Equivalent Focal-Length, Aperture and Speed of Camera Systems
Lens Reviews -
Over the last few years we have received several messages asking about and disputing the system equivalence that we are mentioning in our APS-C and Micro-Four-Thirds lens reviews. For the sake of efficiency, it was about time to write an article about it. This will surely not end the discussions but it illustrates our view on this - take it or leave it.
This article is NOT an article promoting full format cameras. In fact, I am not using full format cameras by choice whenever I can. All systems compromise on something (size/weight/image quality/handling)- the important thing is that a system is right for YOU. YOUR preferences are the only ones that matter to YOU. I mention the obvious here because some people are really getting religiously defensive when it comes to a discussion about system equivalence.
Before diving into the details let's make a clear statement first - the focal length and aperture are static physical values. Citing Wikipedia:
Focal length: The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus.
Aperture: In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are. The lens aperture is usually specified as an f-number, the ratio of focal length to effective aperture diameter.
No matter what we are going to discuss below - the focal length and aperture of a lens isn't going so change. e.g. a 50mm f/1.8 lens is a 50mm f/1.8 is a 50mm f/1.8 lens. Whatever we mention in our review, these physical characteristics are NEVER disputed.
Now the problem is ... you don't take images with a lens. A naked lens is nothing more than an expensive paperweight. A lens makes only sense in the context of a camera and THIS is where things are getting complicated when comparing different SYSTEMS. Equivalence is a SYSTEM discussion, not only a lens discussion.
For the sake of simplicity let's pick a concrete example that we'll use throughout this article:
a full format (35mm) camera with a 300mm f/5.6 lens
an APS-C format camera with a 200mm f/4 lens
a Micro-Four-Thirds camera with a 150mm f/2.8 lens
Some of you may already shout in agony but let's swallow this for now ... :-)
Equivalent Focal Length
This is probably the least disputed topic of the whole discussion. The equivalent focal length relates to the crop factor of a smaller sensor relative to a full format sensor.
(*) It is actually slightly less than that in real systems (e.g. 23.5x15.6mm on Nikon, 22.5x15.0mm on Canon)
(vs Full format)
|APS-C||24x16mm (*)||ca. 1.5x (**)||3:2|
(**) It is more like 1.55x to 1.6x in real systems
Simplistically the crop factor is just the ratio between the sensor width (or height) of a system relative to the full format (e.g. 36mm / 24mm = 1.5x for APS-C). Now you may notice that this is actually not so easy for Micro-Four-Thirds because the image ratio is different (4:3 vs 3:2). Most observers have settled for the 2x crop factor here (you can argue between 1.84x to 2.08x depending on how you look at it).
In order to compare the different focal lengths, we have to take crop factor and multiply it with the focal length:
Or we can phrase it differently - when using a smaller format, we have to use the same FOCUS DISTANCE using a SHORTER focal length in order to achieve the SAME FIELD OF VIEW in the final image (camera output) because only a crop of the full format image field is used. Which leads us to the next topic ...
Equivalent Aperture (Depth-of-Field)
Ok, so the above was (hopefully) easy ... let's move on to the equivalent aperture (depth-of-field) which is where the pain starts for some ... ;-)
CLICK HERE to open a depth-of-field calculator.
Enter the specs that we have discusses so far and a focus distance of 10m (could be any):
a full format camera (e.g. Canon EOS 5D III), 300mm f/5.6
an APS-C format camera (e.g. Fuji X-T1), 200mm f/4
a Micro-Four-Thirds camera (e.g. Olympus E-M1), 150mm f/2.8
Then observe the depth-of-field result - it is the SAME. Again, the FIELD-OF-VIEW is IDENTICAL here. Below is a summary:
(*) This value varies a bit because APS-C format sensors are not sized to the ideal 24x16mm. The calculator is also rounding a bit. Also APS-C f/4 * 1.5x = f/6 and not f/5.6. These are still tiny error margins in the grand picture really.
So despite having used a bigger physical aperture, the DEPTH-OF-FIELD is the same. Why? Because you have to use a shorter focal length to achieve the same result. So a 150mm f/2.8 (on MFT) is equivalent to a 200mm f/4 (on APS-C) is equivalent to a 300mm f/5.6 (on FF). Thus the equivalent full format aperture in our example is therefore ... f/5.6.
Note: This calculator simplifies things a bit - the so-called "circle-of-confusion" is kept constant across all systems here.
||Physical Focal Length
The next toad to swallow (one more to come thereafter) is speed. Some may argue that the 150mm f/2.8 (MFT) and 200mm f/4 (APS-C) are faster than the 300mm f/5.6 full format lens. Well, this is true for the naked lens but it is actually a debatable observation when comparing the SAME OUTPUT QUALITY - that is by taking the camera into the equation again.
Let's assume that we have 3 different system cameras with 20 megapixels at ISO 200. I think we can agree on the fact that the image noise is best on the full format camera, followed by APS-C followed by Micro-Four-Thirds, right? Now ... what amount of increased image noise are we talking about here? There are, of course, variations due to different sensor technologies but let's assume for a moment that they all rely on the same ingredients. So ? Well, ISO 800 on full format will give you roughly the same image noise as ISO 400 (more like ISO 340 actually) on APS-C and ISO 200 on Micro-Four-Thirds. Or in other words - based on the same output quality - and this is the only thing that counts - full format has a 2 f-stops advantage over Micro-Four-Thirds and roughly 1 f-stop over APS-C.
Thus ... assuming the SAME OUTPUT QUALITY (same megapixels, same sensor noise) the SYSTEM SPEED is identical for a 300mm f/5.6 on a full format camera, a 200mm f/4 on an APS-C camera and a 150mm f/2.8 on Micro-Four-Thirds. You may argue that image stabilization plays a role but then just take e.g. the Sony A7 II as an example - thus a full format camera which can take advantage of in-body IS plus in-lens IS. Whatever you can do in a smaller format is technically achievable in a bigger format. Current advantages are just a snapshot in time - eventually all systems will pick up new technologies and catch up (or they disappear as Darwin told us).
Wonna have a visual here? Try the comparometer over at dpreview. If you click the link it'll give you a new window showing a comparison between the Nikon D750 (full format, 24 megapixel Sony sensor) and the Nikon D7200 (APS-C, 24 megapixel Sony sensor). Select RAW & ISO 3200 for the D750 and RAW & ISO 1600 for the D7200 (or ISO 6400 vs ISO 3200). Observe the image noise. Result: pretty much identical thus a 1 f-stop advantage for the full format camera here.
Very often you can read that smaller sensor systems give you a substantial size advantage. But keeping the discussion above in mind ... is that actually true? Of course, there'll be many variations depending on the specific comparison (and e.g. whether a lens has been underdesigned or not) but let's pick one:
||Equivalent to ...
|Full Format||Sony FE 70-300mm 4.5-5.6 G OSS||70-300mm f/4.5-5.6||84x143.5mm||875g|
|APS-C||Pentax DA 60-250mm f/4 ED SDM||"90-380mm f/5.6" |
|Micro-Four-Thirds||Olympus M.Zuiko 40-150mm f/2.8 ED||"80-300mm f/5.6"||79.4x160mm||760g |
(w/o tripod collar)
The Pentax lens doesn't really fit there but I couldn't find a more appropriate APS-C example. The Pentax lens is longer but then the equivalent aperture is f/6.2 if we are precise there (f/4 * 1.55 = f/6.2).
Well? Ok, the Sony lens is a little heavier but the Olympus lens is actually a bit longer. We have to take off the tripod mount in case of Pentax - thus 100g or so. However, you may notice that the difference is not huge - it's certainly not a factor of 2 (MFT vs FF).
Another one maybe?
||Equivalent to ...
|Full Format||Sony FE 35mm f/2.8||35mm f/2.8||37x62mm||120g|
|APS-C||Fujinon 23mm f/2||"35mm f/2.8" (f/3.1)||51.9x60mm||180g|
|Micro-Four-Thirds||Leica DG 15mm f/1.7||"30mm f/3.4"||36x58mm||115g|
Surprising, isn't it? Not really. Why? Well, because in order to achieve the same output characteristic in the final image, you have to increase the physical aperture correlated to the smaller sensor. Bigger aperture = bigger glass = higher weight.
Let's do a quick calculation just for fun - a bit more precise this time (for equivalent lenses):
Full format: 50mm f/2.8
APS-C: 32mm f/1.8 (using 1.55x now)
MFT: 25mm f/1.4
What is the diameter of the aperture in mm? 17.8mm ... in all three cases. Now if we assume an idealized lens ... what does this mean ? Right ... :-)
||Equivalent to ...
|Full Format||Sony FE 28-70mm 3.5-5.6 OSS||28-70mm 3.5-5.6||72.5x83mm||295g|
|APS-C||Pentax DA 16-45mm f/4||"24-70mm f/5.6" (f/6.2)||72x92mm||365g|
|Micro-Four-Thirds||Panasonic 12-35mm f/2.8 OIS||"24-70mm f/5.6"||68x74mm||305g|
Closing note ...
So by now I'm sure many people are upset ... ;-). However, you know what? Is the above actually important? Let's take a last example - e.g. Micro-Four-Thirds offers a Leica 100-400mm f/4-6.3 OIS - is such a lens (size/weight) available in full format ? No, it isn't. There are numerous examples like this one. Smaller formats tend to give up some speed for providing smaller, light-weight lenses. YOU have to find the right balance in the grand scheme of things. I, for one, will not carry a full format system around the Himalayas nor will I take family pictures with a heavy 70-200mm f/2.8 full format lens. But this is me. Your mileage may vary and that's Ok for the world.