Understanding objective diameter vs. image circle, and how it relates to sensor size and signal-to-noise ratios in sensors.

[scottelly]

<p>I have been trying to understand why "larger" sensors are supposed to be better. I've read so much about it that I'm not sure if I'm confused or just perplexed. What I seem to be finding is that people are blaming sensor size and pixel pitch for a problem that really equates to the size of the lens objective. Some articles I've read at places like The Luminous Landscape and ClarkVision seem to indicate that it's the size of the photo-sites on the sensors that makes all the difference to signal-to-noise ratios, because of the inherent photonic noise issue, which implies that it's really physics that is the limiting factor in the number of pixels a "good" sensor can have, and we need to consider the balance between pixel size (diameter of photosites or their micro-lenses) and the number of pixels on a sensor's surface. But what about objective diameter? Doesn't THAT matter more? Afterall, isn't a large objective on the lens going to compensate? And what about image circle size? If I use a lens with the same size objective, which collects the same amount of light, doesn't that lens collect the same number of photons? If this is the case, if that lens projects those photons into a smaller image circle, because the lens is designed for a smaller (APS-C) size sensor, won't just as many photons enter the photo-sites, even though the photosites are smaller than the photo-sites on a larger, full-frame sensor with the same number of megapixels? Ultimately it's all about photons, right? Shouldn't we be considering the number of photons reaching the individual photosites to be the main issue, rather than photosite sizes? Yes, I know there is a relationship there (i.e. larger numbers of photosites in the same size sensor means the photons are split up into smaller groups, making them produduce an inherently noiser image), but when considering the difference between, say, a Nikon D300 and a Nikon D700 (both are 12 megapixel cameras offering 14 bit RAW), should I really be so worried about the size of the sensor, if I plan on buying lenses to match the sensor sizes? I realise that if I get lenses for full-frame cameras and put them on a D300, which has a 1.5 crop factor, I will be wasting about half the photons the lens collects, so that is a serious issue, but aren't lenses that are made specifically for APS-C sensor cameras made with higher image quality standards and smaller image circles, specifically to compensate for the fact that the photosites on those lenses are packed closer together? And isn't the real issue about signal-to-noise ratios all about the objective of the lenses on those small-sensor cameras not collecting as many photons?</p>

[markci]

<p>No that's pretty wrong.<br /> <br /> Objective size, by which I assume you mean the diameter of the front element, doesn't really mean a damn thing on its own. It's a function of the lens design and maximum aperture. For long lenses it's very close to being equal to the maximum aperture. For short lenses it generally isn't.<br /> <br /> The important thing is that <em>no, just because a photon hits the front element does not mean it winds up on the sensor</em>. For any lens or any camera. And it certainly doesn't work that way when you have a sensor that is much smaller than the image circle of the lens. When you put a D300 behind the lens instead of a D700, the light is not magically refocused on the smaller sensor.<br /> <br /> Nor is nothing magic about the lenses designed for smaller sensors. If you keep the focal length constant in doing a comparison, the camera with the smaller sensor will be collecting photons from a narrower angle of the scene, thus fewer photons. If you adjust to a shorter lens so that the viewing angle is the same, then you'll have a shorter lens with a smaller aperture (at the same f/stop), thus fewer photons.<br /> <br /> Basically if your argument were true it would be possible for 110 film to produce the same results as 8x10. Guess what: it can't. The laws of physics have not been repealed.<br>

<br /><i> "And isn't the real issue about signal-to-noise ratios all about the objective of the lenses on those small-sensor cameras not collecting as many photons?"</i><br>

<br /> You can sort of look at it that way, but it's completely irrelevant. Small sensors imply small lenses with small aperture diameters. There is no way around it.<br /> <em><br /></em></p>

<p> </p>

[peterblaise]

<p>.</p>

<p>Scott, f/stops are <em><strong>relative</strong> </em> , and there ain't no 6" diameter "objective" lens bringing light into a compact digital camera sensor. After all, that would require a gargantuan f/0.06 aperture or something like that, and f/2.0 is hard enough to make on lenses for small sensors (Minolta released f/1.2 on their little tiny 8mm video cams, by the way, why not adapt them from the used market!).</p>

<p>The goal, as you suggest abstrusely, is to collect more photons, and bigger or more efficient pixel buckets do that, so the next generations of improvement in signal-to-noise ratio requires bigger buckets or more efficient buckets. Sony is an early releaser of such chip improvements, and Canon improves the software to make previous generation chips "keep up". Either way, the goal is pictures that satisfy consumers, and so far, so good.</p>

<p>Also, consider how much detail you want in a picture, that is, how many pixels across you want. Once you know your desired pixel count, then open your wallet and pay for the one that offers the signal-to-noise ratio you want, and larger or more sophisticated buckets, once again, are the only way to give you both the resolution and the signal-to-noise ratio you want.</p>

<p>But, hey, if you can come up with a way to put more than f/2.8 worth of exposure through an f/2.8 pipe and keep everything else photographically controllable and predictable, go for it. Physical reality and the physical sciences will stand back and watch you try, try, try again!</p>

<p>.</p>

[jcoffin]

<p>In theory, yes, you could get by with simply using faster lenses. Realistically no, it won't work.</p>

<p>First of all, the lenses quickly grow quite large, and large objectives (of photographic quality) quickly grow extremely expensive. Just to give some concrete numbers, let's consider a sensor that's limited to ISO 200, but we want to use it in the same light as we'd currently use ISO 3200 at f/1.4 (with the shutter speed held constant).</p>

<p>ISO 3200 is four stops faster than ISO 200, so to compensate we need a lens that's four stops faster than f/1.4. That works out to f/0.35. To do that, the front element has to be a minimum of 50/0.35 = ~143mm (about six inches) in diamater.</p>

<p>Worse, aberrations are proportional to approximately the square of the f/stop, so building such a fast lens would require nearly unbelievable aberration correction to be anywhere close to as sharp as the current 50mm lens. In fact, I'm reasonably certain nobody really knows how to do aberration correction nearly that good (there's a reason the world isn't full of 50/0.35 lenses).</p>

<p>Along with that, you'd have to deal with the fact that for most practical purposes such a lens would have no depth of field at all. You'd no longer be able to "focus on the eyes" -- the curvature of an eyeball would mean you could only pick part of the eyes to focus on.</p>

<p>Even if such a thing could be designed and built, the cost and weight would be almost unbelievable. The front element of a 50/0.35 would be about the size of a 400/2.8. The weight would probably be only marginally lower (maybe 9 pounds instead of a bit over 10 for the 400/2.8). Due to the difficulty of correcting aberrations, the cost would probably be quite a bit higher -- almost certainly more than $10000US.</p>

<p>That's looking at only one specific lens (and probably the simplest case at that) -- assuming you were talking about a camera with interchangeable lenses, you'd need to do the same with <strong>all </strong> the lenses you cared about.</p>

<p>To summarize: while theoretically possible, this approach is grossly impractical. A system would be extremely large and heavy, would cost more than anybody could afford, and would have so little depth of field (when wide open) that you'd only be able to take pictures of (extremely) flat objects anyway.</p>

[scottelly]

<p>O.K. I understand the issue of image size and resolution: you get better resolution out of a larger projected iage size, while all else is equal (grain of the film or pixel density is the same, but there are more, because the area is larger). I also understand that a smaller aperture and different field of view do play a role. But with a lens that's designed to make the same image (say a 50mm) on a small sensor as another lens would on a large sensor (say a 75mm - sorry I don't know of such a lens), and both offer an aperture of f1.8, and both have the same size objective lens, wouldn't the final result be that the photons collected by the lens all end up in the photo-sites of the lens in basically the same proportions? (given the same number of photosites and proportionate diameters of photosites, etc.) Remember that there is a disadvantage of shooting with 8x10 other than it's cumbersome and non-digital nature. MUCH longer exposures are necessary when shooting with an 8x10, right? I don't believe that is just a matter of using smaller apertures (like f16 and f22). I believe that if I use a similar f8 aperture to shoot a scene with my 5 D, I get approximately the same exposure in about half the time or less that I do with my 4x5, using the same ISO settings. I suspect this is due to the relative differences in size of objective lens to film.<br>

Again, am I thinking all contorted and wrong here? Please give me a link that will explain in detail, because your explanation didn't quite work for me Mark.</p>

[scottelly]

<p>Given an f-stop of f8, with a focal length of 75mm in a full-frame lens on a camera with a full-frame sensor, wouldn't the same picture (and number of photons) be achieveable with a 1.5 crop-factor sensor shooting with a 50mm lens at f8 if that lens has the same objective diameter, but a smaller image circle (matched to the 1.5 crop-factor sensor), and isn't this why manufacturers created the special digital lenses in the first place? (Well, they probably did that primarily to make more money, but there ARE other reasons too, right?)<br>

The reason I have brought up this objective lens thing is the fact that Giant Squid have huge eyes for seeing in the dark, and my big Canon 70-200mm f2.8 L IS lens has a very large objective, and the images from it seem to look brighter, even though they are shot at the same ISO, shutter speeds, and aperture as used with other lenses. The view through that lens is brighter too. I realize that the aperture has more to do with it than the objective lens, but for any given aperture, isn't a larger objective lens likely to collect more light? I also remember reading somewhere, when I got started in photography in the 1980s that a larger objective lens does indeed collect more light, which would translate to more photons being transmitted through any given aperture. Is this wrong?</p>

[alec_myers]

<p>Scott,</p>

<p>I think you're both right and wrong. It is all about the number of pixels - the sensor size doesn't matter but the number of pixels and the number of photons to divide over them does.</p>

<p>But that's not just down to objective size, that's down to objective size (very roughly, depending on the lens design) divided into the focal length, which gives you the f-stop. It's only approximate, and then only for some lenses (counterexample: take a 70-200 zoom lens with a 77mm objective which is f/2.8 at the far zoom, but still f/2.8 at the short end, it doesn't make use of all the photons collected by the objective then or it would be f/0.95!)</p>

<p>When you say that 8x10 cameras need much longer exposures, that's *only* because you can't find an f/2.8 lens for them - you have to use much smaller apertures. The reason the f-stop is useful is because it removes variables like the objective diameter and the film stock size from the equation.</p>

<p>"I believe that if I use a similar f8 aperture to shoot a scene with my 5 D, I get approximately the same exposure in about half the time or less that I do with my 4x5, using the same ISO settings."</p>

<p>There, at least, you are incorrect. If you have the same ISO and the same f-stop then perforce the exposure time is the same. (Your hand-held light-meter doesn't need to know the format size does it?)<br /> I think you will find this webpage (relevant, if a bit obliquely so) very interesting:<br /> <a href="http://www.clarkvision.com/photoinfo/dof_myth/">http://www.clarkvision.com/photoinfo/dof_myth/</a><br /></p>

<p>Oh, and this one, too:<br>

<a href="http://www.clarkvision.com/imagedetail/does.pixel.size.matter/index.html">http://www.clarkvision.com/imagedetail/does.pixel.size.matter/index.html</a></p>

 

[markci]

<p>"But with a lens that's designed to make the same image (say a 50mm) on a small sensor as another lens would on a large sensor (say a 75mm - sorry I don't know of such a lens), and both offer an aperture of f1.8, and both have the same size objective lens, wouldn't the final result be that the photons collected by the lens all end up in the photo-sites of the lens in basically the same proportions? "<br>

<br /><br>

(sigh) again with the objective size. Maybe my explanation would work better for you if you actually read it.<br>

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You need to stop worrying about the diameter of the objective. It has very little to do with anything. The quantity that actually matters in terms of light gathering is called the entrance pupil diameter. If you know the focal length and the f/stop then you know the entrance pupil diameter. It happens that with long lenses the front element's diameter is close to the entrance pupil's diameter, but it is not true for wider lenses. Measuring any wide lens should convince you of this.<br>

"But with a lens that's designed to make the same image (say a 50mm) on a small sensor as another lens would on a large sensor (say a 75mm - sorry I don't know of such a lens), and both offer an aperture of f1.8, and both have the same size objective lens..."<br>

<br /><br>

STOP!! RIGHT THERE!! The fact is that THEY WON'T and CANNOT have the same size entrance pupil and they WILL NOT have the same size front element diameter either. Your confusion perhaps stems in part from theorizing lenses that are in fact impossible.<br>

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"I believe that if I use a similar f8 aperture to shoot a scene with my 5 D, I get approximately the same exposure in about half the time or less that I do with my 4x5, using the same ISO settings. I suspect this is due to the relative differences in size of objective lens to film."<br>

<br /><br>

You can believe in fairies and leprechans if you like too, but that doesn't make them exist. Tell me - does the typical light meter include a setting for the diameter of the front element? I wonder why it would be that it would not. If there is a different between your exposure times in the two systems it's because of other factors, like poor light transmission in older lenses, the fact that the ISO of digital cameras is an approximation, etc.<br>

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[scottelly]

<p>Hmmm, you've given me a lot to think about Mark. I guess I'll have to review some more. I'm sure that some time in the past, maybe in college, I learned this stuff. THANK YOU for your help.</p>

[peterblaise]

<p>.</p>

<p>Scott, you're all over the map with (non) scientific unreferenced speculation. Stop and measure something, anything, and try again.</p>

<p>.</p>

[James G. Dainis]

"I believe that if I use a similar f8 aperture to shoot a scene with my 5 D, I get approximately the same exposure in about half the time or less that I do with my 4x5, using the same ISO settings."

 

Let me amplify a point that Alec made.

 

I meter a scene and it calls for f/8 at 1/125 sec. The meter doesn't know if I am using a 35mm camera, a medium format camera or an 8x10 view camera. For f/8, I have to use 1/125 sec shutter speed no matter which camera I am using.

 

I assure you, I use the same hand held meter when using my 35mm camera as when I am using my 8x10 view camera. There is no correction that has to be set on the meter depending on which camera or lens I am using. It works the same for all cameras and lenses, all formats .

[allardk]

<p>Scott, you can indeed lower the noise by keeping the same shutter speed, opening up the aperture and exposing a sensor to more light, without overexposing. This is achieved by lowering the ISO. ISO's are related to actual light intensities. On small pixel cameras, they mean a higher (ADCbit/photon) value than on large pixel sensors.<br>

More photons at the same ISO and a correct exposure means bigger pixels, that's it, period. Nevertheless, there's still a lot of headroom to gain until sensors hit the real physical limits (which would be single photon sensitivity in all colors)<br>

Read this about four times and you may get a bit wiser on how it all works:<a href="http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/index.html"> Noise, Dynamic Range and Bit Depth in Digital SLRs</a></p>

 

[joe_c5]

<p>What you say is close to being correct, but as described in the replies above the aperture must also be very large, not just the objective.</p>

<p>While it may be possible to design lenses with maximum apertures larger than F/1, I don't believe it is practical to design good ones. Even F/1.2 tends to be iffy. While some lenses are better than others, many would not be considered truly "sharp" at wider apertures than F/2.8. Few zoom lenses seem to have larger apertures than F/2.8 either.</p>

<p>So with cost effective lenses a larger sensor can generally collect more light than a smaller sensor.</p>

<p>If cost, size, and weight were no object, the sharpest photographs could be taken with a sensor large enough that the image was diffraction limited at the desired depth of field. Even then, larger pixels would probably still increase dynamic range at the bright end. Note that for wide depths of field, smaller sensors may be quite adequate.</p>

<p> </p>

[scottelly]

<p> I guess what I am most concerned with is the difference between two lenses that have the same objective diameter, similar construction (re. materials and quality of build), the same aperture, yet different image circles. I am thinking specifically of lenses made for APS-C sensor cameras (the "digital only" lenses) vs. lenses like what I use on my Canon 5 D. Wouldn't one of those lenses made for a smaller sensor concentrate the light that it catches into a smaller area, effectively increasing the number of photons entering the photosites on a smaller sensor camera?</p>

<p>I know this would fly in the face of conventional thinking, and I didn't see the affects of this, when I put my Sigma 18-125mm "digital only" lens on my 5 D (amazingly it works just fine, but vignettes horribly), but maybe I'm just not noticing what is going on. It seems obvious to me, after experimentation, that what I am proposing can not be the case, and since if it were, then light meters would not work (at least not without all sorts of complications, requiring adjustments or compensations charts, etc.), but I can't seem to grasp what is happening. Does this optics stuff not work like a telescope? Does not a larger objective translate to a brighter image? Maybe the larger objective in a telescope includes a larger aperture (in fact in many telescopes, I believe the opening where the objective lens is located is called the aperture). Still, I am a little confused by the idea that I can have objective lenses that are the same size, with identical focal lengths and apertures, but when the image circle being projected is smaller that does not translate into a higher concentration of photons.</p>

<p>Thank you all for your comments and patience.</p>

<p>Here are two photos I shot that show what my 5 D records through 1) my 70-200 f2.8 L IS set on 100mm at f5.6 and my Sigma 18-125 set on 100mm at f5.6 - you can see the image from the Canon is actually brighter. What's weird it the fact that it seems that the Sigma is marked in a compensated way. What I don't understand is the fact that when shooting with it on my 20 D I never got a super wide angle image when it was set at 18mm. VERY weird indeed. I wonder what the markings really mean on that lens, after this test (well . . . sort-of test).</p>

<p>http://www.scottvision.com/compare</p>

<p>Check the EXIF data yourself. The two files in that folder were uploaded straight from the memory card.</p>

[scottelly]

<p>Well, that was confusing Allard. Thank you for the link though. Unfortunately what I'm getting at is not about sensor size so much as photon "concentrations" caused by optics. I'm under the impression that a lens works similarly to the way a magnifying glass works (though in a much more complicated multi-lens way). If you use a large magnifying glass and concentrate the Sun's light onto a spot 1 inch in diameter, you will be concentrating photons. You can even see the dark area around the bright spot. With a larger magnifying glass, you can concentrate more light onto the same size spot, effectively increasing the concentration of photons. If you use the same lens, but move it, so it concentrates the light onto a smaller spot, you have suddenly increased the number of photons per square millimeter, right? (I believe this is what happens when a lens is designed to work with a smaller sensor.) Sure, the aperture comes into play, but to what degree? Can more photons be "funneled" through an aperture of the same size, by changing the optics? I don't know, but I sure do wonder. We can change focal lengths without increasing the length of a lens. In fact, the focal length of the lens on my Sony R-1 gets longer, though the front lens element is getting closer to the camera (when I zoom from 24mm to 35mm - these are equivalentcy numbers, to give the magnification level that would match what would be seen with similar lens focal lengths on a full-frame camera with a full-frame lens). The interesting thing is when I look at the numbers in the EXIF info. The lens really has much smaller focal length numbers there (presumably, because Sony is referring to some form of "real" focal length that works with the 1.7 crop factor of the sensor in the R-1).</p>

<p>The more I think about this stuff, the more I wonder what a lens focal length really means. Does it really have anything to do with the magnification or the image circle? I know there are large format lenses that make image circles larger than other lenses made for the same format and with the same focal length. I am not quite sure how their angle of view is measured though. I know that while a 2x extender does not double the actual focal length of a lens, it somehow effectively doubles the magnification or "apparent" focal length, so what really does focal length mean after all? Is focal length really just a measure of magnification? I read in Wikipedia and found that focal length is not as simple as I once thought. Apparently focal length with a simple lens is fairly simple, but when groups of lenses are involved, things change dramatically. According to what I read there, "The focal length of a lens determines the magnification at which it images distant objects." If this is the case, then is my Sigma lens mismarked, or is it just marked for focal lengths that coincide with particular magnification levels that would calculate to match full-frame lenses on full-frame cameras. When being used only on an APS-C size sensor do the number match to what the images would look like if the lens was a full-frame lens on a full-frame SLR? Would it be the same on a Sigma camera, which has a 1.7 crop factor instead of a 1.6 crop factor, or are lenses for those cameras "calibrated" differently? What about mounting a Nikon version of that lens on my camera with an adapter? Would it then be a lens with a different focal length range, because it was designed for a 1.5 crop factor camera instead of a 1.6 crop camera?</p>

<p>How does angle of view and image circle size relate to focal length?</p>

<p>I guess I have many more questions than answers. Maybe I need to go to college and learn about optical engineering. Maybe I should just give up and leave it to those who are more interested in designing optics for cameras than shooting photos.</p>