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PostPosted: Mon Mar 03, 2008 8:45 pm 
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Hi folks,

The thread Will full frame sensors survive? over in the Off-topic section got me thinking about Depth of Field and, of course, that got me confused! What follows was written in an attempt to unconfuse myself!

This is a long post so I'll set out my conclusions, so far.
      Summary
  • Full-frame sensors have better dynamic range: .......... True
  • Full-frame sensors give better image quality: ............. True
  • Full-frame sensors can work at higher ISO numbers: .. True
  • Full-frame sensors give a shallower Depth of Field: ..... True, but they don't have to :!:
Nothing too controversial, I hope, but the DoF question is complicated. I'll explain my reasoning next. Skip to the final paragraph, if you would rather, to see my invitation to continue the conversation.

To set the scene, I will compare two sensors, both with 12 megapixels and assume that the anti-aliasing filters have similar effects. To keep the sums simple one sensor will be full-frame (same as 35mm film) and the other will have a 1.5x crop factor. I will use the terms "detector" to refer to the electronics at each pixel and "sensor" to refer to the whole chip.

For simplicity I will assume that each pixel (cropped-or full-frame sensor) captures all the light arriving in its bit of the sensor (in other words the microlenses are 100% efficient). The detector at each pixel is just a device for detecting incoming photons and adding the liberated electrons into temporary storage (the "well") as they arrive. The process isn't 100% efficient by any means but the number of electrons stored will be proportional to the number of photons that have arrived provided the well hasn't been totally filled (blown highlights). After the exposure is complete the number of electrons in each well is measured (or read out). I will assume that differences in thermal and readout noise between the full-frame and cropped sensors are not major factors compromising what follows. EDIT: In the light of subsequent posts in this thread such differences cannot be ignored but would appear to be only second order effects.

      Full-frame sensors have better dynamic range
    No argument here, I believe, as the larger geometry of each pixel's detector in a full-frame sensor typically allows a greater full-well capacity (number of photons "converted" into electrons). Note that I am defining dynamic range here as the ratio between the largest number of electrons from each pixel and the smallest number of electrons which is above the noise level. Of course you can have all the dynamic range in the world but if the A/D (analog to digital) converters don't have sufficient precision that dynamic range is wasted. Hence the recent move from 12 to 14 bit A/D.

      Full-frame sensors give better image quality
    Now it gets trickier! The answer is, of course, that they do but the reason is interesting. It's to do with the dynamic range advantage discussed above but greater dynamic range is only useful if the camera can supply enough photons to each pixel. Let's assume that a scene is captured by the cropped sensor using a 40mm focal length lens at f/4. To capture the same amount of the scene on a full-frame sensor we would use a 60mm lens (applying that 1.5x factor) and, being simple souls, we might opt to continue to use f/4 so, given both cameras are working at the same ISO, achieving similar shutter speeds. But remember that both full-frame and cropped sensors have 12 MP and that each microlens is assumed to feed all of the light falling on it to its detector. Of course the 60mm f/4 lens is collecting 2.25 times as much light as the 40mm f/4 lens (1.5 squared) so the full-well capacity of each detector on a full-frame sensor has to be bigger than that of a cropped sensor. So the better image quality of the full-frame sensor is simply down to the fact that it typically gets more photons when capturing the same scene using the same f-number, ISO and shutter speed.

      Full-frame sensors can work at higher ISO numbers
    Exactly the same reasoning applies as in the case above. In fact it's the other side of the same coin but I thought it worth giving a separate heading and now I understand why higher ISO numbers are usable.

      Full-frame sensors give a shallower Depth of Field
    OK, here's the "biggie"! At a simplistic level this is true but if you are seeking to maximise the depth of field (e.g. in a landscape) then the diffraction limited depth of field is pretty much the same - hence my "True, but they don't have to" answer in the summary. Two things are going on here so to start with let's take the example above with a 40mm lens at f/4 on our cropped sensor camera. Using the DOFMaster Depth of Field Calculator we can see that focussing at 20 metres gives acceptable sharpness from 10m to infinity. However on the full-frame 60mm lens at f/4 the best we can do, while retaining acceptable sharpness at infinity, is to focus at 30m giving a closest distance of acceptable focus of 15m. Not nearly so good as the 10m with the 40mm lens on the cropped sensor.

    So from that analysis full-frame sensors give shallower Depth of Field. Yes, but they don't have to! To understand why we need to consider diffraction. Far too big a subject to cover here but a good introduction is the CambridgeInColour article Diffraction & Photography. Towards the bottom of that page there is a Diffraction Limit Calculator. Accept the defaults for print size, viewing distance and eyesight (for why these are relevant see this DoF tutorial) and plug in our 12 MP sensor and click the "Set Circle of Confusion = Twice Pixel Size?" checkbox. With a little experimentation we see that on the 1.5x crop sensor f/8 is the smallest f-number before diffraction becomes an issue while on a full-frame sensor we can go to just under f/13. By the way, this relationship between diffraction limiting f-number and frame size explains why large format (film) landscape photographers can use ridiculously large f-numbers compared to the digital world.

    So, returning to the Depth of Field calculator and focussing at the hyperfocal distance, then taking the 1.5x cropped sensor 40mm lens at f/8 we get sharp focus from 5.1m to infinity and with the 60mm lens at f/12.7 (full-frame) we get sharp focus from 4.8m to infinity, which is near enough exactly the same total DoF. This result is also confirmed by using the Depth of Field Equivalents calculator nearly halfway down the CambridgeInColour article Digital Camera Sensor Sizes. That shows that f/8 on a 40mm lens in front of a 1.5x cropped sensor has an equivalent DoF to a 60mm lens at f/12 in front of a full-frame sensor. No real surprise there (the 1.5x factor applied to f/8 to give f/12).

    In case you think this still gives the advantage to the cropped sensor because it can work at smaller f-numbers and so faster shutter speeds, in my opinion it doesn't. When maximum depth of field is needed, the two sensor sizes are equivalent because for the same image quality you can crank up the full-frame ISO number higher before you get the same levels of sensor noise that you would see from a cropped sensor. And, as discussed, the full-frame sensor can more easily achieve a shallower depth of field than the cropped sensor.

Phew! I hope that made some sort of sense. Please feel free to shoot the arguments above down in flames if they are in error. The purpose of this thread is, hopefully, to explore the pros and cons of full-frame and cropped sensors to help future buying decisions. Please also feel free to add posts discussing other full-frame versus cropped sensor trade-offs which I haven't covered. 8)

Bob.

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Last edited by Bob Andersson on Wed Mar 05, 2008 11:40 am, edited 1 time in total.

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PostPosted: Mon Mar 03, 2008 9:16 pm 
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Weeell,

there is at least one other serious reason for "Full-frame sensors give better image quality"
It's because the stress on the lenses is less: Less resolution, less critical to CA. Why is this? Because the photosites on FF/FX are larger and thus not as dense as on a 1.5-crop sensor. The only negative being that the light fall-off in the corners might be stronger if the lens is not built for FF/FX. But that can easily be corrected in p-p.

As to higher dynamic range: I'm not sure whether the electric noise of a larger photo-site might be proportional higher than of the smaller size (more silicon to make noise) or even lower :? Have not read anything about this potential effect...

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Last edited by Thomas on Sat Dec 13, 2008 10:26 pm, edited 1 time in total.

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PostPosted: Mon Mar 03, 2008 9:35 pm 
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Hi Thomas,

Excellent point about lens performance. Thank you.

Bob.

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PostPosted: Tue Mar 04, 2008 1:57 am 
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Thanks for the topic and the link to that site, Bob.

I learnt some GOOD things!


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PostPosted: Tue Mar 04, 2008 2:26 am 
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Hey Bob,

Excellent work there Mr. Andersson and a very interesting read.

Could it be boiled down to a simple analogy?

A bigger bigger eye and a smaller eye, with the same glass in front of it - the bigger eye will:
1) See better in the dark (high ISO)
2) Be able to focus in finer increments (potentially shallower DOF)
3) Better be able to resolve color nuances (dynamic range)
4) Be able to handle more input before overloading (whiteout)

It does seem "logical" that a larger sensor - with ALL else equal - should be able to do resolve more, due to it's larger sensor-points and wider range before being overloaded. When you think about it, High ISO noise-handling is also a process of resolving details.

Cheers :-)


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PostPosted: Tue Mar 04, 2008 8:26 am 
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Thanks Bob! I learnt quite a bit!

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PostPosted: Tue Mar 04, 2008 9:24 am 
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Am I going out on a limb to say that Nikon/Canon and perhaps Sony/Pentax will offer a $1000ish full frame camera by PMA 2012?

How long do you think it will take for full frame to be common place in DSLRs?

Best Regards
Matt


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PostPosted: Tue Mar 04, 2008 11:05 am 
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Hi folks,

Thanks for the encouraging feedback.

Thomas wrote:
...As to higher dynamic range: I'm not sure whether the electric noise of a larger photo-site might be proportional higher than of the smaller size (more silicon to make noise) or even lower :? Have not read anything about this potential effect...

Hi Thomas,

I only had time for a very quick reply last night and so couldn't address the electric noise issue. As you know, I'm into astrophotography and am a bit of a fan of Chrisitian Buil's site. He wrote an evaluation of the full-frame Canon EOS 5D with respect to astrophotography and did some tests with the 5D and compared the results with the cropped sensor EOS 10D, 20D and 350D/XT cameras. Not quite "apples with apples" but both the 20D and 350D have pixel areas of 6.42 μm while the 5D has a pixel area of 8.20 μm.

The original article (here) is in French but Google's language tools can provide a readable English version here and (I hope) a readable German version here.

The analysis is complex but I think that on the basis of his summary of the noise reading results where he states "Les EOS 20D, 350D et 5D ont des caractéristiques de bruit très semblables", which in Googlish reads "The EOS 20D, 350D and 5D have noise characteristics very similar", my assumption that "differences in thermal and readout noise between the full-frame and cropped sensors are not major factors" is probably OK.

Bob.

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PostPosted: Tue Mar 04, 2008 6:45 pm 
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Only if the underlying silicon-technology* of those three cameras are practically identical OR if electrical noise is noticably below the 1 photon impact, so that 1 and 0 is easily discernible.

*AFAIK different technologies even with the same geometry can yield differences in electrical noise.

Don't want to invalidate your assertion. But the proof is somewhat so-so unless we can put a lid on those other noise components :roll:

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Last edited by Thomas on Tue Mar 04, 2008 9:53 pm, edited 1 time in total.

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PostPosted: Tue Mar 04, 2008 7:03 pm 
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I agree it's not proof but bear in mind that the process technologies in the cameras tested by Buil are from the same manufacturer (Canon) and were deployed over similar time periods. I'll also turn the argument around and suggest that the better image quality that we actually see from full-frame sensors tends to support the assertion that "electric" noise figures from full-frame sensors is not significantly worse. Not quite sure why you are persisting with this one, Thomas. Where's your evidence that there is a significant difference? :?

Bob.

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PostPosted: Tue Mar 04, 2008 10:05 pm 
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Well I've seen measurement from comparable sensors that have clearly different dynamic range (comming out of the pipeline at the end after readout and A/D conversion). To the effect of 1-2 stops :shock:
So there are other factors that might influence the dynamic range other then the sensor geometry. So we can not infer backwards and say: because someone attests to higher dynamic range of a FF/FX-camera you cannot necessarily imply that comes from the larger photocells.
The ability to capture masses of photons is one determinant of DR, but if larger noise of larger photosites cancels out the effect you end up with inherently the same DR.
That is why the Q "do larger photosites generate more electrical noise" matters.

As an aside: From my time when I built hifi-amplifiers you always made sure that you did not take "oversized" transistors for the pre-amp for two reasons: the big iron was slower and had more noise :x

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PostPosted: Wed Mar 05, 2008 12:19 am 
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Hi Thomas,

Thanks for taking the time to lead me along. Having to rely on Google's English translation of Christian Buil's tests makes life difficult but, hey, nothing ventured nothing gained!

      Noise Reading
    Looking at Table 4 then for the 5D under his test conditions he sees a noise level from the detector of 3.74 electrons and a noise level from the electronic circuitry of the amplifier stage of 1.73 electrons. By comparison the figures for the 20D are 3.69 and 2.09 respectively. Christian remarks that:

      The EOS 20D .. and 5D have noise characteristics very similar. Nothing separates determining these cameras, the differences are close to the margin of error of measurements. Only the noise fixed 5D tested seems very slight progress.

      Signal to Noise
    The machine translation makes this section of Buil's test even more difficult to follow so I'll just take a few quotes from his conclusions.

      The 5D also has a performance signal to noise ratio of 12% higher than a 20D
      .
      The large size of the pixels of 5D allows this device to deliver images less noisy, cleaner appearance, than the .. 20D
      .
      Increased performance 5D, however, is not commensurate with the increase in the size of the pixels, as we have already emphasized, which is a shame.
      .
      It is however no doubt that the quantum yields of sensor 20D and 5D are identical, and that the gain observed for the latter is solely related to geometric factor for increasing the size of the pixels.
    What to make of this? The pixel size of the 5D is about 28% larger than the pixel size of the 20D so the fact that the 5D only has a signal to noise ratio 12% better goes very much to the point you were making that "there are other factors that might influence the dynamic range other then the sensor geometry".

Would you settle for us both being right, but you being slightly more right! My initial analysis would have suggested a 28% improvement in S/N ratio of the 5D compared to the 20D but measurements show that just over half of this improvement is lost, presumably down to the factors you suggest. 8)

Bob.

P.S. I have been comparing the 5D and 20D here because, according to Buil, they have detectors with similar quantum efficiencies.

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PostPosted: Wed Mar 05, 2008 9:13 am 
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Ok, Bob. Let's close our dispute about DR with a draw: You're half-right and my points seem half-valid. But I concede:
All other things being equal: A sensor with larger photosites has the potential for larger DR. :!:
It's just that we don't know exactly how "equal" the other things are :wink:
So much for splitting hairs
:lol: :lol: :lol: :lol: :lol:

But I stumbles across two other factors that might influence electrical noise of the sensors afaik :shock:
- Heat increases noise. A larger sensor might be hotter (more current to carry) or colder (more area to give heat off)
- Higher speed increases noise: so a sensor optimized for high-speed readout might induce more noise (regardless of the size).

These are pure (speculative) examples to show that sensor-development is far from trivial and there might be some positive surprises coming in the future from sensors large and small!
:D :D :D :D :D

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PostPosted: Wed Mar 05, 2008 9:48 am 
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So that this is not just a 2 handed discussion :)

I think there is plenty of room in sensor development.
If you look at computer CPU and GPU development with now 45nm substrates which produce less heat, consume less power and......generate less noise.

My feeling is that the greatest potential lies in Foveon sensors with developments in CMOS sensor technology, to me that is where it can best be exploited.

It will be interesting to see where it leads - there is a quantum step to be made somewhere, probably hinging on filter elimination.
I wonder to what extent there are filtering differences in these 2 size formats that have an impact? I simply have no idea.

To get back to the differences in sensor sizes vis-a-vis full format sensors, my instinct says there is greater dynamic range to be hand in the larger sensor, and perhaps in saturation theshold as well.

But then, isn't it amazing how often things are counter-intuitive? :lol:


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PostPosted: Wed Mar 05, 2008 11:55 am 
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Hi MU51CL,

The more the merrier. That was my hope when I started the thread. I certainly agree that there is room for improvement in sensor design. Canon certainly believe that there is some way to go yet (50MP sensors, 16 bit A/D and clean 6400 ISO similar to today's 1600 according to one rumour site).

We had an interesting conversation about Foveon X3 sensor technology over in the Sigma DP1 thread. While a discussion of the pros and cons of Foveon technology may be a bit off-topic for this thread (which is meant to discuss the pros and cons of full-frame) it is frustrating that we don't see Foveon sensors with higher physical pixel counts (even with the x3 factor accounted for) let alone full-frame versions.

I am not aware of any significant differences in the colour filters of the Bayer matrix which result from going from cropped to full-frame sensors, but that may be down to my own ignorance. I believe it is true that the anti-aliasing filters in front of the sensor are less aggressive on full-frame sensors but that this is down to the fact that with it's Pro models Canon expect the photographs will be more likely to be post-processed which allows a "software" AA filter to be applied to eliminate any resultant moiré patterns if the shot demands it. Not sure about Nikon's approach, I'm afraid.

Bob.

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OM-D E-M5, H-PS14042E, Gitzo GT1541T, Arca-Swiss Z1 DP ball-head.
Astrophotography: TEC 140 'scope, FLI ML16803 camera, ASA DDM60 Pro mount.


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