >200nm, a DOF (whatever that is, I don't
"Depth of focus". So my beads sit on the x-y plane, and the depth of focus is in the z-plane and is dictated by my objective lens (and lambda)
>recognize the acronym off the top of my head) of >500nm and an accuracy of 200nm. You bead size is >40% of the DOF and equal to your stated >accuracy.
I can determine focus to within the limits of my z-stage (c.a. 200 nm's). By plotting the measured size against z position (for a through focus set of data), the curve is very smooth and parabolic, so I can obtain best focus quite well (or at least well within the range of sizes that my optical changes make)
>That is far from negligible. The beads might be >small enough to be considered as point sources >for determining the general behaviour, and the >overall form of the diffraction pattern, but >that is quite different from the detailed >analysis you are trying for.
Why is it - the perfect system contains 83.6% of its total energy within the first dark ring. Im using a similar measure.
>Encircled energy is a perfectly good measure -- >for some purposes. If you were looking to focus >a laser beam then it would be an appropriate >measure of how good your focusing was. But that >is not your task.
But it is, we need the peak intensity as high as possible and I cannot change how tha analysis works - its better for higher peak intensities. As we randomly populate a slide with these beads, any ringing reduces the contrast and also screws up our alorgrithms.
>Your task is resolving images -- something very >different.
Not really, its identifying the locations of objects and deciding in which channel the signal is strongest.
The energy in the rings is irrelevant to that resolution (the amplitude is, but because of the size of the rings a negligible amplitude can still represent significant energy.
>And why should you not consider a focus that is >not quite the theoretical focal plane but does >result in a narrower central peak? "defocusing" >to improve resolution and contrast is not >exactly an unknown nor unused technique.
Yes this is a away to improve resolution, but see attached - its at the expense of contrast.
Whatever happens, my audience want to see a method where I can then reproduce what we see on the camera - compare raw blocky image with reconstructed blocky image.
Thanks
Jason