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 Post subject: Size Matters
PostPosted: Tue Jan 11, 2011 6:22 pm 
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Hi folks,

Here are a few more ideas from yours truly. Feel free to shoot them down... 8)

Executive summary: Everything else being equal, the larger the crop factor of the camera body you buy the faster the glass you need for each situation where shallow DoF, fast shutter speeds and/or low light ability is key.

I've offered a few posts over the years exploring the implications of sensor size when choosing a camera and recently came to the conclusion that the only parameter that truly determines a camera's performance, for the typical sensors in use in the larger cameras today, is the maximum diameter of the entrance pupil a lens can accept. For simplicity I'll refer to this as the "lens diameter" in what follows. In summary:

  • For a given field of view the ability to generate a shallow DoF is dependent on lens diameter and not sensor size.
    Have large sensor cameras reached their limit? refers.

  • For a given detector efficiency and field of view the ability to "stop the action" is dependent on lens diameter.
    Stopping the action requires a particular shutter speed and one needs to be able to record the arrival of enough photons in that time to ensure a particular image quality (lack of image noise).

  • For a given detector efficiency and field of view the ability to work in low light is dependent on lens diameter.
    It's the same deal as above: one needs a certain number of photons per pixel to get the noise level down and for the number of photons to be the same the lens diameter can't change.

  • For a given pixel count and field of view the ability to avoid diffraction softening while offering maximum DoF is dependent on lens diameter used (actual).
    Full-frame or Cropped Sensors: Which is best for Landscapes? refers.


From the above it would seem that the sensor size has nothing to do with the prime concerns of a photographer and that a 50mm f/2 lens in front of a full-frame sensor performs identically to a 25mm f/1 lens in front of a crop factor 2 sensor or even a 10mm f/0.4 lens in front of a crop factor 5 sensor as found in some of the larger compacts. Each combination provides the same ability to give shallow DoF and the same photon collecting power. The output is indistinguishable in terms of the images we extract from the memory card, right? Well no, not quite!

There are two stumbling blocks, the last of which is probably insurmountable. The first is that as you shrink the sensor the area of silicon that can be devoted to each pixel also shrinks. While that may not affect the ability to convert photons into free electrons it does, with current fabrication techniques, limit the number of electrons that can be stored before the storage is full and that limits the maximum dynamic range. Technology may overcome this but the second limitation, below, is a deal breaker.

In the last case above, with a crop factor of 5, to maintain the capabilities I mentioned at the start one needs a lens of 10mm focal length and an f-number of 0.4. Lenses even as fast as f/1 are rare beasts and incredibly pricey. Even though the sweet spot needed for a crop factor 5 sensor is a lot smaller I doubt we'll ever see an f/0.4 lens as a mainstream product. There are limits to what can be made!

As an aside, the lens diameter argument is why compact/superzoom cameras, which are great little tools in their own right, will always be at a photographic disadvantage when compared to their larger cousins in every way except for size.

The same logic, driven by the lens diameter, also applies to medium format cameras so one could argue that for pixel counts typically found in today's DSLRs there's no advantage optically in such a camera as one can achieve all the advantages one needs with the sort of glass already available for those DSLRs. But if higher pixel counts are needed then the sensor fabrication argument above would indicate that medium format is the way to go unless and until there's a breakthrough in storing those electrons. Of course there's much more to any lens than its diameter (entrance pupil) so one has to read the reviews to determine optical and mechanical quality but however good a lens is in these respects the lens diameter still limits what can be achieved.

With this in mind and looking at the current crop factor 2 to 1.5 cameras, field of view considerations mean that crop factor 2 lenses can have focal lengths that are shorter than their 1.5 to 1.6 equivalents by very roughly about 25%. But the same "lens diameter" argument implies that they should also be about 25% faster (minimum f-number about 25% smaller) to enable them to achieve similar DoF or light-gathering power for a particular field of view. A very cursory glance through the lens catalogues tells me that this isn't typically the case so kudos to a third party manufacturer like Voigtländer for spotting the gap and offering their Nokton F0,95/25mm.

Before the micro four-thirds community rise up in arms I'll offer that not only are there some great micro four-thirds cameras around but Canon, to take just one example, do exactly the same with their EF-S lenses. They are designed to work solely with their 1.6 crop factor cameras so one might hope that they would be 1.6 times faster than their full-frame equivalents (lenses with focal lengths 1.6 times longer). Not so, though Canon might defend themselves by pointing to the various fast primes they have on offer. No doubt the micro four-thirds community can point to their legacy lenses as well. 8)

So, right at the start, I offered that:

Quote:
Everything else being equal, the larger the crop factor of the camera body you buy the faster the glass you need for each situation where shallow DoF, fast shutter speeds and/or low light ability is key.

That statement doesn't mention the lens diameter (maximum entrance pupil) directly but, of course, it follows directly from it. The "each situation" part implies a particular field of view and that implies shorter focal lengths as the crop factor increases. Add a requirement for constant lens diameter to the mix and the f-number has to go down in proportion to the crop factor.

So far as purchasing decisions are concerned it does seem bizarre that it's often true that the full-frame cameras are typically less limited when it comes to selecting fast glass. :?

Bob.

Edit: Corrected typo.

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Olympus OM-D E-M1 + M.Zuiko Digital ED 12-40mm f/2.8, Lumix 7-14mm f/4, Leica DG Summilux 15mm f/1.7 ASPH, M.Zuiko Digital 45mm 1:1.8, M.Zuiko Digital ED 75mm 1:1.8.
Leica D Vario-Elmar 14mm-150mm f/3.5 - f/5.6 ASPH.
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.


Last edited by Bob Andersson on Wed Jan 12, 2011 11:03 am, edited 1 time in total.

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 Post subject:
PostPosted: Tue Jan 11, 2011 8:54 pm 
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Bob Andersson wrote:
Before the micro four-thirds community rise up in arms


All 4 of them? :lol:

No I'm just kidding. Very interesting read. I can also imagine larger sensors to be less taxing on the glass.

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 Post subject:
PostPosted: Tue Jan 11, 2011 10:28 pm 
Interesting as always, thanks Bob


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 Post subject:
PostPosted: Wed Jan 12, 2011 10:50 am 
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.
Thanks guys. I've been wondering about the psychology of the usual fixation on sensor size (and I'm confining myself to a fixed pixel count here) as a measure of goodness. Maybe part of it is that, as photographers, we tend to view the world from our camera outwards when taking a picture. The bit closest to us and which actually captures the image is the sensor so that's what we think of as most important. But so far as the scene being shot is concerned the most important bit, the lens, is the bit that initially captures the photons and everything else is just data processing.

No surprise when considered from the viewpoint of the scene being shot that DoF is determined primarily by the diameter of the entrance pupil for a given angular field of view. It's a similar situation when considering how well a lens performs in gathering up photons. As photographers we are used to talking about the f-number and often refer to it rather misleadingly as aperture when what it really is is the ratio of the entrance pupil to the focal length. Astronomers when referring to aperture are talking about the size of the entrance pupil (diameter of the objective lens or primary mirror), a much more correct use of the term in my opinion.

Of course f-number is an excellent measure when applied to a changing field of view of a normal scene (extended rather than point like source of light) when that scene illuminates a fixed sensor as we know that zooming in or out at a constant f-number means the shutter speed can remain broadly the same. But f-number is totally misleading when we are comparing sensor sizes and a fixed field of view which is the thrust of this thread. An f/2 lens in front of a crop factor 2 sensor only gathers light at one quarter of the rate of an f/2 lens in front of a full-frame sensor when the focal lengths of the lenses used are adjusted to give the same field of view. This isn't just theory either: when I put my EF 24-105mm f/4L IS USM lens on my EOS 5D Mark II it can gather light at up to 2.56 times the rate it can when put on an EOS 40D, assuming I can adjust the zoom to get the same field of view on both cameras. :shock:

But maybe that's too much of a purist point of view. The usual mantra that full-frame is better, as in it offers potentially shallower DoF and less image noise, works as a rule of thumb even though the reason it works is largely down to the lenses available rather than any inherent property of the sensor. Why it works might interest me when I've got my anorak on but as a rule of thumb I guess "if it works don't fix it" applies. I chose the title of this thread "Size Matters" with some care! 8)

Bob.

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Olympus OM-D E-M1 + M.Zuiko Digital ED 12-40mm f/2.8, Lumix 7-14mm f/4, Leica DG Summilux 15mm f/1.7 ASPH, M.Zuiko Digital 45mm 1:1.8, M.Zuiko Digital ED 75mm 1:1.8.
Leica D Vario-Elmar 14mm-150mm f/3.5 - f/5.6 ASPH.
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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 Post subject:
PostPosted: Thu Jan 13, 2011 12:40 am 
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Hi Bob, interesting read as always.

Apologies if you already mentioned it, but don't forget the resolution / accuracy of the lens itself. Small, high resolution sensors have a very small pixel pitch, which demands very high quality lenses to resolve sufficient detail. So even if you could create a 10mm f0.4 lens, it would have to also have sufficiently high resolution to resolve detail for the fine pixel pitch of the sensor behind it.

This has always been one of the lesser mentioned benefits of a larger sensor - namely the lower demands placed on the resolution of the lens. It's ironic most full-frame bodies tend to be coupled with the most expensive lenses, when in terms of resolving power, such optics are needed more urgently for smaller sensors with finer pixel pitches.

Of course there are other optical issues like vignetting and field-flatness to consider, but lens resolution is important.


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 Post subject:
PostPosted: Thu Jan 13, 2011 10:23 am 
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Hi Gordon,

I did make the briefest of references to lens quality about halfway down the opening post but you are absolutely right to emphasise the point. For the purposes of the thread I was assuming best quality lenses but in the real world there are always compromises.

As my thesis is that it's the size of the (maximum) entrance pupil that matters, for a given field of view, rather than sensor size I was wondering how to make a prediction, in the scientific sense, that could be tested. Not so easy to do as I could always check the results first and then make a "prediction". But I'm an honest chap so I'll offer the following and state that I haven't checked the results:

Assume: An EF-S 17-55mm f/2.8 IS USM offers about the same field of view range on an EOS 7D as an EF 24-105mm f/4L IS USM does on a 5D Mark II once you take account of the 1.6x crop factor on the 7D. Consider the EF-S lens on a 7D at an actual focal length of 50mm and at f/2.8 - the diameter of the entrance pupil is 17.86mm. For the same field of view the EF lens on a 5D2 must be zoomed to 80mm and at f/4 that means the diameter of the entrance pupil is 20mm. Let's assume both lenses are focussed at a point some five metres away.

Prediction: For this shot the DoF of the EF lens + 5D2 will be about 10% shallower (17.86/20) than the DoF of the EF-S + 7D combination. The f/4 lens on the 5D2 offers potentially shallower DoF, and a brighter image, than the f/2.8 lens on a 7D. I usually use the DoF calculator here to check these things but I haven't done so in this case.

So would anyone care to check that result and see if I've got it about right? If I have then I think I will have made my point that it's the diameter of the entrance pupil that's key, though one does need to know the crop factor of the sensor in order to work out the equivalent focal lengths for a particular field of view. If I'm wrong then I'll accept public humiliation in the CameraLabs Stocks. :)
    Image
Bob.

Edit: Originally I worked out that 17.86/20 came to about 5%. Well, I've put some new batteries in the calculator and, of course, the figure is about 10% so I've edited the prediction. See my post below...

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Olympus OM-D E-M1 + M.Zuiko Digital ED 12-40mm f/2.8, Lumix 7-14mm f/4, Leica DG Summilux 15mm f/1.7 ASPH, M.Zuiko Digital 45mm 1:1.8, M.Zuiko Digital ED 75mm 1:1.8.
Leica D Vario-Elmar 14mm-150mm f/3.5 - f/5.6 ASPH.
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.


Last edited by Bob Andersson on Thu Jan 13, 2011 4:41 pm, edited 1 time in total.

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 Post subject:
PostPosted: Thu Jan 13, 2011 4:27 pm 
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Hi folks,

Either nobody wanted the challenge or they were too polite to point out my mathematical error. In the original post immediately above I'd decided that 17.86/20 came to about 5% and not the (roughly) 10% it actually is. :oops:

I discovered the error when I decided to test my "prediction" this afternoon. Using DoF Master:
  • 5D Mark II, 80mm, f/4, Focus at 5 m -- DoF = 0.93 m
  • 7D, 50mm, f/2.8, Focus at 5 m -- DoF = 1.08 m

    That's a difference of about 14%. Maybe the different pixel count is factored in?
Or using the CambridgeInColour DoF calculator:
  • 5D Mark II, 80mm, f/4, Focus at 5 m -- DoF = 0.994 m
  • 7D, 50mm, f/2.8, Focus at 5 m -- DoF = 1.123 m

    That's a difference of about 11.5%

The actual DoF that the two sites offer differs but the sense and the magnitude of the DoF difference between the two camera plus lens combinations is, I hope you'd agree, in the right ballpark. Result! :P 8)

Back to the real world, if the choice is between a crop sensor camera of factor 1.5 or 1.6 then to shoot the same scene with the same DoF one needs a lens that can go just over one stop faster than a full-frame camera needs. And if you buy a crop factor 2 model then you need a lens that can go two stops faster than a full-frame camera needs. Food for thought?

Bob.

P.S. I think I've just avoided a trip to the Stocks, though maybe it was a narrower squeak than I'd expected due to my inability to do sums! Phew. :)

_________________
Olympus OM-D E-M1 + M.Zuiko Digital ED 12-40mm f/2.8, Lumix 7-14mm f/4, Leica DG Summilux 15mm f/1.7 ASPH, M.Zuiko Digital 45mm 1:1.8, M.Zuiko Digital ED 75mm 1:1.8.
Leica D Vario-Elmar 14mm-150mm f/3.5 - f/5.6 ASPH.
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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PostPosted: Thu Jan 13, 2011 9:09 pm 
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We forgive you Bob!

It is interesting to see the DOF calculation for the different formats. Anyone who wants the shallowest DOF should take note...


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PostPosted: Thu Jan 27, 2011 9:34 am 
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Hi folks,

Hey, it seems that one of the DPR reviewers has been reading this thread. :P

From their Olympus XZ-1 Review:
    It's sometimes hard to work out how much or little depth-of-field a lens will produce, thanks to
    differing sensor sizes (and the unclear manner in which they are often designated), but
    the key factors are the physical size of the aperture and the angle-of-view.
The ultimate accolade? Certainly not as I'll reserve that honorific for CameraLabs but it's good to see the word's getting out. :twisted:

Bob.

_________________
Olympus OM-D E-M1 + M.Zuiko Digital ED 12-40mm f/2.8, Lumix 7-14mm f/4, Leica DG Summilux 15mm f/1.7 ASPH, M.Zuiko Digital 45mm 1:1.8, M.Zuiko Digital ED 75mm 1:1.8.
Leica D Vario-Elmar 14mm-150mm f/3.5 - f/5.6 ASPH.
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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