# Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions
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Re: Diffraction Limit Discussion Continuation

bobn2 wrote:

That seems eminently sensible. I note pixel size doesn't come into it.

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Bob

He didn't even look at pixel size. There is zero investigation there of whether or not pixel size makes a difference. given that the photo.net page that lays out the calculations refers to film I'm guessing that whoever put that page together wasn't looking to see if pixel size doesn't impose any additional limitations.

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Re: Cutting to the chase.

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal.

As I've repeatedly said, including in the post you quoted, indeed the very line you quoted, I'm referring to the peak visible resolution, not the peak resolution. There's an important difference.

At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed,

That's exactly what I've been claiming the whole time in this thread.

none of which has anything, whatsoever, to do with being "diffraction limited".

Diffraction causes a decrease in resolution, agreed?

When resolution drops due to stopping down from the peak aperture, that is due to diffraction, agreed?

At the aperture at which diffraction is reducing resolution, you can say that diffraction is limiting the resolution of the final image, agreed?

If resolution appears to be the same at an aperture smaller than the peak aperture then diffraction doesn't become the dominant factor in limiting resolution until later than the peak aperture, agreed?

Therefore, for practical purposes, as far as the eye can see, a system where resolution visibly drops immediately after peak aperture is more limited by diffraction than a system where the visible drop happens later. Agreed?

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Re: Cutting to the chase.
1

Jonny Boyd wrote:

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal. At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed, none of which has anything, whatsoever, to do with being "diffraction limited".

+1. The formula Johnny uses can be justified under some assumptions, like a Gaussian blur. But it proves him wrong, as the plots illustrate (the formula, too, but I guess formulas are out of fashion nowadays).

And where exactly does it prove me wrong? It would be helpful if you elucidated rather than making bald assertions.

The maximum is always at f/4, despite your efforts to spin it. GB explained it well, that is why I did not add anything. It can be also seen from the formula.

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Re: Diffraction Limit Discussion Continuation
3

Jonny Boyd wrote:

bobn2 wrote:

That seems eminently sensible. I note pixel size doesn't come into it.

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Bob

He didn't even look at pixel size.

Indeed, that's one reason he's being sensible.

There is zero investigation there of whether or not pixel size makes a difference.

Simply not true. Of course, it depends what the 'difference' is that you're referring to, but if it's the f-number for peak resolution, the theory would suggest that it makes no difference (since the system PSF is the convolution of lens and camera PSF, and only the lens is f-number dependent to any significant degree), moreover none of the lens testing sites which have tested the same lens on different pixel count cameras shows any shift in the peak with pixel size.

given that the photo.net page that lays out the calculations refers to film I'm guessing that whoever put that page together wasn't looking to see if pixel size doesn't impose any additional limitations.

Until someone comes up with some evidence that this shift in the peak with f-number exists (evidence, you know the stuff, made up from real observations, not made-up numbers) there really isn't any point 'looking to see'. It'd be more productive looking for the yeti.

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Bob

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Re: Diffraction Limit Discussion Continuation
1

Hi Jonny,

Jonny Boyd wrote:

bobn2 wrote:

That seems eminently sensible. I note pixel size doesn't come into it.

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Bob

He didn't even look at pixel size. There is zero investigation there of whether or not pixel size makes a difference. given that the photo.net page that lays out the calculations refers to film I'm guessing that whoever put that page together wasn't looking to see if pixel size doesn't impose any additional limitations.

I've thoroughly considered pixel size, but there's absolutely no need to consider it when calculating the f-Number at which diffraction begins to inhibit a desired print resolution at an anticipated enlargement factor.

I ended that post with an invitation to keep reading...

With both CoC (defocus) and f-Number "limit" (diffraction) calculations relying on user-specification of a "desired print resolution," further reading is available here: http://www.dpreview.com/forums/post/40100820

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Re: Diffraction Limit Discussion Continuation

You're making an excellent point, Steen.

Steen Bay wrote:

Mike Davis wrote:

Yes, enlargement factor and desired print resolution are the only variables affecting the selection of a CoC diameter for DoF calculations (assuming you have considered viewing distance when specifying your desired print resolution). And they are the only variables affecting the f-Number at which diffraction will begin to inhibit a desired resolution.

What about the resolution of the sensor/system? Think it's necessary to take the max potential resolution in account too if we want to know at which point the resolution will be visibly affected. Both when calculating DoF and 'diffraction limit' at 100% view (equivalent to a large print). Guess that app. 2x pixel size/pitch is 'appropriate' in both cases.

I ended an earlier post with an invitation to keep reading...

With both CoC (defocus) and f-Number "limit" (diffraction) calculations relying on user-specification of a "desired print resolution," further reading is available here: http://www.dpreview.com/forums/post/40100820

Quoting myself from that post:

Before you can select a "desired" final image resolution, you have to be realistic when selecting an enlargement factor.

For example, the Nikon D300's 15.7 x 23.7mm sensor captures 4288 x 2848 pixels (12.21 MP) at a moderate pixel density of 181 pixels/mm.

Taking into account the loss of resolution caused by the RGBG Bayer algorithm and AA filter, typically a 30% loss relative to actual pixel count, if you "desire" to record subject detail in the final image at a resolution of 5 lp/mm, you'll be limited by pixel count to the following print dimensions:

Max. 5 lp/mm Width: 4288 pixels / 360 dpi = 11.91 inches
Max. 5 lp/mm Height: 2848 pixels / 360 dpi = 7.91 inches

Assuming you plan to make 7.91 x 11.91-inch prints (where the Pixel Count will support a desired print resolution of 5 lp/mm), your enlargement factor (without cropping) would be 11.91 inches / 23.7mm = 302.54 mm / 23.7mm = 12.8x

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Re: Cutting to the chase.

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal. At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed, none of which has anything, whatsoever, to do with being "diffraction limited".

+1. The formula Johnny uses can be justified under some assumptions, like a Gaussian blur. But it proves him wrong, as the plots illustrate (the formula, too, but I guess formulas are out of fashion nowadays).

If you really want a formula, then here we go. Bob, you should red this too.

We're going to consider two camera systems with sensors with resolution b and s when b > s.

We're also going to consider a lens with resolution at peak aperture of l_p.

We'll us units such that l_p = 1. If the resolution at ant aperture is l then 1 => l > 0.

If we want to compare the resolution of the two systems then we can use the formula

1/system resolution^2 = 1/lens resolution^2 + 1/sensor resolution^2

The resolution for sensor b is therefore r_bl = sqrt [(l^2 * b^2) / (l^2 + b^2)] which at peak aperture will be r_bp = sqrt [b^2 / (1 + b^2)]

Similarly for sensor s, r_sl = sqrt [(l^2 * s^2) / (l^2 + s^2)] which at peak aperture will be r_sp = sqrt [s^2 / (1 + s^2)]

When stopping down the lens, the relative drop in resolution for sensor b will be: Drop_rel_b = 1 - (r_bl / r_bp)

Similarly for sensor s, the drop will be: Drop_rel_s = 1 - (r_sl / r_sp)

The difference between these two relative drops is:

Drop_rel_b - Drop_rel_s = 1 - (r_bl / r_bp) - 1 + (r_sl / r_sp) = (r_sl / r_sp) - (r_bl / r_bp)

If this is equal to zero, then when stopping down to the same aperture then resolution drops at the same relative rate e.g. by 5% of peak resolution. If it is greater than zero, then the higher resolution sensor (b) experiences a greater drop relative to its peak resolution. Since its peak resolution is also great than for the lower resolution sensor (s), this will also equate to a great absolute drop.

So is there a greater relative drop i..e is Drop_rel_b - Drop_rel_s > 0?

Drop_rel_b - Drop_rel_s = (r_sl / r_sp) - (r_bl / r_bp)

= sqrt ([(l^2 * s^2) / (l^2 + s^2)] / [s^2 / (1 + s^2)]) - sqrt ([(l^2 * b^2) / (l^2 + b^2)] / [b^2 / (1 + b^2)])

= sqrt [(l^2 + l^2 * s^2] / (l^2 + s^2)] - sqrt [(l^2 + l^2 * b^2] / (l^2 + b^2)]

= l * ( sqrt [(1 + s^2] / (l^2 + s^2)] - sqrt [(1 + b^2] / (l^2 + b^2)])

= (l / sqrt [(l^2 + s^2) * (l^2 + b^2]) * (sqrt [l^2 + b^2 + l^2 * s^2 + b^s * s^2] - sqrt [l^2 + s^2 + b^2 * l^2 + b^2 * s^2])

If sqrt [l^2 + b^2 + l^2 * s^2 + b^s * s^2] > sqrt [l^2 + s^2 + b^2 * l^2 + b^2 * s^2] then Drop_rel_b - Drop_rel_s > 0

l^2 and b^2 * s^2 appear on both sides, so taking them out, if b^2 + l^2 * s^2 > s^2 + l^2 * b^2 then Drop_rel_b - Drop_rel_s > 0.

X = b^2 + l^2 * s^2 - s^2 - l^2 * b^2

If X > 0 then Drop_rel_b - Drop_rel_s > 0.

X = b^2 + l^2 * s^2 - s^2 - l^2 * b^2

= b^2 * (1 - l^2) - s_2 (1 - l^2)

= (b^2 - s^2) * (1 - l^2)

As established earlier, l <=1, therefore (1 - l^2) > 0.

Also as established earlier, b > s, therefore (b^2 - s^2) > 0.

Therefore X > 0 and Drop_rel_b - Drop_rel_s > 0.

Therefore the relative drop in resolution is great for a higher resolution sensor than a lower resolution one.

Therefore the absolute drop is also bigger.

The final implication of this is that as sensor size decreases, the drop in resolution when stepping down constantly decreases. Given that human eyes have finite ability to distinguish resolution, there will come a point where the resolution at an aperture lower than the peak aperture will be indistinguishable from the resolution at peak aperture to the human eye.

That's exactly what I've said with words, illustrated with numbers and charts and have proved with numbers.

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Re: Cutting to the chase.

Just another Canon shooter wrote:

Jonny Boyd wrote:

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal. At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed, none of which has anything, whatsoever, to do with being "diffraction limited".

+1. The formula Johnny uses can be justified under some assumptions, like a Gaussian blur. But it proves him wrong, as the plots illustrate (the formula, too, but I guess formulas are out of fashion nowadays).

And where exactly does it prove me wrong? It would be helpful if you elucidated rather than making bald assertions.

The maximum is always at f/4, despite your efforts to spin it. GB explained it well, that is why I did not add anything. It can be also seen from the formula.

So you think that the human eye will always perceive a resolution difference when stopping down to any aperture, using any resolution of sensor to capture the image?

No-one disputes that the maximum is always at the same aperture. That has repeatedly been said. I'm talking about whether in the real world you will notice any difference and whether you can then actually stop down further than the peak without incurring any perceived loss of resolution.

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Re: Diffraction Limit Discussion Continuation

bobn2 wrote:

Jonny Boyd wrote:

bobn2 wrote:

That seems eminently sensible. I note pixel size doesn't come into it.

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Bob

He didn't even look at pixel size.

Indeed, that's one reason he's being sensible.

If you assume that pixel count makes no difference and make no attempt to investigate whether pixel count makes a difference, how can you authoritatively say that pixel count makes no difference? That's utterly illogical.

There is zero investigation there of whether or not pixel size makes a difference.

Simply not true. Of course, it depends what the 'difference' is that you're referring to, but if it's the f-number for peak resolution, the theory would suggest that it makes no difference (since the system PSF is the convolution of lens and camera PSF, and only the lens is f-number dependent to any significant degree), moreover none of the lens testing sites which have tested the same lens on different pixel count cameras shows any shift in the peak with pixel size.

You're completely dodging the point. Again. No-one disputes that the peak resolution occurs at the same f-number regardless of the sensor used. The dispute is whether the pixel count makes any difference to perceived resolution. If you can't tell the difference between resolution at peak aperture and resolution at a smaller aperture, then for all practical purposes, they have the same resolution and pixel size does make a difference. Do put agree with that or not?

given that the photo.net page that lays out the calculations refers to film I'm guessing that whoever put that page together wasn't looking to see if pixel size doesn't impose any additional limitations.

Until someone comes up with some evidence that this shift in the peak with f-number exists (evidence, you know the stuff, made up from real observations, not made-up numbers) there really isn't any point 'looking to see'. It'd be more productive looking for the yeti.

I've given you realistic, representative numbers which you can't seem to find any particular fault with. I've plotted charts. I've tried to explain things with words. I've also done a fair bit of mathematics, using the rule of thumb formula in the way in which you indicated it should be used. I'm at a loss to understand why you can't see the truth here.

I have five questions below that summarise the key points of my argument. Perhaps if you can point out where you disagree with one of the key points, we can see where the problem is.

1) If you take two cameras, one with a high-res sensor and one with a low-res sensor and put the same lens on them, then step down the aperture form peak resolution, the higher res sensor will experience a greater relative drop in resolution (i.e. drops to a lower percentage of the peak resolution) - yes or no?

2) If it does experience a greater relative drop in resolution, it must also experience a greater absolute drop in resolution - yes or no?

3) There is a limit to the resolution that the eye can perceive - yes or no?

4) There is a limit to the difference in two similar resolutions that the eye can perceive - yes or no?

5) If the relative and absolute drop in resolution both become smaller with lower resolution sensors, and if the ability of the eye to tell the difference in resolution is finite, then there will eventually come a point where the sensor resolution is sufficiently small that stopping down the aperture produces no visible decrease in resolution - yes or no?

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Re: Cutting to the chase.
1

Jonny Boyd wrote:

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal. At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed, none of which has anything, whatsoever, to do with being "diffraction limited".

+1. The formula Johnny uses can be justified under some assumptions, like a Gaussian blur. But it proves him wrong, as the plots illustrate (the formula, too, but I guess formulas are out of fashion nowadays).

If you really want a formula, then here we go. Bob, you should red this too.

We're going to consider two camera systems with sensors with resolution b and s when b > s.

We're also going to consider a lens with resolution at peak aperture of l_p.

We'll us units such that l_p = 1. If the resolution at ant aperture is l then 1 => l > 0.

If we want to compare the resolution of the two systems then we can use the formula

1/system resolution^2 = 1/lens resolution^2 + 1/sensor resolution^2

The resolution for sensor b is therefore r_bl = sqrt [(l^2 * b^2) / (l^2 + b^2)] which at peak aperture will be r_bp = sqrt [b^2 / (1 + b^2)]

Similarly for sensor s, r_sl = sqrt [(l^2 * s^2) / (l^2 + s^2)] which at peak aperture will be r_sp = sqrt [s^2 / (1 + s^2)]

When stopping down the lens, the relative drop in resolution for sensor b will be: Drop_rel_b = 1 - (r_bl / r_bp)

Similarly for sensor s, the drop will be: Drop_rel_s = 1 - (r_sl / r_sp)

The difference between these two relative drops is:

Drop_rel_b - Drop_rel_s = 1 - (r_bl / r_bp) - 1 + (r_sl / r_sp) = (r_sl / r_sp) - (r_bl / r_bp)

If this is equal to zero, then when stopping down to the same aperture then resolution drops at the same relative rate e.g. by 5% of peak resolution. If it is greater than zero, then the higher resolution sensor (b) experiences a greater drop relative to its peak resolution. Since its peak resolution is also great than for the lower resolution sensor (s), this will also equate to a great absolute drop.

So is there a greater relative drop i..e is Drop_rel_b - Drop_rel_s > 0?

Drop_rel_b - Drop_rel_s = (r_sl / r_sp) - (r_bl / r_bp)

= sqrt ([(l^2 * s^2) / (l^2 + s^2)] / [s^2 / (1 + s^2)]) - sqrt ([(l^2 * b^2) / (l^2 + b^2)] / [b^2 / (1 + b^2)])

= sqrt [(l^2 + l^2 * s^2] / (l^2 + s^2)] - sqrt [(l^2 + l^2 * b^2] / (l^2 + b^2)]

= l * ( sqrt [(1 + s^2] / (l^2 + s^2)] - sqrt [(1 + b^2] / (l^2 + b^2)])

= (l / sqrt [(l^2 + s^2) * (l^2 + b^2]) * (sqrt [l^2 + b^2 + l^2 * s^2 + b^s * s^2] - sqrt [l^2 + s^2 + b^2 * l^2 + b^2 * s^2])

If sqrt [l^2 + b^2 + l^2 * s^2 + b^s * s^2] > sqrt [l^2 + s^2 + b^2 * l^2 + b^2 * s^2] then Drop_rel_b - Drop_rel_s > 0

l^2 and b^2 * s^2 appear on both sides, so taking them out, if b^2 + l^2 * s^2 > s^2 + l^2 * b^2 then Drop_rel_b - Drop_rel_s > 0.

X = b^2 + l^2 * s^2 - s^2 - l^2 * b^2

If X > 0 then Drop_rel_b - Drop_rel_s > 0.

X = b^2 + l^2 * s^2 - s^2 - l^2 * b^2

= b^2 * (1 - l^2) - s_2 (1 - l^2)

= (b^2 - s^2) * (1 - l^2)

As established earlier, l <=1, therefore (1 - l^2) > 0.

Also as established earlier, b > s, therefore (b^2 - s^2) > 0.

Therefore X > 0 and Drop_rel_b - Drop_rel_s > 0.

Therefore the relative drop in resolution is great for a higher resolution sensor than a lower resolution one.

You do like wasting your own time. I don't think anyone has disputed that would be the case.

Therefore the absolute drop is also bigger.

Also probably true.

The final implication of this is that as sensor size decreases, the drop in resolution when stepping down constantly decreases.

Pixel count, you probably mean. Best not to complicate things with different sensor sizes at this point.

Given that human eyes have finite ability to distinguish resolution,

That statement is very ill formed, so much so as to be meaningless. What do we mean by 'resolution' and how does one 'distinguish' it? Best to stick with measurable things rather than make unevidenced and undoubtedly simplistic assumptions about human perception. What, for instance, is the role of acuity in all this? Is MTF50 a good model for perceived resolution?

there will come a point where the resolution at an aperture lower than the peak aperture will be indistinguishable from the resolution at peak aperture to the human eye.

However, I would hazard a guess that is probably true. So what? When the image is degraded so much that you can't distinguish between one f-number and another, are we really interested at all? Remember, the decision we're trying to inform here is the trade between DOF and resolution. Just thinking about that trade presupposes a concern for image quality which certainly won't be satisfied by a system so un-diffraction-limited that diffraction has ceased to be a player in resolution at any f-number (and interestingly, this 'diffraction limited' you're talking about has become precisely the reverse of what it means in an astronomical or microscope context). Let's just be clear, as camera with those properties is a dreadful camera, one no serious photographer would want.

That's exactly what I've said with words, illustrated with numbers and charts and have proved with numbers.

You've 'proved' nothing with numbers - working fictitious numbers cannot prove anything. Working fictitious anything can't prove anything.

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Re: Cutting to the chase.

bobn2 wrote:

Therefore the relative drop in resolution is great for a higher resolution sensor than a lower resolution one.

You do like wasting your own time. I don't think anyone has disputed that would be the case.

You seemed to be highly sceptical of everything I've previously posted.

Therefore the absolute drop is also bigger.

Also probably true.

Then I don't understand why you kept disagreeing with me.

The final implication of this is that as sensor size decreases, the drop in resolution when stepping down constantly decreases.

Pixel count, you probably mean. Best not to complicate things with different sensor sizes at this point.

I meant pixel count, yes.

Given that human eyes have finite ability to distinguish resolution,

That statement is very ill formed, so much so as to be meaningless. What do we mean by 'resolution' and how does one 'distinguish' it? Best to stick with measurable things rather than make unevidenced and undoubtedly simplistic assumptions about human perception. What, for instance, is the role of acuity in all this? Is MTF50 a good model for perceived resolution?

How exactly is it 'ill-informed'? It's a general statement about the ability of the human eye to resolve detail, saying that it has limits. I'm trying to establish what the limits are, merely that they exist. It would be ill-informed to suggest that the human eye has no limit on its ability to perceive detail or differences in resolution.

there will come a point where the resolution at an aperture lower than the peak aperture will be indistinguishable from the resolution at peak aperture to the human eye.

However, I would hazard a guess that is probably true.

Why guess? I did the maths for you. I've outlined the logic. Why guess?

And if you agree, why did you keep trying to tell me I was wrong?

So what? When the image is degraded so much that you can't distinguish between one f-number and another, are we really interested at all?

Without looking at actual examples that's an entirely speculative question. I was merely establishing that the principle that at some point resolution becomes too low to distinguish between the peak aperture and another aperture.

Remember, the decision we're trying to inform here is the trade between DOF and resolution. Just thinking about that trade presupposes a concern for image quality which certainly won't be satisfied by a system so un-diffraction-limited that diffraction has ceased to be a player in resolution at any f-number (and interestingly, this 'diffraction limited' you're talking about has become precisely the reverse of what it means in an astronomical or microscope context).Let's just be clear, as camera with those properties is a dreadful camera, one no serious photographer would want.

I've established a principle, I haven't run numbers to say whether such a camera would always be dreadful. To a extent that's a subjective statement.

That's exactly what I've said with words, illustrated with numbers and charts and have proved with numbers.

You've 'proved' nothing with numbers - working fictitious numbers cannot prove anything. Working fictitious anything can't prove anything.

The numbers illustrated the exact mathematics I did above. If the mathematics you seem to now agree with are correct, then the numbers are examples of what resolution looks like for certain combinations of sensor and lens. If you took a sensors with some of those resolution, and a lens with that resolution, you would get those results, or something close enough since the formula is only a rule of thumb.

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Re: Cutting to the chase.
1

Jonny Boyd wrote:

Just another Canon shooter wrote:

Jonny Boyd wrote:

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

So you think that the human eye will always perceive a resolution difference when stopping down to any aperture, using any resolution of sensor to capture the image?

No-one disputes that the maximum is always at the same aperture. That has repeatedly been said. I'm talking about whether in the real world you will notice any difference and whether you can then actually stop down further than the peak without incurring any perceived loss of resolution.

You will not notice much difference if you open up more, either. All this based on you idea that a 5% drop from, say, 1200 is the same, visually, as 5% drop from 2400, which is a very bold assumption and flat out wrong at moderate viewing sizes.

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Re: Cutting to the chase.

Just another Canon shooter wrote:

Jonny Boyd wrote:

Just another Canon shooter wrote:

Jonny Boyd wrote:

Just another Canon shooter wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

So you think that the human eye will always perceive a resolution difference when stopping down to any aperture, using any resolution of sensor to capture the image?

No-one disputes that the maximum is always at the same aperture. That has repeatedly been said. I'm talking about whether in the real world you will notice any difference and whether you can then actually stop down further than the peak without incurring any perceived loss of resolution.

You will not notice much difference if you open up more, either. All this based on you idea that a 5% drop from, say, 1200 is the same, visually, as 5% drop from 2400, which is a very bold assumption and flat out wrong at moderate viewing sizes.

And where exactly is that assumption? I am concerned with the general principle that lower resolution sensors experience lower relative and absolute drops in resolution than higher resolution ones. I don't know exactly where the limit would be for when the eye would no longer perceive a difference, but as long as there are limits, then a point will eventually come where the change in resolution is indistinguishable.

I repeat: I am making no claims about when this would happen, merely that it would happen  if you kept reducing the sensor resolution relative to the lens resolution.

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Re: Cutting to the chase.
3

Jonny Boyd wrote:

bobn2 wrote:

Therefore the relative drop in resolution is great for a higher resolution sensor than a lower resolution one.

You do like wasting your own time. I don't think anyone has disputed that would be the case.

You seemed to be highly sceptical of everything I've previously posted.

I've been very sceptical of the methodology of your 'proof','demonstration', whatever it was. What I've said is that it doesn't prove anything, not least the thing you think that it proves, which is that the f-number of the peak moves with pixel size. That doesn't mean that some of the random assumptions that you built in don't accord with reality.

Therefore the absolute drop is also bigger.

Also probably true.

Then I don't understand why you kept disagreeing with me.

I only disagreed with the bits where you were clearly wrong, or your line of reasoning made no sense or your method for demonstrating the 'truth' was nonsense. I have a strong aversion to bogusly quantitative demonstrations, because they fool a lot of people into thinking they're based on reality. McHugh's 'diffraction limit calculator' falls into exactly the same category.

The final implication of this is that as sensor size decreases, the drop in resolution when stepping down constantly decreases.

Pixel count, you probably mean. Best not to complicate things with different sensor sizes at this point.

I meant pixel count, yes.

Given that human eyes have finite ability to distinguish resolution,

That statement is very ill formed, so much so as to be meaningless. What do we mean by 'resolution' and how does one 'distinguish' it? Best to stick with measurable things rather than make unevidenced and undoubtedly simplistic assumptions about human perception. What, for instance, is the role of acuity in all this? Is MTF50 a good model for perceived resolution?

How exactly is it 'ill-informed'?

I said and meant 'ill formed', not 'ill informed'.

It's a general statement about the ability of the human eye to resolve detail, saying that it has limits.

Now you say 'detail', then you said 'resolution'. Which do you mean? Again, when you say 'finite' you are suggesting something quantitative - that 'resolution' or 'detail' could be measured, and there is some result which says that below some limit of this metric, the eyes cannot resolve. So, which do you mean, how is it measured and where is the perceptual evidence o back up what you say?

I'm trying to establish what the limits are, merely that they exist.

You haven't even done that. Clearly the human visual system has its limits, but so far you have given no information about their nature. I raised the word 'acutance' in a previous post. Is this important? Does the perception of 'detail' or 'resolution' depend on light levels? Does it depend on the type of image? Human perception is a complex thing, and the existence of a simple limit, where you could say that at some point something is invisible based just on an MTF50 measurement, is not a given.

It would be ill-informed to suggest that the human eye has no limit on its ability to perceive detail or differences in resolution.

No-one said 'ill informed'. But it is indeed 'ill informed' to assume that human perception has very simple limits that can be predicted with a metric like MTF50, especially when there can be such variety in viewing conditions, which have not been stated.

there will come a point where the resolution at an aperture lower than the peak aperture will be indistinguishable from the resolution at peak aperture to the human eye.

However, I would hazard a guess that is probably true.

Why guess? I did the maths for you. I've outlined the logic. Why guess?

The maths was done based on fictitious figures, the logic was fallacious - therefore your exercised shows nothing. That doesn't mean that some of the results you were purporting to show don't stack up in the real world.

And if you agree, why did you keep trying to tell me I was wrong?

I told you that your experiment was bogus beginning to end, see above about its relationship to real world results.

So what? When the image is degraded so much that you can't distinguish between one f-number and another, are we really interested at all?

Without looking at actual examples that's an entirely speculative question.

Take it as a hypothetical. Does your running the numbers show you just how low a pixel count a camera would need to take diffraction out of the picture? Is that a pixel count most serious photographers would be content with?

I was merely establishing that the principle that at some point resolution becomes too low to distinguish between the peak aperture and another aperture.

You just had to say it - that isn't controversial.

Remember, the decision we're trying to inform here is the trade between DOF and resolution. Just thinking about that trade presupposes a concern for image quality which certainly won't be satisfied by a system so un-diffraction-limited that diffraction has ceased to be a player in resolution at any f-number (and interestingly, this 'diffraction limited' you're talking about has become precisely the reverse of what it means in an astronomical or microscope context).Let's just be clear, as camera with those properties is a dreadful camera, one no serious photographer would want.

I've established a principle,

Not at all. The 'principle' you established - that you can reduce pixel count to the point where diffraction is the least of your worries - was pretty obvious to everyone. But that wasn't the 'priciple' you purported to be establishing, which was that there would be a 'plateau' which would effectively move the peak resolution. You never established that.

I haven't run numbers to say whether such a camera would always be dreadful. To a extent that's a subjective statement.

To an extent Let's go back to your own numbers. We seem to get a pretty flat line when the 'sensor resolution' is 30. 30 what, you don't say, but we can make an estimate, because the lens resolution for the lens at f/22 is 60 of whatever they are. f/22 in practice is usually diffraction limited and seems to give an MTF50 of 30 lp/mm on lenstip's methodology (http://www.lenstip.com/392.4-Lens_review-Olympus_M.Zuiko_Digital_12-40_mm_f_2.8_ED_PRO_Image_resolution.html). So '60' means 30 lp/mm, which means that '30' means '15'. So we're talking about 15 lp/mm or 30 pixels/mm, or 200k pixels on a mFT sensor. Do you think that is a resolution anyone here is seriously going to aim for?

That's exactly what I've said with words, illustrated with numbers and charts and have proved with numbers.

You've 'proved' nothing with numbers - working fictitious numbers cannot prove anything. Working fictitious anything can't prove anything.

The numbers illustrated the exact mathematics I did above. If the mathematics you seem to now agree with are correct,

I don't agree that the 'mathematics' are 'correct'. As i said, you used a sometimes useful approximate formula, ran some unrealistic numbers with it, and came out with a bogusly quantitative result which did no more than show what was obvious before you did it. You wasted your time and brought nothing new to the discussion. The fact that I agree that the obvious was all along obvious in no way validates your 'mathematics'.

then the numbers are examples of what resolution looks like for certain combinations of sensor and lens. If you took a sensors with some of those resolution, and a lens with that resolution, you would get those results, or something close enough since the formula is only a rule of thumb.

200kP is your measure of quality? Why, exactly, do you have an interest in mFT equipment?

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Re: Cutting to the chase.
1

Jonny Boyd wrote:

Just another Canon shooter wrote:

You will not notice much difference if you open up more, either. All this based on you idea that a 5% drop from, say, 1200 is the same, visually, as 5% drop from 2400, which is a very bold assumption and flat out wrong at moderate viewing sizes.

And where exactly is that assumption?

You are applying 5% threshold for low density sensors and for higher one. This does no prove existence of a limit but let us play that game for a moment. Why fixed percentage? Why not measure it absolute terms? Why not on a log scale?

Now, one can say that at a higher resolution 5% matters less because we cannot benefit much from that high resolution anyway, depending on how we view the result, of course. Then you should choose, say, 10% threshold at higher densities instead. And the results may surprise you.

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Re: Diffraction Limit Discussion Continuation

Interesting thoughts...  at least from the point of view of those who wrote them. Fortunately, it's a lovely spring day and I might just slap a couple ND filters on my camera and shoot at f20 all afternoon.

Diffraction shmaction.

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Re: Diffraction Limit Discussion Continuation
2

Jonny Boyd wrote:

). ) Anders W wrote:

Jonny Boyd wrote:

Anders W wrote:

Jonny Boyd wrote:

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.

I never denied that.

Yes you did. Do you want me to look up the specific posts where you denied it or are you going to acknowledge it voluntarily?

There was a post (Re: Nope.) where I said that peak resolution for a lens affected only by diffraction, would be wide open. Other optical effects would limit that. The lens itself will have an inherent peak aperture and I made that point that as you increase the aperture and the resolution of the lens drops, cameras become less and less able to take advantage.

The way I described was over simplified because I forgot to take into account the fact that you do still gain advantage from having a sensor resolution higher than the lens resolution. If you had three sensors with resolution s_1 > s_2 > s_3 then when the lens is stopped down to reduce the resolution to about 3 * s_2, then you get no meaningful advantage from using s_1 instead of s_2, though you're still better using them than s_2. Stop down so that the lens resolution is about 3 * s_1 and there's no meaningful difference between the resolution of the sensors. That's due to diffraction, so that's the practical limit imposed by diffraction if you're trying to decide whether it's worth using a higher resolution camera or not. That seemed to me to be the practical point of asking where diffraction causes a limitation.

As I said, in that particular post I forgot to account for higher resolution sensors being useful up to a point and left out the factor of 3, but otherwise the broad point I was making was still correct.

In this post (Re: So, what are the m4/3 diffraction limits?) I said that for a sensor with much loser resolution than the resolution of the lens, then there would be a plateau of sharpness, rather than a peak. I've modelled that and put on a chart which demonstrates exactly that. I'm guessing the disagreement here is over the definition of peaks and plateaus, so I probably should have clarified that I wasn't talking about a perfectly flat sharpness, but rather a peak is so spread out, with minimal drop across multiple f-stops, certainly much flatter than the curve for higher res images, that it's virtually indistinguishable from flat. If system resolution only drops 1% between peak aperture and f/22, then that's a plateau compared to a system where resolution drops 40% between peak aperture and f/22.

In retrospect I should have taken more time to spell out exactly what I meant by plateau.

I said that at low resolutions it's more of a plateau that a peak, so you effectively get the same resolution at smaller apertures.

No you didn't say that. You said the peak would occur at different apertures depending on sensor resolution (just as Cambridge in Colour). Do you want me to look up the specific posts for you?

I havent read everything on the CiC site, but the bit I agreed with, which I thought was in dispute, was when diffraction begins to degrade detail, which is a different discussion to the question of when it limits you so much that you may as well use a lower resolution camera. CiC is right that diffraction becomes noticeable at wider apertures for higher resolution sensors and therefore degrades their detail sooner. As I've repeatedly said in many posts, that's not the same as saying that those higher resolution cameras don't still have a detail advantage.

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.

You felt it necessary to assign blame and point fingers when I had hoped the conversation could have a fresh start.

Look! A number of us took time to teach you (I don't apologize for the expression) what things are actually like.

Your first reply to me basically ignored the length post I'd written to try and work out where disagreement originated, and instead of engaging with any of the points, you basically said 'Here's a formula that shows why you're wrong. Go work out why.'

What I actually said was:

"If you work out the implications of the formula, you'll see that Bob is right. Let me know if you have any questions/problems."

http://www.dpreview.com/forums/post/53161275

Maybe you didn't mean it that way,

No, I certainly didn't mean it that way. I simply took you on your words. You said you had a degree in physics so I assumed you were familiar with formulas and in a position to work out the implications for yourself (as eventually, but not initially, turned out to be the case). Math is there for a reason and for those who are reasonably familiar with the language of mathematics, it is a far more precise and less ambiguous way to get the message across in cases like the present than verbal expressions.

but it came across as rather arrogant with the lack of engagement and disinclination to explain things.

See the offer to help out with any questions/problems in my initial response quoted above. Moreover, I immediately responded to your request for further information in the form a point-by-point response to the argument you had outlined as well as a first description of the implications. I did so in spite of the fact that your initial reply was anything but gentle. See here:

http://www.dpreview.com/forums/post/53162094

We were rewarded by all sorts of insults.

Really? Where? I suggested that your first reply was unhelpful for reasons that I've outlined again here, and elsewhere suggested that you didn't understand diffraction and disagreed with the laws of physics (Re: So, what are the m4/3 diffraction limits?). In retrospect that was probably a misunderstanding over the word limit. I was talking about diffraction limiting the amount of detail that could be resolved while you were saying that higher res sensors would always improve detail. I thought you meant that you could get more detail than what diffraction effects limit you to i.e. the system resolution could exceed the diffraction-imposed lens resolution, but presumably you actually meant that you could always get closer and closer to that limit? Similarly you thought I was saying that higher resolution sensors stop adding detail at a point, when I meant that there's a level of detail that no sensor can exceed and the gains you get, at a certain point, are so negligible that you can ignore them.

In so far as I may have misunderstood you or failed to express myself clearly, I apologise.

OK. You did misunderstand and you did fail to express yourself clearly but the apology is accepted.

Now we are somehow made up as the guilty party just because you not man enough to stand up and say you made a mistake.

I've stated quite clearly several times now that I regard the problems in the previous thread as largely being down to misunderstanding and had no interest i pointing the finger at anyone, preferring to make a fresh start. You're the one who thought it necessary to point the finger and assign blame, so I find your comments here rather ironic.

Not recognizing that you are wrong when you are implicitly puts the blame equally on both sides alike (and I certainly don't think that's appropriate in the present case). This in turn makes it more difficult to accomplish what you say you wanted: a "fresh start".

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).

I'm not interested in dissecting the previous discussion.

For pretty obvious reasons.

Yes, the reason I stated: I would rather move forward with the discussion and add to the forum, rather than dig up the past and waste people's time. I'm sure other comemnters would rather read about photography than our personal disagreements, so can we get back the actual discussion?

No problem with that.

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Re: Diffraction Limit Discussion Continuation
2

Jonny Boyd wrote:

Anders W wrote:

Jonny Boyd wrote:

I said that at low resolutions it's more of a plateau that a peak, so you effectively get the same resolution at smaller apertures.

No you didn't say that. You said the peak would occur at different apertures depending on sensor resolution (just as Cambridge in Colour). Do you want me to look up the specific posts for you?

I forgot to add the following quotes from CiC:

Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the f-number of your lens, and on the wavelength of light being imaged. One can think of it as the smallest theoretical "pixel" of detail in photography. Furthermore, the onset of diffraction is gradual; prior to limiting resolution, it can still reduce small-scale contrast by causing airy disks to partially overlap.

In practice, the diffraction limit doesn't necessarily bring about an abrupt change; there is actually a gradual transition between when diffraction is and is not visible. Furthermore, this limit is only a best-case scenario when using an otherwise perfect lens; real-world results may vary.

This should not lead you to think that "larger apertures are better," even though very small apertures create a soft image; most lenses are also quite soft when used wide open (at the largest aperture available). Camera systems typically have an optimal aperture in between the largest and smallest settings; with most lenses, optimal sharpness is often close to the diffraction limit, but with some lenses this may even occur prior to the diffraction limit. These calculations only show when diffraction becomes significant, not necessarily the location of optimum sharpness (see camera lens quality: MTF, resolution & contrast for more on this).

n MTF of 1.0 represents perfect contrast preservation, whereas values less than this mean that more and more contrast is being lost — until an MTF of 0, where line pairs can no longer be distinguished at all. This resolution limit is an unavoidable barrier with any lens; it only depends on the camera lens aperture and is unrelated to the number of megapixels. The figure below compares a perfect lens to two real-world examples:

The aperture corresponding to the maximum MTF is the so-called "sweet spot" of a lens, since images will generally have the best sharpness and contrast at this setting. On a full frame or cropped sensor camera, this sweet spot is usually somewhere between f/8.0 and f/16, depending on the lens. The location of this sweet spot is also independent of the number of megapixels in your camera.

I don't think CiC says what you think it says, if you believe it claims that peak aperture depends on the sensor resolution rather than just the lens resolution.

It's calculator clearly does, as indicated already at the very beginning of the previous thread:

http://www.dpreview.com/forums/post/53151553

Just look at the calculator itself here

http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

and additionally consider what Bob says for example here

http://www.dpreview.com/forums/post/53176717

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Duck, duck, goose.
1

Jonny Boyd wrote:

Great Bustard wrote:

Jonny Boyd wrote:

The universal claim I'm disproving is that peak visible resolution always occurs at the same aperture.

You didn't disprove that the peak resolution always occurs at the same aperture, all else equal.

As I've repeatedly said, including in the post you quoted, indeed the very line you quoted, I'm referring to the peak visible resolution, not the peak resolution. There's an important difference.

Did you define the "peak visible resolution"?  I mean, since display size, viewing distance, and visual acuity play such important roles in that, I would imagine you discussed them somewhere in your definition.

At best, you've said that if the resolution is low enough and/or the photo is displayed small enough, there will be a large range of apertures where the loss of resolution either due to lens aberrations for apertures wider than the peak aperture or due to diffraction for apertures more narrow than the peak aperture, will not be noticed,

That's exactly what I've been claiming the whole time in this thread.

Has anyone argued against that?  Link and quote, if you'd be so kind.

none of which has anything, whatsoever, to do with being "diffraction limited".

Diffraction causes a decrease in resolution, agreed?

Agreed.

When resolution drops due to stopping down from the peak aperture, that is due to diffraction, agreed?

Agreed.

At the aperture at which diffraction is reducing resolution, you can say that diffraction is limiting the resolution of the final image, agreed?

Agreed.

If resolution appears to be the same at an aperture smaller than the peak aperture then diffraction doesn't become the dominant factor in limiting resolution until later than the peak aperture, agreed?

Agreed.

Therefore, for practical purposes, as far as the eye can see, a system where resolution visibly drops immediately after peak aperture is more limited by diffraction than a system where the visible drop happens later. Agreed?

Not agreed, and am surprised you do not understand this.  For example, let's say for a particular display size, viewing distance, and visual acuity, I can resolve 1000 lw/ph.  All else equal, the photo from the lower MP sensor will dip below that threshold before the higher MP sensor.

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Re: So is this one

gollywop wrote:

TomFid wrote:

Probably best to stick to just eyeball the raw data, and be satisfied with its 1 stop interval. Or, build a model with a sensible functional form and fit it to a larger sample of body/lens combinations.

As to inventing a curve by eyeballing the data, the results are completely without value. Indeed, the best estimate we have for a maximum is the maximum we have, not one based on speculation. You can then do some half hearted Bayesian modification by saying that you have a diffuse prior that, when taken into account, would suggest that that maximum could be in a range around the data maximum -- maybe even 1 stop. But there's no value to eyeballing a curve.

I think we're in violent agreement, as I intended "be satisfied with its 1 stop interval" to be equivalent to your clearer "the best estimate we have for a maximum is the maximum we have," not inventing a curve.

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