Large sensors and Image Noise

[facts_please]

It is an observed fact that SLR cameras using relatively large sensors perform substantially better than point-and-shoot cameras in low light situations. The most common explanation is that the much larger sensors in SLR style cameras gather more light in proportion to their larger area – typically 4 times that of the smaller sensors found in point and shoot cameras.

Careful thought suggests this explanation is a wrong – one of those myths that if repeated often enough comes to be regarded as fact. The reason that SLR cameras perform better in low light situations is almost entirely due to their larger lenses, which gather more light. The larger area sensor does not inherently have anything to do with it, except for a slight second order benefit due to the fact that the dead area of a larger sensor is a slightly lesser proportion of the total sensor area.

Before justifying my statement above, I need to define clearly what I mean by the aperture of a lens. In this discussion, aperture means the effective diameter of the iris that controls how much light passes through the lens. Forget about ‘f-numbers’ in this discussion – I will refer only to aperture diameter, which of course is expressed in length units such as millimeters.

It is essential to state clearly what constitutes a fair image noise comparison between two cameras that are identical in all respects except sensor size. Firstly, the number of pixels must be the same. The shutter speed must also be the same. Both cameras must be at the same distance from the same object, and the image of this (identically sized) object must exactly fill both sensors, which of course means that the focal length of the lenses will be set differently for each camera. Further, both lenses must be set to the same aperture, or otherwise it is perfectly obvious that one lens will gather more light, which would not make for a fair comparison between the different sizes of sensor. With identical apertures set for both cameras, the depth of field and diffraction limited resolution will also be the same for both cameras, again making for a fair and equal comparison. Correct exposure for both cameras being compared is obtained by adjusting the camera ISO setting. The numeric ISO reading thus obtained is irrelevant. Thus we have a truly fair ‘apples versus apples’ comparison between two cameras with different sized sensors, totally relevant to the real world. Both cameras are ‘doing the best they can’ under identical conditions and constraints, with the only variable being the size of the sensor. I contend that the total amount of light striking the sensor will be the same for both cameras, despite one sensor having a greater area, and that the image noise performance will therefore also be essentially the same.

This conclusion makes good sense. All else equal, the amount of light gathered by the lens is proportional to the area of the lens aperture, and this same amount of light is delivered to the sensor, regardless of sensor size. In other words, for a larger sensor, the same amount of light is simply spread over a larger area. The electrical signal level registered by the sensor is proportional to the total number of photons arriving at the sensor which, as discussed, is independent of sensor size in a properly structured comparison. This is not rocket science. This is common sense.

Note that the superior low light performance of SLR style cameras is not in dispute – what is in dispute is the reason for this superiority, and the reason is mainly because SLR style cameras have physically large lenses which gather more light. It may be correctly deduced from this discussion that compact point-and-shoot cameras will always have inherently poor low light performance, not for the most part because they use a small sensor, but because compact cameras must necessarily use a physically small lens. Judging from the statements that I commonly read in camera reviews, implying that low light performance of point and shoot cameras could be greatly improved if only the sensor was much larger, this point does not seem to be well understood.

The described method of comparing cameras with different sensor sizes is lens independent, as it should be when the object of the test is to compare only the effect of sensor size. That is, the test is genuinely measuring the signal to noise of different sized sensors, with the lens in both cases delivering the same total number of photons to the sensor. If such testing is performed in the real world, I would expect larger sensors to produce only a slightly better result (less noise in image) on account of a lesser proportion of ‘dead’ sensor area, with diminishing returns beyond a certain sensor size. A camera comparison of this type would be meaningful and revealing, yet unfortunately I have not seen camera comparisons performed in this way.


One final point. The comparison method described above gives no credit for the ‘speed’ of the lens, which is appropriate when the object of the test is to compare only the effect of sensor size. However, if the object of the comparison is to compare the low light and image noise performance of the camera as a whole, including lens, then the lens aperture should be fully open on both cameras under comparison, that is, both cameras are doing their absolute best to gather as much light as possible. As previously, correct exposure for both cameras being compared is obtained by adjusting the camera ISO settings. Needless to say, in this case superior low light performance will usually be accompanied by a poor depth of field, as expected from a ‘fast’ lens operating at a large aperture. If testing is done in this way, I would expect SLRs to perform very significantly better (lower image noise) than a point and shoot camera, NOT because of the larger sensor, but because of the larger aperture of the SLR lens, which collects more light.

In summary, it is true that SLR style cameras generally outperform compact point and shoot cameras in low light conditions. However, despite popular belief, the reason for this superiority has little to do with sensor size, but is due to the larger lenses on SLR style camera that gather more light.

Comments?

[McQ]

Hi Colin. Thanks for your thoughts on the sensor size vs. image noise topic. Take a look around and feel free to chime in on other forum topics as well. First, please take a look at this earlier in-depth discussion: Camera sensor size: noise & depth of field trade-offs

The reason that SLR cameras perform better in low light situations is almost entirely due to their larger lenses, which gather more light. The larger area sensor does not inherently have anything to do with it, except for a slight second order benefit due to the fact that the dead area of a larger sensor is a slightly lesser proportion of the total sensor area.

This is true: everything else being equal, a larger sensor does not necessarily mean that it will have better low light performance. However, one could argue that real-world design limitations come into play when determining what aperture range is available for a given sensor size. For example, a relatively standard 50 mm lens at f/2.0 on a full frame 35 mm camera would require a 10 mm lens at f/0.6 on a compact camera with a 1/1.8" sensor size! The largest aperture consumer lenses are really no more than f/0.9 at the very largest, and you pay dearly to get something like that. Of course, depth of field equivalence is another factor (if needed), so overall, a larger sensor size does at least give more low light *flexibility*.

It is essential to state clearly what constitutes a fair image noise comparison between two cameras that are identical in all respects except sensor size. Firstly, the number of pixels must be the same. . . .

I contend that the total amount of light striking the sensor will be the same for both cameras, despite one sensor having a greater area, and that the image noise performance will therefore also be essentially the same.

This conclusion makes good sense. All else equal, the amount of light gathered by the lens is proportional to the area of the lens aperture, and this same amount of light is delivered to the sensor, regardless of sensor size. In other words, for a larger sensor, the same amount of light is simply spread over a larger area. . .

The number of pixels can even be different for this comparison. I agree that the total amount of light reaching each sensor will be the same if the depth of field is kept identical (everything else being equal). The flux of light on the larger sensor will be less though, but the larger sensor will have lower apparent noise (at a given print size, not necessarily 100% on screen) for a given ISO sensitivity (pretty much regardless of megapixel count). This lower apparent noise for a given ISO will for the most part cancel out any decrease in light flux.

Note that the superior low light performance of SLR style cameras is not in dispute – what is in dispute is the reason for this superiority, and the reason is mainly because SLR style cameras have physically large lenses which gather more light. It may be correctly deduced from this discussion that compact point-and-shoot cameras will always have inherently poor low light performance, not for the most part because they use a small sensor, but because compact cameras must necessarily use a physically small lens. Judging from the statements that I commonly read in camera reviews, this point does not seem to be well understood.

The described method of comparing cameras with different sensor sizes is lens independent, as it should be when the object of the test is to compare only the effect of sensor size. That is, the test is genuinely measuring the signal to noise of different sized sensors, with the lens in both cases delivering the same total number of photons to the sensor. If such testing is performed in the real world, I would expect larger sensors to produce only a slightly better result (less noise in image) on account of a lesser proportion of ‘dead’ sensor area, with diminishing returns beyond a certain sensor size. A camera comparison of this type would be meaningful and revealing, yet unfortunately I have not seen camera comparisons performed in this way.

I think most camera reviews are only concerned with rough accuracy in their statements and testing, such that the explanations and results make clear and intuitive sense to the readers. I don't think there's necessarily anything wrong with that as long as it is for the most part accurate. I agree though that sometimes a little bit too much "marketing hype" creeps in when touting the merits of a larger sensor size -- after all, these are the much higher price bracket items with better margins, and often represent the flagship models of a given camera company.

One final point. The comparison method described above gives no credit for the ‘speed’ of the lens, which is appropriate when the object of the test is to compare only the effect of sensor size. However, if the object of the comparison is to compare the low light and image noise performance of the camera as a whole, including lens, then the lens aperture should be fully open on both cameras under comparison, that is, both cameras are doing their absolute best to gather as much light as possible.

Something else to consider is that two camera lenses do not necessarily let in the same flux of light -- even if their apertures are set identically. The Canon 24-105 mm f/4L IS lens lets in maybe 1/2-2/3 of a stop less light than the average lens at f/4, for example. Fortunately, I've seen many camera review websites note this fact and take it into account when comparing noise levels between camera models.

[facts_please]

Hi McQ,

Hi Colin. Thanks for your thoughts on the sensor size vs. image noise topic. Take a look around and feel free to chime in on other forum topics as well. First, please take a look at this earlier in-depth discussion: Camera sensor size: noise & depth of field trade-offs

Thanks for your welcome. I had already looked briefly at this previous thread, though must admit I cringed when I read :-

1. Yes, sensor size is the dominant factor when considering image noise.

No. The dominant factor is the size of the lens, or more precisely the lens aperture.

This is true: everything else being equal, a larger sensor does not necessarily mean that it will have better low light performance. However, one could argue that real-world design limitations come into play when determining what aperture range is available for a given sensor size. For example, a relatively standard 50 mm lens at f/2.0 on a full frame 35 mm camera would require a 10 mm lens at f/0.6 on a compact camera with a 1/1.8" sensor size! The largest aperture consumer lenses are really no more than f/0.9 at the very largest, and you pay dearly to get something like that. Of course, depth of field equivalence is another factor (if needed), so overall, a larger sensor size does at least give more low light *flexibility*.

Yes, I did not mention this originally because my original post was already long. Consistent with my original post, if you want better low light performance then fundamentally you need a larger lens with a larger aperture, to gather more light. However, it turns out to be difficult to build large aperture lenses with short focal lengths, so in practice if you need a larger lens then you may need to go with a longer focal length, which in turn will require a larger sensor, whether you like it or not. You could say that a larger sensor permits the use of a larger aperture lens, but let us be clear, it is the larger lens that provides the improvement in low light performance, NOT the larger sensor. I love large sensors, by the way ....

I agree that the total amount of light reaching each sensor will be the same if the depth of field is kept identical (everything else being equal). The flux of light on the larger sensor will be less though, but the larger sensor will have lower apparent noise (at a given print size, not necessarily 100% on screen) for a given ISO sensitivity (pretty much regardless of megapixel count). This lower apparent noise for a given ISO will for the most part cancel out any decrease in light flux.

You make it sound so complicated .... Under identical conditions, the total amount of light reaching both sensors is the same - on that we agree. The pixels on both sensors detect the same number of photons, and the (mainly shot) noise on both sensors will also be the same. Signal-to-noise ratio is therefore the same for both sensors. As per my posting, you adjust the ISO knob on both camera for correct exposure - you don't get to choose this as an independent variable. The underlying SNR is already set long before you twiddle the ISO knob - all the ISO gain will do is scale the electrical output from the sensor so as to match the A/D converter, the number of bits available for encoding, and so on. Unless I am missing something, both cameras will produce a near identical image in terms of noise, ignoring second order effects such as different active area ratio. 'Apparent noise' and 'print size' and 'given ISO sensitivity' simply don't come into it, to my simple minded way of looking at things. Am I missing something? I may well be, and I would welcome further discussion until we are in agreement.

Actually, we seem to agree on most points, and I am just being my usual picky self.

[McQ]

Thanks for your welcome. I had already looked briefly at this previous thread, and must admit I cringed when I read :-

1. Yes, sensor size is the dominant factor when considering image noise.

No. The dominant factor is the size of the lens, or more precisely the lens aperture.

Yes, lens f-number is the central factor, but that was not part of the earlier discussion, which I think was taken a bit out of context. There were also many qualifiers after that sentence. The answer you quote was from a member who was only asking about the trade-off between pixel density and sensor size. We were also focusing on the issue of perceived noise at 100% onscreen versus at a given print size.

[facts_please]

1. Yes, sensor size is the dominant factor when considering image noise.

Yes, lens f-number is the central factor, but that was not part of the earlier discussion, which I think was taken a bit out of context. There were also many qualifiers after that sentence. The answer you quote was from a member who was only asking about the trade-off between pixel density and sensor size. We were also focusing on the issue of perceived noise at 100% onscreen versus at a given print size.

To be more precise, it is the absolute lens aperture diameter (or area, if we want to absolutely correct), not the f-number, that determines how much light is gathered by the lens, and therefore sets the image noise.

I do apologise for taking your original sentence out of context. Agreed that much changes when the discussion includes different numbers of pixels, and pixel density .... it was a different thread and I should have been more careful.

[McQ]

I think we are in agreement on pretty much everything; the points are just written a little differently.

With regards to f-number versus absolute aperture diameter, I would have to respectfully disagree though. A 400mm f/2.8 lens has a MUCH larger absolute aperture diameter than a 100mm f/2.8 lens, for example, yet both lenses let in the same amount of light (due to identical f-numbers). This is why I changed the wording from lens aperture (which could be either f-number or absolute aperture diameter) to f-number.

[facts_please]

With regards to f-number versus absolute aperture diameter, I would have to respectfully disagree though. A 400mm f/2.8 lens has a MUCH larger absolute aperture diameter than a 100mm f/2.8 lens, for example, yet both lenses let in the same flux of light (due to identical f-numbers). This is why I changed the wording from lens aperture (which could be either f-number or absolute aperture diameter) to f-number.

Ooops! You are, of course, perfectly correct for the common situation where the sensor size is fixed, and the focal length is varied to adjust the ‘zoom’, or field of view.

My only defence is that my mind was still stuck on the different situation that I described in my original posting, where two cameras with different sized sensors are being compared re their low light performance. In this situation the field of view is constant for the two cameras being compared, and the sensor size is different. In this situation the amount of light gathered by the lens and delivered to the sensor is indeed a function of the absolute aperture.

[McQ]

No problem. It was an interesting discussion. Hope to hear from you more in other threads in the future...

[facts_please]

With regards to f-number versus absolute aperture diameter, I would have to respectfully disagree though. A 400mm f/2.8 lens has a MUCH larger absolute aperture diameter than a 100mm f/2.8 lens, for example, yet both lenses let in the same flux of light (due to identical f-numbers). This is why I changed the wording from lens aperture (which could be either f-number or absolute aperture diameter) to f-number.

Ooops! You are, of course, perfectly correct for the common situation where the sensor size is fixed, and the focal length is varied to adjust the ‘zoom’, or field of view.

My only defence is that my mind was still stuck on the different situation that I described in my original posting, where two cameras with different sized sensors are being compared re their low light performance. In this situation the field of view is constant for the two cameras being compared, and the sensor size is different. In this situation the amount of light gathered by the lens and delivered to the sensor is indeed a function of the absolute aperture.

It would be good to clean this issue up properly, as knowing how much light is delivered to the sensor, in the general case of different sized sensors and different focal lengths, is important.

In the general case, I contend it is neither the f-number nor the absolute aperture that matters. The general expression is :-

Total light striking sensor depends on S(D/L)

where:
D is absolute aperture diameter
L is the focal length
S is the sensor dimension


Let's check to see if this consistent with both of our quoted statements.

In your example, for a given camera where sensor size is constant, the expression reduces to :-
Total light striking sensor depends on (D/L)
but (D/L) is just the reciprocal of the f-number, so the general expression is indeed consistent with what you wrote.

In my example, where the field of view is constant, we note that the field of view is proportional to(S/L). Think about that, if sensor size is doubled, then focal length is also doubled to maintain same field of view. If (S/L) is constant, then the expression reduces to :-
Total light striking sensor depends on D
And so the general expression is indeed also consistent with what I wrote.

Excellent! I hate untidy ends.

[cav]

However, if the object of the comparison is to compare the low light and image noise performance of the camera as a whole, including lens, then the lens aperture should be fully open on both cameras under comparison, that is, both cameras are doing their absolute best to gather as much light as possible.
Comments?

An interesting and thought provoking argument.

With the limitations of compact camera lenses being what they are, it might be an idea to photograph a very bright subject using a very small aperture. This would, in effect, eliminate the lens from the equation as it approaches a pinhole with minimum aberration allowing a more transparent analysis of the sensor performance.

Do digital sensors suffer form reciprocity law failure?

[McQ]

With the limitations of compact camera lenses being what they are, it might be an idea to photograph a very bright subject using a very small aperture. This would, in effect, eliminate the lens from the equation as it approaches a pinhole with minimum aberration allowing a more transparent analysis of the sensor performance.

Yes, that would be helpful to minimize any effects due to depth of field, or the light angle when it strikes the sensor. If the pinhole sizes capture equivalent light for both the small and large sensor, then this would also help when testing noise levels in two different cameras. It all comes down to whether you want to try and isolate the effects of the sensor, or test the entire lens to sensor optical system...

Do digital sensors suffer form reciprocity law failure?

Not to anywhere near the same degree as film (it's pretty much non-existent). However, digital has a new problem: fixed pattern noise.

[Radu Dinu Cordeanu]

The discussion was very interesting and I thank you all.Digging deeper we find the quality of the electronic amplifier but I think a good picture depends on place,light, brain ,eye and hand and in a small part on camera.
RaduDinu.

[Dave Humphries]

it might be an idea to photograph a very bright subject using a very small aperture.

Hi all,

That might be a problem, my big (ish) lens on a compact sized sensor bridge camera only stops down to f8 , a feature I assumed was deliberate to prevent the diffraction effect becoming too evident in the pictures.

I am not sure if I am right about that, or whether the smaller lens on a point'n'shoot compact affects it in anyway; e.g. cannot resolve as much so diffraction would be less noticeable.

Any thoughts?

Cheers,

[facts_please]

DaveH: (A very small aperture) might be a problem, my big (ish) lens on a compact sized sensor bridge camera only stops down to f8 , a feature I assumed was deliberate to prevent the diffraction effect becoming too evident in the pictures.

There is a common misunderstanding that point and shoot camera can't stop down the iris as far as SLRs or 35mm film camera.

In this case, you need to stop thinking about f-numbers, and consider that what actually matters from the point of view of depth-of-field, diffraction and how much light gets to the sensor for a given field of view, is the absolute aperture diameter.

To obtain an f-number that is equivalent to a 35mm film camera, in terms of absolute effective aperture, you need to scale down the fnumber by the crop factor.

As the crop factor for your S5600 point-n-shoot is around 6, that means that at F8, the absolute effective aperture is the same as a 35mm camera at F48!!!!

Now you see why there is no point in having greater than F8 on that camera!! and diffraction could be an issue.

Wait a minute, ColinS has terrible problems with too much light in his landscape shots. He would surely give his left arm to get hold of your camera, going to an equivalent of F48! Why don't you strike a deal with him - maybe he would swap his camera for yours ....

[Dave Humphries]

Colin,

If that factoring of f numbers is true (first time I've heard of it - but I suppose it would be to qualify as a common mis-understanding), then my wide open at f3.5 - f5.6 (depending on zoomed FL) explains your earlier comment about the lens "throwing a lot of the light away". I reckon the multiplier is about 5 rather than 6, but I take the point, so then I have about f20 to f32 wide open.

So why is the range between fully open and closed so small?

And doesn't this scaling and the other one effectively cancel out, meaning things ARE comparable, number for number, on say, noise between different sensor sizes? It's getting late here, maybe my mind is wandering.

I'll look a-fresh tomorrow, cheers,

[McQ]

In this case, you need to stop thinking about f-numbers, and consider that what actually matters from the point of view of depth-of-field, diffraction and how much light gets to the sensor for a given field of view, is the absolute aperture diameter.

To obtain an f-number that is equivalent to a 35mm film camera, in terms of absolute effective aperture, you need to scale down the fnumber by the crop factor.

The flux of light reaching the camera sensor is only a function of the f-number. If the sensor is cropped, then for a given f-number, the flux of light hitting the sensor remains the same, but the total amount hitting the sensor is proportional to the area of the cropped sensor divided by are of the reference (full frame) sensor. This is equivalent to using an aperture on the cropped sensor that ensures the same depth of field as the uncropped sensor.

However, since a compact camera has a much greater depth of field for a given f-number, it can open up the lens more to lower it's noise levels. If one chooses an aperture that makes the depth of field between the large and small sensors the same, then the noise levels will also be similar.

Technical Note: strictly speaking, when we say that everything "cancels out" with respect to noise in a compact vs SLR camera, this is only speaking of random noise. In reality, there's many other sources of noise, including sensor read-out noise and black body noise, which all become much more prominent in the shadow tones of an image. When considering this fact, larger sensors definitely have a noise advantage -- even at the same depth of field / exposure.

As the crop factor for your S5600 point-n-shoot is around 6, that means that at F8, the absolute effective aperture is the same as a 35mm camera at F48!!!!

Now you see why there is no point in having greater than F8 on that camera!! and diffraction could be an issue.

This is all true: compact cameras have vastly better depth of field at a given aperture when compared to SLR cameras. You can calculate the equivalent aperture and focal length for (nearly) any two different sensor sizes at this tutorial: Digital Camera Sensor Sizes

Wait a minute, ColinS has terrible problems with too much light in his landscape shots. He would surely give his left arm to get hold of your camera, going to an equivalent of F48! Why don't you strike a deal with him - maybe he would swap his camera for yours ....

Well, Colin's SLR camera can use tilt/shift lenses for better depth of field placement. Further, I would opt for the vastly greater depth of field control from f/1.4-f/32 in SLR cameras compared to the typical f/2.8ish-f/8 in compact cameras any day. And this is all ignoring the fact that the SLR camera will (nearly) always have more dynamic range . . .

[McQ]

If that factoring of f numbers is true (first time I've heard of it - but I suppose it would be to qualify as a common mis-understanding), then my wide open at f3.5 - f5.6 (depending on zoomed FL) explains your earlier comment about the lens "throwing a lot of the light away". I reckon the multiplier is about 5 rather than 6, but I take the point, so then I have about f20 to f32 wide open.

So why is the range between fully open and closed so small?

Mostly cost/design issues. High quality zoom lenses with a very large max aperture require exotic glass elements (UD/aspherical/flourite/etc, which dramatically increase the cost.

And doesn't this scaling and the other one effectively cancel out, meaning things ARE comparable, number for number, on say, noise between different sensor sizes? It's getting late here, maybe my mind is wandering.

I'll look a-fresh tomorrow, cheers,

Yes, it all effectively cancels out *IF* you want to achieve the same depth of field.

Note: by "cancels out" I am referring to the trade-off between noise, exposure and depth of field. Dynamic range will almost always be greater for the larger sensor camera, whereas the smaller sensor camera will be able to achieve equivalence using much smaller/lighter/cheaper lenses.

[facts_please]

Hi McQ,

Note: by "cancels out" I am referring to the trade-off between noise, exposure and depth of field. Dynamic range will almost always be greater for the larger sensor camera, whereas the smaller sensor camera will be able to achieve equivalence using much smaller/lighter/cheaper lenses.

As far as I can tell, we agree on everything, but with the interesting observation that we look things from a slightly different angle, and explain things differently. I suspect that is because you are a photographic expert and I am not - I know essentially nothing of photography per se, and am figuring out the technical details as I go using an underlying knowledge of general physics. It is significant that two different approaches come to the same conclusions - that is the beauty of science.

However, I'm not sure if I agree with your above quote - depends on what you mean by equivalence. I would define equivalence as being when the cameras being compared are the at the same distance from the same object, the same object completely fills both sensors (ie, same FOV), and both cameras are achieving essentially the same noise, depth of field and shutter speed, and the F-numbers will be differerent so as to provide the same total amount of light on each sensor, as required for same noise. Thus, the performance of the two camera is the same. However, I dispute that the smaller sensor camera will be able to avhieve this equivalence using 'much smaller/cheaper/lighter lenses'. In fact, I believe that if anything the opposite is true. The absolute aperture of both lenses will be the same, thus roughly similar size and weight, but the lens on the smaller sensor camera will require a smaller F-number, which is usually more expensive to manufacture.

Originally Posted by facts_please
Wait a minute, ColinS has terrible problems with too much light in his landscape shots. He would surely give his left arm to get hold of your camera, going to an equivalent of F48! Why don't you strike a deal with him - maybe he would swap his camera for yours ....

Well, Colin's SLR camera can use tilt/shift lenses for better depth of field placement. Further, I would opt for the vastly greater depth of field control from f/1.4-f/32 in SLR cameras compared to the typical f/2.8ish-f/8 in compact cameras any day. And this is all ignoring the fact that the SLR camera will (nearly) always have more dynamic range . . .

You do realise, of course, that my comments here were totally tongue-in-cheek. The professional camera/lens used by ColinS is worth an awful lot of money, and he won't be swapping it for a Finepix 5600 any time soon .... However, you must admit there is an irony in using such a superb lens almost exclusively at F11 to F22, when most of the complexity, size, weight and cost has gone into providing the capability of going to F1.4, or did ColinS even mention F1.2 ! Guess I'm just jealous that I don't own lenses like that.

PS. I am constantly confused by the intended meaning of the word 'aperture'. How about we standardize on the term 'F-number' to mean F-number, and let 'aperture' mean the absolute aperture diameter. Or I'm happy with any other suggestion, so long as it avoids confusion.