Are Perceptual Megapixels stupid?

Erik Kaffehr said:

chrisfisheye said:

RCicala said:

SrMi said:

In the often-referenced appendix Why Perceptual Megapixels are Stupid, Roger Cicala explains why claiming that a lens can resolve a certain number of megapixels does not make sense.

On the other hand, Leica’s Peter Karbe said in a presentation that Leica’s SL-APO lenses are prepared for more than 100MP sensors.

ProfHankD also disagrees with Roger. I wondered about ProfHankD’s statement that the 45MP FF sensor will out-resolve most lenses wide open, and his answer was (DPR post):

I don't disagree with Roger very often, but his simple MTF math is a little too simple. First off, "MTF maxes at 1.0" makes no sense in terms of resolution -- it maxes at 1.0 for contrast. We normally quote resolution at a fixed contrast (e.g., MTF30 is 30%) or contrast at a fixed resolution; multiplying contrasts at a fixed resolution doesn't tell you at what resolution your target contrast threshold will be reached. It's simply not that linear. Beyond that, the Perceptual MP numbers are supposed to be system MTF numbers approximating human perception (whatever contrast ratio that means; DxOMark created the PMP metric, but doesn't document the exact computation) -- from DxOMark, the same lens often gets a different PMP rating on a different body. So, yes, quoting a single PMP number for a lens independent of body used would be wrong.

Is Roger wrong? Can sensors out-resolve lenses?

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Well, first off, Roger's wrong all the damn time. Sometimes, like this time, he even knows it as he writes it, so to speak.

As Jack pointed out, I was aiming for as simple as possible, and gave up accuracy to try to get understanding among the group who were losing their minds over DxOMark's metric, and the "you have to buy a new lens for your new camera" marketing.

As an oversimplified generalization my math pretty well holds for decent lenses on reasonable cameras, but there would be lots of exceptions, especially towards the extremes of high resolution sensors and inadequate lenses. I didn't mean it with anything like scientific accuracy. But the argument that I was fighting was "if you put your 20 perceptual megapixel lens on a 20 megapixel sensor, you get 20 megapixels. If you put it on a 40 megapixel camera you still get 20 megapixels".

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Hello,

In your article, you give a more extreme example (I mean a mlre important difference between resolutions), a camera sensor with 61mp while the lens resolves 30mp..

I guess that to an extent, when you increase the sensor resolution, there is a limit you can find for the resulting resolution and you can define this limit as being the lens resolution.

So why can't you say that a sensor outresolves a lens ? I consider this is the case when its resolution is far superior to the lens resolution.

I had already found an equation, not sure about its validity, maybe it derives from the MTF equations:

1/l = 1/ls + 1/ll

Where l represents the linear resolution, ls linear resolution for the sensor and ll linear resolution for the lens.

So for instance in the case ls=ll , we have l = ls/2.

This means that in terms of spatial resolution, putting a lens that resolves 20mp on a 20mp sensor would give 5mp total resolution.

Why not ? I do not consider it discredits the terminology about perceptual resolution of each part (lens or sensor) taken alone. But I agree the interpretation is a bit misleading.

By the way, can somebody tell me about the validity of the equation I show ? I have no idea, I give it by memory but the model looks quite good !.

Erik Kaffehr said:

I will take full responsibility for using oversimplified and somewhat inaccurate math, but I want full credit for being more accurate than DxOs pseudoscience. At least I showed my "formula"

All that being said, though, perceptual megapixels are stupid. Even the name is stupid.

Roger

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Hi,

I am not sure those resolution formulas make any sense.

The way I would see it, images are passing trough a chain affecting image quality, where each stage adds some blur. Lenses have some blur, all lenses are affected by diffraction when stopped down. Many sensors have some OLP filter and the sensor itself blurs the image by it's pixel size.(*)

The last part depends on the sensor. Higher resolution sensors have smaller pixels, so they add less blur. Smaller pixels will also have narrower OLP filters.

But, if the image projected on the sensor is much more blurry than the blur caused by the pixel, pixel size would not matter a lot.

In the real world, things are a bit more complex. Sharpening is coming into the equation. We seldom use images with no sharpening at all.

Higher sensor resolution may be helpful in sharpening.

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Add to the mix AI-based sharpening tools that interpolate an image and manufacture detail that "looks natural" but isn't, and the question of the resolution of a digital imaging system becomes both more complex and less clear.

Bill Ferris said:

Add to the mix AI-based sharpening tools that interpolate an image and manufacture detail that "looks natural" but isn't, and the question of the resolution of a digital imaging system becomes both more complex and less clear.

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Resolution is typically defined by detail captured, not guessed. It characterizes the data collected, well, in terms of what can be extracted from it.

J A C S said:

chrisfisheye said:

J A C S said:

chrisfisheye said:

J A C S said:

chrisfisheye said:

Hello,

Thanks Erik and Jack for your answers and for the reference of these formulas, I had no idea where I had found them...

Even if it may be incorrect, I find them interesting. This formaula looks consistent:

• For the limits, when a sensor outresolves the lens (or the contrary) it works.
• When both resolution are equal, it gives a linear resolution divided by 2 which looks consistent with Nyquist-Shannon

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No, the Nyquist limit (needed for perfect sampling) would be the worst of the two, and

if they are equal, it would be equal to each one of them.

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If they are equal, to get the most of the lens resolution, you have at least to double the sensor resolution. I do not understand your point but please clarify.

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You multiply two MTF curves each one having “finite support” in math terms, the support of the product is the intersection of the two. In other words, if one lives in the band range [0,B1], and the other one in [0,B2], then the product will live in [0,B] with B=min(B1,B2).

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We certainly don't use the same model, but if the lens resolves 20mp, then you get the information thanks to the sensor, by sampling, so the final resolution will decrease unless you have a sensor which outresolves by far the lens.

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lf the lens resolves 20mp by sampling theory standards, then you need a 20mp sensor to catch that. You do not get 10mp combined.

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If you shoot a grid of 20mp with a 20mp sensor you loose in average information (unless you are perfectly aligned with the grid). You need more pixels to get all the information.

If always need to sample with a higher frquency that the frequency information of the data you want to capture.

I am sure you know that but I am just explaining that in my understanding, this is based on this model. I am convinced that this model is not that bad

J A C S said:

J A C S said:

This model looks consistent to me. How to link it with the MTF, I have no idea, maybe it is a simplistic model but not uninteresting.

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chrisfisheye said:

J A C S said:

chrisfisheye said:

J A C S said:

chrisfisheye said:

J A C S said:

chrisfisheye said:

Hello,

Thanks Erik and Jack for your answers and for the reference of these formulas, I had no idea where I had found them...

Even if it may be incorrect, I find them interesting. This formaula looks consistent:

• For the limits, when a sensor outresolves the lens (or the contrary) it works.
• When both resolution are equal, it gives a linear resolution divided by 2 which looks consistent with Nyquist-Shannon

Click to expand...

No, the Nyquist limit (needed for perfect sampling) would be the worst of the two, and

if they are equal, it would be equal to each one of them.

Click to expand...

If they are equal, to get the most of the lens resolution, you have at least to double the sensor resolution. I do not understand your point but please clarify.

Click to expand...

You multiply two MTF curves each one having “finite support” in math terms, the support of the product is the intersection of the two. In other words, if one lives in the band range [0,B1], and the other one in [0,B2], then the product will live in [0,B] with B=min(B1,B2).

Click to expand...

We certainly don't use the same model, but if the lens resolves 20mp, then you get the information thanks to the sensor, by sampling, so the final resolution will decrease unless you have a sensor which outresolves by far the lens.

Click to expand...

lf the lens resolves 20mp by sampling theory standards, then you need a 20mp sensor to catch that. You do not get 10mp combined.

Click to expand...

If you shoot a grid of 20mp with a 20mp sensor you loose in average information (unless you are perfectly aligned with the grid). You need more pixels to get all the information.

Click to expand...

A 20mp grid has an infinite Nyquist limit. If you want a 1-1 correspondence of grids to Nyquist, they have to be sinusoidal.

chrisfisheye said:

If always need to sample with a higher frquency that the frequency information of the data you want to capture.

I am sure you know that but I am just explaining that in my understanding, this is based on this model. I am convinced that this model is not that bad

chrisfisheye said:

chrisfisheye said:

This model looks consistent to me. How to link it with the MTF, I have no idea, maybe it is a simplistic model but not uninteresting.

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Click to expand...

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chrisfisheye said:

If you shoot a grid of 20mp with a 20mp sensor you loose in average information (unless you are perfectly aligned with the grid). You need more pixels to get all the information.

Click to expand...

Since MTF out of a sensor is not shift invariant this is a problem that can only be swept under the carpet by assuming a natural image with more or less randomly distributed detail. In practice it boils down to the Nyquist frequency being a moving target depending on the given scene as shot.

However, for purposes of comparing the performance of photographic hardware, we can get around this issue by ensuring that what you suggest does not happen. Enter for instance the slanted edge method.


Jack

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

SrMi said:

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

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My simplest way to see it:

• Lens outresolves the sensor -> aliasing
• Sensor ouresolves the lens -> no aliasing

Real life may be a bit different. One of those things is that colors are sampled at half frequency compared to luminance, especially if we regard 'G' and 'G2' channels to be separate.

Best regards

Erik

SrMi said:

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

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Note that the ‘ outresolves’ argument does not fit in DXO’s P-MP’s which cannot be higher than the MP-s of the sensor used for measuring

Erik Kaffehr said:

SrMi said:

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

Click to expand...

My simplest way to see it:

• Lens outresolves the sensor -> aliasing
• Sensor ouresolves the lens -> no aliasing

Real life may be a bit different. One of those things is that colors are sampled at half frequency compared to luminance, especially if we regard 'G' and 'G2' channels to be separate.

Click to expand...

You described the positive effect when the lens is outresolved by the sensor (less aliasing = better IQ).

I was wondering about the negative effect when using such a lens with high vs. low resolution sensors.

My question is motivated by the regularly heard disqualification of lenses because they are outresolved by sensors. I believe that disqualification is wrong.

Erik Kaffehr said:

Best regards

Erik

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SrMi said:

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

Click to expand...

A sensor outresolves a lens when higher resolution sensor does not really improve anymore the resulting resolution. It means we are close to the limit that could be reached by a virtual infinite resolution sensor.

I think anyway that if we draw the curves of the resulting resolution depending on the sensor resolution, the curve becomes all of a sudden flat. For a 20mp perceptual lens I would expect that a sensor outresolves the lens with something like 80mp sensor (twice the linear resolution) , this does not mean it does not improve anymore but that only slight improvements can be expected.

Jack Hogan said:

chrisfisheye said:

If you shoot a grid of 20mp with a 20mp sensor you loose in average information (unless you are perfectly aligned with the grid). You need more pixels to get all the information.

Click to expand...

Since MTF out of a sensor is not shift invariant this is a problem that can only be swept under the carpet by assuming a natural image with more or less randomly distributed detail. In practice it boils down to the Nyquist frequency being a moving target depending on the given scene as shot.

However, for purposes of comparing the performance of photographic hardware, we can get around this issue by ensuring that what you suggest does not happen. Enter for instance the slanted edge method.

https://www.strollswithmydog.com/the-slanted-edge-method/

Jack

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This is a discussion about how the MTF of a sensor+lens is measured (allegedly) with a particular method, not about what they are in the first place. We model sampling of a sensor as a superposition of a convolution by the light sensitive area of a pixel, and pointwise sampling after that. The former has a Nyquist limit (infinite, actually but for all practical purposes it is finite), while the latter has Nyquist limit in a different sense - the one that the sampling rate can possibly support. Nyquist of the light sensitive area exceeds that dictated by the sampling rate, so it is the latter that is left.

In a nutshell, a sensor has no MTF but it does have a Nyquist limit.

chrisfisheye said:

SrMi said:

When someone says that a camera sensor outresolves a lens, what does that mean in practice?

When someone mentions that a sensor outresolves a lens, it is typically implied that:

• Such a lens will perform worse or equally on high as on a low-resolution sensor.
• Using such a lens is wasted on high-resolution sensors.

Based on my experience, both statements are wrong.

If those statements are wrong, what are P-MPs good for?

Click to expand...

A sensor outresolves a lens when higher resolution sensor does not really improve anymore the resulting resolution. It means we are close to the limit that could be reached by a virtual infinite resolution sensor.

I think anyway that if we draw the curves of the resulting resolution depending on the sensor resolution, the curve becomes all of a sudden flat. For a 20mp perceptual lens I would expect that a sensor outresolves the lens with something like 80mp sensor (twice the linear resolution) , this does not mean it does not improve anymore but that only slight improvements can be expected.

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A factor other than total megapixels and lens optical quality that sets a resolution limit on a photo, is the virtual aperture of the lens. For example, the 200-500mm zoom I sometimes use to photograph the Moon has an entrance pupil diameter of about 89mm. That aperture has a theoretical resolution limit of about 1.4 arcsecond. In this photo of a first quarter Moon, the smallest resolvable detail is roughly 2 arcseconds in size: https://www.dpreview.com/galleries/4703428257/photos/4355765/quarter-moon

Now, the 200-500 isn't an exotic prime. I'd guess that the lens elements are figured via an automated process with little, if any, hand-figuring involved. In other words, it's a good consumer zoom but nothing special.

Would an exotic prime or zoom lens of a similar or greater aperture make photos significantly sharper or better resolved? Well, that depends in part on the conditions in which that lens would be used. A 500mm f/4 prime has a virtual aperture of 125mm and a theoretical resolution potential of 1 arcsecond. When photographing the Moon and shooting through miles of air, another limiting factor that needs to be considered is atmospheric steadiness or seeing. A lens with an aperture of 125mm or greater will resolve 1-arcsecond or smaller details only if the air through which the subject is being imaged allows for it. There's no guarantee those conditions will be present.

In my experience, the greatest benefit of using a larger aperture to make observations is not necessarily the increased potential angular resolution. It's the improved contrast detection that comes with using a larger aperture. You can see this night sky imaging that stacks multiple exposures of the same subject into one image. The additional light improves signal-to-noise ratio and reduces the threshold for the lowest contrast feature visible in the final image.

So, while it's all well and good to seek a means of quantifying how lenses of the same focal length and f-stop but of differing optical quality would impact the amount of detail visible in a single exposure, there's also the question of how differences in optical quality affect the presentation of low contrast details. These are details that aren't difficult to detect by virtue of being small in size. They're difficult to detect because they're low in contrast. This isn't a megapixel thing but is relevant to the discussion of what distinguishes one lens from another or one imaging system from another.

Sorry, are you saying that there are specific situations—like long distances through atmospheric haze—where a particular strength of a lens might give it an advantage over a lens with the same resolving ability? IOW that there's more to the issue than just plain lp/mm?

Or am I completely misunderstanding?

Bill Ferris said:

So, while it's all well and good to seek a means of quantifying how lenses of the same focal length and f-stop but of differing optical quality would impact the amount of detail visible in a single exposure, there's also the question of how differences in optical quality affect the presentation of low contrast details. These are details that aren't difficult to detect by virtue of being small in size. They're difficult to detect because they're low in contrast. This isn't a megapixel thing but is relevant to the discussion of what distinguishes one lens from another or one imaging system from another.

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RichardSwearinger said:

Sorry, are you saying that there are specific situations—like long distances through atmospheric haze—where a particular strength of a lens might give it an advantage over a lens with the same resolving ability? IOW that there's more to the issue than just plain lp/mm?

Or am I completely misunderstanding?

Bill Ferris said:

So, while it's all well and good to seek a means of quantifying how lenses of the same focal length and f-stop but of differing optical quality would impact the amount of detail visible in a single exposure, there's also the question of how differences in optical quality affect the presentation of low contrast details. These are details that aren't difficult to detect by virtue of being small in size. They're difficult to detect because they're low in contrast. This isn't a megapixel thing but is relevant to the discussion of what distinguishes one lens from another or one imaging system from another.

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Atmospheric seeing - steadiness of the through which the subject is being observed - is a factor that impacts an optic's ability to resolve to the theoretical limit of its aperture.

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

Bill Ferris said:

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

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How is that different from an increased resolution?

J A C S said:

Bill Ferris said:

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

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How is that different from an increased resolution?

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It's not resolving fine detail. It's resolving low contrast.

Bill Ferris said:

J A C S said:

Bill Ferris said:

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

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How is that different from an increased resolution?

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It's not resolving fine detail. It's resolving low contrast.

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Are you referring to lower shot noise making the contrast swings more discernible? That would be a function of Exposure.

If so, noise (hence Exposure) affects the standard deviation of the resulting MTF curve. I seem to recall reading that empirical observations have shown that the standard deviation of the MTF curve is more or less proportional to the standard deviation of the noise in the image. With a bar target it tended to be proportional to the square root of the spatial frequency.

Jack

Bill Ferris said:

J A C S said:

Bill Ferris said:

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

Click to expand...

How is that different from an increased resolution?

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It's not resolving fine detail. It's resolving low contrast.

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If you take MTF as a measure of resolution (at all frequencies) it is contrast at given frequency, so it combines them both. You are talking perhaps about low frequency MTF. Still part of resolution. BTW, that would hardly get visibly better if you open the aperture.

There is also loss of contrast coming from light not part of the frame. MTF does not capture that, and it is typically worst wide open.

Jack Hogan said:

Bill Ferris said:

J A C S said:

Bill Ferris said:

Also, resolution of fine detail isn't the only benefit of using a larger aperture optic. As aperture increases, lower contrast details become visible. This is an often overlooked and underappreciated advantage.

Click to expand...

How is that different from an increased resolution?

Click to expand...

It's not resolving fine detail. It's resolving low contrast.

Click to expand...

Are you referring to lower shot noise making the contrast swings more discernible? That would be a function of Exposure.

If so, noise (hence Exposure) affects the standard deviation of the resulting MTF curve. I seem to recall reading that empirical observations have shown that the standard deviation of the MTF curve is more or less proportional to the standard deviation of the noise in the image. With a bar target it tended to be proportional to the square root of the spatial frequency.

Jack

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It's not strictly an exposure issue. There's a combination of exposure and image scale at play. While an f/4 shutter actuation at some focal length, X, has the same exposure as an f/4 shutter actuation at a focal of 10X, the longer focal length and larger entrance pupil diameter allow for a larger image scale, better resolution of both fine detail and lower contrast detail that won't be discernable in the wider angle, reduced image scale photo made with the same exposure.

SrMi said:

Is Roger wrong? Can sensors out-resolve lenses?

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Roger is never wrong, but perhaps sometimes not accurate as he explained above ;-)

I do not know if this was referred to in any of the posts above, but with only a few days left of DPReview, there is no time to check + :-(

The link below gives an approximation of a formula for total system resolution, i.e. the combination of camera and lens : https://www.pbase.com/lwestfall/image/52085939

So

1/Res(total) = 1/Res(sensor) + 1/Res(lens)

Some formulas use the square for all the resolutions.

In any case, it shows that even if one part has a higher resolution than the other, both still contribute to the total resolution.

However, it also shows that if one is much much greater than the other, the total resolution will be largely limited by the part with the lowest resolution.

I.e., if both sensor and lens have arbitrary resolution values of 10, then total system resolution will be 5, but if the lens resolution is 10 and the sensor resolution is 100, then total system resolution will be 9.1 - probably an extreme case, but mathematically possible

In the latter case some might argue that the sensor out-resolved the lens, but other might argue that is does not as total system resolution is not 10.

--
Kjeld Olesen
http://www.acapixus.dk