Could somebody help me understand this paragraph explaining the relationship between noise and sensor size?

Question

According to this article from dpreview, which compared noise between a full-frame camera with a full-frame lens (the D810), the same full-frame camera with an APS-C lens, and an APS-C camera with the same APS-C lens just mentioned (the D7000), at the same aperture, shutter speed, distance, framed the same way (so I'm assuming at different focal lengths), at various ISOs, if I understand the article correctly, the article seems to suggest that the D810, that is, the full-frame camera with the APS-C lens, performs better in terms of noise than the D7000, the APS-C camera with the same APS-C lens. Am I understanding this correctly?

Here is the paragraph in question:

Now we see the effect of all the extra light captured: the outer cone in the diagram at the top of the page [this is in reference to the diagram near the beginning of the article which shows how some of the light reflected by a full-frame lens that would normally reach a full-frame sensor won't reach an APS-C sensor because of the latter sensor's smaller size]. The APS-C camera and APS-C crop still look the same but the extra sensor area (all exposed to the same light intensity [as measured by aperture and shutter speed]) allows the full frame image [to] look better overall.

I should probably also mention that according to the article, both cameras used in the test, the D810 and the D7000, have sensors with similar pixel sizes.

The reason I'm asking whether the D810 with the APS-C lens performs better in terms of noise than the D7000 with the same lens is because I'm having a hard time seeing the difference between the two test shots at various ISOs (full-frame with APS-C lens vs. APS-C with APS-C lens).

I also believe for comparison purposes, only the images taken with the full-frame camera with the full-frame lens were resized, in order to compare those images to the images taken with the full-frame camera with the APS-C lens, as well as the images taken with APS-C camera with the APS-C lens, but I could be wrong, so you might have to take a quick peek at the article.

I can clearly see that the test shots taken with the full-frame camera with the full-frame lens are less noisier than either the test shots taken with the full-frame camera with the APS-C lens or the APS-C camera with the APS-C lens, but I'm having trouble understanding why the test shots taken with the full-frame camera with the APS-C lens are supposed to be less noisier than the test shots taken with the APS-C camera with the APS-C lens, as the article seems to suggest.

Answer 1

If I understand right, bigger sensors have more room for pixels than smaller ones, so you can either have a higher feasible pixel density leading to crazy high resolutions with basically nonexistent noise until you get to higher ISOs, eg. 50MP+ on a newer a7R series body or a lower-end G-mount one, or 100MP+ on higher-end G-mount and other medium-format bodies, or a lower pixel density leading to a lower resolution but insane sensitivity, eg. 12MP but the sensitivity maxes out at ISO409600 on the a7S line, however if you try to achieve crazy resolutions like mentioned on a smaller sensor, the noise floor just goes to crap because you can only fit so many pixels on, say, a 1/2.3" sensor vs. a 1", 4/3, APS-C, or full-frame sensor before you start to have to sacrifice somewhere, typically in noise floor, eg. a photo taken in high-res mode at ISO100 on a Galaxy S20 Ultra looks like a 16MP photo taken at ISO1600 from an older 4/3 ILC.

Answer 2

One sentence in the article says

And, since their pixels are very similar in size and they feature similar technology, the pixel-level performance is essentially identical across all three cameras.

They then say that people won't care about the sensor size when choosing how to present a picture, they will choose a size they like for other reasons. They rescale the pictures to a common number of pixels. For example, my laptop display is 1980 x 1080 or about 2MP. The full frame camera has about 2.25 times more pixels in its image. When rescaled to a common number of pixels the image coming from the D810 uses 2.25 times more input (camera) pixels to make each output (display) pixel. This is effectively using a 2.25 times larger pixel and results in less noise. I would expect a similar result if the D810 were only a 16MP camera. There would be less noise on the camera pixel level then but similar reduction in noise when going to output.

Answer 3

(Based on the images in the article)

If all images are taken from the same distance, as the article states, then there's a much longer focal length being used for the FF images. If the same focal length were being used, the FF images would show a much larger area of the test chart, not a much smaller area. I couldn't find anywhere in the article that explains this discrepancy.

With the same aperture setting, a longer focal length has a larger entrance pupil, and thus lets more light into the camera than the same f-number with a shorter focal length lens. That's why the FF image has a better signal to noise ratio, and thus less perceived noise.

I'm having trouble understanding why the test shots taken with the full-frame camera with the APS-C lens are supposed to be less noisier than the test shots taken with the APS-C camera with the APS-C lens, as the article seems to suggest.

The article does not seem to me to be suggesting that at all. It's claiming the FF image taken with the FF lens that uses the full area of the FF sensor has less noise than either image taken with the smaller image circle and cropped on the FF camera to match the size of the APS-C camera.

Answer 4

You shouldn't use full frame cameras with APS-C lenses.

If you manage to use a full frame camera with an APS-C lens (for example by using a Sigma or Tamron lens on Canon body -- the third-party lenses won't block the invalid connection), you will see only the middle of the image. A cropped sensor, therefore, even though the camera is full frame one. Some mirrorless full frame cameras automatically give you a cropped picture, detecting the lens to be a crop lens.

If you crop the resulting image to filter away areas outside the crop circle, you will get useful area of the sensor that has the same size as the APS-C sensor.

If you then consider the noise, both cameras will have equal noise in that useful image area.

However, that's not how the full frame camera is supposed to be used. If the 1.6x crop lens is 50mm f/1.8, then you are supposed to use 80mm f/1.8 lens on the full frame camera. It will give the same field of view but will use more of the sensor area. You will therefore capture more light, so at the same ISO, the noise is lower on the full frame camera.

Also if you use 50mm f/1.8 full frame lens, both on the crop camera and the full frame camera, so that it's a full frame lens not an APS-C lens, then the full frame field of view will be bigger. It will see more light. Therefore, on the full frame camera, at the same ISO, noise is lower.

Another question: you take a 6000 x 4000 pixel picture of a bird, but find the focal length not to be enough. You will crop the image to 1500 x 1000 image. Did you increase the noise when cropping? Yes you did, magnifying the image will magnify noise too.

A third question: you have a 70-200 f/2.8 and are considering whether to use a 2x teleconverter. You are worried that 140-400 f/5.6 would be too slow, creating too much noise. Therefore you use the lens as 70-200 f/2.8 and do the teleconverter thing in post-processing by cropping, because "then it's a fast f/2.8 lens". Did you achieve anything useful by avoiding the teleconverter? No you didn't, taking 25% of image area is equal to using a 2x teleconverter: in both cases, you magnify noise. (Assuming each and every image is cropped to 25%, as you could theoretically when cropping only crop those images that require cropping and leave the rest uncropped.)