# Lens Resolution fact or fiction?



## duydaniel (Jun 30, 2013)

Hi guys,

Lens resolution is something very often discussed, especially on DXO site.
However, I feel that it is fictional and here is why:

Look at p&s cameras, they often come with low quality zoom lens (compare to DSLR ones)
yet they offer a very high resolution out put images. If you zoom in those images, you can 
definitely see details and they are not bad.

If you get the ratio of megapixel from a p&s and the area of light projected on the sensor by the lens and multiply that ratio multiple times until you meet the size of your DSLR sensor, I am sure you can get a much higher lens resolution from your DSLR (not sure if this make sense) than one from DXO.

So if that is the case, then the DXO resolution measurement is a total BS
What do you think?


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## WillThompson (Jun 30, 2013)

duydaniel said:


> So if that is the case, then the DXO resolution measurement is a total BS
> What do you think?



I totally agree that DXO is mostly BS but not for the reasons you mention!


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## Mt Spokane Photography (Jun 30, 2013)

Resolution is a feature that can be measured, and it makes a huge difference, otherwise why not use a coke bottle?

What a lot of people don't realize that the resolution of point and shoot lenses is not only very high, but is higher than a typical DSLR lens. It has to be higher because of the tiny sensor. Since the lenses are small, they can be made to high resolutions more easily and cheaply. They have pretty much reached the practical limit, so there is no magic formula to keep improving them by any large amounts.

That doesn't mean that the resolution of the final images is higher, but, if you were to measure the mtf of the lens, it will usually be higher. 

Panavision used to have a supurb presentation about the subject, but have since taken it down. It still lives on the internet in places like this. I'd strongly recommend this for all photographers, since it explains the significance of MTF and what resolution as we think of it really is.

http://www.freshdv.com/2008/05/demystifying-digital-camera-specs.html


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## Radiating (Jun 30, 2013)

duydaniel said:


> Hi guys,
> 
> Lens resolution is something very often discussed, especially on DXO site.
> However, I feel that it is fictional and here is why:
> ...



I think that your premise defies the most basic logical checks. 

If lenses do not have resolution then how can we consistently measure their resolution? Magic?


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## johnhenry (Jul 8, 2013)

Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.

You also need to be able to take advantage of that resolution.

I do have to laugh a bit at people who use phones with outrageous number of pixels and expect to get the same results as a camera with a lens meant for optimal capture of images.

First off, the ULTIMATE resolution of a lens is based on its linear size, the larger the front element, the higher the resolution the lens is capable. You can stick on a CCD/CMOS with more pixels but if the lens is incapable of the resolution, the added data is simply an upsampled version of what was there. IE No meaningful improvement.


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## Mt Spokane Photography (Jul 8, 2013)

johnhenry said:


> Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.
> 
> You also need to be able to take advantage of that resolution.
> 
> ...


 
Resolution of a lens has nothing to do with its physical size. Where did you hear that??


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## Quasimodo (Jul 8, 2013)

Mt Spokane Photography said:


> Resolution is a feature that can be measured, and it makes a huge difference, otherwise why not use a coke bottle?
> 
> What a lot of people don't realize that the resolution of point and shoot lenses is not only very high, but is higher than a typical DSLR lens. It has to be higher because of the tiny sensor. Since the lenses are small, they can be made to high resolutions more easily and cheaply. They have pretty much reached the practical limit, so there is no magic formula to keep improving them by any large amounts.
> 
> ...



Thank you for the link, looking forward to watch and get further educated.

G


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## Drizzt321 (Jul 9, 2013)

Quasimodo said:


> Mt Spokane Photography said:
> 
> 
> > Resolution is a feature that can be measured, and it makes a huge difference, otherwise why not use a coke bottle?
> ...



Fantastic set of videos, thanks!


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## risc32 (Jul 9, 2013)

johnhenry said:


> Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.
> 
> You also need to be able to take advantage of that resolution.
> 
> ...



say whaa?


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## jrista (Jul 9, 2013)

duydaniel said:


> Hi guys,
> 
> Lens resolution is something very often discussed, especially on DXO site.
> However, I feel that it is fictional and here is why:
> ...



The problem is that DXO is not actually measuring just lens resolution. DXO's tests are "camera system resolution" tests. The final output resoution of any camera is a _*convolution*_. Lenses don't simply project...they also modify. Sensors don't simply record...they too also modify. The image projected by a lens is then further "convolved" by the sensor, producing a result that has a lower resolution than either the lens (as depicted by its mathematically generated MTF) or the sensor (as determined by it's raw spatial resolution...pixel pitch for raw luminance-only "detail" resolution.)

An example would be to take a *perfect* f/4 lens, one that is diffraction limited and not aberration limited, and thus capable of resolving 173 lp/mm (line pairs per millimeter), and let's say a high resolution P&S camera also capable of 173 lp/mm spatial resolution (which, assuming ideal circumstances and say a foveon-style sensor with 2.8 micron pixels, is plausible). The final output resolution of an image produced by this camera setup will be lower than 173 lp/mm. Because of the fact that the real-world image is convolved into a digital image, we cannot actually achieve that maximum theoretical resolution. 

Total "system resolution" is closely approximated by computing the root mean square (RMS) of each component in the system. Technically speaking, each and every specific piece, such as individual lens elements, air pockets, filters in the lens and in the stack above the sensor, as well as the sensor itself, should be taken into account. We can reasonably approximate total system resolution by just taking the RMS of each major component...the lens and the camera. In this case, our "blur circle" size is the same for the lens and the sensor...2.8 microns. The RMS would be:


```
tsr = sqrt(2.8^2um + 2.8^2um) = sqrt(7.84um + 7.84um) = sqrt(15.68um) = 3.96um
```

The pixel pitch and diffraction limited blur of the lens and sensor is 2.8 microns, however the final system blur is 3.95 microns. A larger blur leads to lower resolution. In terms of spatial resolution (lp/mm):


```
tsrSpat = 1l / (3.96um / 1000um/mm) / 2l/lp = 126lp/mm
```

The actual output of a camera setup that uses a PERFECT f/4 lens (something highly unlikely in a P&S, but for demonstration purposes) and a high resolution sensor that uses 2.8 micron pixels, is 126 lp/mm. That is about 73% the maximum potential resolution either the lens or the sensor is capable of (again, assuming ideal circumstances). The ACTUAL resolution of such a setup with real-world parts would still be lower. One can assume that the lens is not perfect...let's say 10% less than perfect. The bayer nature of most CMOS image sensors will also impact results, possibly shaving off another 25%. That would give us a lens capable of 155lp/mm, and a sensor capable of 130lp/mm. That results in a total system resolution of 100lp/mm.

Now, keep in mind...this is for a camera with a very good lens, and a sensor with much smaller pixels than the average DSLR. If we run the numbers for, say, the 5D III and a high end L-series lens at f/4, we get even lower results. Assuming we get the same 155lp/mm out of the lens, the sensor now has 6.25 micron pixels. Assuming the same 25% loss due to the bayer array on the sensor, and the final system resolution comes out to 57lp/mm. 



Before DXO moved to their new way of presenting lens tests, most of the higher end L-series lenses were getting 40-55lp/mm resolution results with cameras like the 5D II, 5D III, and 1D IV. That is right in line with the math I've demonstrated above. My 10% and 25% weights for lens and sensor are a bit optimistic and rather simplistic, one will usually experience greater losses, further diminishing resolution.

Additionally, one has to understand DXO's test setup. They test lenses in extremely low light, much lower than the kind of light people will photograph in. This has the effect of severely hurting any lenses that are not ultra fast (i.e. f/2 or faster) because the "transmission" factor takes a serious hit. The only logical conclusion I can come to is that to maintain a "consistent" test setup (consistent by DXO standards anyway), a lower light level had to be used in order to test ultra fast lenses (i.e. f/1.2 or faster) without over-exposing. Again, this is similar to DXO's other tests, and one particular factor has an overbearing impact on the total "score" of the lens in the end...and undue impact, and one that does not fairly or appropriately demonstrate the true quality of many lenses. (An example of that would be Canon's new 200-400 f/4 1.4x TC lens...which scores a mere 24 on the DXO scale, when it is a superb lens with excellent resolution and excellent characteristics in general. The SOLE detractor? TRANSMISSION!!!)

(NOTE: I would actually offer that DXO's lens tests are fundamentally flawed when it comes to their transmission factor. I do not believe they are actually testing "light transmission"...if they were, then it shouldn't matter what the aperture is...all that would really matter is how much of a known quantity of a small column of light transmitted through the center of the lens actually reached the back of the lens. Technically speaking, such a test should work even at the minimum aperture, as aperture should not play a role in testing the light transmission of a lens at all...however in the case of DXO's tests, it clearly does.)


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## Mort (Jul 9, 2013)

@ jrista

I was looking at your other replies from back in 2012 that I thought was pertinent to the discussion. I was wondering where you have learned the math from that. I am an engineer and the only times I've seen stuff like that was during the small time when we talked about optical physics. I would love to research more on that subject. Optics fascinate me (I guess it's good I like photography)

As for the resolving test, I feel the DxO tests are good "general guidelines" of how lenses perform. Of course there is something to be said for the camera lens combo. When the 5d mkiii first came out, DxO ripped on it saying the D800 blew it away, but when real world examples came in, it was much closer. They then looked at the lens & camera system as a whole and found out that the 5d mkiii comes out much closer to the D800 outside the lab. 

Also somebody correct me if I'm wrong, but I have felt that resolving power is very closely tied to the sharpness; not that they are the same, but very closely related.


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## jrista (Jul 9, 2013)

Mort said:


> @ jrista
> 
> I was looking at your other replies from back in 2012 that I thought was pertinent to the discussion. I was wondering where you have learned the math from that. I am an engineer and the only times I've seen stuff like that was during the small time when we talked about optical physics. I would love to research more on that subject. Optics fascinate me (I guess it's good I like photography)



Well, I stole the RMS approximation from Ctein, from one of his articles from a few years back. In reality, the math is far more complex, assuming you actually have the benefit of richer information. If you wish to research more for yourself, search "Point Spread Function". Every element in an optical system has some impact on the image it affects. Each element of glass, the diaphragm, even the filter stack over the sensor and the sensor itself. They all spread light out. In actuality, the PSF of a given lens rarely results in a perfectly spherical result...usually a more complex pattern emerges. If you have an accurate mathematical model of a lens, then there are powerful tools that can run the complex math for you, and simply present you with plots of what the blur circle looks like at a theoretical sensor plane, for each aperture you test. At wider apertures, a multitude of optical aberrations will usually contort the PSF into odd shapes. At very narrow apertures, diffraction will usually produce a more patterned shape that is more spherical in nature (although it really depends on the number of blades in the aperture.) 



Mort said:


> As for the resolving test, I feel the DxO tests are good "general guidelines" of how lenses perform. Of course there is something to be said for the camera lens combo. When the 5d mkiii first came out, DxO ripped on it saying the D800 blew it away, but when real world examples came in, it was much closer. They then looked at the lens & camera system as a whole and found out that the 5d mkiii comes out much closer to the D800 outside the lab.



I wouldn't say DXO's tests are not useful in any capacity. My problem with DXO is ultimately their scalar scores. It is impossible to "score" things that differ wildly on a linear scale...it just doesn't make sense. Especially when you have a bogus factor like "Transmission" playing such a critical role. For example, Canon's 200-400 should score far higher than "24", and it should have superb transmission thanks to Canon's SWC nanocoating (usually used on internal elements.)

The variety of detailed information from DXO is useful...plots like the vignetting and sharpness ones are no more or less useful than the same from DPR. I would just be very careful of using the DXO score as anything that even remotely resembles a realistic assessment of a lens. To be plain...it doesn't. It's a fundamentally flawed result that doesn't accurately represent anything, and is overly weighted on maximum aperture.



Mort said:


> Also somebody correct me if I'm wrong, but I have felt that resolving power is very closely tied to the sharpness; not that they are the same, but very closely related.



Remember that resolving power for a lens is a variable. Technically speaking, a proper evaluation of a lens (i.e. MTF) takes into account sharpness and contrast across the area of the lens (center to corner) at at least a couple key apertures (i.e. max and f/8). Depending on how you shoot and what you shoot, an evaluation of a lens at it's maximum aperture may not be useful to you if you shoot landscapes and are rarely wider than f/11, let alone f/8. I think DXO tends to offer "best aperture", which is the aperture at which sharpness in that particular test, with that particular camera, for that particular AFMA setting, peaked.



There is a lot of difficulty in testing lenses...there are SO many factors that affect the results, some of them that vary from sample to sample and whether lens samples are appropriately calibrated to body samples. The amount of repetition in a test (i.e. we tested each lens sample with each body sample three times, and aggregated and averaged the results) also matters, and affects the accuracy. I figure DXO is probably pretty thorough, but I have always had a problem with their approach...for both sensors and lenses. They don't weight critical factors well, or as in the case of transmission, they critically weight factors that are either improperly evaluated, or just plain not useful in the end (i.e. in stills photography, an f/4 lens is an f/4 lens...there will be slight variations in what that actually means, but in the end it won't affect the final outcome enough to matter. Transmission is far more critical in cinematography, as you often pre-plan everything, right down to when, where, and how focus and aperture are changed...so knowing exactly how much light and therefor exactly what the final exposure will be after each change is important.)


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## Don Haines (Jul 10, 2013)

risc32 said:


> johnhenry said:
> 
> 
> > Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.
> ...


I have a 30 year old 800mmF5.6 at work. My 70-200 resolves greater detail of distant objects....and is certainly a lot smaller chunk of glass.... Resolution is a function of how precise the glass is ground and shaped, plus the constancy of the index of refraction of that glass.


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## jrista (Jul 10, 2013)

johnhenry said:


> Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.
> 
> You also need to be able to take advantage of that resolution.
> 
> ...



Umm...this is so flawed I don't even know where to begin. First, lens resolution is ULTIMATELY determined by diffraction, assuming otherwise perfect characteristics. In the case of a lens that is not *diffraction limited*, optical aberrations, of which there are a great variety, ultimately determine the limit of resolving power. 

The size of the front element has absolutely nothing to do with resolving power. The front element really has to do with _light gathering power_. The front element of a lens must be at least as large as the entrance pupil from a distance of "infinity", but may be larger. Being large, however, does not necessarily mean higher resolution. There are a multitude of lenses that offer diffraction limited characteristics at wide apertures that are also very small, even diminutive in size. From a limitations standpoint, it is actually easier to correct optical aberrations with a smaller lens, meaning the center to corner performance curve at the very least becomes flatter, and the overall MTF can usually be maximized _more easily_. That is not to say that large lenses cannot be optimally designed (pick up any one of Canon's mark II great white primes), however it is usually a much tougher problem to solve...hence the significant expense.

It is also completely incorrect to state that when either a lens or sensor are "incapable" of achieving a certain resolution, that there is no point in using a higher resolution counterpart. If you have a sensor capable of resolving 80lp/mm, and already have a lens that is capable of resolving 120lp/mm at f/4, here is ABSOLUTELY a benefit from moving to a better lens, say one capable of resolving 140lp/mm at f/4. The final output resolution, that system resolution I talked about in my previous reply, increases as it is the result of a *convolution* of _ALL ELEMENTS INVOLVED IN THE SYSTEM_.

Sorry bub, but not a single thing you said is even remotely accurate. Laugh all you want, but the joke is on you. :


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## bdunbar79 (Jul 10, 2013)

johnhenry said:


> Resolution of a lens is fine, but you need to have a sensor with enough pixels to capture it.
> 
> You also need to be able to take advantage of that resolution.
> 
> ...


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