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# Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
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Re: Diffraction Limit Discussion Continuation
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Jonny Boyd wrote:

Anders W wrote:

Jonny Boyd wrote:

I think part of the problem in the previous thread is people talking about different things using the same terms, or the same thing using different terms, or disagreeing about which tiny mathematical improvements should be regarded as real world differences, and which should be viewed as negligible changes. Rather than rehash the existing discussion, I'd like to approach things from a slightly different tack.

If we take the system resolution equation r = (l^-1/2 + s^-1/2)^-1/2 where r is the system resolution, l i the lens resolution, and s is the sensor resolution, then we can draw the following conclusions:

As l tends towards infinity, r approaches the limit s, as s tends towards infinity, l approaches the limit r, and when l and s are roughly equal r = l * 2^-1/2 = s * 2^-1/2.

In other words, as you improve sensor resolution, the overall system resolution increases, but can never be greater than the lens resolution. Similarly, as lens resolution improves, overall system resolution improves, but can never exceed the sensor resolution. In other words, there are hard limits on the resolution of the system.

Now imagine a system with resolution r_1 featuring a lens with resolution l_0, and a sensor with resolution s_1 = l_0 * 10^1/2. Also imagine a system with resolution r_2, featuring the same lens, but a different sensor with resolution s_2 = l_0 * 10^-1/2. Therefore s1 = 10 * s_2

r_1 = l_0 * (10/11)^1/2

r_2 = l_0 * (1/11)^1/2 = s_2 * (10/11)^1/2

The resolution of r_1 is effectively equal to the resolution of the lens, while the resolution of r_2 is effectively equal to the resolution of the sensor s_2.

Increasing the resolution of the sensor by an order of magnitude results in a swing from system resolution being determined predominantly by the resolution of the sensor to the system resolution being determined primarily by the lens.

Both systems should have their peak sharpness at about the same aperture, but the limiting factor in the resolution will be different for the two systems. Increase sensor resolution further beyond s_1 and won't get a high resolution than l_0 so it's effectively diffraction limited. Decrease the resolution below s_2 and it's predominantly the sensor resolution that determines the system resolution so diffraction is largely irrelevant. Hence some of us saying that r_1 is more limited by diffraction than r_2 even if peak sharpness is at the same aperture and r_1 is always greater than r_2.

Glad to see that you finally worked out the implications of the formula I gave you.

there,s nothing there that I hadn't already said to you in other ways.

There most certainly is: The recognition that the point along the aperture range where peak image resolution occurs is independent of sensor resolution.

Substantively, I have only two comments: That peak sharpness will occur at exactly rather than approximately the same aperture and that "my/our" side is hardly the one to blame for any conceptual or terminological misunderstandings.

Anders, I avoided assigning blame to anyone and put it down to misunderstanding.

Yes I saw that. So I pointed out what was missing.

Don't be in ass in response.

I am not being an ass. You decidedly are by calling me one for absolutely no good reason.

If you substantively agree then you'll also agree that when the sensor resolution drops below a certain level, the aperture size won't perceptibly reduce the system resolution in the same way as a system with a sensor resolution similar to the lens resolution. And once you get to a high enough sensor resolution, diffraction overwhelmingly determines system resolution so that the whole system is effectively diffraction limited from wide-open.

What I substantively agree with is the following:

When the sensor resolution is much lower than lens resolution, variations in lens resolution will have but a small impact on image resolution (but still always such that increased lens resolution leads to increased image resolution). When it is the other way around (lens resolution much lower than sensor resolution), variations in lens resolution will have a much stronger impact on image resolution.

I tried to put that to you earlier, but you seemed dismissive of the idea. I'm unclear about whether that is still the case..

Where was I dismissive about the idea as I spelled it out above? Please provide specific references (the post/posts you have in mind and the passage/passages in those posts).

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