# Iso, noise, extenders, cropping, and 600mm f/6.3 vs 500mm f/5.6 zooms

#### AlanF

##### Canon 5DSR II
Another one of my geek notes that may be of some practical use.

This has been stimulated by discussion in the threads about 600mm f/6.3 vs 500mm f/5.6 telephoto lenses. It is usually thought that the larger f-number of the longer lens means either a slower shutter speed or introducing more noise by having to increase the iso, which is a disadvantage for the longer lens. I’ll show that the 600mm doesn’t suffer from those apparent disadvantages.

I am analysing the situation that is the usual one of using telephoto lenses with the output Images of crops blown up to the same viewing or printing size from different focal lengths and apertures, or from smaller sensors or crops blown up to the same size images from larger sensors.

Crop vs Full-Frame Sensors
Let’s start in our comfort zone with something that most of us do know from practice and maybe as well from theory: the images from smaller sensors are inherently noisier than large ones and have lower dynamic range when viewed at the same image size. The qualitative reason for this is that the image from the smaller sensor has to be enlarged more to give the same size image as from a larger sensor. This amplifies the noise in the image as well as any defects and lowers effective dynamic range.

In terms of physics, there is noise in an image because of fluctuations in the amount of light or number of photons, n, hitting the sensor. From statistics (the Poisson Distribution), the signal to noise (S/N) = sqrt(n). The more the light, the higher sqrt(n) and so the better S/N. We can calculate the difference in number of stops (ev) using logarithm to base 2, log(2), applied to the change in area of sensors. For a crop factor of 1.6 for FF vs APS-C.

Number of stops = log(2)(1.6x1.6) = 1.36ev.

So, all else being equal, a crop APS-C sensor has 1.36 stops more photon noise than full frame. That is equivalent to setting the iso of the crop 2.56x higher in terms of noise (1.6x1.6, and increasing the iso increases noise). Or, we need a lens that is has an f-number 1.36 wider to let in more light to compensate.

A common mistake is to consider just the f-number of the lens as being the only factor that determines the amount of light in an image. The f-number does determine the intensity of light hitting a sensor, but the degree of enlargement of the image from the sensor is another key factor.

Cropping
Cropping, as we know from practice, increases noise in an enlarged image, and it follows the same principles as crop vs FF sensors. We need to work at progressively lower isos to keep noise under control the more we crop.

Using a 1.4x and other Teleconverters
Putting a 1.4xTC on our telephoto increases its focal length by 40% but increases its f-number by one stop. People sometimes complain that using a larger f-number at the same shutter speed means increasing the iso to compensate and so increases the noise. Alternatively, it is thought we can maintain the iso by lowering the shutter speed, but that could be bad. But, increasing the focal length by 40% increases the area of the image by 1.4x1.4 = 2 times. So, we have to blow up the image from lens without the TC 2x in area to be the same size as with the TC. This is equivalent to lowering the iso noise with the TC by = log(2)(2) = 1 stop.

So, double the iso at the same shutter speed when shooting with a 1.4xTC and we will have only the same noise as without the TC and twice the number of pixels on target blown up to viewing size!
Fewer people know that.

500mm f/5.6 vs 600mm f/6.3
Let’s compare the size of images produced. The image of an object from the 600mm is 1.2x1.2 times larger in area. So, the 500mm image has to be enlarged 1.44x in area, which is log(2)(1.44) = 0.53 stops. The image of the 600mm f/6.3 lens is 0.33 stops dimmer than the 500mm f/5.6. However, raising the iso by 0.33 stops when working with it at f/6.3 and the same shutter speed as the 500/5.6 actually gives an improvement in noise 0.53-0.33 stops = 0.2 stops better.

So, all things being equal, shooting the 600mm f/6.3 at the same shutter speed as a 500mm f/5.6 but at 0.33 stops higher iso puts 44% more pixels on target and slightly better noise when viewing images at the same size!

Diffraction effects

Very briefly, the diameter of the 600mm lens is actually slightly larger than that of the 500mm.
Diameter of 600mm f/6.3 entrance pupil = 95.2mm.
Diameter of 500mm f/5.6 entrance pupil = 89.3mm.
This means that when even when fully diffraction limited, the the 600mm gives better resolution. Its Airy disk is 6.3/5.6 = 1.125x larger but the linear separation is 1.2x larger.

In conclusion, I would prefer a 600mm f/6.3 zoom to a 500mm f/5.6. Although, for primes I would prefer the larger field of view of the 500mm, whereas the 600mm zoom can be zoomed out to 500mm or shorter if needed.

Thank you!

mikekeck

Thank you Alan.

mikekeck

#### Jack Douglas

##### CR for the Humour
Alan, are you taking over for Neuro? Haven't seen much from him lately.

I'll believe you since I can't get that engaged in such things but fully appreciate your insights.

One thing that also sometimes gets ignored is that cropping after the fact doesn't allow for the same "in the field" viewing and AF point accuracy. I find it to be very helpful to have my subject as large as possible when I'm focusing and thus prefer having the teleconverter on (assuming I'm not fighting to keep the subject in the viewfinder, such as BIF).

Jack

AlanF

#### slclick

##### 135L
Alan, are you taking over for Neuro? Haven't seen much from him lately.

I'll believe you since I can't get that engaged in such things but fully appreciate your insights.

One thing that also sometimes gets ignored is that cropping after the fact doesn't allow for the same "in the field" viewing and AF point accuracy. I find it to be very helpful to have my subject as large as possible when I'm focusing and thus prefer having the teleconverter on (assuming I'm not fighting to keep the subject in the viewfinder, such as BIF).

Jack
He did jump in to answer a question last week for someone, but yeah, he's been semi-awol.

#### Don Haines

##### Beware of cats with laser eyes!
He did jump in to answer a question last week for someone, but yeah, he's been semi-awol.
Life can get in the way..... here’s hoping that he has found something way more fun and interesting to consume his time.

#### AlanF

##### Canon 5DSR II
Alan, are you taking over for Neuro? Haven't seen much from him lately.

I'll believe you since I can't get that engaged in such things but fully appreciate your insights.

One thing that also sometimes gets ignored is that cropping after the fact doesn't allow for the same "in the field" viewing and AF point accuracy. I find it to be very helpful to have my subject as large as possible when I'm focusing and thus prefer having the teleconverter on (assuming I'm not fighting to keep the subject in the viewfinder, such as BIF).

Jack
No, he knows much more about photography than me and I can't match his turn of phrase. But, I like trying to understand things and, when I do, to share the information. My approach is to think through problems and when I get an analog solution in my mind put the maths around it.

#### Joules

##### EOS 7D MK II
Very nice topic and a well formulated opening post.

Another way to think about it is just in terms of the light that your subject is emitting, how much of that gets through your lens and over how much effective area it is spread out.

Light of the subject is constant, unless the lighting conditions change.

How much gets through the lens depends on the lenses aperture (not the f-number, but the actual hole where light comes through).

And how much it gets spread out effectively is determined by the focal length, the use of TCS or cropping in the same way. For a given light, aperture and shutter speed, all ways of spreading the light will result in the same degree of noise. For cropping the downside is of course a loss of detail, unless your resolution is so high that you are beyond the diffraction limit in each case anyway.

It would be cool to see how the use of big whites and TCS changes once we get to the resolution that are diffraction limited at mist high f-numbers.

Raptors and AlanF

#### Joules

##### EOS 7D MK II
In conclusion, I would prefer a 600mm f/6.3 zoom to a 500mm f/5.6.
I came away with the opposite conclusion in a post in the other thread. Since they are so close in theory, it depends a lot on how the practical implementations look

If it is harder to correct and makes the lens slightly longer to go for 600 mm, I'd prefer a 500 mm. That's mostly just a feeling based on the observation that my Sigma 150-600 mm C performs amazing at 500 mm and slightly less so at 600 mm. That's of course not much to base anything on, but it feels like if they had stopped at 500 mm with that large opening you get at the 600 mm end, the lens could have been a tad lighter (in terms of the momentum it puts in your arm) and just as good optically.

#### AlanF

##### Canon 5DSR II
I came away with the opposite conclusion in a post in the other thread. Since they are so close in theory, it depends a lot on how the practical implementations look

If it is harder to correct and makes the lens slightly longer to go for 600 mm, I'd prefer a 500 mm. That's mostly just a feeling based on the observation that my Sigma 150-600 mm C performs amazing at 500 mm and slightly less so at 600 mm. That's of course not much to base anything on, but it feels like if they had stopped at 500 mm with that large opening you get at the 600 mm end, the lens could have been a tad lighter (in terms of the momentum it puts in your arm) and just as good optically.
True about size - 500mm does have less inertia against rapidly moving. I am not advocating the Sony 200-600mm as I have no intention of buying one but Sony has rewritten the book for IQ quality of 600mm zooms. There is much compelling evidence from reliable posters on sites that the lens is very sharp at 600mm. A couple of reliable review sites that make MTF measurements show that 600mm keeps up the IQ throughout the focal length range.
https://www.pcmag.com/review/368812/sony-fe-200-600mm-f5-6-6-3-g-oss
https://uk.pcmag.com/sony-fe-200-600mm-f5-6-63-g-oss/123501/sony-fe-200-600mm-f56-63-g-oss
And TDP has tested it.

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#### degos

##### EOS RP
The image of an object from the 600mm is 1.2x1.2 times larger in area.
Be careful in attempting to do precise maths with imprecise marketing numbers. Sigma's 600mm 6.3 C is actually 583mm...

However, raising the iso by 0.33 stops when working with it at f/6.3...
No digital camera has linear noise through third-stops. In some cases the noise increase is as much or more as for the next full stop, which is why some photographers disable third-stops.

#### AlanF

##### Canon 5DSR II
Be careful in attempting to do precise maths with imprecise marketing numbers. Sigma's 600mm 6.3 C is actually 583mm...

No digital camera has linear noise through third-stops. In some cases the noise increase is as much or more as for the next full stop, which is why some photographers disable third-stops.
I am discussing general principles and it’s irrelevant that a particular lens has a focal length that is shorter. In fact, it’s not the precision of the focal length that is important, but the the area of the entrance pupil. The 100-400mm II isn’t 400mm either. If the noise is not linear through third stops and a third stop gives more noise than a full stop, the one of the next thirds must lead to no increase in noise or even a decrease. So, it could even be advantageous to increase by a third of a stop by your arguments depending on where you are in the iso curve. Again, I am discussing general principles for good lenses on good bodies.

Joules

#### Jack Douglas

##### CR for the Humour
True about size - 500mm does have less inertia against rapidly moving. I am not advocating the Sony 200-600mm as I have no intention of buying one but Sony has rewritten the book for IQ quality of 600mm zooms. There is much compelling evidence from reliable posters on sites that the lens is very sharp at 600mm. A couple of reliable review sites that make MTF measurements show that 600mm keeps up the IQ throughout the focal length range.
https://www.pcmag.com/review/368812/sony-fe-200-600mm-f5-6-6-3-g-oss
https://uk.pcmag.com/sony-fe-200-600mm-f5-6-63-g-oss/123501/sony-fe-200-600mm-f56-63-g-oss
And TDP has tested it.
Interesting to see the Sony X1.4 and 400 DO II X2 - what's your take on off centre performance? I looked because one of my primary reasons for owning the 400 was X2.

Jack

#### AlanF

##### Canon 5DSR II
Interesting to see the Sony X1.4 and 400 DO II X2 - what's your take on off centre performance? I looked because one of my primary reasons for owning the 400 was X2.

Jack
I suppose you are talking about the Sony +1.4xTC at 840 f/9 vs 400 DO II + 2xTC on the 5DSR at f/8 in

where the Sony is much sharper in the centre. My personal experience with just one copy of the 2xTCIII is that it was fine with larger pixels, like on the 300mm f/2.8 II on the 5DIII, OK on the 5DIV with the 400mm DO II, and only passable on the 5DSR. However, I think this is more general. The Swedish site objektivtest, for example, tested the 1.4x and 2xTC IIIs and found whereas the 1.4x took a small hit of about 10% loss of MTF, the 2xTC took a big hit, ~30%, on the higher resolution APS-C/5DSR sensors. So, I think with your 1DXII the 2x set up is great but your experience might be like mine if you go to a high resolution sensor of preferring to stop at the 1.4xTC. From what I have read, the Nikon 1.4xTC is great but the 2x is meh. However, the Sony looks good. I find the Nikon 1.4xTC on the Nikon 500/5.6 PF to be optically excellent at 700mm. I expect the new Canon RF extenders to be first rate.

#### Jack Douglas

##### CR for the Humour
Thanks Alan. Exactly what I was looking for. I can't see me at this point in my existence springing for another very expensive long RF lens but if it were exceptional, I might. I'm leaning towards the R5 but once a person has spent time with a 1D it might be tough to accept some missing features. In other words I'm not too secure in my impending decisions right now. I haven't been helped by my upgrade to a 32" 4K monitor!

I'll add that my photos tolerate more sharpening than I would have expected with the 400 X2 and I guess if the detail is there with the 1DX2, this is to be expected but won't hold true with higher resolution cameras. Here we go again; more compromises.

Jack

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