If you are here to understand (why) equivalence (is wrong) then read this: https://dtmateojr.wordpress.com/2014/09/28/debunking-equivalence/
Before you start reading this post, I highly recommend that you read my previous post because it explains the very basic concept of f-stop. Failure to understand this basic concept is what leads to nonsense.
It turned out that the myth I mentioned in the last paragraph of my previous post became a hot topic in one of the forums. This guy who owns a full frame, a D800 to be more specific, started arguing about the superiority of his camera vs the APS-C sensors. What’s even funnier is that this was a Pentax forum. You know that brand that doesn’t have a full frame camera yet (cough! cough!). I don’t even know why he was lurking in there.
Anyway, as the myth goes, a full frame sensor has less noise compared to a smaller sensor because it can gather more light. The basic premise is that all things being equal (lens, sensor, processor, incident light), the size of the sensor is the single most significant factor that affects noise because of its superior light gathering capacity. As I have mentioned in my previous post, this is not true. In fact, in reality, a full frame sensor gathers less light than a smaller sensor and I will expain this later.
First, let’s see what this myth really is in greater detail. Here’s the link that is supposedly the authority of this myth: http://www.josephjamesphotography.com/equivalence/#aperture
I would like to quote the following:
The concepts of, and connections between, total light, DOF, and noise, are much more easily understood in terms of aperture rather than f-ratio, especially when comparing different formats. While the same f-ratio will result in the same exposure (where exposure is the density of light that falls on the sensor — photons / mm²), regardless of the format, the aperture diameter, together with the shutter speed, determines the total amount of light that falls on the sensor, where the same total amount of light falling on the sensor results in the same noise in the photo, for equally efficient sensors.
I can already see where this is going. The argument is that since a larger sensor requires a longer focal length to cover the same FoV then it follows that for the same f-stop, it will have a larger aperture and therefore allow more light in. ROFL! Seriously?! You just can’t make that up you know 🙂
” Luminance noise is a function of the total amount of light falling on the sensor, and the efficiency of the sensor. The photon noise (often referred to as “shot” noise) is determined by how much light the sensor records. This, in turn, is determined by the total amount of light falling on the sensor (Total Light = Exposure · Effective Sensor Area)”.
You can read that from here: http://www.josephjamesphotography.com/equivalence/index.htm#noise
The first statement totally ignores the fact that distance plays a very important role in the intensity of light. Look at our sun for Pete’s sake. There are more stars way larger than our sun and yet it’s much much brighter than any other light source above our atmosphere because of distance. Even if you go out at night in the open (large aperture), it’s still way brighter inside a room with a single window (smaller aperture) during daytime. I have not even started arguing photographically yet.
Allow me to debunk this myth using a very simple example. Consider the simplest lens of all: a pinhole. Put a pinhole in front of a full frame and a crop sensor. Do you think that the pinhole is any brighter because it’s in front of a full frame? Of course not. Now here’s the problem: if the pinhole is too close to the sensor, it won’t illuminate the whole sensor. What do you do? You move the pinhole away from the sensor of course. Now anyone with half a brain will quickly realize that the larger the sensor the farther the pinhole should be. Refer to my crappy illustration below:
The distance D1 and D2 of the pinholes are proportional to the size of the sensor that needs to be illuminated below. Can you see how this relates to our sun and stars argument above? The farther pinhole is giving lesser light to the the sensor. Unfair to the full frame isn’t it? How do we make this fair to both sensors? Make the farther pinhole bigger. Obvious isn’t it?
How does this relate to a real lens? The size of the pinhole is your aperture, the distance from the sensor is your focal length and their ratio is your f-stop. That’s why a f-stop is a f-stop and gathers the same amount of light for any sensor size. Same amount of light means same SNR for the same type (not size) of sensor!
Now to counter the other statement on sensor area, refer to the illustration below. If we are to use the same lens at the same aperture then we will arrive at something like this for different sensor sizes:
So now we have the same distance and the same aperture therefore the same amount of light entering the sensor chamber. Does this mean the larger sensor is capturing more light? Of course not! It’s not like the individual sensels can share their signals with other sensels. Whatever light falls on each sensel is as is. The SNR for each sensel is (more or less) constant for a given incident light.
Look closely at the illustration above again because now I will go further into saying that in fact, the larger sensor is capturing less light in this situation. Now why is that? Because lenses aren’t perfect. Light diminishes as you move away from the center of the lens. You want proof? Wide open, the same lens will produce vignettes on a full frame while it looks perfect on a crop sensor. A vignette can be as bad as two stops down at the corners. That’s four times less light!!! If truly a full frame captures more light then there won’t be vignetting.
Consider this thought experiment:
Supposing that you have a D800 sensor under any lens. Keep the same lens but now cover one half of the sensor with a completely opaque material therefore exposing only half of it. Do not cover the lens; just the sensor. If the myth is true, then it follows that this sensor half (a crop) will now gather less light and therefore produce more noise. Now uncover this half and cover the other half. Again, if the myth is true then this second half would also gather less light and, just like the other half, will produce more noise. It follows that if you fully uncover the full frame sensor, it’s really just a combination of two more noisy halves! The myth is telling us that two noisy half-sensors will produce one clean full frame sensor?! This is absurd!
This thought experiment is not just a thought experiment. It actually happens every time you click your shutter. At fast shutter speeds, the shutter curtain does not actually fully open and close. Instead, the shutter curtain behaves like a very small slit that glides over the sensor. Therefore, the sensor is not exposed as a whole at the same time but in chunks defined by the curtain slit size. This slit is way smaller than half a sensor. Since this slit exposes only a part of the sensor at any given time, your full frame is really acting like a combination of multiple smaller sensors! If the myth is true then a full frame sensor is really just a combination of multiple very small noisy sensors!!!
We can continue this experiment by further subdividing the sensor until we come to a point where all we have left is just one sensel. If the myth holds then this sensel will be hopelessly noisy. It follows that a full frame sensor is composed of individual hopelessly noisy sensels! That is insane! That is beyond reason! This is just wrong, people!
The only conclusion is that sensor size does NOT matter! Note that half of a full frame is your APS-C sensor. Therefore full frame and APS-C have the same light gathering capacity and therefore exhibit the same noise profile!
What affects light gathering capacity (among other factors) is the size of the sensels. The K5/D7000 and D800 have practically the same sensel pitch and therefore have the same light gathering capacity. Again, it’s NOT the sensor size but SENSEL size! That is why the SNR of the D7000 and K5 are the same as the D800. That is why the SNR of the D700 and D4 are better than the D800. (https://dtmateojr.wordpress.com/2014/04/21/rain-can-teach-us-photography/)
Note: re-editing since my update disappeared mysteriously when I accessed it using the wordpress iPad app 😦
With the recent discussions that happened in the comments below I could not help but to conduct my own real experiment on this. According to the myth, as long as the same shutter speed and same physical aperture are used, the resulting images should have the same amount of noise and so I made an experiment.
Here are the parameters:
35mm, f5.6, ISO 200 VS 100mm, f16, ISO 1600
Why those settings? Because they produce the same aperture sizes:
35mm/5.6 = 6.25mm
100mm/16 = 6.25mm
Since f16 is 3 stops slower than f5.6, I boosted the brightness in-camera by using ISO 1600.
I used the low-light monster Nikon D700. My lens of choice was the Tamron 24-135/4-5.6. I chose this lens because of the following reasons:
1. It covers the focal range I required for the experiment without hitting the extreme zoom limits of the lens.
2. It has focal length markings at 24, 35, 50, 70, 100 and 135.
3. It locks to infinity focus.
Item #3 is very important because my subject and light source are very far. I used the clear night sky as my subject and my light source. The sky is very wide and uniformly lit that differences in AoV are immaterial. I shot the scene approximately 30 minutes after sunset.
Without further ado, let me present to you the results:
Above photo was taken at 35mm, f5.6, 30s, ISO 200.
Above photos was taken at 100mm, f16, 30s, ISO 1600.
As you can see, the first shot is very clean. The second shot has very visible luminance and chroma noise. Admittedly, I expected a lot worse from the second shot but I guess this is testament to how good the D700 is in low light situations. The blurry white lines are stars. The long exposure has created star trails. As expected, the longer focal length has produced longer trails.
I think that at this point, this myth has been truly busted. As always, comments are more than welcome.