Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?

Started Jun 13, 2012 | Discussions
Al_10D
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Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
Jun 13, 2012

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.
I wonder how many pixel needed to match the lens resolution?

Is it 3 pixels per lp? If so, 28Mpx sensor resolution would be alredy limited by lens.

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Peter 13
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.

That is whatever lines per mm on some particular sensor. Change the sensor, you get different data. Also, those are MTF-20 figures, if I remember well. Change the MTF value, and the result changes. They have the whole curves there. Also, resolution is color dependent.

I wonder how many pixel needed to match the lens resolution?

Is it 3 pixels per lp? If so, 28Mpx sensor resolution would be alredy limited by lens.

There is no such thing as matching the resolution. The total blur is a combination of lens blur and AA/pixels blur (excluding motion blur and a few other factors). You improve each one, you improve the total resolution but the gain be very small at extreme pixel densities. See, even going from 18mp to 24mp on crop gives you a visible resolution gain but it is not enough to remove the AA filter. So my guess is that somewhere near 250mp on FF would be a good pixel count to realize the full potential of the lenses with "minimal'" loss, whatever minimal means.

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yabokkie
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Peter 13, Jun 13, 2012

So my guess is that somewhere near 250mp on FF would be a good pixel count to realize the full potential of the lenses with "minimal'" loss, whatever minimal means.

+1, I'm thinking of several hundred MPs but don't have a single number.
a simple number maybe 1 GP.

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Al_10D
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Peter 13, Jun 13, 2012

Peter 13 wrote:

Al_10D wrote:

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.

That is whatever lines per mm on some particular sensor.

I'm talking about resolution of the lens, 60 lp/mm lens should resolve no more than 1440 x 2160 lp on any FF sensor. (60 lp/mm * 24mm) x (60 lp/mm * 36 mm).

My question actually is: how many pixel needed to resolve 1 lp ? 2? 3? 4?

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Luke_S
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Theoretically you need 2 pixels per 1 mm of sensor height/width to resolve resolution equal 1 lp/mm (assuming that there is no AA filter and lens resolution is sufficient enough), but this refers only to horizontal and vertical resolution, not diagonal.

In practice you need much more. Conventional modern sensors with moderate AA filters resolve approximately 75% (+ - 10%) of their potential resolution according to my observations. If you've asked this question a few years ago I would say it was 60% due to lower pixel count demanding stronger AA filters.

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Al_10D
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to yabokkie, Jun 13, 2012

yabokkie wrote:

So my guess is that somewhere near 250mp on FF would be a good pixel count to realize the full potential of the lenses with "minimal'" loss, whatever minimal means.

+1, I'm thinking of several hundred MPs but don't have a single number.
a simple number maybe 1 GP.

250MP resolution on FF sensor is about 13000 x 19000. That sensor would require a lens to be able to resolve 180 lp/mm. For 1 GP sensor double that number, 360 lp/mm.

Are Canon lenses that capable ? Somehow I doubt that.

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Peter 13
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

Peter 13 wrote:

Al_10D wrote:

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.

That is whatever lines per mm on some particular sensor.

I'm talking about resolution of the lens, 60 lp/mm lens should resolve no more than 1440 x 2160 lp on any FF sensor. (60 lp/mm * 24mm) x (60 lp/mm * 36 mm).

They do not measure resolutions of lenses, as simple as that. They measure the combined resolution of lenses mounted on a specific body.

My question actually is: how many pixel needed to resolve 1 lp ? 2? 3? 4?

This question has no meaning, really. As I explained, above, you always get some improvement, and when you set some limit of acceptable loss, you get your numbers. It is like in statistics - how many people do you need to poll to get a correct answer who will win if the elections were held today? Well, all of them. But if you accept a margin of error, say, 2%, then you get a reasonable number.

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Peter 13
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

yabokkie wrote:

So my guess is that somewhere near 250mp on FF would be a good pixel count to realize the full potential of the lenses with "minimal'" loss, whatever minimal means.

+1, I'm thinking of several hundred MPs but don't have a single number.
a simple number maybe 1 GP.

250MP resolution on FF sensor is about 13000 x 19000. That sensor would require a lens to be able to resolve 180 lp/mm. For 1 GP sensor double that number, 360 lp/mm.

On the blue channel (which happens to be the most resolving optically), it is about 1/2 of that per mm. But again, there are no lines really. You are talking about the value of the Fourier Transform at one frequency, which is what the MTF basically measures.

Are Canon lenses that capable ? Somehow I doubt that.

The D800 shows clear aliasing (and I am not even talking about the D800E) with their 50/1.4 at f/4. Doubling the linear resolution would probably make it better, with the same AA filter. This is 144mp already. If you want to remove the AA filter, you need to double the resolution again, I guess. So my 250mp was too conservative, I am afraid.

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yabokkie
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Peter 13, Jun 13, 2012

If you want to remove the AA filter, you need to double the resolution again, I guess. So my 250mp was too conservative, I am afraid.

exactly. a camera with no AA filter, and claim there will be never ever any lens sharper enough to cause problem, then we are about at the end of the "MP war", but this is only the output.

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gdanmitchell
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

I'm going to not quite answer the question you asked, but perhaps address some things that might be more important as background to your question and whether or not you want to pursue it too far.

Lens resolution is not a binary as it "X can resolve something and Y cannot." It isn't. for example, that some lens "can resolve 2000 lp/mm and cannot resolve 2001 lp/mm." The ability to resolve "rolls off" beyond (and before, actually) some arbitrary measurement based on some standard of the amount of contrast maintained between two line pairs.

In terms of the relationship between what you might term lens resolution and sensor resolution, we can imagine three possibilities:

  1. Sensor and lens resolution are equal - This is essentially a practical impossibility. Lens resolution varies at different apertures and in various parts of the frame. Is the "lens resolution" standard the very best portion of the very best lens you own at the aperture optimized for that portion of the frame? Is it the very best you can imagine for the very best lens made? Something else? Essentially, lens and sensor resolution can never be equal in the real world.

  2. Lens outresolves sensor - It is possible that this could happen with some lens at its best aperture and the right focal length and portion of the frame. In this case you might imagine the you are "wasting the resolution" of your lens. Perhaps, and you might wish that the sensor would be fully capable of handling the best that your best lens can do in its best circumstance.

  3. Sensor outresolves lens - This is probably the best place to be. Not only is there some literal value in this situation (remember that lens resolution is not an either/or thing) such that you might still see a better image (if you are really picky and making a very, very large print), but as long as their is no other significant downside in terms of sensor performance, the sensor now permits you to use your lens at its most effective performance level.

Meanwhile back in the real world, this sort of musing rarely has much practical meaning...

Dan

Al_10D wrote:

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.
I wonder how many pixel needed to match the lens resolution?

Is it 3 pixels per lp? If so, 28Mpx sensor resolution would be alredy limited by lens.

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Al_10D
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Peter 13, Jun 13, 2012

They do not measure resolutions of lenses, as simple as that. They measure the combined resolution of lenses mounted on a specific body.

Yeah, I did not think about it, I just took 60 lp/mm number as actual measurement of the lens resolution, you are right.

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Press Correspondent
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In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

I wonder how many pixel needed to match the lens resolution?
Is it 3 pixels per lp?

The answer to your question is given by the Nyquist Theorem. If the sensor was black and white (or monochrome) with no Bayer pattern, the answer would be that 2 lines of pixels are sufficient to resolve one line pair.

However, Bayer makes it color sensitive and interpolated. The resolution in green is roughly double of that in red or blue. Then there are different wavelengths, so the resolution in blue is more than in red. Plus in white Bayer creates wrong colors and moire. So there usually is an AA filter to remedy the artifacts at the expense of the resolution. Plus there are gaps between pixels of the same color, making the lp/mm measure wrong, as you would miss random details even if you can resolve straight lines.

Overall, you still usually get close to 2 pixel lines per line pair (sometimes 2.5 to 3). However, the true real life resolution is about only a half of that, except for Foveon whose resolution is about twice better than interpolated Bayer. (You do not lose much detail by downsizing Bayer twice). A good rule of thumb is that the true resoluttion of a sensor roughly equals its number of green photocells that matches the Foveon resolution, but is only a half of Bayer.

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Great Bustard
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The question, as posed, is unanswerable.
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

The best Canon lenses resolve abput 60 lp/mm (according to DXOMARK) or 1440 lp per height and 2160 lp per width of FF sensor.

Like all "lens" tests, DxOMark's "lens" tests are system tests. That is, how well does a particular lens resolve on a particular sensor of a particular size with a particular number of pixels and a particular AA filter.

I wonder how many pixel needed to match the lens resolution?

An infinite number of pixels. Typically, system resolution is calculated as follows:

1 / (R system)² = 1 / (R lens)² + 1 / (R sensor)² + 1 / (R low bypass filter)² + ...

The system resolution is limited by the lowest resolution of the elements in the imaging chain. So, for the system resolution to match the lens resolution, the lens must be the lowest resolving portion of the chain, and the other elements in the chain have to be perfect not to result in less resolution still.

Is it 3 pixels per lp? If so, 28Mpx sensor resolution would be alredy limited by lens.

The question is not answerable unless we know the resolutions of all the elements in the chain.

However, the Canon 50 / 1.4 macro on a 5D2 (21 MP FF):

http://www.photozone.de/canon_eos_ff/564-canon50f14ff?start=1

is resolving 3740 lw/ph in the center of the frame at 50% contrast with the processing (coversion) that PZ has applied to the photo, which is 78 lp/mm on the sensor, and 3.7 lp/mm on a 20x30 inch print.

Compare and contrast with the 50D (15 MP 1.6x):

http://www.photozone.de/canon-eos/565-canon50f14apsc?start=1

where we have 2598 lw/ph in the center, and thus 2.6 lp/mm on a 20x30 inch print vs the 350D (8 MP 1.6x):

http://www.photozone.de/canon-eos/159-canon-ef-50mm-f14-usm-test-report--review?start=1

where it falls to 2064 lw/ph in the center, and thus 2.0 lp/mm on a 20x30 inch print.

So, on 1.6x, we see that an 87.5% increase in the pixel count resulted in a 26% increase in resolution, and a 60% increase in sensor width combined with a 40% increase in pixel count results in a 44% increase in resolution. At least, in the center, and at the sharpest aperture for the center.

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John Sheehy
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

yabokkie wrote:

So my guess is that somewhere near 250mp on FF would be a good pixel count to realize the full potential of the lenses with "minimal'" loss, whatever minimal means.

+1, I'm thinking of several hundred MPs but don't have a single number.
a simple number maybe 1 GP.

250MP resolution on FF sensor is about 13000 x 19000. That sensor would require a lens to be able to resolve 180 lp/mm. For 1 GP sensor double that number, 360 lp/mm.

Are Canon lenses that capable ? Somehow I doubt that.

The problem with these discussions is that the figures are not meaningful without of definition of what it means to resolve. If the goal is to have high pixel contrast, then the number of MPs isn't anywhere near as high as if the goal is to resolve the red and blue channels without aliasing or distortion.

Case in point; I have a Casio superzoom with 1.5 micron pixels that gives RAW output. Even at f/8, the blue channel can be severely aliased. It might take pixels as small as 0.75 microns or smaller not to have aliasing or distortion in the blue channel at f/8. That's 1.5GP or more, full-frame, and that's at f/8. What about high-end lenses that are diffraction-limited at f/5.6 or f/4?

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John Sheehy
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Re: Sensor vs lens resolution Q or how many pixel needed to resolve 1 LP ?
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

My question actually is: how many pixel needed to resolve 1 lp ? 2? 3? 4?

Define "resolve".

Yes, you could have one row of pixels dark, the next light, the next dark, etc, with a bit of luck of alignment, but shift that relationship 1/2 pixel vertically, and what do you get? All gray. Do you call that resolution, when it is so fragile? I don't. And what happens with a 3:2 (pixels:lines)? Uneven grouping of the lines; is that resolution? At 4:2, things get a little saner, but the weight of the lines is still uneven, and jagged if you're talking about diagonals. This is all for B&W or luminance. What happens if you need an accurately resolved blue channel, with blue pixels only in every other line of pixels? I chose blue because blue has the least diffraction. It also has the most atmospheric diffusion, but that is irrelevant at short distances.

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tony field
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Currently popular formulae
In reply to Great Bustard, Jun 13, 2012

Great Bustard wrote:

Typically, system resolution is calculated as follows:

1 / (R system)² = 1 / (R lens)² + 1 / (R sensor)² + 1 / (R low bypass filter)² + ...

what ever happened to the old calculation of system resolution which used to be around for many more than the past 50+ years I have been in photography:

1 / (R system) = 1 / (R lens) + 1 / (R sensor) + 1 / (R low bypass filter) + ...

If (R lens) = 100 and (R sensor) = 300, the numerical difference is "large" but maybe not significant?

1 / (R system)² = 95
1 / (R system) = 75
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Al_10D
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Thank you all for the info. Nother Q.
In reply to Al_10D, Jun 13, 2012

What is a practical limit on Mp for FF sensor and current Canon EOS lenses?

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Its RKM
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Re: The question, as posed, is unanswerable.
In reply to Great Bustard, Jun 13, 2012

Great Bustard wrote:

I wonder how many pixel needed to match the lens resolution?

An infinite number of pixels.

Well it is large, but it certainly isn't infinite. An f/0.5 lens has an infinitely large aperture, so we know that no practical lens can ever have better diffraction limited resolution than an f/0.5 lens. I have seen a couple of diffraction limited f/0.7 lenses, but they were very impractically priced. Probably diffraction MTF for f/1 or thereabouts is a practically realizeable maximum lens resolution for minimum resolved contrast.

Typically, system resolution is calculated as follows:

1 / (R system)² = 1 / (R lens)² + 1 / (R sensor)² + 1 / (R low bypass filter)² + ...

And even that is only a crude approximation which fails on exactly the same assumption as the OP's initial assessment: what is "R lens"? Is that MTF-50? MTF-20? Typically, in my line of work, I use MTF-05 but, occasionally, even that isn't low enough contrast. What if your subject has several stops or even orders more contrast than your sensor - we had a thread here recently about how to photograph an astronomical event that certainly fell into that category, and that was followed two weeks later by yet another, so it isn't that improbable.

Adding resolutions in inverse quadrature is a very crude approximation which may be reasonable for matched dynamic range capabilities, however the nest approach is to multiply the MTF curves of the significant system elements - lens, AA filter, pixel, spatial filter etc. - and threshold the product curve at the contrast you can discern by eye.

The system resolution is limited by the lowest resolution of the elements in the imaging chain.

Agreed, but that isn't always the lowest "resolution" for any specific MTF, let alone scene contrast.

The question, however, is answerable as posed since every optical solution has an MTF0 - a resolution at which the lens reproduces no contrast at any transmitted or responded wavelength, irrespective of the contrast in the scene.
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Great Bustard
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Re: Currently popular formulae
In reply to tony field, Jun 13, 2012

tony field wrote:

Great Bustard wrote:

Typically, system resolution is calculated as follows:

1 / (R system)² = 1 / (R lens)² + 1 / (R sensor)² + 1 / (R low bypass filter)² + ...

what ever happened to the old calculation of system resolution which used to be around for many more than the past 50+ years I have been in photography:

1 / (R system) = 1 / (R lens) + 1 / (R sensor) + 1 / (R low bypass filter) + ...

If (R lens) = 100 and (R sensor) = 300, the numerical difference is "large" but maybe not significant?

1 / (R system)² = 95
1 / (R system) = 75

http://www.bobatkins.com/photography/technical/rrs.html

This relationship is quoted in many texts, including publications by Kodak (P315 - Scientific Imaging) and in "Image Clarity" by John Williams. It is certainly a relationship which can give a decent approximation of system resolution under some conditions. However it is not based on any sound theory and can, in fact, be shown to give erroneous results when used improperly. There is no reason why the exponent should be 2. Some studies have shown a better fit with smaller exponents in the region of about 1.5, but even then, it's still empirical - it applies only under the conditions used for the experiment in which it was determined.

Might want to give the whole link a read for more on the issue.

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tony field
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Re: Thank you all for the info. Nother Q.
In reply to Al_10D, Jun 13, 2012

Al_10D wrote:

What is a practical limit on Mp for FF sensor and current Canon EOS lenses?

IMHO (and certainly not technically qualified), my guess that that practical limits in which some tangibly useful increase in image recording detail might be seen is in the order of 50 to 80 mp. Of course, that implies your concept of "practical" parallels mine
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