Are Perceptual Megapixels stupid?

SrMi · Mar 20, 2023

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?

Jack Hogan · Mar 21, 2023

When reading the Appendix it seems clear that Roger is assuming a particular spatial frequency when he says 'the camera at MTFx is multiplied by the lens at MTFy'. He kept the explanation to a bare minimum, understandably so given the mostly unsophisticated audience he is writing for.

And the perceptual megapixel is probably a weighted combination of camera and lens MTF curves, which is how many single metric sharpness metrics work. I assume it provides an estimate of the perceived sharpness produced by that lens with that camera, a more sophisticated version of what Roger is talking about.

So I think they both have their place in such a discourse.

The 'lens outresolves the camera' or vice versa is undefined. One way to look at it could be where, in terms of spatial frequencies, the MTF curve of one is higher than the other.

For instance, this horizontal/vertical MTF curve in red - for a 12MP 2/3" sensor with 3um pixel pitch, 100% fill factor and 0.7c/p AA - 'outresolves' the MTF of the lens as measured (blue and green curves) throughout the shown range.

Loading…

www.dpreview.com

Jack

Erik Kaffehr · Mar 21, 2023

Jack Hogan said:
When reading the Appendix it seems clear that Roger is assuming a particular spatial frequency when he says 'the camera at MTFx is multiplied by the lens at MTFy'. He kept the explanation to a bare minimum, understandably so, given the mostly unsophisticated audience he is writing for.

And the perceptual megapixel is probably a weighted combination of camera and lens MTF curves, what many single metric sharpness metrics do. I assume it provides an estimate of the perceived sharpness produced by that lens with that camera, a more sophisticated version of what Roger is talking about.

So I think they both have their place in such a discourse.

The 'lens outresolves the camera' or vice versa is undefined. One way to look at it could be where (in terms of spatial frequencies) the MTF curve of one is higher than the other.

Jack

I think that it is a bit miss leading concept. Lens resolution varies over the field. Most decent lenses resolve pretty fine detail near center, but many lenses loose sharpness off center.

So, the central part needs a high resolution sensor to resolve all detail, but the more peripheral parts may be a bit blurry. So, technically, a high resolution sensor may be needed to correctly resolve the center, say 3.8 micron pitch, but many lenses may not be able to utilize that pitch.

On the other hand, I think it is reasonable to use some contrast criteria for resolution, say resolution at 20% MTF. But we would need to keep in mind that 20% MTF is plenty to achieve pretty bad aliasing for high contrast subjects with fine detail.

In the end, it is always a combination of lens and sensor, with subject and probably also photographers being limiting factors.

Best regards

Erik

Jack Hogan · Mar 21, 2023

Good point about aliasing and the changing performance of lenses throughout the field of view - and direction of detail there, Erik. So 'as measured' becomes an essential qualifier in the plot above. And an indication of the Nyquist frequency for the expected scene should be part of it (probably off-scale above).

Jack

J A C S · Mar 21, 2023

RCicala · Mar 21, 2023

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?

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".

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

Bill Ferris · Mar 21, 2023

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?

Click to expand...

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".

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

Here's something you got right in the article, "Assumptions are the dark matter of the internet; we can’t see them, but we know they account for most of the mass."

Tru dat.

chrisfisheye · Mar 21, 2023

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?

Click to expand...

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".

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 !.

RCicala 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

Erik Kaffehr · Mar 22, 2023

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?

Click to expand...

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".

Click to expand...

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 !.

chrisfisheye 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

Click to expand...

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.

Best regards

Erik

Jack Hogan · Mar 22, 2023

chrisfisheye said:
chrisfisheye wrote: [...] 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.

[ ---] 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 !.

That is what I believe is referred to as the Fuji version, then there is a Kodak version where each term is squared, then...

However, they are really combining apples and oranges, since if you are only given the spatial frequency at which MTF is equal to xx for both curves - but not the rest of the curves - it is just an educated guess,

For example, take the red and top green curve in the plot above at MTF70, say 95lp/mm and 35 resp. According to your formula MTF70 for the system should be 25.6lp/mm. Using Kodak's 32.8lp/mm. To get the correct answer multiply the two curves together frequency-by-frequency and see where MTF70 lands.

Jack

chrisfisheye · Mar 22, 2023

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

To repeat myself, I am not "shocked" that a 20Mp sensor with a lens resolving 20mp results in a resolution lower than 20mp. The model of perceptual megapixels remains consistent, in my opinion. I am not saying that the formula is correct but more that it is consistent with the general model.

J A C S · Mar 22, 2023

Jack Hogan said:
Jack Hogan said:

chrisfisheye wrote: [...] 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.

[ ---] 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 !.

Click to expand...

That is what I believe is referred to as the Fuji version, then there is a Kodak version where each term is squared, then...

However, they are really combining apples and oranges, since if you are only given the spatial frequency at which MTF is equal to xx for both curves - but not the rest of the curves - it is just an educated guess,

For example, take the red and top green curve in the plot above at MTF70, say 95lp/mm and 35 resp. According to your formula MTF70 for the system should be 25.6lp/mm. Using Kodak's 32.8lp/mm. To get the correct answer multiply the two curves together frequency-by-frequency and see where MTF70 lands.

Jack

As Joofa mentioned years ago, this formula, with the squares, applies if you take the standard deviation as a measure of the blur (assuming it is finite). In particular, it is true for two Gaussian blurs superimposed.

J A C S · Mar 22, 2023

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

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.

chrisfisheye · Mar 22, 2023

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

J A C S said:
if they are equal, it would be equal to each one of them.

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.

J A C S · Mar 22, 2023

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.

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).

chrisfisheye · Mar 22, 2023

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).

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.

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.

RCicala · Mar 22, 2023

I think all the above have merit and and are correct depending on specific circumstance.

What does NOT have merit was the way the general community was interpreting perceptual megapixels, which was basically the lowest of camera resolution or lens resolution was what the overall resolution would be. Basically, they were saying "if a lens perceptual megapixel is 20, then there's no reason to have a camera greater than 20 megapixels; it won't make a difference". This got encouraged by the not-so-subtle manufacturer's "lens rated for 40 megapixels" marketing.

I was simply (oversimply for this subforum, but consider who I was writing to) trying to walk people back from that ledge and point out that they would indeed see a significant difference with either a better lens OR a better camera.

My off the cuff formula definitely breaks down at very high resolution or with very bad lenses, but given a starting point of adequate lens on adequate camera, I think it's pretty accurate as a general description of consumer range equipment.

chrisfisheye · Mar 22, 2023

RCicala said:
I think all the above have merit and and are correct depending on specific circumstance.

What does NOT have merit was the way the general community was interpreting perceptual megapixels, which was basically the lowest of camera resolution or lens resolution was what the overall resolution would be. Basically, they were saying "if a lens perceptual megapixel is 20, then there's no reason to have a camera greater than 20 megapixels; it won't make a difference". This got encouraged by the not-so-subtle manufacturer's "lens rated for 40 megapixels" marketing.

I was simply (oversimply for this subforum, but consider who I was writing to) trying to walk people back from that ledge and point out that they would indeed see a significant difference with either a better lens OR a better camera.

My off the cuff formula definitely breaks down at very high resolution or with very bad lenses, but given a starting point of adequate lens on adequate camera, I think it's pretty accurate.

Agree 100% with your post !

J A C S · Mar 22, 2023

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.

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

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.

J A C S · Mar 22, 2023

Your formula was based on the correct notion that MTF curves multiply but that does not mean that the MTF-50 (or so) values multiply, as Jack pointed out.

Are Perceptual Megapixels stupid?

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