Long Lenses & Low Light

[fcotterill]

I think the OP supported his original thesis with facts and examples,

As @DRwyoming explains it and I've tried.... The OP's examples fall short, notwithstanding debates about the real world variables that it's clear have to be compared to evaluate lens performance...
No free lunches

and I'm convinced within my non math or optical engineering limits. If someone who disagrees could give an example where the lens with the smaller entrance pupil provided more total light or less noise after all the required equivalency, that would help me understand.

Real World comparison: compare a 200 f2G Nikkor to a 500 f5.6 PF for photographing wildlife subjects.

What is the advantage of the 11mm wider Window Ф of the 'Fat Man' ?

 

[Bill Ferris]

Without getting into all the equivalence issues and different sensor sizes, can we say this:

At the same focal length, a faster lens will get you more light wide open and hence may generally be better for low light, all other things being equal (which they rarely are). Of course it might be too large/heavy, too expensive or you may need to stop down for DOF.

That is correct. At the same focal lengths, lenses working at different f-stops will have different-sized entrance pupils. The fastest lens (lens with the smallest f-number) will have the larger entrance pupil and collect more light energy from the subject.

At the same time, that may not be true in all cases when comparing a faster shorter lens to a longer slower lens. For example, a 400 mm f2.8 lens is not better for low light than a 600 mm f4 lens, both used wide open and at the same distance, if you have to crop the image from the 400 mm lens or use a TC with the 400 mm lens to get a FOV similar to that obtained with the 600 mm lens.

Yes.

Another example would be a comparison of 400mm f/4.5 and 600mm f/6.3 lenses. If a photographer is struggling to choose between them and the source of that indecision is the belief that the shorter, faster lens will be better in low light, a follow up question to ask is if they would plan to fill the frame at 400mm, or add a TC or crop the photo to match the 600mm framing. If they'd plan to crop or TC the 400mm f/4.5, its 89mm entrance pupil isn't collecting any more light from the subject than the 600mm f/6.3's 95mm entrance pupil. There's no low-light noise advantage in choosing the faster lens.

If you can get closer with the 400 mm lens and hence avoid the need to crop or use a TC, again the faster lens would generally be better for low light.

There's also the potential that being closer to the subject positions the photographer within the minimum focus distance for the longer lens. If that's the case, the longer lens would not be usable.

I think this was what Steve was saying in his video comparing the 400 mm TC and 600 mm TC lenses.

Is there something more I am missing. If this is it, it seems simple enough.

That's what I've gathered watching Steve's videos, as well. If you ever want to calculate a percentage difference in light-gathering, a comparison of entrance pupil sizes makes that pretty easy.

 

[Bill Ferris]

The entrance pupil AND the angular field of view based on focal length determine how much light is collected from the subject. It's not just entrance pupil as two different focal length lenses with the same entrance pupil will gather different amounts of light from the same uniformly lit and uniformly toned subject based on their respective fields of view.

You can't just toss out the collection area on the object side of the lens when discussing captured photons it's an important part of the process.

Actually, you can toss out the size of the subject in the frame. Whether we're talking about a point source (e.g. a star) or a the Moon filling the frame at a 2000mm focal length, the size of the virtual entrance pupil determines how many photons will be collected from that subject.

Object size in the frame will alter the exposure but not the total light energy collected from the subject.

 

[DRwyoming]

Actually, you can toss out the size of the subject in the frame. Whether we're talking about a point source (e.g. a star) or a the Moon filling the frame at a 2000mm focal length, the size of the virtual entrance pupil determines how many photons will be collected from that subject.

Object size in the frame will alter the exposure but not the total light energy collected from the subject.

I think I see where you're coming from, so let's put overall exposure aside for now.

Take two lenses, say a 500mm f/4 and a 1000mm f/8. By definition they have the same 125mm entrance pupil and let's assume their design and manufacturing resulted in 100% optical efficiency so their T stops are T4 and T8 respectively.

Now point them both at the same bright celestial body or even bright terrestrial object surrounded by dark elsewhere in both frames. I think we'd both agree they'd capture the same number of photons from that bright subject with the rest of their respective fields of view being dark enough to ignore.

Now since they have the same entrance pupils are you asserting they deliver the same signal to noise ratio and same object brightness on a digital sensor located at the image plane? Maybe I misunderstood what you've posted but this seems to be the assertion that the signal to noise ratio on the sensor for the area associated with the object will be the same because entrance pupil is the same.


But the same sized object will occupy 4 times the area on the sensor when shot with the 1000mm lens vs the same object shot with the 500mm lens.

That means that same finite number of collected photons is now distributed across a larger area of the sensor and those photons are now spread across 4 times as many photo sites assuming a sufficiently high resolution sensor. In other words each photo site will now respond to 1/4 as many photons from the 1000mm lens than when the same object was photographed with the 500mm lens. Do you agree with this that at the image plane the image shot with the longer focal length lens takes up substantially more of the sensor area and thus those captured photons are spread across more photosites?

In this scenario each photo site will capture 1/4 the number of available photons compared to the shorter focal length lens.

How can we say the object exposure or signal to noise will be the same when each photo site on the sensor is recording fewer photons? The sensor photo sites associated with the longer focal length lens are clearly capturing fewer photons and operating closer to their inherent noise floor.

In this example the longer focal length lens delivers 1/4 the number of photons to each sensor which corresponds exactly the difference in exposure predicted by f/ stops even though their entrance pupils are identical.

Does this make sense to you as to why entrance pupil alone cannot predict exposure or signal to noise ratio without any focal length information?

 

[Dinusaur]

I think I see where you're coming from, so let's put overall exposure aside for now.

Take two lenses, say a 500mm f/4 and a 1000mm f/8. By definition they have the same 125mm entrance pupil and let's assume their design and manufacturing resulted in 100% optical efficiency so their T stops are T4 and T8 respectively.

Now point them both at the same bright celestial body or even bright terrestrial object surrounded by dark elsewhere in both frames. I think we'd both agree they'd capture the same number of photons from that bright subject with the rest of their respective fields of view being dark enough to ignore.

Now since they have the same entrance pupils are you asserting they deliver the same signal to noise ratio and same object brightness on a digital sensor located at the image plane? Maybe I misunderstood what you've posted but this seems to be the assertion that the signal to noise ratio on the sensor for the area associated with the object will be the same because entrance pupil is the same.


But the same sized object will occupy 4 times the area on the sensor when shot with the 1000mm lens vs the same object shot with the 500mm lens.

That means that same finite number of collected photons is now distributed across a larger area of the sensor and those photons are now spread across 4 times as many photo sites assuming a sufficiently high resolution sensor. In other words each photo site will now respond to 1/4 as many photons from the 1000mm lens than when the same object was photographed with the 500mm lens. Do you agree with this that at the image plane the image shot with the longer focal length lens takes up substantially more of the sensor area and thus those captured photons are spread across more photosites?

In this scenario each photo site will capture 1/4 the number of available photons compared to the shorter focal length lens.

How can we say the object exposure or signal to noise will be the same when each photo site on the sensor is recording fewer photons? The sensor photo sites associated with the longer focal length lens are clearly capturing fewer photons and operating closer to their inherent noise floor.

In this example the longer focal length lens delivers 1/4 the number of photons to each sensor which corresponds exactly the difference in exposure predicted by f/ stops even though their entrance pupils are identical.

Does this make sense to you as to why entrance pupil alone cannot predict exposure or signal to noise ratio without any focal length information?

To restate, what you said, in another way; a 1000mm lens has twice as long focal length as 500mm lens. This means light has to travel twice as much distance inside in order to reach the sensor. From basic physics we know that intensity of light follows inverse square law, light disperses with distance. In your example, despite receiving the same amount of light due to the same size of the entrance pupil, with 1000mm lens the camera's image sensor will receive 1/4 (1/2^2) of light compared to 500mm as it is twice as long. I don't think there's any way around it.

 

[SCoombs]

To restate, what you said, in another way; a 1000mm lens has twice as long focal length as 500mm lens. This means light has to travel twice as much distance inside in order to reach the sensor. From basic physics we know that intensity of light follows inverse square law, light disperses with distance. In your example, despite receiving the same amount of light due to the same size of the entrance pupil, with 1000mm lens the camera's image sensor will receive 1/4 (1/2^2) of light compared to 500mm as it is twice as long. I don't think there's any way around it.

- and this would be a more technical way of stating what I took from the more "colloquial" explanation offered in the Gerald Undone video.

 

[BillW]

To restate, what you said, in another way; a 1000mm lens has twice as long focal length as 500mm lens. This means light has to travel twice as much distance inside in order to reach the sensor. From basic physics we know that intensity of light follows inverse square law, light disperses with distance. In your example, despite receiving the same amount of light due to the same size of the entrance pupil, with 1000mm lens the camera's image sensor will receive 1/4 (1/2^2) of light compared to 500mm as it is twice as long. I don't think there's any way around it.

Doesn't the focusing of light by the lens elements inside the lens change this so that we do not have a simple inverse square law for light traveling inside the lens? I'm not sure what the does to the results we are discussing.

 

[Bill Ferris]

I think I see where you're coming from, so let's put overall exposure aside for now.

Take two lenses, say a 500mm f/4 and a 1000mm f/8. By definition they have the same 125mm entrance pupil and let's assume their design and manufacturing resulted in 100% optical efficiency so their T stops are T4 and T8 respectively.

Now point them both at the same bright celestial body or even bright terrestrial object surrounded by dark elsewhere in both frames. I think we'd both agree they'd capture the same number of photons from that bright subject with the rest of their respective fields of view being dark enough to ignore.

Now since they have the same entrance pupils are you asserting they deliver the same signal to noise ratio and same object brightness on a digital sensor located at the image plane? Maybe I misunderstood what you've posted but this seems to be the assertion that the signal to noise ratio on the sensor for the area associated with the object will be the same because entrance pupil is the same.

The SNR and noise level of the subject will be the same because the same number of photons is collected from the subject by both lenses. Noise is proportional to the square root of the signal.

But the same sized object will occupy 4 times the area on the sensor when shot with the 1000mm lens vs the same object shot with the 500mm lens.

That means that same finite number of collected photons is now distributed across a larger area of the sensor and those photons are now spread across 4 times as many photo sites assuming a sufficiently high resolution sensor.

Yes, the image of the subject projected by the longer focal length lens will have the same number of photons but, as a result of covering a larger area, will have a lower exposure.

In other words each photo site will now respond to 1/4 as many photons from the 1000mm lens than when the same object was photographed with the 500mm lens. Do you agree with this that at the image plane the image shot with the longer focal length lens takes up substantially more of the sensor area and thus those captured photons are spread across more photosites?

The number of photo sites isn't a factor determining of exposure or total light collected from the subject. It's the area across which the photons are distributed that will determine the exposure. Use the same focal length lens and same exposure settings to photograph a scene, first with a 45MP camera and then with a 6MP camera of the same format, and both sensors receive the same exposure. That both lenses are working with the same size entrance pupil and collect the same number of photons from the subject ensures both sensors will receive the same total light energy from the subject.

In this scenario each photo site will capture 1/4 the number of available photons compared to the shorter focal length lens.

How can we say the object exposure or signal to noise will be the same when each photo site on the sensor is recording fewer photons? The sensor photo sites associated with the longer focal length lens are clearly capturing fewer photons and operating closer to their inherent noise floor.

Image noise is a function of the total light energy used to make a photo; not of the light energy received per pixel.

In this example the longer focal length lens delivers 1/4 the number of photons to each sensor which corresponds exactly the difference in exposure predicted by f/ stops even though their entrance pupils are identical.

Does this make sense to you as to why entrance pupil alone cannot predict exposure or signal to noise ratio without any focal length information?

Exposure doesn't directly determine the total number of photons projected on the sensor or the noise in that signal. This is easily demonstrated by comparing photos made at the same exposure with medium format and smartphone cameras. The much smaller surface area of the smartphone camera sensor will receive much less light than the larger medium format sensor. The smartphone camera lens, while working at the same f-stop, will project much less light from any subject in the frame than a lens mounted to the medium format camera working at the same f-stop. That difference in light transmission is due to the substantial difference in the size of the respective entrance pupils being used.

 

[bleirer]

As @DRwyoming explains it and I've tried.... The OP's examples fall short, notwithstanding debates about the real world variables that it's clear have to be compared to evaluate lens performance...
No free lunches

Real World comparison: compare a 200 f2G Nikkor to a 500 f5.6 PF for photographing wildlife subjects.

What is the advantage of the 11mm wider Window Ф of the 'Fat Man' ?

I don't know the answer, I was hoping Bill would tackle it as an example. How do you know it isn't slightly better to use the f2?

 

[DRwyoming]

Yes, the image of the subject projected by the longer focal length lens will have the same number of photons but, as a result of covering a larger area, will have a lower exposure.

I agree with this statement which is exactly what @SCoombs experiment of side by side images demonstrated that you previously seemed to take issue with.

I also agree it's possible to evaluate lens choices for their light gathering on the basis of entrance pupil but it seems much easier to do so basing on f/ stop as it incorporates both entrance pupil and focal length information and is more easily understood by most photographers.

Again on the exposure issue I may have misunderstood your earlier posts but the statement quoted at the top of this post and Shane's experiment both indicate that subject exposure is not determined by entrance pupil alone and that focal length plays a big role which is why the concept of Relative Aperture or what we call f/ stop originated in the first place.

I understood your point and your push back on Shane's experiment to suggest the f/5.6 lens with the larger entrance pupil would provide higher exposure at the image plane than the smaller entrance pupil f/2.8 lens. If that's not your stance then perhaps we're in agreement. If that is your stance then we've arrived at the agree to disagree point of this conversation.

 

[bcgnz]

I think it makes more sense to compare lenses having the same aperture and different focal lengths to illustrate OP’s point.

A 500mm f/5.6 and an 800mm f/5.6 would collect the same amount of light, and they will achieve the same exposure given the same camera, the same shutter speed, and the same ISO. However, if one were to crop into the 500mm f/5.6, then the effective exposure and noise would be worse compared to the 800 f/5.6. But if you don’t crop, the noise and exposure would be exactly the same, even though their entrance pupil is different.

In this regard, under the same lighting conditions, a particular aperture value will always correspond to the same exposure, regardless of entrance pupil size. This is why sometimes people complain about small aperture in low light situations - there is no way around it. A larger entrance pupil will not be able to somehow improve the exposure in low light while the aperture remains small. A f/2.8 is always brighter than f/5.6 given the same sensor size and ISO - UNLESS YOU CROP THE f/2.8 IMAGE

This goes back to the northern polar bear’s point -buy the focal length you need to fill the frame and the largest aperture you are willing to spend and carry…

 

[bcgnz]

Another way to illustrate OP’s point might be that

Even on a 400mm f2.8, the effective exposure you can achieve on a localized area of the image can be similar to 800mm f5.6, since they have the same entrance pupil. In that regard, the 800mm f5.6 is no worse than the 400mm f2.8 in low light conditions.

The catch here is that while the 400mm f2.8 is able to capture a full scene, the 800mm f5.6 is only able to capture a localized area. If all you want is a particular localized area, then the 800mm f5.6 is equally good in low light.

There is no free lunch. You don’t get to capture the full scene with the 800mm f5.6.

This goes back to the northern polar bear’s point… choose the focal length you need FIRST and then buy the largest aperture you are willing to spend and carry.

Others please correct me if my impressions are wrong. I think the frustrations many have with OP’s point is that he seems to suggest entrance pupil is somehow a more superior and universal metric. But no, choose the focal length FIRST and then get the largest aperture possible. Don’t choose a lens based on entrance pupil alone ever…

Another way to say this is that don’t buy an 800mm f5.6 instead of a 500mm f5.6 just because the 800mm f5.6 has a larger entrance pupil while what you actually need is the 500mm f5.6

 

[SCoombs]

Since I mentioned it previously, let me try to provide an example of the first hand experience that makes me by default inclined to doubt the claim under discussion here.

Here are two shots from a soccer game I photographed this fall. I unfortunately don't have as many good examples of this at various shutter speeds/ISO levels as I would have a week ago as I just went through and cleared out a large number of non-keepers from the past few months and, as one might imagine, photos that turned out poorly due to noise were frequently non-keepers!

Here is a shot taken with my 70-200 f2.8. It was shot at a shutter speed of 1/1600 with a focal length of 150 mm and aperture of f/2.8 yielding an entrance pupil of 53mm. The camera's matrix metering put the auto-ISO at 1800. This photo was cropped in post to 2009*2511 pixels, meaning it was a massive crop throwing away about 89% of the pixels. I have turned off noise reduction before exporting. I think that it doesn't look half bad - certainly good enough for the use case that is usually the end goal of these sorts of photos, and it looks a lot worse here because the forum is displaying it so large compared to how it would normally be used.

You can only see EXIF info for this image if you are logged in.

Now, here is another photo from the same game in the same lighting shot with my 180-600. It was shot with a shutter speed of 1/1250 - so if anything a little bit better light-wise. The matrix metering gave it an auto ISO of 10,000, due in large part to the aperture that was 2 + 1/3 stops darker. It was shot at 340mm and f/6, yielding an entrance pupil of 56mm. It should, according to the entrance pupil method of judging this sort of stuff that we have been discussing, have a very similar and ever so slightly better SNR than the other shot. Now, if I give this one less of a crop, not 89% but only 49% - basically a DX crop - it has, to my eye, slightly worse noise, but I'll admit it's close:

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If I crop this one in to the same size as the first one, the noise is much, much worse, even though if I haven't misunderstood previous comments in the thread cropping to the same size should yield the "correct" comparison:

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So those are two photos, one taken with an entrance pupil of 53, the other of 57, and the one with the slightly larger pupil has MUCH worse noise when we view portions of the photo of the same size.

Here's another, this one also at 1250 SS, ISO 14400, 600mm at f/6.3 for an entrance pupil of 95mm, one which is nearly twice as large as the f/2.8 lens in this case, yet the noise is in this case so much worse that it is noticeable even without cropping to the same dimensions as the f/2.8 shot:

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If I crop this one to the same size as the f/2.8 shot, the noise is obviously much, much worse.

Let's go back to the f/2.8 lens, this one shot with an entrance pupil of 71 (200mm) at 1/600. This one is an especially massive crop: it is only 3.2 MP, having thrown away 93% of the pixels. (I keep choosing extreme crops from the f/2.8 to emphasize the point, by the way)

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Is it noisy? Yes. It's a huge, ridiculous crop, of course. Yet it's still not as noisy as the 600mm yields with a much more reasonable crop. Let's pull this one back to a crop that is similar in size to that 600mm shot above:

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I can't even really tell there's noise anymore. It looks great!

For me, this stuff really overshadows everything else. Ultimately what I care about is how to get the best photo I can of stuff I need or want to get a photo of. I'm not all that concerned with the various intricacies of equivalency, which to me is certainly interesting as far as it goes and I do enjoy reading about it but I still see it as ultimately irrelevant to what I care about since I don't worry about figuring out how to exactly replicate a shot or a look from one camera to the other. I care about getting the best looking photo I can, and over the course of thousands of shots at soccer and other sporting events I have learned from experience that the lens with the larger aperture and the smaller maximum entrance pupil gives me that over the lens with the smaller aperture but the larger entrance pupil.

Now unfortunately the light levels are not 100% consistent here, at least as far as the camera's metering was concerned (really the light didn't change much that day). The second shot here and the first are very close, 1/3 stop apart. That's a difference, but I don't think it's nearly enough to explain the drastic difference in noise.

The biggest outlier here is the worst shot - the third one - which seems to have been a full stop darker based on the settings. The third one is closer. As I said, I'd have had a lot more to choose from to demonstrate this a week ago as there were a ton of shots at perfectly equivalent lighting levels showing the same thing. I still think that some kf these are close enough in lighting and far enough in noise to help illustrate the point.

 

[macwalter]

This is all very interesting but one thing I have have found is how depth of field plays into actual use. An f2.8 focal length is very short and I find often even with a 600mm f6.3 getting the whole bird in focus can be very difficult when trying to get close. For me the main advantage I find with faster glass is the ability to shoot at higher shutter speeds to get action shots and here the f2.8 and f4 are clearly superior to my 600 f6.3. As Steve P said getting a sharp image is more important than how much noise. My fastest lens is the 400 f4.5 and although it is twice as fast as my 600 f6.3 I have to get closer or crop more which tends to negate the image quality except when I find I can shoot fast enough to freeze more of the image. So in lower light I will tend to prefer the 400 f4.5 and try to get closer. Having an exotic 600mm f4 would be a dream come true but is beyond my budget. also it’s a beast to handhold. I would imagine though that the info from the discussion above would help explain why the big glass has better IQ and contrast.