What is equivalence? If you haven’t heard of this term used in photography before then don’t bother; you didn’t miss anything. (Part two is here)
If you are curious though, it simply means that different formats or sensor sizes require different settings in order to produce “the same” or equivalent images. Usually, equivalence proponents use the 35mm full frame sensor as the “reference standard”. For example, for a m43 sensor and full frame sensor to have the same angle of view (AoV), the m43 will have to use a 25mm lens and the full frame a 50mm lens because the m43 sensor is smaller; four times smaller to be exact. It doesn’t end there. Since a 25mm lens has a shorter focal length compared to a 50mm there will be differences in depth of field (DoF). The shorter 25mm will have to shoot at f/4 to get the same DoF as a 50mm at f/8.
There are other “parameters” involved in this “equivalence”. For more details, refer to this article in dpreview: http://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care
That dpreview article is funnily entitled “What is equivalence and why should I care”. Should you really care about equivalence? Most photographers don’t care about equivalence. Real photographers’ shooting techniques vary depending on the camera that they brought with them. Give a photographer a mobile phone and he will capture fantastic images without pretending that he is carrying a DSLR. I own a mobile phone, several point-and-shoot cameras, a few m43’s, an APS-C and full frame cameras. I know exactly what each one of them are capable of doing and I shoot accordingly. I don’t expect shallow DoF with my iPhone so every time I shoot portraits with it I need to be careful that the background does not distract from the main subject. Here is an example of how you can capture professional-looking portraits with a simple iPhone 3GS: https://fstoppers.com/editorial/iphone-fashion-shoot-lee-morris-6173.
Bottom line is, gear does not matter. If gear does not matter, equivalence does not matter.
But let’s not stop there. There is more to that equivalence article. To be precise, there are a lot of incorrect information in that article that are very misleading if you are not careful. The biggest misinformation that equivalence proponents spread in forums is that of “total light captured”. I will try to debunk equivalence in the next few paragraphs.
For the sake of example, let’s compare a m43 and a full frame (FF) sensor. By now you should already be aware that a FF sensor is four times larger than a m43 sensor. The m43 crop factor is therefore 2x. It follows that to shoot “the same image” we will have to use different lenses and use different f-stops like so:
m43: 25mm at f/5.6
FF: 50mm at f/11
This will result in the same AoV and DoF. Now what about the rest of the exposure triangle? This is where equivalence-fu starts becoming really stupid. The proponents insist that you could use the same shutter speed for both m43 and FF and still arrive at the same image. They insist that the same shutter speed must be used so that both images will result in the same “blurring” due to subject motion (ROFL!!!). The example above then becomes:
m43: 25mm, f/5.6, 1/125s
FF: 50mm, f/11, 1/125s
Wait, doesn’t that underexpose the FF image? Indeed it does. By two stops, to be exact! Didn’t I say it was stupid? In what world do two images, two stops apart, are considered “the same”? One is obviously darker. Much darker. Equivalence proponents must have something up their sleeves 🙂 You probably guessed it already. They say that you can bump up the ISO of the full frame shot so that it will be of the same brightness as the m43 shot! So now the example becomes:
m43: 25mm, f/5.6, 1/125s, ISO 100
FF: 50mm, f/11, 1/125s, ISO 400
Seriously?!!! Let’s be very clear about this. Bumping up the ISO does not increase light. ISO has absolutely no effect on exposure. Learn about that here. So why do you think that equivalence-fu proponents are suggesting that this ISO bump will make both images equivalent? Their reasoning is quite simple and stupid: because both sensors have gathered “the same total amount of light”!!! Recall that each stop of exposure means twice the amount of light. Since a m43 sensor is four times smaller than a FF sensor it means that underexposing the FF by two stops (4x amount of light) will still result in the same TOTAL light captured by each sensor. If that isn’t stupid then I don’t know what is.
Let’s discuss this further by using a simple experiment. Supposing that we have a m43 camera and we shoot a scene using a 25mm lens. We can produce a full frame equivalent image of the same scene with the same AoV using the same m43 camera by stitching four shots from a 50mm lens. Refer to the illustration below:
As you can see, the smaller single shot image captured with a 25mm lens will look exactly the same as the larger stitched image which is equivalent to what a full frame sensor would have captured. The narrower AoV of the 50mm lens means that we need four shots stitched side by side to arrive at the same AoV as the 25mm shot. Again, this shows that a FF sensor is four times larger than a m43 sensor. Same AoV, same DoF but different image sizes due to the different sensor sizes.
Now let’s be stupid for a while and assume that equivalence is correct 🙂 In order for the single shot image and the stitched image to have the same total amount of captured light, we will have to underexpose by two stops, each of the four individual shots that we used to stitch the larger image. Since these four images are now much darker we will have to bump their ISO by two stops to arrive at the same brightness as the single shot image. At this point, we now have two “equivalent” images: the smaller, properly exposed m43 image and a larger full frame image that was produced by stitching four underexposed m43 shots.
Common sense will tell you that the larger stitched image is every bit inferior to the single shot image. Two stops inferior to be exact. If you sample a quarter chunk of that larger image it will always turn out much worse than the reference m43 shot. Take a quarter chunk from the top, bottom , sides, or center and every single one of them will look much much inferior to the original properly exposed m43 shot. We can therefore say that the larger image is inherently much inferior compared to the single shot m43 image. So how can equivalence proponents honestly say that the underexposed FF shot is “the same” as a properly exposed m43 shot? You don’t need half a brain to realise that this is plainly stupid.
The stupidity does not stop here though. The equivalence-fu followers have something else to support their “theory”. They suggest that if you print or view the smaller properly exposed m43 image and the larger severely underexposed FF image at the same size, they will look exactly the same. Well maybe they would look the same up to a certain extent. Recall that when you view or print an image at a smaller size than its original size then the effects of downsampling will take effect and will result in a lesser perceived noise: https://dtmateojr.wordpress.com/2014/05/19/megapixel-hallucinations/. This, however, has absolutely got nothing to do with light gathering. As we have shown in our example, the underexposed FF image is much much darker than the reference m43 image if it were not for the ISO bump. Equivalence proponents are using image size to circumvent the destructive effects of underexposure and they think that image size and light are one and the same. Image size has got nothing to do with light. A 41Mp Nokia phone camera has a larger image size compared to a full frame 36Mp D800 although the former has much much lesser total amount of light captured. This is why if you are not careful these equivalence-fu “photographers” will easily mislead you.
Let’s take this circus show to a higher level. Assume that total light and image size are equivalent and related. In that case, we could, in a sense NOT increase the ISO of the underexposed full frame image but instead downsample it to the same size as the m43 image and they should result in the same brightness, right? Simply because the same total amount of light has now been projected into the same image area which should result in the same exposure (total light over total area). But we know that this doesn’t work because downsampling or upsampling has no relationship to total light and that is why the downsampled FF image remains two stops darker. So how could equivalence proponents honestly equate total light and image size? :-O
So now we know that equivalence-fu relies on resampling to work around underexposure. Does this always work? No, it doesn’t. If you recall the discussion in the “Understanding Exposure” article that was linked above, bumping up the ISO does not increase light. It only increases gain. The analogy was that of the process of boiling water. Increasing ISO is like boiling water. Boiling pushes water to the top of the container but it does not increase the amount of water. If you underexpose, you will come to a point where there is no more light being captured. It’s like a container with no water. Bumping the ISO or boiling a container that does not contain water does absolutely nothing. Image noise is more pronounced in darker areas. Underexposure will only worsen the noise in those darker areas. When you have no signal, there is nothing to resample. Downsampling will not always save you.
The nasty effects of bumping up the ISO can not be ignored. Increasing the ISO will also result in hot pixels, banding and other nasty artifacts. Why do you think are cameras limited by how high you can set the ISO sensitivity? Why can’t we not bump the ISO indefinitely? Because the truth is, high ISO sucks regardless of sensor size. Imagine an ISO 6400 shot from a m43 Olympus E-M5 compared to an ISO 25600 shot from a full frame Nikon D800. How much worse does it get if you now compare a point-and-shoot camera with 5x crop factor to that D800. Five stops underexposure is A LOT and really bad. I mean really, try underexposing a night shot on your D800 by 5 stops then bump it up in Photoshop. Crash and burn baby!
If you think that’s bad then consider shooting with slide film. How big is a sheet of film for a 8×10 view camera compared to a measly 35mm camera? For the sake of argument let’s just say that the size difference is 5x. Do you really believe that if I shoot Fuji Velvia on 35mm and then I underexpose Velvia on the 8×10 camera by five stops and push it during development that the images will look “the same”? If this was negative film then maybe you can get away with it but don’t even attempt that kind of circus act with slide film. Slide film is very unforgiving when it comes to exposure. Five stops is almost the entire usable dynamic range of slide film!!! If a photographic “theory” fails miserably with film then that “theory” is simply wrong. In the case of equivalence, it’s bullshit, plain and simple.
So to answer that dpreview article’s question: “should you care about equivalence?”. Not if it’s wrong and stupid.
I can’t believe that people keep on spreading this nonsense. Here’s another funny equivalence-fu fauxtographer: equivalence for embeciles
Examine his illustration on the effect of different apertures f/8 and f/4. He is totally oblivious to the effect of focal length on light intensity. Note that although f/8 and f/4 here have the same physical aperture size, the longer focal length of the f/8 lens causes the light to be projected much wider into the sensor. The net effect is that each sensel behind the longer f/8 lens receives much lesser number of photons than the sensels behind the shorter f/4 lens. The result is underexposure which is seen as a darker image. Two stops (or 4x light) of underexposure to be exact. This obviously corresponds to noisier sensel output and therefore noisier image.
How can two images with different exposures be equivalent?! Such an idiotic explanation is the result of the epic failure to understand very basic photography. Exposure is totally independent of sensor size. The same f-stop results in the same total number of photons per sensel regardless of imaging format. Always. Same f-stop means same exposure meaning the same brightness.