Tag Archives: equivalence

Debunking the Myth of Full Frame Superiority (Again)

 

FFvAPSC

Equivalence does not prove the superiority of full frame (FF) over crop sensor (APS-C, M43) cameras. In fact, equivalence shows that equivalent photos are equivalent in terms of angle of view, depth of field, motion blurring, brightness, etc…including QUALITY. Yes, equivalent photos are equivalent in quality.

Refer to the illustration above where we have a full frame lens (BLUE) on a full frame sensor (GREEN). Some full frame sensors are now capable of shooting in crop mode (APS-C) where only the area in RED is used. When a crop sensor LENS is used on a full frame sensor, only the area in RED is illuminated and the rest of the areas in GREEN are in complete darkness and therefore do not contribute to light gathering. This is also true when the full frame is forced to shoot in crop mode with a full frame lens; the camera automatically crops the image to the area in RED and the rest of the areas in GREEN are thrown away.

As per the illustration above, we can see that the central half of the full frame sensor is really just an APS-C sensor. If indeed, a crop sensor is inferior in terms of light gathering then logic will tell us that every center of a full frame shot will be noisier than the rest of the frame. We know this is not true. The light coming in from the lens spreads evenly throughout the entire frame. Total light is spread over total area. As a matter of fact, the central half is the cleanest because lenses are not perfect and become worse as you move away from the center.

Now suppose we have a full frame 50mm lens in front of a full frame sensor. Notice that the crop mode area (RED) does not capture the entire image that is projected by the 50mm lens. The angle of view is narrower than full frame (GREEN). There are several ways we can capture the entire 50mm view while using crop mode:

  1. move backward
  2. use a wider lens (approx 35mm)

Both methods allow the RED area to capture more of the scene. A wider scene means more light is gathered. It means that if we force the RED area (APS-C) to capture exactly the same image as the GREEN area (FF) we will be forced to capture more light! More light means less noise! In equivalent images, APS-C is actually cleaner than full frame!!!

For example, if we go with option #2 using a wider lens, equivalent photos would be something like this:

RED (APS-C): 35mm, 1/125, f/5.6, ISO 100
GREEN (FF): 50mm, 1/125, f/8, ISO 200

This is exactly what the equivalence theory proposes. The difference in f-stop is to ensure that they have the same depth of field given the same distance to subject. The faster f-stop for APS-C (f/5.6) guarantees that TWICE more light is gathered. Notice that the full frame is now forced to shoot at a higher ISO to compensate for the lesser light coming in due to a narrower aperture given by f/8. So if we are to use the same camera for both shots, say, a Nikon D810 to shoot in normal mode with a 50mm lens and in crop mode using a 35mm lens, the crop mode image will be noticeably better. In equivalent photos, crop mode comes out one stop better. In equivalent photos, the smaller sensor results in BETTER quality!!!

The story does not end here though. The full frame shot has twice the area of the crop mode shot. If both images are printed at the same size, the crop mode shot will need to be enlarged more than the full frame shot. Enlargement results in loss of quality and the full frame image will have an advantage over the crop mode image. Whatever the crop mode shot gained by the increase in gathered light is lost by a proportional amount during enlargement. In the end, both full frame and crop mode shots result in exactly THE SAME print quality!!!

Bottomline, full frame will not give you cleaner images than crop sensors, assuming that they are the same sensor technology (e.g. D800, D7000, K5). They will result in equivalent print quality if forced to shoot equivalent images.

Full frame superiority busted!

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Debunking Equivalence Part 2

In my previous post Debunking Equivalence I covered in detail the major flaws of this concept called “equivalence”. Mind you, not everything in equivalence is wrong. Equivalence in field of view and depth of field make total sense. What does not make sense is the equivalence in exposure. This “exposure equivalence” is what full frame fanbois sell to unsuspecting gear heads. It is supposed to prove that full frame is superior to APS-C, m43 and smaller sensor cameras. 

In this post, I will use basic math to debunk the myth. Just enough math that I learned when I was in first grade — seriously.

Recall the equivalence comparison between m43 and full frame:

m43: 25mm, f/5.6, 1/125s, ISO 100

FF: 50mm, f/11, 1/125s, ISO 400

Ignore the ISO settings for now. Let us concentrate on the f-stop and shutter speed settings. The reason, they say, that f/5.6@125 is equivalent to f/11@125 is that both gather the same amount of light by virtue of the difference in focal length. The longer 50mm lens will have the same entrance pupil diameter as the 25mm lens. The difference in focal length of course is proportional to the sensor size. 

Now let us use arbitrary units of measure and consider the ratio X/Y, where X is the total amount of light and Y is the sensor size. Supposing that for m43 we have the ratio 4/8, a full frame sensor (4x area), according to equivalence, would have a ratio 4/32. Again:

m43 = 4/8 vs FF = 4/32

So total light is constant at 4 units and the denominators are the respective sensor size units 8 and 32 for m43 and full frame respectively. Still with me? Obviously, they are not the same. Not in any known universe. This is why for the same amount of light, the full frame will come out two stops underexposed. And this is why equivalence fanbois will insist that an increase in ISO is necessary; the full frame shot is very dark! Now we know that bumping the ISO does not increase the amount of light but will make the image brighter. I’m not sure how to represent that in numbers because nothing has changed really in terms of light. ISO bump is fake. It’s a post-capture operation that does not change the exposure or captured light. Furthermore, an ISO bump introduces noise and that is why equivalence forces the comparison to be performed at the same print size. This method of cheating does miracles for the fanbois. Let’s see how it works:

If we agree to compare at the same print size of 16 units, we now have 

m43: 4/8 upsampled to 4/16

FF: 4/32 downsampled to 4/16

Magic!!! They are now the same! They are equivalent! This is true for any print size therefore equivalence is correct!!! Therefore full frame is superior because at the same f-stop it will have gathered more light! 

Well, not so fast! The amount of light did not change. It was constant at 4 units. The apparent changes in signal performance was not due to light but due to resampling. Do not equate resampling to total light. They are not the same and are completely independent of each other. Resampling is like changing your viewing distance. I can make my crappy shot look cleaner simply by viewing it farther away. Did I change total light by moving away from the image? Stupid isn’t it?

That is the very naive reasoning behind equivalence. Not only is the conclusion stupid but the assumption here is that there is absolutely NO NOISE! Noise is ever present. Noise is present and proportional to the incoming light and a property of the sensor itself. Let’s see what happens when we introduce noise. 

Supposing that noise is 1 unit. We now have:

m43: signal = 4/8, noise = 1/8

FF: signal = 4/32, noise = 4/32

Therefore the signal to noise ratio (SNR) are as follows:

m43 = 4:1

FF = 4:4 or 1:1

The full frame is obviously inferior! It makes sense because it was underexposed by two stops (4x)!!! If you boost the signal by increasing the ISO you are boosting noise as well. In low light situations where noise is more pronounced, a 4:2 SNR for m43 will be 4:8 for full frame. There is more noise than signal in the full frame image! At 4:4 SNR for m43, full frame is at 4:32. There is nothing but noise in the full frame. You just can’t underexpose indefinitely and bump the ISO! That doesn’t work in all situations. This is why images at higher ISOs look bad. There is more noise than signal in low light situations. Yet, equivalence fanbois will try to convince you that ISO 6400 on m43 is the same as two stops underexposure plus ISO 25600 in full frame. It’s not. 

So again, the equivalence fanbois could not accept this fact. At the sensor level, equivalence has made the full frame look really bad. What can they do? Cheat again! Force the comparison to use the same print size. At a print size of 16 units, noise will be increased or decreased proportional to how much you upsample or downsample. We have:

m43: signal = 4/16, noise = 2/16

FF: signal = 4/16, noise = 2/16

So now the SNR for both are equal at 4:2! Can you see how they manipulate the numbers? They are using image size (number of pixels) to circumvent noise and stupidly equate this to light gathering. The total amount of light has not changed. How could anyone possibly attribute the changes in SNR due to resampling to light? It does not make any sense at all! Look closely though because this SNR is for the entire image. Most of the signal will be concentrated on the brighter areas. In the darker areas noise will show its teeth. In instances were full frame is severely underexposed (SNR 4:32) there is no saving it. It would look crap. M43, on the other hand will happily chug along with 1:1 SNR or better. 

This is why when you start comparing two full frame cameras with different resolutions you will notice variations in SNR results at different print sizes (Megapixel Hallucinations). If the SNR changes even when the sensor size is held constant then obviously sensor size does not matter. Therefore total light, being proportional to sensor size, by itself does not tell the whole picture. What matters is the RATIO of total light to sensor size, otherwise known as EXPOSURE. For SNR to be the same, exposure must be the same for sensors with the same properties (i.e. sensel pitch, efficiency, etc…). Size does not matter. 

Equivalence debunked…again!

Debunking Equivalence

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:

Screen Shot 2014-09-28 at 10.31.50 pm

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.

Update:

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.