rjlittlefield wrote: ↑Fri Dec 02, 2022 6:32 pm
mjkzz wrote: ↑Fri Dec 02, 2022 4:31 pm
OK, that looks long post
Ah yes, the TL;DR problem. I don't know how to solve that.
and it seems you are looking at this thing from a different angle.
Perhaps I misunderstood. Your thread title was "Relationship Between Magnification vs Depth of Field". so I assumed that's what you were interested in.
That relationship turns out to be simple IF you hold Feff constant: DOF ∝ 1/m^2
If you don't hold Feff constant, then the relationship gets complicated and I can't do anything about that.
only geometric analysis is valid
The geometric models are fine as long as you're operating far away from the diffraction limit, that is, if your images are mainly limited by the resolution of sensor, display, or viewer.
The more a system is affected by diffraction, the less accurate the geometric models become.
In the limit of a system that is totally limited by diffraction, the geometric models simply give wrong answers, unless you re-parameterize them using C = Airy disk diameter and then they become OK again.
--Rik
No I am not questioning your logic. But I think we have one thing we interpret differently, let me explain.
I have asked my niece in Boston to look up the formula, it is from MicroscopeU. I do not have it, but it looks like this:
DOF = oc + g/M
oc is the diffraction term. For a given objective, ie, the one on the zoom, it should be constant. g is a geometric term, once an CoC is picked, it should be constant for an (or given) infinite objective (on the zoom), complicated for finite and normal lenses.
So from here, I totally understand your argument that,
The geometric models are fine as long as you're operating far away from the diffraction limit, that is, if your images are mainly limited by the resolution of sensor, display, or viewer.
This is indisputable from the MicroscopeU formula. Also this is indisputable:
In the limit of a system that is totally limited by diffraction, the geometric models simply give wrong answers, unless you re-parameterize them using C = Airy disk diameter and then they become OK again.
In fact all of your analysis are right, no doubt here. Except one thing
When people say relationship between magnification and DOF, particularly in the context in your other thread, they are asking, for a given setup, if they change the magnification, ie, change the zoom, what happens to the DOF? They are not asking how to determine DOF which has diffraction stuff there, they are asking the change of DOF due to zooming in and out.
So in that context, diffraction stuff becomes irrelevant, this is true if you look at the first order derivative with respect to magnification, the contribution for the diffraction terms to the change of DOF is zero! (they stay the same and get subtracted out if you perform numerical analysis with a computer, which I think you have done before) So changes will be solely due to geometric parameters. And if you look at the quick experiment done by the other member, at considerable magnification the change is less observable but it is there, this is due to the 1/M^2 factor in the first order derivative. But if M is considerable less, this will be so much apparent, same logic.
BTW, magnification itself is a unitless geometric parameter. So geometric analysis is in play as soon as it is mentioned in an argument
I think you are looking at it from determination of DOF rather than change of DOF. Hope this helps.
PS, I am not thrashing at all, if you read through them, those posts are process of my thoughts which I think can be good for others, be it right or wrong.