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Comparing FF to APS-C: What difference does the bigger sensor make?
Posted By: dosdan, 06-03-2011, 09:42 PM

It is often mentioned that a FF sensor has 2.3x as much area as APS-C. So it should be able to capture a lot more light than an APS-C sensor and be better in low-light situations. This has many people craving for FF because it will allow them to shoot in tougher conditions. But this "advantage" is not as usable as it first seems. Let's look deeper.

FF vs APS-C (1.5x CF) has a 1.2 stops theoretical SNR advantage: https://www.pentaxforums.com/forums/photography-articles/129754-comparison-sn...ml#post1347917

I'll compare the Nikon D7000 to the D700, but you could just as easily substitute the Pentax K-5 in this discussion.

Due to the superior technology in the D7000's sensor compared to the D700, the advantage in FF SNR at true ISO200 is 1 stop. See the relative difference in the ISO200 18% SNR in Table 1: https://www.pentaxforums.com/forums/photography-articles/129754-comparison-sn...ml#post1346567

However, if you compare the two formats at the same DOF & FOV, then the FF camera will have to use a 1.2 stops smaller aperture to match the FOV & DOF of the APS-C camera.

Consider the following setups:
  1. 50mm FL, f/1.4 on APS-C at 7.5m subject distance
  2. 50mm FL, f/1.4 on FF at 5m
  3. 75mm FL, f/2.1 on FF at 7.5m
First off, FOV. Due to the "magnification" (1.5x Crop Factor) caused by the smaller sensor in the APS-C camera, to get the same FOV you either have to get closer with the FF camera, if using the same FL, or at the same subject distance, use a higher FL.

So for equiv. FOV:
  1. 50mm FL on APS-C @ 7.5m = 3.6m wide FOV
  2. 50mm FL on FF @ 5m = 3.6m wide FOV
  3. 75mm FL on FF @ 7.5m = 3.6m wide FOV
See: Dimensional Field of View Calculator at http://www.tawbaware.com/maxlyons/calc.htm

Now include consideration of DOF into these equivalent FOV situations:
  1. 50mm FL, f/1.4 on APS-C @ 7.5m = 1.26m total DOF
  2. 50mm FL, f/1.4 on FF @ 5m = 0.83m total DOF. Stopped down to f/2.1 = 1.26m total DOF
  3. 75mm FL, f/2.1 on FF @ 7.5m = 1.26m total DOF

So you can see that, when you include equiv. FOV & DOF, the FF setup has to reduce the aperture to f/2.1 to match the f/1.4 lens on APS-C. This is approx. 1 stop. So you lose FF's sensitivity advantage when you maintain FOV & DOF equivalency.

The only ways you can use FF's greater sensitivity are if you can accept either a shallower DOF or a wider FOV (you need to move the 50mm FL, f/1.4 on FF @ 5m, back to 6.1m to obtain a 1.26m DOF, at which distance you get a FOV width of 4.39m, so your subject is now smaller), or a bit of both.

The topic of APS-C & FF equivalency is covered in great detail in Joseph James' essay on Equivalence

Dan.

Last edited by dosdan; 12-04-2011 at 02:47 AM.
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06-11-2011, 07:39 AM   #16
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suggestion

QuoteOriginally posted by rparmar Quote
So far I have neglected to mention that I came across this article only because I have written my own on the subject: Equivalence of Camera Systems. I would be happy for readers to critique that article, as it is my attempt at making these thorny matters as simple as possible.
I like what you said and how you said it.

One thing I think you might reconsider is the appropriate relationship for image quality.

So far image noise is concerned the square root of sensor area is the best descriptor since Signal/Noise (for inherent shot noise) is proportional to Sqrt(Number of photons). This is true either for the total image or individual pixels - ie. either display quality or pixel peeking quality.

A good case can also be made that Image Clarity (subjective image quality) is proportional to a linear measure of pixel or image size.

Using a linear (ie. sqrt(area)) rather than area relation between IQ and sensor/pixel dimension would further simplify your conclusions.

Dave

06-11-2011, 08:15 AM   #17
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Dave: I do indeed use the sqrt(area) measure as you suggest: it's the last column in the table and the one I conclude is most appropriate.
06-11-2011, 08:27 AM   #18
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QuoteOriginally posted by rparmar Quote
Dave: I do indeed use the sqrt(area) measure as you suggest: it's the last column in the table and the one I conclude is most appropriate.
Paragraph 4 - last sentence theatre of noise: Equivalence of Camera Systems
QuoteQuote:
...All else being equal, a larger sensor produces better IQ, and the measure of this difference is the ratio of sensor areas...
and
QuoteQuote:
Summary
1. Lens Focal Length and Aperture are invariant no matter what sensor they are attached to.

2. A smaller sensor acts exactly like a cropped version of a larger sensor (all else being equal). The image quality decreases in proportion to the amount of the crop{nb usually given as a linear measure}, that is, the ratio of sensor areas.
I mentioned it in the context of "image quality" and noise but it also holds as you point out for diffraction, fov, and dof.

Dave

PS I know this seems like nit-picking but I think it helps internal consistency and consistency with what I think is usually implied by "Image Quality".

Last edited by newarts; 06-11-2011 at 09:52 AM.
06-11-2011, 01:07 PM   #19
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QuoteOriginally posted by toooldtocare Quote
The differences are small if you only print 13x19 or smaller, but if you crop or blow up really large a full frame sensor wins hands down on sharpness.
You would know better than i if there is sharpness differential between FF and aps, all i know is one can print sharp aps images up to 36" maximum dimension. Because i've sold at least 8 framed prints in that dimension that were taken with my K20. I've seen a K20 image shown in these forums that was enlarged to 48".

The other factor that hasn't been mentioned here, is that due to the much greater numbers of aps cameras that are being sold, there is more development money to develop aps sensors than there is to develop FF sensors. Its the "unwashed masses" that are driving the market Of course, i assume that some new breakthru found in aps sensor development would eventually be exported to FF sensors. Will FF sensors eventually be as cheap as today's aps sensors - i suppose.

06-11-2011, 02:41 PM   #20
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No, Dave, you are not nitpicking -- thanks for pointing out these statements. I think actually I was trying to simplify too much. I have removed these references from the article and will reserve talking further about image quality until another instalment because I need to introduce pixel size in order to talk about quality in any meaningful way.
06-11-2011, 02:56 PM   #21
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QuoteOriginally posted by rparmar Quote
No, Dave, you are not nitpicking -- thanks for pointing out these statements. I think actually I was trying to simplify too much. Now, I need to reconsider what to do with this article.
It is hard to edit one's own writing I find.

I think the article is nicely written & helpful.

The diffraction stuff might be moved in with the equivalence article by simplifying it to "diffraction onset begins around pixel pitch (micrometers) ~ f-number". This is an important limit often omitted in equivalence discussions. It is hard to know how simple to be and when to stop.
06-12-2011, 11:21 AM   #22
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QuoteOriginally posted by newarts Quote
It is hard to know how simple to be and when to stop.
Well, that's for sure. My thinking was that there were already a lot of detailed and confusing articles on the web, and also some that are too simplistic or biased. Having recently joined some MFT boards I am dismayed to see people arguing their sensors are no worse than larger sensors. It seems to me healthier to know what compromises one is making when shooting a particular camera system, and to be happy with those compromises... or find a better system!

Since I am writing on a blog the particular articles appear when I get around to finishing them. The difficulty is then having some sort of organisation readers can follow. For this reason I am not against going back to finished articles and updating them. I will soon do this once more in order to provide links to related articles.
07-29-2011, 01:36 AM   #23
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Am I missing something here? I think the first premis in the first paragraph of your article is wrong, the amount of light falling on each pixel is exactly the same, if I use the same lens on a Canon 5D (APS sensor) and a 1D (Full frame) set Aperture priority, set f8 and the shutter speed is exactly the same for each camera, the image is not 1/2 a stop brighter on the full frame.

As I understand it the reason why a full frame has lower noise is because the sensor is physically larger and doesn't get as warm as an APS sensor (heat generates spurious noise in any electronic component). Also the pixel density is less.

One thing I do know is that my K5 gives less noise than either of the two Canons'!

Or am I wrong?

Chris

07-29-2011, 02:38 AM   #24
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QuoteOriginally posted by ChrisJ Quote
Am I missing something here? I think the first premise in the first paragraph of your article is wrong, the amount of light falling on each pixel is exactly the same, if I use the same lens on a Canon 5D (APS sensor) and a 1D (Full frame) set Aperture priority, set f8 and the shutter speed is exactly the same for each camera, the image is not 1/2 a stop brighter on the full frame.
Chris, the 5D has a FF-sized sensor. See the specs here:
http://en.wikipedia.org/wiki/Canon_EOS-5D

The 5D sensor is very close to the FF size of 36mm x 24mm.

The 1D does not have FF-sized sensor. Its sensor is 28.7 mm x 19.1 mm (see http://en.wikipedia.org/wiki/Canon_EOS-1D). Compared to FF, FF has a 1.57x bigger sensor and the CF of the 1D is 1.26x.

However, if we were comparing FF to APS-C with a 1.53x CF, the difference in areas (see http://en.wikipedia.org/wiki/Image_sensor_size) is approx. 864 mm2 to 370 mm2 = 2.34x bigger. Taking the square root of 2.34 to get the relative difference in diagonal length = 1.53x (hence the crop factor difference).

Now say these two sensors have the same sensel size and technology, and let's assume the APS-C sensor is 10 MP. The FF version with the same sized sensels would have to have 2.33x more sensels to fill the bigger sensor area, hence 23.3 MP. In such a case, swapping the same FF lens between both cameras should result in the same amount of light falling on each sensel in both cameras. If you consider these sensors at the pixel level (aka 100% zoom - I'm using the term "sensel" for the photo-electronic conversion element in the sensor, and the term "pixel" for the output after the demosaicing of sensel output to decode the Bayer CFA), each camera should have a similar noise performance in a raw file. This is the DxOMark's "Screen" tab on their charts.

However, say we want to compare the noise performance of both sensors when resizing/printing to the same size, say 6"x4", 8"x10" or A4. In such a situation, the fact of the 2.33x greater area of FF produces a superior noise performance. The difference due to this "normalisation" of output size is the square root of the ratio of the areas, hence 1.53x better noise performance from FF compared to APS-C. Expressed as Stops, this is 2 log2 (1.53) = 1.2 Stops better SNR for FF. This normalised output-size comparison is shown in the DxOMark "Print" tab. I find this the most useful tab to use when comparing both within & between formats as the difference in the number of sensels in each camera becomes less significant (at the same technology level, smaller sensels, when considered individually, will be more noisy than large sensels) - it's the quality of final output image that's the most important thing.

Going back to your original quote, at the same F-number, at the same shutter speed & ISO sensitivity, you will get the same exposure since the LV (Light Value) is the same. Or considered the other way around, at the same LV and using the same shutter speed & ISO sensitivity, an f/4 lens (regardless of focal length, FOV & DOF) will produce the same level of exposure on both FF & APS-C. But at the same exposure level (and assuming equivalent levels of sensor technology), the FF version should have 1.2 stops better 18% SNR.

The situation changes when you match DOF & FOVs on the two formats.

Dan.

Last edited by dosdan; 07-29-2011 at 03:56 AM.
07-29-2011, 07:06 AM   #25
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Ah, I am missing something, not only that the 5D should have read 550D, for which I apologise.

So if the Mp's are similar, of course the sensel (nice term that) will be larger on the FF sensor, occupy more of the surface area and receive more light.

I really should stop replying to these just after I get up, I need at least 2 cups of tea before the brain meshes.

Chris
07-29-2011, 08:01 AM   #26
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QuoteOriginally posted by ChrisJ Quote
I need at least 2 cups of tea before the brain meshes
those Englishmen...
07-29-2011, 02:53 PM   #27
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QuoteOriginally posted by ChrisJ Quote
So if the Mp's are similar, of course the sensel (nice term that) will be larger on the FF sensor, occupy more of the surface area and receive more light.
Working at the sensel level, I think "pixel pitch" (distance between the centre of the sensels), rather than the actual sensor size, is usually quoted. Problem here when comparing sensors, particularly for different years, is that the fill-factor was much lower in older cameras due to either no micro lenses or more primitive implementations of them. So a lot less of the total sensor area was converting light to electricity, leading to much lower efficiency and more noise.

The problem with looking at individual sensels is that it's easy to develop a "more mega pickles is worse" mentality, whereas its the total sensor, compared at similar output size, that is more significant.

I much prefer to work at a normalised output size/DxoMark "Print" tab level where the output quality of two sensors is equally compared, regardless of sensel count and sensel size.

Dan.

Last edited by dosdan; 07-29-2011 at 02:58 PM.
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