FF v Crop Sensor hypothetical question ...

[DrJon]

Re: FF v Crop Sensor hypothetical question ...

BTW Tony was just explaining equivalence rather than inventing anything himself.

Remember light is inherently noisy (as photons are emitted at random intervals). The noise is proportional to the square root of the light intensity. Hence if you have 4x the light you get 2x the noise and so the amount of noise relative to signal is halved. This is just in the light and has nothing to do with the sensor. Hence 4x the sensor size you get half the photon shot noise for the same exposure.

While I'm at it dynamic range is the capacity of the pixels (few k to over a 100k electrons) divided by the read noise of the pixel (an electron or two on good sensors like the 6D) then log base 2 to convert to stops. Hence big pixels will be better in similar technology (more capacity and they seem to be good at low read noise these days).

I think sensors have improved somewhat, but noise reduction has improved a lot more. It would probably be interesting to run DXO 9.5 over some old noisy 20D images sometime.

There is a good point about usage - I think how much you care about noise etc. depends a lot on what you want to do with the photo, and that can vary shot-to-shot almost. Interestingly there are a lot of people on the Internet convinced no sensor smaller than their choice is any use whatsoever and all the bigger ones and just antique bulky systems for dinosaurs. In reality there is no perfect camera unless you don't care about size, weight and cost, plus probably not even then...

[AndyMulhearn]

Re: FF v Crop Sensor hypothetical question ...

Remember light is inherently noisy (as photons are emitted at random intervals). The noise is proportional to the square root of the light intensity. Hence if you have 4x the light you get 2x the noise and so the amount of noise relative to signal is halved. This is just in the light and has nothing to do with the sensor. Hence 4x the sensor size you get half the photon shot noise for the same exposure.

Eh? I'm not sure what you mean here but noise is not related to photons in that way, or in fact in any way that I'm aware of. There are two sources of electrons that are recorded by a photo site in a sensor. First is the result of incident photons and second is stray electrons released as a result of the characteristics of the semi-conductor used in the sensor. Of the two, the incident photons are the ones you want to capture, the noise is the one you want to avoid.

Sensors are generally made of similar materials so will have similar noise characteristics, i.e. for each unit area there will be a similar level of average noise. But FF sensors are much bigger than APS-C or smaller sensors so they can capture more photons for the same exposure values than the smaller sensors, hence the bigger the sensor, the better signal the signal to noise ratio and the less noise you see in the shot.

If you want, you can try an experiment. Stick a lens cap on and take a 30second exposure. There will be no photons on the sensor as there is light path to the sensor. There will be noise however which proves noise and incident photons are not related.

[DrJon]

Re: FF v Crop Sensor hypothetical question ...

Light is inherently noisy as Photons are emitted randomly (Quantum Physics and all that), although they will come at an average rate for a particular level of illumination. Hence if you get an average of 100 photons per micro-second reflected from a certain area of uniformly gray surface (i.e. a camera pixel's worth) you can't guarantee exactly 100 will show up, just that will be the average, so looking at a bunch of equally illuminated areas you might get 98, 101, 99, 102, 99, 101 per micro-second. If you graph it you get a bell-curve (i.e. a gaussian). The more light you capture the more the noise from the random nature of photons is evened out, so in this example doubling the area (pixel size gets) 199, 201, 200.

Another example will be dropping frozen peas onto a covered bucket (as light is quantised into photons). You might drop an average of 100 per second but the gaps will be slightly random and so someone uncovering the bucket to capture a second's worth might get a few more or less.

...Pause to Google...

http://thelivingimage.hamamatsu.com/resources/photon-shot-noise/

...Another pause to look in my bookmarks...

http://theory.uchicago.edu/~ejm/pix/20d/tests/noise/index.html#shotnoise

"An important characteristic of fluctuations obeying Poisson statistics is that their standard deviation -- the typical fluctuation away from the average in the typical count -- is equal to the square root of the average count itself. That is, if 10000 photons are collected on average, the typical fluctuation away from this average number of photons will be about 100 -- the counts will typically range from about 9900 to 10100. If instead on average 100 photons are collected, the variation from count to count will be +/- 10. Thus, as the signal grows, the photon shot noise also grows, but more slowly; and the signal-to-noise ratio increases as the square root of the number of photons collected. The higher the illumination, the less apparent the shot noise; the lower the illumination, the more apparent it is."

I'm not saying there aren't other noise sources in digital cameras, you get read noise (typically 1-2 electrons per pixel for recent sensors), thermal noise, pattern noise (the 6D is really good for this, unlike a D800 say) plus noise between capturing the electrons and digitising them - Canon are really bad for this, they take a 15.5 stop sensor in the 6D and reduce it to just over a 12 stop sensor by noise from their analogue-to-digital path. This is why Sony/Nikon have more Dynamic Range at low ISO, at high ISO the amplified read noise dominates so it doesn't matter as much.

Example:

Let's say you drop 170,000 photons into a 1Dx pixel (operating at ISO 100). The Quantum Efficiency of the 1Dx sensor is 47% so you get about 80,000 electrons. This is good as the pixel will hold just over 90,000.
You'll get about 200 electrons of Photon Shot Noise, 1.3 electrons of read noise and 38.2 electrons of noise from combined read noise and noise from digitising the signal. This is why you care about the noise in the light and how big your sensor is so how much light it gathers.

For a 70D the numbers are 53,000 photons, 24000 electrons (the pixels hold over 26,000 electrons and using the same % of a full pixel as the 1Dx, assuming that means the same exposure), 150 electrons of Photon Shot Noise, 2.3 electrons of read noise and 13.5 electrons of combined read/digitisation noise.

Hence:

1Dx Photon Shot Noise to Signal ratio = 200/80000 = 0.0025
70D Photon Shot Noise to Signal ratio = 150/24000 = 0.00625 = 150% more noise than the 1Dx

1Dx Read and Digitisation Noise to Signal ratio = 38.2/80000 = 0.0004775
70D Read and Digitisation Noise to Signal ratio = 13.5/24000 = 0.0005625 = 17.8% more than the 1Dx

1Dx Photon Shot Noise to Read/Digitisation Noise ratio = 5.23x
70D Photon Shot Noise to Read/Digitisation Noise ratio = 11.1x
The smaller the sensor the more the Photon Shot Noise is the dominant noise source at decent light levels. Even with the big sensor it's still the main thing.

So inherently (in this example) the 70D's is 17.8% noisier than a 1Dx but if you look at the noise in the light you are gathering it's more than 150% noisier, "more than" as you need to combine the two noise sources. Remember this is all at ISO 100 and a particular exposure, it's not general. Also it will appear better than that in reality as you need to start playing with logarithms to allow for human visual response.

Note I rounded a few numbers to make for easier reading. Also a few things are simplified as otherwise it would be unreadable (like not converting noise to dB or stops). Note noise doesn't add with a + sign, but for numbers this different the Photon Shot Noise dominates so much you can pretty much ignore the rest.


P.S. What the heck... converting to Stops...

Signal/Noise due to Photon Shot noise -
1Dx: log10(80000/(200))/log10(2) = 8.6 stops
70D: log10(26000/(150))/log10(2) = 7.4 stops

Signal/Noise due to Read and Digitisation noise -
1Dx: log10(80000/38.2)/log10(2) = 11.03 stops
70D: log10(26000/13.5)/log10(2) = 10.91 stops

Difference including the Photon Shot Noise only = (log10(80000/200)/log10(2))-(log10(26000/150)/log10(2))
= 1.2 stops (including a fair bit of rounding)

Difference in sensor size in stops = log10((36*24)/(22.5*15))/log10(2)
= 1.35 stops

Q.E.D.


P.P.S. Sorry for anyone suffering mental trauma through reading this.

[jk224]

Re: FF v Crop Sensor hypothetical question ...

What the..... That's it, I'm going back to film!

[S_J_P]

Re: FF v Crop Sensor hypothetical question ...

Thanks for that DrJon, it's good to see the math behind the throw-away comments about larger-pixels being "better"

[DrJon]

Re: FF v Crop Sensor hypothetical question ...

Strictly you need to add it up over the whole sensor, so larger sensors are better (the noise in the smaller pixels, being random, looks less bad at the same overall image size as it averages out). However as noise goes up larger pixels get relatively better than smaller ones, so they score big at really low light/high ISO when the read noise is a big part of the total (or so I'm told).

Remember as you turn the ISO up you amplify the signal, its shot noise and the read noise (but not the digitisation noise), at ISO 51,200 the 1Dx's pixel's capacity is 163 electrons, as that is as much as you can get that when you amplify it you do not go over the top of the digitiser's range. Now you really begin to care about the Read and Photon Shot noise.

If you have the same % gray as before (although with tons less scene illumination) you get 144 electrons from incoming light, hence rather handily (amazingly in fact) 12 electrons of photon shot noise and 1.7 electrons of read+digitisation noise. (You still have 30+ electrons of digitisation noise, but as that doesn't get amplified it's only a teeny part of an electron when scaled to the signal size. So if you amplify the signal by 512x the digitisation noise is 1/512 as big relatively compared to the unamplified signal and noise - the signal is amplified to 144*512, shot noise to 12*512 and the read noise to 1.3*512.)

Roger is a great source on this in addition to my already quoted linked ones:

http://www.clarkvision.com/articles/digital.sensor.performance.summary/index.html

http://www.clarkvision.com/articles/does.pixel.size.matter/

Note I used DXO's numbers (stripped out by sensorgen.info) in my example, rather than his, although they tend to agree pretty well.
I see I said Gaussian when I meant Poisson too - still they are pretty similar, err -ish...

[AndyMulhearn]

Re: FF v Crop Sensor hypothetical question ...

Hmm, not ignoring this but thinking deeply about it and doing some reading.