Effective focal length of some telephotos

[AlanF]

A current thread on the resolving power of lenses has got me thinking about how to compare the resolution of lenses using MTFs in terms of line pairs. Here is an attempt to rationalise this, which may be wrong. So, if it is wrong or it is of any use, please comment. The basic idea is to use the data that the Photozone and lenstip sites give for the maximum resolution of a lens and the observed resolution at different f-stops in terms of line pairs.

We know that if you get closer to a subject, you get better resolution. From simple optical theory, the resolution depends upon (1/distance) from the subject because the size of the image depends on 1/distance. If you are at half the distance, the image will be twice the size and you have effectively doubled the resolution of the lens. So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens. So, I calculated the ratio of observed/maximum for different lenses and multiplied the ratio by the stated focal length. This then gives the effective telephoto length. In the following Table, the effective focal length is the distance you would have to stand from the subject to get the resolution stated by the manufacturer. OK, I know there are caveats depending on AA filters, breathing, stated focal lengths being an exaggeration etc, but there some interesting trends.

Lens focal length f number Effective focal length (mm)

400L 400 5.6 324
400L 400 8.0 330
100-400L 400 5.6 325
100-400L 400 8.0 330

300L f/4 300 4.0 235
300L f/4 300 5.6 254
300 f/4L+1.4xTC 420 5.6 265
300 f/4L+1.4xTC 420 8.0 273

300 f/2.8 II 300 2.8 282
300 f/2.8 II 300 4.0 293

Sigma 150-500 370 6.3 257
Sigma 150-500 370 8.0 265
Sigma 150-500 370 11.0 273
Sigma 150-500 500 6.3 261
Sigma 150-500 500 8.0 299
Sigma 150-500 500 11.0 315

The Sigma at 500mm gives only the resolution of a 300mm lens. Adding a 1.4xTC to the 300mm f/4 gives only an effective 1.1xTC. The 400L and 100-400L are equivalent to a perfect 330mm lens.

The agreement between lenstip data and photozone was pretty for overlaps - I used a maximum of 46 for the lenstip data.

 

[ajfotofilmagem]

Re: Effrective focal length of some telephotos

I swear I tried to understand its concept but could not. First, the concept of "perfect lens" that definitely does not exist in the real world. The comparison of a lens distance "y", and half "y". A comparison of lenses is only fair comparing the size of the object in the picture (magnification) equal. Attempts to compare a photo with distance "X" with another that has the double distance "X" does not seem really valid.

 

[AlanF]

Re: Effrective focal length of some telephotos

I swear I tried to understand its concept but could not. First, the concept of "perfect lens" that definitely does not exist in the real world. The comparison of a lens distance "y", and half "y". A comparison of lenses is only fair comparing the size of the object in the picture (magnification) equal. Attempts to compare a photo with distance "X" with another that has the double distance "X" does not seem really valid.

We all know that there is no such thing as a "perfect" lens. But, lenses like the 300mm f/2.8 II come pretty close to it. Indeed, at f/4 lenstip measured its resolution to be 97.8% of the maximum (which fits in with Canon's MTF charts). All such calculations require some degree of approximation, and saying 97.8% is close enough to 100% for the calculations is good enough for me. If you want 100.000000%, then read no further.

It is perfectly valid to compare lenses at different distances. All we are asking is: if a (near) perfect lens can only just resolve 2 lines which are at, say for an argument, 1 mm apart, how close do you have to get with a less good lens to resolve them? From my simple calculations, if you are standing 293 metres from the subject with a 300mm f/2.8 II lens at f/4, you would need to stand at 235 metres away with the 300mm f/4L lens to capture the same detail

 

[ajfotofilmagem]

Re: Effrective focal length of some telephotos

I swear I tried to understand its concept but could not. First, the concept of "perfect lens" that definitely does not exist in the real world. The comparison of a lens distance "y", and half "y". A comparison of lenses is only fair comparing the size of the object in the picture (magnification) equal. Attempts to compare a photo with distance "X" with another that has the double distance "X" does not seem really valid.

We all know that there is no such thing as a "perfect" lens. But, lenses like the 300mm f/2.8 II come pretty close to it. Indeed, at f/4 lenstip measured its resolution to be 97.8% of the maximum (which fits in with Canon's MTF charts). All such calculations require some degree of approximation, and saying 97.8% is close enough to 100% for the calculations is good enough for me. If you want 100.000000%, then read no further.

It is perfectly valid to compare lenses at different distances. All we are asking is: if a (near) perfect lens can only just resolve 2 lines which are at, say for an argument, 1 mm apart, how close do you have to get with a less good lens to resolve them? From my simple calculations, if you are standing 293 metres from the subject with a 300mm f/2.8 II lens at f/4, you would need to stand at 235 metres away with the 300mm f/4L lens to capture the same detail

Now I understand your argument. If you use a lens with very high spatial resolution, can then apply more crop because it has more clarity than other lens sharpness reasonable. It makes sense to some extent, but in actual use photographed with tele lens because we can not or do not want to walk up close to the object. It is similar to a decision between optical zoom and digital zoom.

 

[takesome1]

Re: Effrective focal length of some telephotos

While it was somewhat interesting to read I do not think you are on to anything.
If anything it could possibly mislead someone.

I say this because I know that the 300mm f/2.8L II with or without a 1.4x III is (300mm f/2.8 II> all other lenses listed).

 

[AlanF]

Re: Effrective focal length of some telephotos


Now I understand your argument. If you use a lens with very high spatial resolution, can then apply more crop because it has more clarity than other lens sharpness reasonable. It makes sense to some extent, but in actual use photographed with tele lens because we can not or do not want to walk up close to the object. It is similar to a decision between optical zoom and digital zoom.
[/quote]

I think it tells you more than that. For example, the Sigma 150-500mm at 500mm and f/6.3 on a 5DIII will have no significantly better resolution of a distant object than the 300mm f/4L at f/5.6 on a 5DIII of the guy standing next to you.

 

[AlanF]

Re: Effrective focal length of some telephotos

While it was somewhat interesting to read I do not think you are on to anything.
If anything it could possibly mislead someone.

I say this because I know that the 300mm f/2.8L II with or without a 1.4x III is (300mm f/2.8 II> all other lenses listed).

Please explain the last sentence as it makes no sense to me.

 

[takesome1]

Re: Effrective focal length of some telephotos

While I understand what you are trying to show with your chart, it does not reflect the true quality of the lens.
If you look at the effective focal length numbers you displayed it gives you an illusion that these other lenses may be closer in quality to the 300mm f/2.8L II than they really are.

I suppose you could re arrange the chart to have equal comparisons. Same aperture at the same focal length.

Still, given all of the long lenses you listed which do you go with?

 

[Loswr]

Re: Effrective focal length of some telephotos

I think it tells you more than that. For example, the Sigma 150-500mm at 500mm and f/6.3 on a 5DIII will have no significantly better resolution of a distant object than the 300mm f/4L at f/5.6 on a 5DIII of the guy standing next to you.

The ratio of the effective FL to the actual FL seems analogous to DxOMark's P-Mpix measurement, basically showing the decrement from the theoretical maxmium.

 

[chromophore]

Here's the problem with this type of measurement, and why we do not quantify the resolving power of a lens in this fashion: the data is right-censored at the Nyquist frequency for a given sensor-lens combination, so inverting it in this way would result in some error. It would, as you inadvertently have done, lead to the erroneous statement that a lens with half the resolution of a "perfect" lens would resolve the same if it were twice as close to the subject. This is not actually the case, because the highest observable spatial frequency from the perfect lens is determined by the sensor, not by the lens itself.

Furthermore, consider that resolving power as a function of subject distance is itself not constant in real-world lenses, and that this even can change with image height.

 

[Pi]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

OK, I know there are caveats depending on AA filters, breathing, stated focal lengths being an exaggeration etc, but there some interesting trends.

Also, depends on the mp count and on the MTF value. Which makes it pretty much useless, as way to characterize a lens vs. a lens+body at a given MTF value.

 

[AlanF]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

OK, I know there are caveats depending on AA filters, breathing, stated focal lengths being an exaggeration etc, but there some interesting trends.

Also, depends on the mp count and on the MTF value. Which makes it pretty much useless, as way to characterize a lens vs. a lens+body at a given MTF value.

A perfect lens does not have infinite resolution - read about Abbe's law - http://en.wikipedia.org/wiki/Diffraction-limited_system. The wave nature of light dictates that resolution is limited by the size of the Airey disk - see http://en.wikipedia.org/wiki/Airy_disk. Infinite resolution would require that the f number is 0 - ie the lens has an infinite diameter.

 

[AlanF]

Re: Effrective focal length of some telephotos

While I understand what you are trying to show with your chart, it does not reflect the true quality of the lens.
If you look at the effective focal length numbers you displayed it gives you an illusion that these other lenses may be closer in quality to the 300mm f/2.8L II than they really are.

I suppose you could re arrange the chart to have equal comparisons. Same aperture at the same focal length.

Still, given all of the long lenses you listed which do you go with?

It should not be an illusion: the third column gives the nominal focal length, the last column the effective focal length. I go with the 300mm f/2.8 II since its nominal focal length is 300mm and the 0.978 MTF means the effective focal length is very close to 300mm at 293mm.

 

[AlanF]

Here's the problem with this type of measurement, and why we do not quantify the resolving power of a lens in this fashion: the data is right-censored at the Nyquist frequency for a given sensor-lens combination, so inverting it in this way would result in some error. It would, as you inadvertently have done, lead to the erroneous statement that a lens with half the resolution of a "perfect" lens would resolve the same if it were twice as close to the subject. This is not actually the case, because the highest observable spatial frequency from the perfect lens is determined by the sensor, not by the lens itself.

Furthermore, consider that resolving power as a function of subject distance is itself not constant in real-world lenses, and that this even can change with image height.

You are absolutely right that the sensor also determines the resolving power. According to the Nyquist limit, in practical terms a pair of lines (1 black and 1 white) would have to span at least 2 pixels to be resolved. So, if a good lens like the 300mm f/2.8 would produce a suitable image at say 293 metres distance, a poorer lens would blur the image of the pair so that they invade each others pixel. So, if the resolution is 25% less than that of the 300mm f/2.8, the target pair of lines would have to be at ~75% of the distance away to compensate for the broadening of the width of each line by blurring.

 

[Loswr]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

A perfect lens does not have infinite resolution - read about Abbe's law - http://en.wikipedia.org/wiki/Diffraction-limited_system. The wave nature of light dictates that resolution is limited by the size of the Airey disk - see http://en.wikipedia.org/wiki/Airy_disk. Infinite resolution would require that the f number is 0 - ie the lens has an infinite diameter.

+1

Perhaps Pi's judgement was clouded by his fondness irrational numbers, and other things that are infinite.

 

[AlanF]

Re: Effrective focal length of some telephotos

I think it tells you more than that. For example, the Sigma 150-500mm at 500mm and f/6.3 on a 5DIII will have no significantly better resolution of a distant object than the 300mm f/4L at f/5.6 on a 5DIII of the guy standing next to you.

The ratio of the effective FL to the actual FL seems analogous to DxOMark's P-Mpix measurement, basically showing the decrement from the theoretical maxmium.

Thanks Neuro. I have checked it out on the DxO site and it does appear analogous. There is a difference in that my measure is a linear relationship for resolution. The Dx0 does it in area using Mpix, which varies as linear squared, so the two scales should be related by my scale = sqrt((P-Mpix)lens1/(P-Mpix)Lens2)). The data are there for the 300mm f/4L (13 P-Mpix) and the 300mm f/2.8 II (21 P-Mix) on the 5DII on the DxO site. Sqrt of 13/21 = 0.79. My scale gives 235/282 = 0.83, which is pretty good agreement.

Yippee - there is something in my calculations!

ps - just checked again for data on the 5DIII, the DxO ratio is 15/22, the square root of which is 0.83, even better agreement. All of these numbers are the same within experimental error and rounding off.

 

[Don Haines]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

I think I will wait for the Mark II perfect lens which should have more than infinite resolution

 

[AlanF]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

I think I will wait for the Mark II perfect lens which should have more than infinite resolution

It will be fitted to the 7DII

 

[AlanF]

So, if you have a lens that has half the the resolution of a perfect lens, then if you stand at half the distance away as you would with a perfect lens, you would obtain the same resolution as would the perfect lens.

A perfect lens has infinite resolution, and half of it it is still infinity.

A perfect lens does not have infinite resolution - read about Abbe's law - http://en.wikipedia.org/wiki/Diffraction-limited_system. The wave nature of light dictates that resolution is limited by the size of the Airey disk - see http://en.wikipedia.org/wiki/Airy_disk. Infinite resolution would require that the f number is 0 - ie the lens has an infinite diameter.

+1

Perhaps Pi's judgement was clouded by his fondness irrational numbers, and other things that are infinite.

An equation that I always find remarkable is e^(iπ) = -1, where e is irrational, as is π(pi), and i is an imaginary number, the square root of -1.

 

[Pi]

A perfect lens does not have infinite resolution - read about Abbe's law - http://en.wikipedia.org/wiki/Diffraction-limited_system. The wave nature of light dictates that resolution is limited by the size of the Airey disk - see http://en.wikipedia.org/wiki/Airy_disk. Infinite resolution would require that the f number is 0 - ie the lens has an infinite diameter.

I never said that a perfect lens exists. A perfect lens is an abstraction.