Does the lens or sensor limit the resolution of an image?

[TonyW]

Hi Ted,

I have done what you suggested. Here is the picture of the square. The behaviour at the edges is similar to what I had before. I would be pleased to see anything you can deduce.

I would add that my original comments are not just of academic interest. If my results are correct, it gives me a more objective way of knowing if images are as sharp as possible. I still don't know any way of measuring what the effects of anti-aliasing are.


square by tonyw36, on Flickr

The jpg file with its full resolution should be available if you use the link to flickr. Flickr would not accept the raw file but that should be available from https://www.dropbox.com/s/kj4rbqgetmbnlzz/056A3591.CR2 (it's a 28MB file though).

[revi]

@Andre:
The amont of photons absorbée by the sensor determines the brightness of the image, but has no influence on sharpness, un les you really overload the sensor.

Detail and resolution are directly related: finer details require a higher resolution to be visible. And the amount of detail is one aspect of sharpness.

Sharpening can increase the size of a jpeg file, but not of an uncompressed image, as you don't increase the number of pixels of the image

[dje]

Hi Tony

I hope my previous response didn't come across as too "dismissive". I guess my concern with your test is the uncertainty in what you are actually looking at. I take your point about using different magnifications to try and eliminate the sharpness of the transitions in the subject. I had a look at your raw file in a little program called "RawDigger" which allowed me to have a look at the values of each pixel in the vicinity of a transition from white to black. Or at least I had a look at the green channel values, some of which would be actual sensor values and some of which would be estimated values from the de-mosaicing process. The transition seems to be gradual over about 5-7 pixels. However I'm not certain what I'm looking at even with this. And I think I've just branded myself as a true pixel peeper !

The more I think about it, I think there are two limitations which can't be avoided. One is the anti-aliasing filter that Colin mentioned but I don't know how much softening this will contribute. The other is the de-mosaicing process and once again, the effect of this is somewhat unknown when you get down to this level of precision.

If you had a camera without an anti-aliasing filter and colour mosaic filter, it might be possible to get some more certainty in the measurements. (I believe the Nikon D800E has no AA filter)

Dave

[xpatUSA]

Hi Ted,

I have done what you suggested. Here is the picture of the square. The behaviour at the edges is similar to what I had before. I would be pleased to see anything you can deduce.

Hi Tony,

I downloaded the jpeg. Perfectly adequate for the purpose. I used QuickMTF to analyze the top, left, bottom, right edges. The results are listed hereunder as: edge spread 10-90% in pixels, The fraction and (LPH) at which MTF = 50%, the MTF at the Nyquist fraction (0.5):

top: 3.58px, 0.142 (1094), 2%
right: 3.86px, 0.132 (1018), 2%
bottom: 4.48px, 0.115 (883), 1%
right: 3.93, 0.132 (1018), 4%

There is a little CA on the left and right edges.

Before the real-worlders start rolling their eyes, I will try to explain what these results mean. There is softness. In one sample at the bottom, I actually got zero MTF at Nyquist and it took over 10px to go from the black value to the white value. However the image is 5760px x 3840 px and you did shoot at f/8 (your lens' sweet spot?). If I were to down-sample (bi-cubic) the image to e.g. 1440px wide and re-test, the results would be much, much sharper.

Might do that after some coffee . . .

[xpatUSA]

Might do that after some coffee . . .

Yep, downsized in two steps of 50% to 1/4 size, using bi-cubic re-sampling. No sharpening was applied to the final image.

I measured a very respectable 1.51px rise, 0.335 at MTF50, and a whopping 17% MTF at Nyquist.

Anything much less than 1.51 and overshooting (halos) will be starting to appear.

An MTF50 of 0.335 means good contrast at reasonable detail frequencies.

17% at Nyquist says that any Moire caused by downsizing will be quite visible.

[pnodrog]

Sort of on the same subject I have found due to moving from a D200 (10megapix) to a D800 (36megapix) to achieve the same apparent sharpness when viewed at full screen I need to sharpen the D800 far more aggressively. (reduce the masking, increase size and leave % about the same) The D800 has far more resolution but unless you are viewing at over 50% it appears softer than the D200. Sharpening appropriately for size of reproduction is far more critical simply because the range of acceptable sizes is greater.

[Polar01]

I stated rolling my eyes about the 2nd post, I do find it interesting, do not completely understand it in my world, but interesting.

Cheers: from a real-worlder

Allan

[xpatUSA]

Hi Ted,
If my statement [which was 'Resolution will be determined by the amount of photons a sensor can absorb'] is indeed incorrect and misleading you should not let it pass. An explanation as to why you say it is incorrect and misleading will be appreciated. You should not challenge any statement without an explanation.

Well that sure told me off . . .

OK, in retrospect, you might have meant 'radiometric' resolution. (my best quess).

Challenge withdrawn!

My turn: we should not use the word 'resolution' without some sort of qualifier.

Looking forward to better understand[ing] your view of how high resolution is produced.

I too am looking forward to that

[pnodrog]

Well that sure told me off . . .

OK, in retrospect, you might have meant 'radiometric' resolution'. (my best quess). Challenge withdrawn!

My turn: you should not use the word 'resolution' without some sort of qualifier.



I too am looking forward to that.

Probably a good guess but the sensitivity, dynamic range of the sensor and of course the resolution of the A/D converter are as I understand it not part of the question posed by the thread. So Ted my initial reaction to Andre's statement was similar to yours.

It reminds me of the story of the blind men and an elephant where they all disagree about what an elephant is because they are each touching a different part.

[AB26]

Hi Ted and L.Paul:

Ted, I see you edited your original post. I am glad you challenged my statement, it forced me to do some serious research.

I did not make a statement that “the more photons a sensor can capture the better the resolution will be” due to some thumb sucking or wild assumptions. I will explain shortly.

Going back to what defines “resolution”, the following: When we as a community of photographers talk about resolution we talk about how “smooth” an image can rendered without “pixilation” and/or noise. Resolution will also determine how much an image can be enlarged before showing any “artefacts”.

The technical “definition” of resolution might be how close line pairs can be together per any given measurement, and be visibly resolved. That would be a technical definition of resolution. The question would be if that definition can be applied in digital imaging systems? Does it not rather apply as a measure of determining resolution rather than be a definition of resolution?

Digital imaging resolution is determined by dots per any given measurement on a horizontal axis and how many lines of dots there are on the vertical axis. DPI refers to dots per inch, PPI to pixels per inch. The more PPI a sensor has per any given measurement, the higher the resolution will be that the sensor can render. A 36MP full frame Sony Exmor R sensor WILL render much higher image resolution than a 10MP full frame Sony Exmor R sensor. (compare Apples with Apples)

Getting back to my statement:
Photons are the electromagnetic light particles entering the camera trough the lens and hitting the sensor at the speed of light. At Sony, the clever Japanese engineers have been working on technology, to reduce the amount of photons deflected, before entering the photosite and being “absorbed” in the silicon substrate in the photosite. At Hasselblad those clever Swedish engineers have been working on technology turning a 50MP sensor into a sensor capable of rendering the resolution of a 200MP sensor.

The only conclusion that is logical to me is that these clever engineers have been working on technology to capture more photons per photosite. Gathering more photons per photosite will render higher resolution with less noise. When capturing an image and under exposing you will notice the image has less resolution than a properly exposed image. A properly exposed image consist of more photons than an under exposed image. Therefore I have to conclude it has to be the amount of photons captured by the sensor that will determine the resolution rendered by any given image sensor. In other words, my statement that the more photons an image sensor can capture the higher the resolution will be should not be considered incorrect and/or misleading.

Does the sensor determine resolution rendered in an image? YES it does! Does the lens determine resolution rendered in an image? NO it cannot! (provided the lens cap is off)

[TonyW]

Hi Ted,

Thanks for the analysis that you have reported here. It seems to me that it supports in more detail my results. One question about the terminology: what does "LPH" stand for?

This has been a desperate scramble up a steep learning curve to me but I think I am succeeding in understanding thinks like MTF, resolution, sampling theorem, etc. Somebody pointed me to the link
http://software.canon-europe.com/fil...Book_10_EN.pdf
which has a lot of relevant information.

It is still not clear how to differentiate between the effect of the lens itself and anti-aliasing.

I have not yet been able to determine where the "sweet spot" of the lens is. Perhaps some more tests like this would help to find out but as someone else has said it may be time to get back to photography.

[dabhand]

I'm a little confused by this thread. Andre you say -"

Going back to what defines “resolution”, the following: When we as a community of photographers talk about resolution we talk about how “smooth” an image can rendered without “pixilation” and/or noise. Resolution will also determine how much an image can be enlarged before showing any “artefacts”. "

But surely, with pixelation especially, resolution is a much broader issue - surely the lens has a part to play through its ability to resolve the separation of two points and form an image of them - that then leads to the ability of a sensor to be able to record that difference, which in turn leads to the output devices ability to portray that level of detail.

In other words, the best resolution that can be achieved is only that of the 'weakest' link in the above chain.

[AB26]

surely the lens has a part to play through its ability to resolve the separation of two points and form an image of them

You need not have a clear image recorded by the sensor to "define" resolution. An OOF image can also be rendered as a high resolution image. If you understand what buttery bokeh means you will understand what I mean.

[chauncey]

Referencing the "weakest link"...it has been shown in numerous tests that a superior lens mounted on an inexpensive camera body will cough out a "better" image than will a cheap lens on a superior body.
Regarding the MTF charts, it would appear the "sweet spot" of the lens is the center-most portion...before where those horizontal lines start their downswing.
That is the reason that I have, occasionally, been an advocate for a crop sensor which only utilizes the centermost portion of the lens, the sweet spot.

[dabhand]

You need not have a clear image recorded by the sensor to "define" resolution. An OOF image can also be rendered as a high resolution image. If you understand what buttery bokeh means you will understand what I mean.

But that surely that uses the out-of-focus regions of an image - thus differences in lens design and quality will result in 'good' or 'bad"' bokeh, so the end result is still a function of the 'weakest link'.

Oh well, time to forget the theory and time for me to do some practical.

[AB26]

That is the reason that I have, occasionally, been an advocate for a crop sensor which only utilizes the centermost portion of the lens, the sweet spot.

Only if you use a FF lens on a crop sensor camera!!

Edit: PS. The other option is to get a Hasselblad that renders no vignetting, no chromatic aberration and no "fall off" to the edges of the image.

[xpatUSA]

Hi Ted,

Thanks for the analysis that you have reported here. It seems to me that it supports in more detail my results. One question about the terminology: what does "LPH" stand for?

It stands for Lines Per image Height, not my favorite units but some folks like 'em! My main problem with 'LPH' is sometimes a 'line' is meant as a pair of lines (typically alternating black/white) and sometimes just one line. Unlike cycles per mm which is quite specific. Or even cycles per radian but we won't go there

This has been a desperate scramble up a steep learning curve

You'll get there . . trusssst me.

It is still not clear how to differentiate between the effect of the lens itself and anti-aliasing.

It took me a long, long time to make a similar differentiation.

I see the lens effect as resulting in a 'virtual' image which hangs in space right in front of the sensor but is completely unaffected by the sensor which could even be a piece of toilet paper, for all we care. In other words, the image produced by the lens needs to be completely disassociated in the mind from the properties of the sensor.

In a similar vein, what the sensor does with the image is determined only by the properties of the sensor. Toilet paper gives a very poor image, even if viewed from the back. My 3.4MP SD9 sensor has no anti-aliasing (AA) filter and, in LO res mode, gives the 'sharpest' image on the planet - but only because LO res means 18.24um pixels (that's big) and a 0.8MP image (that's small). Lots of potential for jaggies and moiré (both forms of aliasing). On the other hand, my 12MP GH1 sensor has a mild AA filter and 4.33um pixels and, at a pixel-peeping level can be a bit blurry. Not one property of any of these, or other, sensors affects the image cast by the lens. Equally, no matter what lens you select, or what zoom or focus or f-number you apply, the properties of the sensor remain un-affected.

Now, to compare a lens versus a sensor, it is best to fix the sensor. Let's choose a sensor with a 8.45um pixel pitch (like a D700). This sensor samples the virtual image directly in front of it at 118 pixels/mm. The sensor is limited by the Nyquist frequency 118/2 = 59 cycles per mm at the sensor face and nowhere else. Now we know the sensor limit - i.e. detail above 59 cy/mm will not be shown correctly.

The lens limit is less easy to determine because everyone and his dog have their own ideas about that. Let's take a perfect lens at an effective aperture Na = N*(1+m) of f/5.6. For green and black subjects, the perfect lens blurs everything (zero contrast or MTF) at 322 cy/mm, referred to the image plane, and this is the lens limit. Now 322 cy/mm is quite a bit more than 59 cy/mm, so the perfect lens should show something at that lower frequency, right?

So here's where your question gets answered after all the foregoing.

a) The lens limits the contrast resolution (MTF), as you have already read, due to abberration and diffraction.

b) The sensor limits the spatial resolution (cycles per pixel) per sampling theory, Nyquist, Abbe, et al.

Therefore, the detail (not 'resolution' in my book) of the image out of the camera is limited by both the lens and the sensor.

When I plug 59 cy/mm into my spreadsheet it tells me the lens MTF at that frequency is 77%, pretty good. In other words, when the D700 sensor has run out of spatial resolution, the perfect lens has excellent contrast and is ready for more. Even a less-than-perfect lens will likely have contrast in hand on a D700, I reckon. So the sensor is limiting detail more than the lens.

When I pick up a point-and-shoot with, say, 2.3um pixels, it's Nyquist limit is 217 cy/mm. If I set the lens to f/16, its zero contrast limit is 113 cy/mm. In which case, the lens is limiting detail more than the sensor.


Perhaps, after you've absorbed the above, we could devise a suitable test . .

I have not yet been able to determine where the "sweet spot" of the lens is. Perhaps some more tests like this would help to find out but as someone else has said it may be time to get back to photography.

If, by 'sweet spot' you meant the best f-number for detail contrast then how about:

Take the square that you printed and put it up on the wall, this time vertically. Put the cam on a tripod. Take shots at f-numbers from smallest (number) up to say f/11. Take raw shots and convert neutrally without sharpening and re-focus for each each shot as best you can. You should see blurring at the smallest f-number which gets less as the f-numbers increase but over a certain f-number blurring will increase due to diffraction. What some call the 'sweet spot' is the f-number at which the blur is least. Somewhere between f/4 and f/11 for most lenses. A trip to http://slrGear.com/reviews/ will show you an interactive graph for many popular lenses.

[Davey]

unsure if I have wrong end of stick but I've thought about this before and it seems like a double issue on the same thing from a logic POV. The lens projects the scene and the sensor captures this projection; ie. it is linear process in that the lens always factors into equation followed by sensor. Obviously there is no scene for the sensor to capture other than the one "made" by the lens so the lens will always be a limiting factor.

So it seems like they both limit it. If the lens can only resolve so much then sensors can only capture that much. Comparing image produced with average lens on average pix count sensor to on a high count (of equal size) would prob see improvement as the sensor isn't adding as much bias to the end image in terms of resolving power that is.

Obviously real world isn't so simple due to CA and so on, noise considerations from silicon pitch changes, other imperfections and laws of physics. Throw in different aa filters and so on and it gets messy working out specifics plus a headache from thinking about it. I'm no expert so totally open to correction on this, just the way it seems to me.

[xpatUSA]

Thanks 'Davey',

Always good to get a fresh view on things and to be reminded of the Real World which exists in spite of all those pesky technicalities!

[Colin Southern]

Obviously there is no scene for the sensor to capture other than the one "made" by the lens so the lens will always be a limiting factor.

Personally, I wouldn't say "limiting factor" - probably more "contributing factor" (in real world terms). In theoretical terms it probably comes down to whether the imperfections offered by the lens are less than the camera can resolve or not; if they're not, then they wouldn't contribute anything to the limits.

In real-world terms there are other factors that make one hundred fold more difference to image quality though (many of which many photographers seems blissfully unaware of).