Diffraction Limit Discussion Continuation

Started 6 months ago | Discussions thread
Jonny Boyd
Forum MemberPosts: 89
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Re: Check your maths
In reply to Just another Canon shooter, 6 months ago

Just another Canon shooter wrote:

Jonny Boyd wrote:

Just another Canon shooter wrote:

Jonny Boyd wrote:

So where does delta_w become too small to notice a change in resolution? When delta_w < w_0.

What if that happens when delta_w/w_p<w_0 (which is approximately d(log w)<w_0)? Imagine all the colors then!

I don't have a maths degree, but I'm pretty sure you can't compare units with different dimensions, so asking if delta_w/w_p (dimensionless) is less than w_0 (length) is nonsensical.

It is, if you put there a constant that changes with the units, like the gravitational constant in Newton's law.

Let me revise it then, if R is the "resolution" in fixed units, why not dR/R^2<0.05. That would be d(log R)/R<0.05, i.e., the rate of change of R on a log scale. And yes, 0.05 would change if you change the units, and whether this is the right law or not, can be decided by experiments with people. It is not such a strange low if you think about it, it reflects the expectation that when you start increasing R too much, you notice that less and less. If you do not like log, I can replace it with your favorite function with a decreasing derivative.

To clarify, do you mean -d/dL ([log (R)] / R) where R = (1/L^2 + 1/S^2)^-1/2 ?

If so, then I think it looks like this (though my calculus is admittedly rusty):

If the threshold under certain viewing condition was 0.05, then a sensor in the range of l_p*10^-0.25 to l_p*10^0.5 would show a noticeable drop in resolution when the lens resolution drops to 0.95*l_p. Higher and lower resolution sensors wouldn't exhibit any noticeable change, presumably because every image from the higher res sensors would be too high to show change and the lower resolution ones wouldn't show enough change to be noticeable.

If under different viewing conditions the threshold was 1.5, then for sensors with resolution l_p or worse, you could stop down as far as 0.65*l_p while a camera with resolution roughly a third of the lens would never show any visible loss in resolution.

BTW, I am still playing your game, in which I do not believe to begin with.

I'm not sure what 'game' that's supposed to be, or why you don't 'believe' in it.

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