A 34MP Fx Sensor and Diffration Limit

[jvora]

Hello :

Anyway to predict what which f/stop Diffraction Limit would be reached for a 34 MP FX Sensor ? Are there any such mathematical formulas that can provide this information ?

Thanks,

Jai

[Christoph C. Feldhaim]

The diameter of the Airy disc (diffraction disc) is about 1.35µm * F-Stop (at about 550 nm wavelength light).
34 MP at 3*4 aspect ratio would be about 5050*6733 Pixel.
34 MP at 2*3 aspect ratio would be about 4761*7141 Pixel.
An FX Sensor is 24*36 mm if I'm right.
So - the pixel pitch would be 24mm/4761 pixel = about 5 Micron
Now it depends where you would see the limit:
The Airy disk diameter equaling the pixel size? -->5=1,35*Fstop => F3.7
Or 2*2 Pixels enclosing an Airy Disk? -->Diameter=10 =>F7.4
Or the Airy disk enclosing a pixel? Diameter = 1,41*Pixelpitch = 7,1µ => F 5.3

The devil is in the detail as usual.


Link: http://en.wikipedia.org/wiki/Airy_disk

You should also keep in mind this is a rough calculation for a diffraction limited system.
Depending on the lenses aberrations your systems sweet spot can be at higher F-Stops.

After reading a lot of stuff on this and especially the MTF papers from Zeiss in their lens camera news I came to the conclusion that there will never be a real theoretical alternative to self testing a lens/camera/sensor system ....

Link: http://www.zeiss.com/C12567A8003B58B9/Contents-Frame/15C75F926592E5C1C1256CED0054968D
Issues 30 and 31 of their magazine ...

[ErikKaffehr]

Hi,

I agree, with a couple of additions:

1) We will have diminishing returns. The incremental improvement may be less than we would expect. Better but not much better.
2) Oversampling may have advantages, like less need of OLP (Optical Low Pass) filtering

Resolution is proportional to the square root of megapixels so going from 24 to 34 MPixels gives like a 19% improvement, may not be very visible.

Best regards
Erik

The diameter of the Airy disc (diffraction disc) is about 1.35µm * F-Stop (at about 550 nm wavelength light).
34 MP at 3*4 aspect ratio would be about 5050*6733 Pixel.
34 MP at 2*3 aspect ratio would be about 4761*7141 Pixel.
An FX Sensor is 24*36 mm if I'm right.
So - the pixel pitch would be 24mm/4761 pixel = about 5 Micron
Now it depends where you would see the limit:
The Airy disk diameter equaling the pixel size? -->5=1,35*Fstop => F3.7
Or 2*2 Pixels enclosing an Airy Disk? -->Diameter=10 =>F7.4
Or the Airy disk enclosing a pixel? Diameter = 1,41*Pixelpitch = 7,1µ => F 5.3

The devil is in the detail as usual.


Link: http://en.wikipedia.org/wiki/Airy_disk

You should also keep in mind this is a rough calculation for a diffraction limited system.
Depending on the lenses aberrations your systems sweet spot can be at higher F-Stops.

After reading a lot of stuff on this and especially the MTF papers from Zeiss in their lens camera news I came to the conclusion that there will never be a real theoretical alternative to self testing a lens/camera/sensor system ....

Link: http://www.zeiss.com/C12567A8003B58B9/Contents-Frame/15C75F926592E5C1C1256CED0054968D
Issues 30 and 31 of their magazine ...

[stever]

from my experience with Canon cameras i agree that it's unlikely that resolution will increase in proportion to linear pixel pitch closer than 6 microns

the increase in resolution from the 5D to 5D2 (6.4 micron) was pretty nearly proportional to the linear pixel increase.  the increase from the 20D (6.4 microns, same as 5D2) to 40d (5.8 microns) is measurable with very good lenses, but not really noticeable.  the improvement from the 40D to 7D (4.3 micron) is similarly measureable (and maybe noticeable) but not close to proportional even with the best lenses.  the linear pixel increase from the 20D to the 7D is almost 50%, but the measurable resolution increases by about 15% with the best lenses (e.g. 100L macro which has maximum resolution between f4 and f5.6)

i believe that silicon progress has outrun lens design and (particularly) manufacturing.  both Canon and Nikon are introducing new lenses to address the problem, but i believe these lenses will not realize the potential of the next generation of ff cameras (and aren't even close for crop-frame).  is there a market for Leica quality (and price) lenses for Canon and Nikon?

[ErikKaffehr]

Hi,

One thing I see is that with a bit aggressive sharpening I get staircase effects and aliasing on diagonal structures which means that the lens can still outresolve the sensor. I'd suggest that even a Quadrupling of Megapixels would make sense, that is going down to 3 microns. We would not be able to resolve much more, but it may results in better reproduction of what we can resolve.

Whatever the megapixels they are hard to utilize fully. Autofocus may not be dead on, lens and sensor may not be perfectly aligned and we also have camera vibration.

The new translucent mirror technology from Sony makes a lot of sense, at least potentially. Elimination of a moving mirror makes adjustment of autofokus simple and electronic viewfinder should make Live View based focusing easier.

Best regards
Erik

from my experience with Canon cameras i agree that it's unlikely that resolution will increase in proportion to linear pixel pitch closer than 6 microns

the increase in resolution from the 5D to 5D2 (6.4 micron) was pretty nearly proportional to the linear pixel increase.  the increase from the 20D (6.4 microns, same as 5D2) to 40d (5.8 microns) is measurable with very good lenses, but not really noticeable.  the improvement from the 40D to 7D (4.3 micron) is similarly measureable (and maybe noticeable) but not close to proportional even with the best lenses.  the linear pixel increase from the 20D to the 7D is almost 50%, but the measurable resolution increases by about 15% with the best lenses (e.g. 100L macro which has maximum resolution between f4 and f5.6)

i believe that silicon progress has outrun lens design and (particularly) manufacturing.  both Canon and Nikon are introducing new lenses to address the problem, but i believe these lenses will not realize the potential of the next generation of ff cameras (and aren't even close for crop-frame).  is there a market for Leica quality (and price) lenses for Canon and Nikon?

[rsn48]

Whatever happened to the guys who said 6 megapixels are enough, haven't heard from them in a while.

[Christoph C. Feldhaim]

The 6 megapixels are only valid if you

- don't crop
- don't go nearer to the image than 1.5 diagonals
- don't fight moiré
- don't use certain postprocessing (like Erik pointed out with the aggressive sharpening and such...)

Basically they were right, but as I like to say: The devil is always in the details.

[Bart_van_der_Wolf]

One thing I see is that with a bit aggressive sharpening I get staircase effects and aliasing on diagonal structures which means that the lens can still outresolve the sensor. I'd suggest that even a Quadrupling of Megapixels would make sense, that is going down to 3 microns. We would not be able to resolve much more, but it may results in better reproduction of what we can resolve.

Hi Erik,

Indeed, many lenses clearly outresolve the sensors although the lenses may exhibit reduced resolution closer to the edge of the image circle (=corners of the image) due to residual lens aberrations. Even with reduced resolution and/or diffraction, increased sampling density will allow smoother gradients and more accurate postprocessing. Reduced dynamic range as a result of smaller sensel pitches (and thus storage capacity) remains to be an issue though, so it is more likely that its the balance between resolution and dynamic range that is going to determine the 'sweet spot'. Here only a physically larger sensor array (e.g. MF) can provide a solution, unless a technological breakthrough allows to significantly increase the storage capacity in e.g. doped silicon.
 

Whatever the megapixels they are hard to utilize fully. Autofocus may not be dead on, lens and sensor may not be perfectly aligned and we also have camera vibration.

While true, lack of camera handling technique is not to be blamed on the sensor. Also, it is possible to restore all sorts of blur more accurately in postprocessing when sampling density is higher.

The new translucent mirror technology from Sony makes a lot of sense, at least potentially. Elimination of a moving mirror makes adjustment of autofokus simple and electronic viewfinder should make Live View based focusing easier.

I think that the loss of sensitivity caused by permanently splitting off a part of the luminous flux is the biggest drawback. Maybe future technology will allow to electronically switch an optically inert layer between almost transparent and reflective. Another drawback will be that the addition of an optical element in the image forming beam will lead to aberrations. Only lenses that consider such a layer of known properties in the design could avoid aberrations to a minimum. A mirrorless system which avoids all that seems to be a more likely direction of development.

Cheers,
Bart

[Christoph C. Feldhaim]

I think that the loss of sensitivity caused by permanently splitting off a part of the luminous flux is the biggest drawback. Maybe future technology will allow to electronically switch an optically inert layer between almost transparent and reflective. Another drawback will be that the addition of an optical element in the image forming beam will lead to aberrations. Only lenses that consider such a layer of known properties in the design could avoid aberrations to a minimum. A mirrorless system which avoids all that seems to be a more likely direction of development.

I believe with the development of sensor and display technology one day we will have an Über-EVF which will fix that ....

[ErikKaffehr]

Bart,

This is a good point. I'm sort of advocating mirrorless systems, but it seems that contrast detecting AF is not good enough right now. So I see translucent as a transitional technology.

I'd probably agree hat adding an extra element in the optical path is less desirable, but I guess that I may prefer it to a moving mirror.

Regarding the DR issue I absolutely agree. On the other hand DR is pretty impressive already.

Regarding the other issues I much appreciate your thoughtful comments, as always.

Best regards
Erik

I think that the loss of sensitivity caused by permanently splitting off a part of the luminous flux is the biggest drawback. Maybe future technology will allow to electronically switch an optically inert layer between almost transparent and reflective. Another drawback will be that the addition of an optical element in the image forming beam will lead to aberrations. Only lenses that consider such a layer of known properties in the design could avoid aberrations to a minimum. A mirrorless system which avoids all that seems to be a more likely direction of development.

Cheers,
Bart

[hjulenissen]

In this talk of "lense outresolving sensor" or "sensor outresolving lense", I guess there is a large area of overlap: where increasing e.g. sensor resolution gives some benefit, but not as much as one would hope.

The diffraction limit can in principle be raised by going for larger aperture lenses, right? (and also increased cost, weight, decreased availability,...)

I have problems understanding the "oversampling" argument. Oversampling is used in A/D and D/A converters to save on analog filtering. How is a 60megapixel sensor any more "oversampling" than a 15 megapixel one? They have the same Bayer pattern, could have the same relative cutoff OLPF,... The only difference seems to be that high-frequency limitations are moved upward in spatial frequency - which is a good thing but also what brought us the "megapixel war".

-h

[Bart_van_der_Wolf]

In this talk of "lense outresolving sensor" or "sensor outresolving lense", I guess there is a large area of overlap: where increasing e.g. sensor resolution gives some benefit, but not as much as one would hope.

It all depends on the particular case. In general though, many decent lenses are capable of resolving patterns in excess of 150 lp/mm. A sensor array is limited to its sampling density, a 6.4 micon sensel pitch cannot resolve much more than 78 cycles/mm unambiguously. So in general a decent lens can outresolve the sensor's capabilities by a factor of 2. Residual lens aberrations can reduce the lens' capabilities. The real issue is that the MTFs of both components combine, and can never be better than the worst of the two. Hence the search for the weakest link. Improve that, and the system performance improves.

The diffraction limit can in principle be raised by going for larger aperture lenses, right? (and also increased cost, weight, decreased availability,...)

The diffraction limit is 'cast in concrete', and is the resultant of wavelength and aperture (diameter/shape). By sampling it with a denser sampling IOW smaller sensel pitch, we only increase the accuracy at which it is going to be characterized in the final image. The per pixel resolution diminishes, so the enlargement potential alone doesn't improve the sharpness, but the blur restoration potential does increase which in turn does help the enlargement potential.

Larger aperture lenses usually also bring along more compromises in optical design. Using wider apertures does reduce diffraction, but usually also increases the visibility of residual lens aberrations. Reduced DOF may also limit the resolution (whether that's bad depends on the image use and it's creative intent). There is an optical compromise somewhere between aberrations and diffraction, and it differs per lens design.

I have problems understanding the "oversampling" argument. Oversampling is used in A/D and D/A converters to save on analog filtering. How is a 60megapixel sensor any more "oversampling" than a 15 megapixel one?

It's not necessarily dependent on the number of megapixels, but rather on the sampling density. When one samples a low resolution (spatial frequency) signal with a significantly (> 2x) higher resolution, then the resolution will not necessarily increase, but the precision will. that increased precision (oversampling) does allow to reconstruct the original/unblurred detail better (e.g. with deconvolution).

Cheers,
Bart

[BJL]

I have problems understanding the "oversampling" argument. Oversampling is used in A/D and D/A converters to save on analog filtering.

One idea is oversampling relative to the resolution of the image delivered by the lens, due to diffraction and more generally due to  the combined resolution limits of the lens. That can reduce or eliminate the need for an OLPF, or in your words, allow the camera maker to "save on analog filtering". With large formats like DMF, good OLPF filter are expensive, so avoiding them can be a significant cost benefit. And without an OLPF, oversampling relative to lens resolution by use of "extreme" pixel counts helps to avoid moiré problems. I believe that Pentax has mentioned the absence of an OLPF in the 645D as motivated in good part by cost savings, but do not have a link for that.

[01af]

Any way to predict at which f-stop Diffraction Limit would be reached for a 34 MP FX Sensor?

There's always a lot of nonsense written on questions like that. As a matter of fact, a hard diffraction limit doesn't really exist. Diffraction is always there, even at wide apertures, and it will gradually increase with smaller apertures. The question when diffraction starts to become objectionable is very similar to the question how far depth-of-field extends. It depends on your personal definition of "objectionable". So what establishes something we consider a limit actually is a matter of convention.

It's a common misconception that diffraction limit depends on pixel pitch. It doesn't. It just depends on image format, lens quality, and on your personal idea of sharpness. Formulas that compute the aperture where an Airy disk's diameter will equal the pixel pitch are amusing but irrelevant.

So for any given image format, the diffraction "limit" at 34 MP will be just the same as at 24 MP will be just the same as at 12 MP will be just the same as on film. For most practical intents and purposes, it's around f/11 for 35-mm full-frame format. If stopping down beyond that, you'll start to see loss of sharpness due to diffraction, no matter what the sensor's pixel count may be. If looking very closely, you can see diffraction losses at any aperture, as long as the lens is good enough (in real life, most lenses aren't) ... again, no matter what the sensor's pixel count may be.

[douglasf13]

 Lens DR should also be mentioned, and it often limits the DR of the sensor.  Internal reflection/flare is an issue with complex lens designs that negatively impacts image DR.

[Bart_van_der_Wolf]

Formulas that compute the aperture where an Airy disk's diameter will equal the pixel pitch are amusing but irrelevant.

I'm always in for a laugh. Why are they irrelevant? Do you mean that you prefer the 'detail' in the f/16 crop versus the f/8 crop below, or are you expressing a very broad generalisation based on a specific situation?



Cheers,
Bart

[01af]

Why are they irrelevant?

I explained it in my previous post. Am I supposed to help you reading, or would a simple repetition of what I wrote be sufficient?

Do you mean that you prefer the 'detail' in the f/16 crop versus the f/8 crop below ...?

No, of course I don't. What makes you ask such a silly question, and in which way would it be related to what I wrote?

[Christoph C. Feldhaim]

It's a common misconception that diffraction limit depends on pixel pitch. It doesn't. It just depends on image format, lens quality, and on your personal idea of sharpness. Formulas that compute the aperture where an Airy disk's diameter will equal the pixel pitch are amusing but irrelevant.

The "diffraction limit" does of course not depend on pixel pitch, since there is no "diffraction limit" - thus it can't be limited ..
But there is a resolution limit and image degradation caused by diffraction .

And there is a point of sensor resolution against F-Stop, where additional megapixels do not add more information and are simply redundant information filling up your memory card or harddisk space. Of course this as well is not a hard limit, but a continuous process.

Is it sufficient to have 1 pixel at the size of an Airy disk? 2x2 pixels, 3x3, 4x4 ...
I think it is safe to agree, that at some point no relevant information is added.

Usually it is said, that the eye cannot resolve more information than 1500-3000 points per image diagonal, depending on the detailed circumstances, like contrast, viewing distance, personal eyesight, etc...
For a 24*36 mm sensor/film this would be

SQRT(24^2+36^2) mm /(1500 to 3000)= 14,4 to 28,8 Micron

Since the size of the 1 ring of the Airy disc is about 1.35*F-Stop *1Micron you see at F11 it starts hitting which is the general experience with that format. ("F11 [sometimes it is said F8] and you'll be there..")

This is also the reason, why I try not to use F-Stops much above F 4.0 with my Canon Powershot G11.

What easily can be seen as well is, that very high resolutions, like 34 Megapixels will only add valuable information and allow for bigger enlargements at near viewing distance (like looking at a 2*3 m print from 50 cm) if very exact technique is used (accurate focusing, tripod, MUP, excellent lenses etc ..) and the aperture is not too small (The F-Number not too high).

[01af]

And there is a point of sensor resolution against f-stop where additional megapixels do not add more information and are simply redundant information filling up your memory card or harddisk space.

This is where the misconception begins.

Is it sufficient to have 1 pixel at the size of an Airy disk? 2x2 pixels, 3x3, 4x4 ...? I think it is safe to agree that at some point no relevant information is added.

No, it's not. In theory, there is no point where no more information is added when increasing the pixel count. More pixels will always yield more information. Of course, the returns will diminish quickly, so there's a point at which theory and practice will diverge for practical intents and purposes. But that point definitely is NOT at 1 pixel per Airy disk. It rather is somewhere in the 5 × 5 to 10 × 10 pixel region, or maybe even higher, depending on your intents and requirements.

And it's the same the other way around. Even when a pixel is larger than the Airy disk diameter, the exact size of the Airy disk still matters. That's why there is no relation between AIry disk diameter and pixel pitch. Smaller Airy disks will always yield sharper images, no matter what the pixel pitch is (as long as the pixel count is high enough to render something like a sharp image in the first place, of course). And higher pixel counts will render sharper images, no matter what the Airy disk diameter is.

So if you're using a certain camera and lens and you find you're starting to lose sharpness due to diffraction when exceeding a certain f-number, then with the same lens on another camera with a higher or lower pixel count you will find you're starting to lose sharpness at the very same f-number. It does not depend on the pixel pitch.

Usually it is said that the eye cannot resolve more information than 1500 – 3000 points per image diagonal, depending on the detailed circumstances, like contrast, viewing distance, personal eyesight, etc ...

For a 24 × 36 mm sensor or film this would be

  SQRT(24^2 + 36^2) mm / (1500 to 3000) = 14.4 to 28.8 micron

Since the size of the 1st ring of the Airy disc is about 1.35 × f-number × 1 micron you see at f/11 it starts hitting which is the general experience with that format. ("f/11 [sometimes it is said f/8] and you'll be there ...")

That's exactly what I said above.

[Bart_van_der_Wolf]

I explained it in my previous post. Am I supposed to help you reading, or would a simple repetition of what I wrote be sufficient?

No, of course I don't. What makes you ask such a silly question, and in which way would it be related to what I wrote?

The fact that you think that references to sensel pitch are humorous, seems to indicate that you are missing the simple fact that the choice for large MP sensor might be inspired by the need for large output. Large output means that the per-pixel microcontrast needs to be as good as one can reasonably get (within the DOF limitations one sets). In that case sensel pitch is of paramount importance, because a diffraction pattern diameter that exceeds the sensel pitch by a certain amount will cause degradation.

Your earlier remark:

If looking very closely, you can see diffraction losses at any aperture, as long as the lens is good enough (in real life, most lenses aren't) ... again, no matter what the sensor's pixel count may be.

also misses the point that a diffraction pattern that's significantly smaller than the sensel pitch cannot be resolved by the sensor (especially in the presence of an OLPF), the diffraction pattern diameter is too small. Yet you suggest otherwise.

Maybe you have some actual examples that unambiguously show this physics defying phenomenon?

Cheers,
Bart