f stop/sensor size realtionship

[jani]

I think that one of the revolutions we'll see in future cameras will be in optics and packaging.

I imagine flexible/semi-liquid lens elements, or better collapsible elements, all inspired by flexible, composite mirrors used in astrophotography.

Optical interferometry may also be usefully miniaturized.

My vision, if I may call it that, is a collapsible SLR-like camera (SLR-like in how you look through the lens, rather than in physical dimensions) that can fit in my pocket, yet when I want to take a picture, it expands to a sensible size and focal length for the shot I want to take.

There'd be no interexchangable lens system, because the built-in lens system would adapt its properties to the momentary requirements.  The sensor could be made bigger than 35mm, if almost everything else can be collapsed into something very and compact.  Professionals would probably have access to bigger models capable of giving better optics, as usual.

A major challenge would be to make the expansion and collapse of the camera user friendly and safe, since quite a few bits and pieces would probably be both sharp and delicate.

I wish I could say "as seen in the SF movie ####", but I don't know about any SF movie depicting something like this.  

This all requires technology that we're on the verge of developing or minituarizing, and maybe we'll see something incorporating ideas like these in 10 or 20 years.

[BJL]

Our 1 micron photosite can hold 1000 electrons, 33 of which are noise. .

The smaller sensor says ...

The big sensor says ...

As I have said before, methods already exist to essentially eliminate the effects of well capacity limits; for example, reading out each well as it approaches being full. Most of your arguments crumble once that is achieved, because it is not possible for a larger format to offer better than the UNLIMITED highlight headroom and dynamic range of a smaller one.

It is then enough for the S/N ratio of a nearly full, small phototsite to be good enough. Kodak says that one get excellent image quality once the S/N ratio at a pixel is 40:1, so that a well capacity of about 2000 is plenty, evn allowng for some dark noise. That is less than 10% of teh smallest DSLR well capacity that I know of, and even slightly sub-2 micron pixels should be able to do that.


Your triumphant responses from large format come down to only the fact that the SAME can be achieved as in a smaller format, but using bigger, more expensive sensors and longer lenses. It is lucky for larger formats that there are better arguments, like the likelihood that smaller formats are at some point limited to lower maximum aperture diameters and thus lower maximum shutter speeds.

Because how do you expect larger foramts to compete when your campaign slogan for them seems to come down to "we're bigger and more expensive, but otherwise just as good?"

[BJL]

I suspect we will be able to  divorce shallow DOF and aperture before long.

Speed is one thing that almost certainly is lost when formats gets too small. We cannot divorce from the ultimate limits on trade-offs between shutter speed, resolution, and noise levels that is set by how fast we can gather light from the subject. As an example, to give our midtone pixels Kodak's "excellent" S/N ratio of 40:1, we need 1600 photons detected at mid-tone pixels, and combined with the currently fashionable 8MP, that needs about 12.8 billion photons total, for any format.

Light gathering rate is limited by the area of the lens opening over which light from the subject is intercepted, and thus by the effective aperture diameter. Whether 35mm format with f=80mm f/8 or 2/3" format with f=8mm, f/2, you have aperture diameter of 10mm, and can gather light at about the same rate.

Thus the speed possible in 35mm with f=80mm, f/2 (40mm aperture diameter) would need that 2/3" format, 10mm lens opened up to f/0.25. I have not seen absolute proof, but I strongly suspect that this cannot be done with good image quality.

I happen to fall at about the 4/3 format level. A limit of f/2 there matches a limit of f/4 in 35mm format digital, and I have little or no need for the combination of less that "f/4 equivalent DOF" and higher shutter speed that a larger format might offer.

[Ray]

Okay! On reflection, I've decided there's a flaw in my reasoning. (Nothing to do with the 1/FL rule though Jonathan).

Since the physical aperture at f10 on the big camera is the same size as f1 on the small camera, there's no major speed advantage at f10 except for maybe a difference in optimal ISO settings. The only advantages I can see are at big apertures where there's less DoF.

[Ray]

Immediately after taking the desired shot move the focus point a fixed percent.  (This could happen very quickly as the camera 'knows where it's going'.)  Take a second shot.

Software (initially in computer, later in camera) could calculate relative distance of objects in the frame.  

The only software I know that does this sort of thing requires many shots at different focussing distances. Any software that could reconstruct full detail from two out-of-focus objects is beyond my comprehension.

If you wanted to take full advantage of the potentially greater resolution of the larger format at large diffraction-limited apertures like f2.8 without sacrificing DoF, then I suspect you'd have to trade off speed for the greater DoF, ie. 10 to 100 shots of focus autobracketing, digitally blended with massive computing power. Seems to me that's very analogous to the method BJL proposed for extending the DR of the small format.

[didger]

so forgive me if I don't want to get into that argument again

Heh, heh, yeah; you never know who might be lurking where when. :laugh:  
Actually, weight was the issue that made me look into the D2X, but I was only hoping that I'd get more or less the same quality as 1ds.  Now that I've taken a few hundred "real life" shots I'm realizing that I might have done it even totally apart from the weight issue.  I'll be posting a few pics after a while to illustrate particular points related to the importance of more DOF and much less high ISO noise, and being able to use a few zooms without quality compromise, and the real life image quality improvement that comes with better ergonomics and display visibility under various lighting conditions.

Now I just hope that the D3X with twice the DR comes along before my 3 year extended warranty for the D2X expires.  That camera is getting USED.  I've never had a more totally happening toy/gadget/tool in my life and I take shelter behind the vast credibility and respect of Thom Hogan to justify my "excessive" enthusiasm.

[Ray]

I seriously doubt that either you or I is in a  position to assess the potential of such technologies; if researchers at Standford University say that it has potential, and the technology has already been put into commerical use, I see little reason to worry just because you are cynical!

BJL,
You're quite right on the first point. I haven't even read of the research you are talking about so it's purely idle speculation on my part.

On the second point, I'm not cynical, I'm skeptical, and for good reason. There are quite a few major innovations in this area that occasionally crop up, cause much excitement and appear to herald the way of the future: the Foveon sensor, for example, Fuji's SR sensor and then the new Olympus group's 4/3rds sensor with newly designed Zuiko lenses which by all accounts are excellent lenses, probably a cut above the equivalent Canon lenses.

But for some reason, the promise of these new technologies is not being fulfilled or at best is developing slowly and what on paper seems a major break-through turns out to be just an incremental improvement.

As to your absurd taunt about 4/3 format, I should not stoop to this nonsensical DPReview forums style rhetoric of "my brand currently sells better than your brand, therefore it and/or its format size are inherently and permanently superior".

Surely you must have realised I wasn't referring to sales? The entire tone of this thread is about comparative performance of image quality. Of course[/i] I meant that you must be disappointed the Olympus 4/3rds system has not yet overtaken in performance and image quality the next format up in size, the Canon 20D.

[BJL]

Ray,

    here is my overall perception. The best format for one's purposes is one that is just big enough to offer
a) good performance out to one's personal needs and limits for shallow DOF, high shutter speed/low light performance, and size and weight of lenses (which all relates to limits on how big the "big glass" needs to get, in terms of maximum aperture diameter and thus front element size).
 adequate pixel count (how small can photosites get?)
c) adequate dynamic range (which might well cease to be a size limit at all)
Going bigger than that just adds "excess capacity" such as larger than necessary electron wells leading to more dark noise.

As with your example: lovers of using f=85mm @ f/1.2 of f/1.4 will probably only ever have one best choice of format: "24x36". Those of us whose DOF goals almost always limit f-stop choice to the range from f/4 up in 24x36mm are probably better served by one of the smaller current DSLR formats, but with 2/3" still to limiting.

[Bobtrips]

I absolutely agree with the 'portability' issue.  I was so tired of the weight of SLRs and multiple lenses that I was ready to either quit shooting (pass on 100% of the shots) when I traveled or take a rangefinder (pass on many of the distance shots).

Then digital became an option.  And walking around with a one pound monster zoom is a joy.

I'm a happy puppy.  But I'm always looking for something even better.  

[Bobtrips]

So Canon comes out with a half-frame, what?  14 megs to beat Nikon?

And that drives the 1DsMkIII to say 20+ megs?

Man, this is going to be interesting.   ::

[Ray]

At the risk of getting shot down in flames for not knowing what I'm talking about, I would say you are essentially correct if, by brightness, you mean the f10.35 lens on the 350D will let in the same amount of light as the f2.8 lens on the FZ20, per unit of time of course. In other words, the physical aperture openings will have the same diameter in each case.

However, since the 350D sensor is around 14x the area of the FZ20 sensor, it will require 14x the amount of light (number of photons) for correct exposure which is approximately what f10.35 on the 350D will produce by requiring an exposure 14x longer.

A fascinating flow on from these basic principles is the possibility of producing ever smaller and smaller sensors of higher pixel density that can match the resolution of much larger sensors using very small lenses with a small f stop. (Well, fascinating for me.)

Where will it end? Will Didger be able to reduce his camera gear weight by yet another few lbs and still get marginally better image quality than the D2X gives him?

Can we break or circumvent those (apparently) immutable laws of physics such as diffraction limitation in lenses, photonic shot noise which has an increasingly more significant effect the smaller the sensor gets, and ultimately produce photosites no bigger than the wavelength of light?

As an after thought, what we might soon get is an ultra lightweight pin-hole camera that produces razor sharp images instead of the very blurry images we associate with pin-hole cameras. The dynamic range would probably be miserably low and such a camera might only be useful for very static subjects where multiple shots could be taken at different exposures and blended with PS CS2's new HDR feature.

[Ray]

But as I said above, the overall scaling between photosite size and total dark noise is not clear, so the "winner" here is not clear either.

What I find interesting here is that dark noise is subject to technological strategies for improvement even if it requires a certain degree of internal cooling (which wouldn't necessarily be difficult with a really tiny camera housed in a much larger body so one can hold the thing).

Photonic shot noise and diffraction limitations seem to be the ultimate barriers to small cameras producing high quality, high resolution images.

I take the point that averaged multiple exposures might reduce the randomness effect of misbehaving photons (you can see I'm not very technical) but I suspect not by much.

Photon noise is proportional to the sqrt of the number of photons impinging upon the photosite. Ie., if the photosite receives 100 photons, noise is 10 photons, or 10% of the signal. If 1000 photons are received by the photosite, noise is represented by a mere 32 photons, about 3.2% of the signal.

Is this a limiting factor as draconian as lens diffraction limitations?

I made the comment that maybe soon we'd have an ultra-small camera capable of matching the DoF of a pinhole camera but with razor sharp images. I can't really see it unless these basic laws of Physics are repealed. (Perhaps the new Pope can do that. Oops! I apologise in advance in case anyone deeply religious is reading this   ).

To clarify the problem, I designed an imaginary small camera to compare with FF 35mm in terms of DoF and resolution. Using the wavelength of red light as the limiting factor for pixel size, and allowing for the usual discrepancy between pixel pitch and pixel size, I used a 1 micron pixel pitch on a 4.5x3mm sensor (keeping the same aspect ratio as 35mm).

Such a sensor would have 15MP and a standard lens, equal to the diagonal of the sensor, would be about 5.4mm in focal length.

To get the same DoF and resolution of a 35mm camera at f8, we'd need a diffraction limited f1 lens. (Not possible now maybe, but with the help of nanotechnology and improved materials, maybe sometime.)

This would clearly be an amazing camera for any subject that requires a reasonable DoF, but with one serious limitation; dynamic range. I can only guess what that might be; 1 stop of undegraded DR described as 3 or 4 stops by the advertisers of such a product?

Let's assume such a camera has just 1 stop of 'clean' DR. To get a DR of 8 stops, we need to blend 8 exposures, the shortest of which for the highlights (which at F1) might be around 1/25,000th of a second on a sunny day. We progressively halve that shutter speed for each of the 7 remaining stops till we reach 1/200th sec for the deep shadows. Bingo! We've got the full DR of a modern DSLR, and more perhaps.

But what about DoF? Well I'm afraid we're stuck with the limitations of diffraction. With such a camera the hyperfocal distance is around 24ft whether it's a 4.5x3mm sensor at 5.4/F1 or a 36x24mm sensor at 43/f8.

Supposing we want a really great DoF comparable to that of a pinhole camera but at the same time sharp. Perhaps we could reduce the aperture opening from F1 to f8 on our miniature camera.

The DoF calculator I've been using at http://www.dofmaster.com/dofjs.html tells me that such a camera I've designed, at f8, will produce a sharp image from 1.5ft to infinity (CoC 0.004 proportional to the program's fixed CoC of 0.03mm for 35mm format). Whatever CoC standard is chosen, the relevant multiplying factor is 8 and the results are the same.

Okay! The assumption is, the lens at f8 can transmit that resolution. Well, of course it simple can't because of diffraction. The sensor in my designed camera has at most a theoretical resolution of 500 lp/mm, but a paractical resolution of maybe 400 lp/mm with a diffraction limited F1 lens. (Guess work of course).

Any image at f8 on such a camera would be no sharper than a 35mm shot at f64.

[BJL]

What's not clear is just what range of charges could such a small photosite, not much bigger than the wavelength of red light, hold?

Clearly there is a lower limit on pixel size, somewhere between 1.8 microns (already achieved) and about 0.6 microns (longest visible wavelengths). So I am sure that it will make you happy to know that a small format like 2/3" is at the fundamental disadvantage of never possibly going beyond resolution of about 5,000 line pairs per picture height, or about 140MP. Darn, camera phones will probably never even get to 50MP!

There seem to be lots of other more immediate practical reasons why formats significantly smaller than the smallest current DSLR format will alway be at significant disadvantages. Some days, when I am in an unusually humble mood, I even believe that the engineers at companies like Kodak, Olympus, Nikon, Sony and Canon know their jobs far better than we do, so that their choices of the new digital SLR formats, from 4/3" to DX, are rationally based on a good understanding of future technical possibilities and limitations, and are not stupid or shortsighted stop-gap measures.


About electron well capacity and/or dynamic range for very small photosites, it is not clear that there is any fundamental limit, even without blending. Let me mention a technical possibility that I have read about recently, and remind you of one that I mentioned some time ago.
 
The new idea is using "nanotechnology" to build photosites that are tall thin towers, literally increasing "well depth", and in practical terms greatly increasing the electron capacity of very closely spaced photosites, giving them very large dynamic range. However, this increases the total "bulk" of each photosite, and so increases at least some sources of dark current, so it is not clear how performance will compare to "wider, shallower" photosites with the same well capacity.

The previously mentioned idea is photosites that are checked repeatedly during an exposure, with the more brightly lit ones read out as they approach being full. Thus highlights get read quickly, shadows more slowly, with the different exposure times for different pixels being taken into account in the final digital conversion of course. It is like taking a sequence of exposures of different durations, but all starting simultaneously.

This might also have a slight bonus over a conventional single exposure using a sensor of higher dynamic range: the better lit parts are exposed more briefly, so motion blur from the longer exposure time needed to hold the shadows does not effect the highlights as much. A slight win over a conventional exposure where highlights are also exposure for the full time.


Finally, I do not see why you keep working so hard to argue that the potential noise advantage of smaller photosites wil become an illusion at some point, because no-one seems to be disagreeing lately. Any advantage or disadvantage will go away if and when dark noise is reduced to an insignificant level, at least when comparing images made with apertures chosen for equal DOF (equal effective aperture diameter). Only until then is smaller potentially "quieter".

[BJL]

Ray,

   firstly, your example of a tiny 4.5x3mm sensor is not of much practical relevance; I think it would make much more sense to stay with the current DSLR formats from 18x13.5 up, or at smallest 2 micron pixel pitch in 2/3" foramt. Indeed photosites about this small are on the market now (2.2 microns in an 8MP 1/1.8" (Sharp?) sensor in the new Ricoh Caplio GX8) or coming soon (under 2 microns in a Matsushita CMOS sensor for mobile phones.)

Secondly, your guess of 1 stop DR for 1 micron pixels is absurdly pessimistic. Current sensors can have well capacities of over 1,000 electrons per square micron, while good shadow performace is got at about 10:1 local S/N or less, needing about 100 photons if dark noise is low enough that shot noise is the main factor (as it would be with such tiny photosites.) From 100 to 1000 is a bit over three stops, and that is a pessimistic estimate of the possibilities. The advertised "engineer's DR" figure could probably be more like 8 stops, since the floor noise level would likely be no more than 4 electrons, giving at least 1000:4 or 250, roughly 2^8.

At 2/3" format and 2 microns, I am fairly sure that the five or size stops needed for scenes of normal subject brightness range will be available as base ISO speed. Then blending just two exposures has the potential for handling great subject brightness range.


Thirdly, and yet again about diffraction limitation: at those equivalent aperture ratios (same effective aperture diameter), diffraction effects are exactly equivalent! f/1 in your tiny format, f/2 in 2/3" format, f/4 in 4/3 and f/8 in 35mm format give exactly the same angular spreading of light by diffraction, since it is diameter of the small hole that light is passing through that determines this. So the diffraction spots with the smaller formats are smaller in exactly the same proportion as the sensor and pixels are smaller, and the same size on same sized prints.

[Ray]

Once highlight headroom is essentially eliminated as a constraint, there is absolutely no DR advantage to a larger format, as the DR is unlimited in either case. That leaves only shadow noise/speed trade-offs, which naturally tend to either a tie or a win for smaller photosites so long as fast enug lenses canb be used.

BJL,
A tie or a win for the smaller photosite? I can't quite follow your reasoning.

Let's consider that a small format (say 2/3rds) through continued technological development could reach a stage of providing adequate resolution for razor sharp poster size prints with superb dynamic range that for all purposes are essentially noiseless.

Isn't this as fanciful science fiction as 'beam me up Scotty'?

At what ISO would this small camera that had conquered all DR constraints operate? ISO 3200? ISO 6400? Maybe even ISO 12800?

Anyone who's tried to take photos in the Vatican Museum without tripod or flash knows that a camera capable of noise-free images at ISO 12,800 would be very handy.

Will your small camera ever be able to do that?

Seems to me the bottom line is this: Whatever remarkable achievements in signal-to-noise, dynamic range and resolution the small-camera designers can pull off, the large-camera designers can do better. If the 2/3rds size sensor eventually gets to 50MP and produces essentially noise-free images at ISO 400 with a dynamic range of 12 stops, then the larger format sensor, through application of a similar degree of technological development, could hypothetically without breaking the laws of physics, reach 200mp and produce essentially noise-free images at ISO 3200.

It's not all to do with signal-to-noise. Two different sized photosites could have the same S/N but one could have a hugely greater dynamic range, and that makes all the difference.

[Ray]

Let me try to make this a little clearer. Let's do a couple of hypothetical but relationally similar examples; my diffraction limited 5.4/F1/4.5x3mm 1 micron 12mp sensor compared with 35mm full frame 43mm/f8/12mp. Resolution and DoF the same in both cases.

Both sensors have taken noise reduction techniques to the limits of the laws of physics, which means that photonic shot noise is the only noise. (Okay! Nothing's perfect! Give or take a couple of electrons. Let's not pixel peep here).

Our 1 micron photosite can hold 1000 electrons, 33 of which are noise. Our 8 micron photosite can hold 64,000 electrons, full well, only 264 of which are noise (is that the right figure - I haven't got my calculator?). We've already got a huge dynamic range advantage of the bigger sensor as well as S/N advantage.

The smaller sensor says, 'Hey! We can build a really deep well that can hold 64,000 electrons and we won't even lose much shutter speed advantage of big brother because we've got F1'. Oops! We've now got more dark noise. Blast it! Never mind! BJL has discovered a way of eliminating all dark noise.

The big sensor says, 'We're aware of BJL's tricks. We've decrypted his 'dark noise removal algorithm' and we can now create a well that holds 512,000 electrons with an S/N that's even less than small sensor.

Small sensor responds.' No worries! We'll blend multiple exposures'. Big sensor retaliates, "So what! We've already done that. We're into the billions of photons old chap. We use huge lenses diffraction limited at f2, schleimflug tilt effects and DoF bracketing. Who kidded you that you could ever compete?

[Bobtrips]

Technological development has an effect of 'trickling down'. Of course more people want little things than big things (photo-wise). But humanity as a whole marches on to ever bigger and better.

I'm not sure but what when it comes to digital camera development things don't trickle up.

And 'bigger and better' got a divorce a long time ago.  

I'll bet there's some minimal size at which there's little market pressure to go smaller, but until we reach that point the movement is likely to be toward smaller packages.  A smaller camera is a camera that's more likely to be carried, thus more likely to bring home the bacon.

I'm pretty convinced (via the previous discussion) that the DR problem is solvable.  DOF is next.  (And if even a simpleton such as me has an idea or two....)  


(And how come we aren't hearing anything about ceramic lenses?)

[BJL]

there will never be a good quality, general purpose, interchangable lens camera system in a format smaller than the current smallest DSLR format, 4/3....

You lost me there....

I am not ruling out quite good cameras in smaller formats like the now fashionable 1/1.8". For example, I like the Olympus C-7070 with its 27mm equivalent or better wide angle coverage.

But there do seem to be lower limits on attainable f-stops, not much below f/2 for zooms, which would limit formats 2/3" and smaller to the DOF options and light gathering speed of not much under f/8 in 35mm format. Even 4/3 seems limited to about "f/4 equivalent zooms", which seems borderline for a flexible, general purpose system.

Clearly, many digicam users live happily with "f/8 equivalent", including some quite serious photographers who simply have little need for shallower DOF or better high shutter speed/low light performance. But it seems too much of restriction for a flexible, interchangable lens system. Especially since the current smaller DSLR formats are already offering such low prices and small sizes.

[Jonathan Wienke]

Can we say that the 1/FL rule should still apply to the 4 and 5mm lenses of small format cameras, or does it completely break down due to the difficulty of holding a small, light object steady?

The 1/F rule applies to the 35mm equivalent focal length, or (actual focal length) * (full-frame crop factor). So a 4mm lens becomes a 20mm or whatever for the purpose of estimating the maximum practical exposure time interval as well as describing FOV.

[Ray]

The indications from the rate of introduction of new sensors and new camera models are of a bottom heavy pattern, with every step up that size ladder having a lower level of activity. This is almost inevitable given the very bottom heavy distribution of sales and revenues.

BJL,
It would certainly seem like that. You probably read more industry analysis reports than I do. Companies in general are obliged to make a profit and it's difficult to make a profit selling products for which there's little demand at a price point which few are interested in. (Unless one has a lucrative contract with the US government  ).

However, when I cast my mind back to the days of the Nikon D1 (and shortly later the Canon D30), I do not see any performance catch-up of the small format. At the top end, we seem to have gone from computer tethered 6MP MF backs with 35mm size sensors to larger format, untethered 25MP backs. In the middle, we've gone from slow 3MP APS-C cameras to much faster 8MP APS-C cameras with significantly less noise at high ISO. At the low end, we've also progressed from noisy and slow, 2 & 3MP P&S cameras to the likes of the 8MP Sony F828 and KM-A200.

Is there not always a price premium for miniaturisation when quality is not to be sacrificed? I don't see any examples of miniature cameras equalling the performance of their larger brothers at any price. Just a few days ago I was looking at a friend's brand new K-Minolta 8mp A200, an upgrade from his Canon G4. Browsing through the review he'd downloaded, I noticed that after a burst of 5 frames in RAW mode the KM A200 leaves one waiting 45 seconds before one can take another shot. 45 seconds? Ridiculous!

The technology you are proposing for the small camera (continuous sampling of each photosite as it fills and discharges) would seem to require fairly massive computing power. It might eventually be cheaper to manufacture a larger camera to accommodate all that extensive processing power. Desktop computers are considerably cheaper than laptops at a comparable performance.