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    Quote Originally Posted by dadoboy View Post
    @ Josh and John Brawley I understand the connection between the limits in size of the Airy disk and photosite size, an am aware of the 2.5 constant for calculations. But why does the physics decide on a 2.5 constant? What does it mean, where does it come from?
    I’m reluctant to continue post here on this topic. My responses are being voted as not helpful.

    There’s a lot of things that affect the real world usefulness of these calculations.

    No one for example has brought up how fill factor affects these calculations. This is the active size of a pixel Vs it’s physical size.

    Things like microlens arrays can factor here too.

    Lens performance as well. An airy desk in a physics model is a perfect circle, but most lenses have some kind of aberrations that means it’s rarely uniform across the airy disk diameter interns of field flatness. (It’s darker often in the middle or the edges depending on the lens)

    It’s getting into some very esoteric ideas. And once you actually go out and shoot enough tests you can get a feel for how much in reality it will affect you in the way you shoot with the cameras you have.

    The general accepted consensus is 2.5x is a good compromise for all these factors.

    JB
    Last edited by John Brawley; 10-25-2020 at 10:58 AM.
    John Brawley ACS
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    www.johnbrawley.com
    I also have a blog


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    Senior Member ahalpert's Avatar
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    Quote Originally Posted by John Brawley View Post
    I’m reluctant to continue post here on this topic. My responses are being voted as not helpful.
    I could be wrong, but I think that some people (not me) downvoted your post where you mentioned that worrying too much maximum resolution would lead to sharp but boring looking movies. Of course you're right, but I'm not sure that Josh Cadmium or anyone else is necessarily advocating for achieving maximum resolution at the expense of other considerations. At any rate, I appreciation your contributions to the discussion


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    John, I appreciate your posts and contributions to the discussion. The info you share is helping us discover vast gap that can exist between theory, experience, and the real world ...there are many layers to the nuance. I can get lost in technical rabbit holes like many others. Locking down on ‘one’ aspect can make us miss the forest. I have to remind myself to step back to consider that beautiful footage isn’t created in laboratories. Art and science need each other to move forward. Between you and Joshua, I’m learning a lot. Thanks!
    Manuel

    Film Scientist
    www.filmscientist.com


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    Quote Originally Posted by John Brawley View Post
    I’m reluctant to continue post here on this topic. My responses are being voted as not helpful.
    John, I wanted to say that I had not downvoted that previous post and I do (as I've said before) highly appreciate your insight and your observations. You are a huge asset to this community. Just because I disagree in some (literally very small) places does not mean that I don't appreciate you.


    Quote Originally Posted by John Brawley View Post
    It’s getting into some very esoteric ideas. And once you actually go out and shoot enough tests you can get a feel for how much in reality it will affect you in the way you shoot with the cameras you have.
    I did want to say that it is one thing to say that what I am posting is esoteric and one thing to imply that I what I am posting is not helpful or perhaps wrong. It might not be helpful to how you shoot (heck, it's probably not going to make much of a difference to how I shoot) but diffraction on this camera is going to have some real world, practical implications, especially when cropping in. At a 2K crop of the sensor you will not be able to use high f stops and still get nearly as sharp of an image. That is not esoteric. It's also testable and agrees with all I've seen so far. If I had the camera in my hands I would certainly test that right now, but I have to rely on physics and math, and what is observable on other sensors.

    I think both of us want Blackmagic to succeed with this camera and one of the reasons why I am talking about this is because I don't want Blackmagic to be blamed for what is just physics. I can easily see some Youtuber say that you should avoid this camera if you want to crop in, or something to that effect, because of what he saw when he was stopped down too much on his lens.


    Quote Originally Posted by John Brawley View Post
    There’s a lot of things that affect the real world usefulness of these calculations. No one for example has brought up how fill factor affects these calculations. This is the active size of a pixel Vs it’s physical size. Things like microlens arrays can factor here too.
    If the active size of the pixel on the 12K is actually less than 2.2um, due to fill factor or the microlens not fully covering, that would have an impact, but it would make it so that diffraction would come more into play, not less. If the active pixel is 2.0mm, for instance, you would need to use an even larger f stop to capture the full resolution of the image.


    Quote Originally Posted by John Brawley View Post
    Lens performance as well. An airy desk in a physics model is a perfect circle, but most lenses have some kind of aberrations that means it’s rarely uniform across the airy disk diameter interns of field flatness. (It’s darker often in the middle or the edges depending on the lens)
    I did bring up aberrations multiple times. When you are dealing with aberrations in a lens, it just means that at some point, what you gain in resolution from stopping down outweighs the losses from diffraction. At another point, that reverses, and what you lose in diffraction, outweighs what you gain from stopping down. However, diffraction limited lenses will always lose resolution when you stop down.

    For another real world example: the Olympus 12-100 f4 will not gain any resolution from stopping down, at every single focal length (as tested on a 16MP 3.7um sensor): https://www.opticallimits.com/m43/10...0f4pro?start=1 . And this is a zoom lens - it's going to have more aberrations than a prime would.


    Quote Originally Posted by John Brawley View Post
    The general accepted consensus is 2.5x is a good compromise for all these factors.
    It's actually not a compromise for all those factors - it's based on the width of the central portion of the Airy Disk, which is 2.44. From there it is just rounded up to 2.5.

    2.44 is a dimensionless number (AKA a ratio - an f stop is also a dimensionless number) and needs the f stop and nanometer of light in order to determine the actual width.

    Take two Airy Disks and place them right next to one another. How far do you need to move one or both in order for them to overlap and then they cease being two Airy Disks? It's just the width of the Airy Disk or 2.44. (In fact, any two identical objects placed next to one another will overlap when moved towards each other 1x the width of the object).

    There is a little more to it than just that (and I'll have a follow up post), but that is why 2.5 is used. It's basically a simple number that tells us where two Airy Disks will meet and overlap each other.


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    Here is a visual example of lens aberration vs. diffraction (the lines are a little wonky - but you get the idea):



    AberrationVsDiffraction.jpg



    You can see that there is a point - a specific f stop - where resolution is maximized. Before that point, in this case f4.2, aberration is limiting the lens from delivering maximum resolution for the sensor. After that point, diffraction is steadily bringing the resolution down from that maximum point.

    But, if you don't need all the resolution a lens and sensor combination can give, then it might not matter to you. In the illustration it shows a yellow required resolution line (for our case, let's say it's a 4K delivery). For the illustration purposes, you could go up to f13.5 and still get the required resolution you need.

    If you move that yellow line up (let's say an 8K delivery or a 2k punch in) you are going to more quickly reach an f stop where you no longer have that much total resolution and things will start to look blurry at the viewing resolution.

    Also, for the lens in the example, as the target resolution increases (as the yellow line moves up) you have to stop down more to reach it - the f stop window for the target resolution narrows. If you wanted to hit 15 lp/mm, for instance, you could only do so in between about f4 and f5.6.

    This chart is just an example, though - don't get too caught up in the exact numbers. Different lens and sensor combinations are going to look different, but they will be similar to this.


    [The chart came from here: https://www.edmundoptics.com/knowled...t-test-target/ . (The rest of the article is not that helpful for what we are talking about.)]
    Last edited by Joshua Cadmium; 10-26-2020 at 12:05 AM.


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    Quote Originally Posted by Joshua Cadmium View Post
    Here is a visual example of lens aberration vs. diffraction (the lines are a little wonky - but you get the idea):



    AberrationVsDiffraction.jpg



    You can see that there is a point - a specific f stop - where resolution is maximized. Before that point, in this case f4.2, aberration is limiting the lens from delivering maximum resolution for the sensor. After that point, diffraction is steadily bringing the resolution down.

    But, if you don't need all the resolution a lens and sensor combination can give, then it might not matter to you. In the illustration it shows a yellow required resolution line (for our case, let's say it's a 4K delivery). For the illustration purposes, you could go up to f13.5 and still get the required resolution you need.

    If you move that yellow line up (let's say an 8K delivery or a 2k punch in) you are going to more quickly reach an f stop where you no longer have that much total resolution and things will start to look blurry at the viewing resolution.

    Also, for the lens in the example, as the target resolution increases (as the yellow line moves up) you have to stop down more to reach it - the f stop window for the target resolution narrows. If you wanted to hit 15 lp/mm, for instance, you could only do so in between about f4 and f5.6.

    This chart is just an example, though - don't get too caught up in the exact numbers. Different lens and sensor combinations are going to look different, but they will be similar to this.


    [The chart came from here: https://www.edmundoptics.com/knowled...t-test-target/ . (The rest of the article is not that helpful for what we are talking about.)]
    Is that for 4K raw, or 4K final from a 6K raw supersample?


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    To summarize about diffraction, I'm just going to quote from here: https://www.edmundoptics.com/knowled...raction-limit/ (a great read, but the video is not that helpful).

    "Every lens has an absolute upper performance limit dictated by the laws of physics. ... This limit is the point where two Airy patterns are no longer distinguishable from each other."

    When looking at resolution and diffraction, it helps to consider them in line pairs per millimeter. Lp/mm helps to determine resolution because it is easy to see when a white line blurs into a black area. Look at the difference in contrast you would see when the Airy Disks start to overlap:


    ContrastLPMMTop.jpg
    ContrastLPMMBottom3.jpg

    [Chart is from here: https://www.edmundoptics.com/knowled...sfer-function]


    --------


    With the Blackmagic 12K sensor, the LINES per millimeter is determined by: 1mm / 2.2um OR 1mm / .0022mm = 454.55 lines. To pair those lines up, just divide by two: 454.55 lines / 2 = 227.3 lp/mm

    Now, at what f stop are those lines completely blurred away - what is the f stop where resolution is absolutely decreased no matter what? The top website link gives us the formula:


    DiffractionLimit.jpg


    So, 227.3 lp/mm = 1000 / (f# * .550) OR f# = (1000/.550) / 227.3 = f8

    That means that for the Blackmagic 12K sensor, f8 is the ABSOLUTE limit for hitting a full 12K worth of the sensor.

    What does absolute limit mean? It means that at f8, contrast is ZERO for the 227.3 line pairs, which have completely blended into one another and formed a completely gray image at that resolution - there are no lines to be seen anymore.


    --------


    Note, though, that at that absolute limit, the white lines we are seeing blurring into one another are not right next to one another - they have one black line in between them. And, if we were absolutely maximizing resolution, one Airy Disk would equal one pixel. So at maximum resolution, the black areas would also be taken up by the width of one Airy Disk.

    I said before that for one Airy Disk to overlap another, one or both need to move a combined total of 1x Airy Disk or 2.44. Now that we are dealing with line pairs, the white portions have to travel further to completely overlap with one another. How far do they have to travel? The width of 2x Airy Disks or 4.88.

    How do I know this? Well, geometry - two equal objects 1x width between one another need to travel 2x width to overlap. Also, because what happens if we now say that 4.88x is the pixel width for diffraction? The math again would be 2.2um*4.88 pixels = 10.736um. To determine f number would be 10.736 / .550 / 2.44 = f8 . The math checks out (it's all related).

    So, to reiterate this, if line pairs (2 pixel widths apart) overlap at 4.88 pixel widths apart, where do lines 1 pixel width apart overlap? Where would a blue line right next to a red line overlap? Divide by two and you would be at 2x less than that, or 2.44 pixel widths.

    This might be hard to wrap your head around, but this was the long way to show why the math and physics get us to that 2.44 (or rounded 2.5x) diffraction number.

    However, and once again, 2.44 is where two lines next to one another completely overlap, not where they start to overlap - not where resolution starts to take a hit.


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    As an addendum: is 2.44 actually the width of an Airy Disk? What actually happens when they overlap, especially on a pixel (photosite) level? That's where it starts to get a little harder and why I was initially bringing up ensquared energy vs. encircled energy.


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    Quote Originally Posted by James0b57 View Post
    Is that for 4K raw, or 4K final from a 6K raw supersample?
    The chart is absolutely NOT for the 12K sensor - it's just an example of how a random lens performs on a random sensor. The numbers don't matter, just that there is always a point in the system where resolution is maximized and an f stop range where target resolution can be achieved.

    You could technically make a chart like that for the 12K sensor, but you would have to make one for every lens you use on it and it would not tell you anything about what the lens is actually doing to the image, except regarding pure resolution.

    In the words of Carl Sagan: "extraordinary claims require extraordinary evidence." Most of what I am posting is counter-intuitive, so I am trying to draw from whatever I can to prove my point.


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    Not sure how "downvoting" works but here's a suggestion: don't allow it to be anonymous. (If we can already see who downvoted then ignore this post - or downvote it.) Can't see why we need downvoting at all. If you disagree, have the cahones to say why politely.


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