[mikesbike]

Took me a while to find this image I had created to visualise the difference. Please excuse the rough graphical approach but it does the job.

Think of this as a focused image circle of a series of concentric lines that are spaced at the maximum resolution capability of the lens. Obviously they get further apart on the edges as the lens performance drops off.
Superimpose the two sensor sizes on it and you can see what I mean that the apsc presents the lens at a lower resolution. It is simple to see that the apsc image has less resolution lines on it.

What this also shows, in reality you get more of a scene in the picture when using the same lens on FF than with APS-C when shooting from the same position. Conversely, if wanting to crop in order to get the same restricted picture that APS-C has gotten, you throw out a lot of pixels, and may wind up with less resolution than the image from APS-C. If instead of cropping, however, you walk closer to get the same framing, then you get the full 36mp benefit in the same shot, or use a longer lens to get the same framing.

[GUB]

What this also shows, in reality you get more of a scene in the picture when using the same lens on FF than with APS-C when shooting from the same position. Conversely, if wanting to crop in order to get the same restricted picture that APS-C has gotten, you throw out a lot of pixels, and may wind up with less resolution than the image from APS-C. If instead of cropping, however, you walk closer to get the same framing, then you get the full 36mp benefit in the same shot, or use a longer lens to get the same framing.

Yes all good stuff and it arises by simply visualising the image circle.
I came from the K01 (16mp) to the K-1 so my pixel pitch is close to identical - therefore an apsc sized crop from my K-1 is essentially identical to the K01.
I often pull back from closeup subjects with the intention of cropping in to gain a little depth of field and have the confidence that I am still on a par with the K01.

[UncleVanya]

I like to think of resolution in practical terms of how well fine details can be resolved.
Hence the description - " Think of this as a focused image circle of a series of concentric lines that are spaced at the maximum resolution capability of the lens."
The red and blue squares sit on the same image circle so it is a no-brainer that the FF image contains more detail (resolution).
Yes the apsc sits on the area of the image with the most detail but the FF also sits over that area as well plus some.

It is easy to fall into the complexity traps but really if you just think about two sensors sitting on the same image circle it is an accurate and simple comparison.

I disagree. Unless the sensors are the same density of pixels the comparison is false. The apsc section should be full of 1.5x the detail in that center.

[GUB]

First of all both resolution of the lens and the megapickles of the camera both contribute to the final image so there is not a black and white answer here.
A good lens is expected to achieve 100 lines per millimetre.
Lets turn that into points of detail 1/100mm square. And yeah I know - a questionable conversion - i think the reality wouldn't be that good.
That converts into a apsc rectangle on the image circle at 3.5 megadots.
So with the K3 that is 3.5 megadots converted to digital with 24megapixels
On the K-1 sensor that would be 5.25 megadots converted with 36 megapixels.
So still a no-brainer.

[Ian Stuart Forsyth]

First of all both resolution of the lens and the megapickles of the camera both contribute to the final image so there is not a black and white answer here.
A good lens is expected to achieve 100 lines per millimetre.
Lets turn that into points of detail 1/100mm square. And yeah I know - a questionable conversion - i think the reality wouldn't be that good.
That converts into a apsc rectangle on the image circle at 3.5 megadots.
So with the K3 that is 3.5 megadots converted to digital with 24megapixels
On the K-1 sensor that would be 5.25 megadots converted with 36 megapixels.
So still a no-brainer.

+1
This can be illustrated even further if hold the number of pixels the same and only change the size ( while this is not prefect as AA filtering strengths
is different for both cameras)



Here is the same lens used on DS and on the K5, with the K5 it has been cropped to 6mp to the same MP count as the DS, only thing that has changed is that the DS is moved closer to the subject
As you can see the larger surface area using the same pixel count can capture finer detail. While this is not a perfect test as we had to change the working distance to hold the same framing we can see a difference



Here is another test this time I am holding the working distance but using another lens on the DS

Again the top is a 6mp crop from the much smaller pixel K5 with the DFA 100 that is a sharp lens.
The bottom is using a M 80-200 on the DS 6mp and shot at the same DOF using the lens at 150mm.
Here you can see using an older Zoom at the same FOV as the prime lens while utilizing the same number of pixels ( only with different size) that they are very close in captured resolution and would say that the edge goes to the zoom with larger pixels of the DS and its stronger AA filter.

I know this may go against what a lot of people think but many times you are better off using FL to increase your reach ( even if its is a lesser lens) than using pixel density to do the same.

[GUB]

+1
This can be illustrated even further if hold the number of pixels the same and only change the size ( while this is not prefect as AA filtering strengths
is different for both cameras)



Here is the same lens used on DS and on the K5, with the K5 it has been cropped to 6mp to the same MP count as the DS, only thing that has changed is that the DS is moved closer to the subject
As you can see the larger surface area using the same pixel count can capture finer detail. While this is not a perfect test as we had to change the working distance to hold the same framing we can see a difference



Here is another test this time I am holding the working distance but using another lens on the DS

Again the top is a 6mp crop from the much smaller pixel K5 with the DFA 100 that is a sharp lens.
The bottom is using a M 80-200 on the DS 6mp and shot at the same DOF using the lens at 150mm.
Here you can see using an older Zoom at the same FOV as the prime lens while utilizing the same number of pixels ( only with different size) that they are very close in captured resolution and would say that the edge goes to the zoom with larger pixels of the DS and its stronger AA filter.

I know this may go against what a lot of people think but many times you are better off using FL to increase your reach ( even if its is a lesser lens) than using pixel density to do the same.

A nice way to look at the issue.

[eric3929]

First of all both resolution of the lens and the megapickles of the camera both contribute to the final image so there is not a black and white answer here.
A good lens is expected to achieve 100 lines per millimetre.
Lets turn that into points of detail 1/100mm square. And yeah I know - a questionable conversion - i think the reality wouldn't be that good.
That converts into a apsc rectangle on the image circle at 3.5 megadots.
So with the K3 that is 3.5 megadots converted to digital with 24megapixels
On the K-1 sensor that would be 5.25 megadots converted with 36 megapixels.
So still a no-brainer.

I apologize if I've missed something obvious - but would you walk me through your math here? How'd you get to 3.5 and 5.25 megadots (and a dot is a 0.01mm x 0.01mm square?)?

---------- Post added 12-01-20 at 09:25 AM ----------

And for clarity - here are the numbers I get on my end.

The KP (APS-C) sensor, it is 235mm x 156mm. This provides an area of 36660 mm^2
The K1 (FF) sensor, it is 359mm x 240mm. This results in an area of 86160 mm^2

Using your assumption that a good lens resolves dots of 1/100mm squares (0.01mm^2) then the KP sensor would read 3666000 dots, or 3.666 Mdots. I got here using sensor area divided by 0.01 (size of your dots).
Using that same math, the K1 would read 8.616 Mdots.

These numbers then translate to 6.5 Megapixels per dot from the KP and 4.2 Megapixels per dot from the K1. So yes - the K1 reads are larger area. But, the area read by the KP has more megapixels per dot, so one might assume more detail could be resolved in that area. Now, of course these are different size pixels, etc. But I'm just trying to follow the math you laid out.

If I am mistaken, and I certainly may be, please correct me.

[GUB]

I apologize if I've missed something obvious - but would you walk me through your math here? How'd you get to 3.5 and 5.25 megadots (and a dot is a 0.01mm x 0.01mm square?)?

---------- Post added 12-01-20 at 09:25 AM ----------

And for clarity - here are the numbers I get on my end.

The KP (APS-C) sensor, it is 235mm x 156mm. This provides an area of 36660 mm^2
The K1 (FF) sensor, it is 359mm x 240mm. This results in an area of 86160 mm^2

Using your assumption that a good lens resolves dots of 1/100mm squares (0.01mm^2) then the KP sensor would read 3666000 dots, or 3.666 Mdots. I got here using sensor area divided by 0.01 (size of your dots).
Using that same math, the K1 would read 8.616 Mdots.

These numbers then translate to 6.5 Megapixels per dot from the KP and 4.2 Megapixels per dot from the K1. So yes - the K1 reads are larger area. But, the area read by the KP has more megapixels per dot, so one might assume more detail could be resolved in that area. Now, of course these are different size pixels, etc. But I'm just trying to follow the math you laid out.

If I am mistaken, and I certainly may be, please correct me.

No you nailed it. I copied pasted from here to another thread yesterday and discovered my maths errors.
K-3III vs K-1II, APS-C vs full frame, which is "best" & price relevance - my thoughts - Page 7 - PentaxForums.com post 100
I am guilty of rounding off in the first instance (3.5 megadots) and then made the atrocious error of multiplying by just the 1.5 crop factor which is a lineal measure -- it should have been x 1.5 x 1.5 as a short cut way .
here is a copy /paste of that correction.

It is a bad day when you have to debunk your own post! How come no one checked my maths!!
so that should read --


" First of all both resolution of the lens and the megapickles of the camera both contribute to the final image so there is not a black and white answer here.
A good lens is expected to achieve 100 lines per millimetre.
Lets turn that into points of detail 1/100mm square. And yeah I know - a questionable conversion - i think the reality wouldn't be that good.
That converts into a apsc rectangle on the image circle at 3.7 megadots.
So with the K3 that is 3.7 megadots converted to digital with 24megapixels
On the K-1 sensor that would be 8.6 megadots converted with 36 megapixels.
So still a no-brainer."

So an even bigger difference - definitely a senior moment.
(Apart from a rounding off error I multiplied by 1.5 to get the FF size when I should have x1.5 x1.5 to calculate on an area basis.)

Using your assumption that a good lens resolves dots of 1/100mm squares (0.01mm^2) then the KP sensor would read 3666000 dots, or 3.666 Mdots. I got here using sensor area divided by 0.01 (size of your dots).
Using that same math, the K1 would read 8.616 Mdots.

That should be "sensor area divided .0001 (size of the dots)" but you ended up with the same answer.
And yes it boils down to which has the most influence on the final image (pixel size, Format or lens resolution) and I differ from you in that I think it is mostly about format and lens resolution.
The other thread discusses it too.