On noise ... A physics point of view

Sep 3, 2009

I would like to post some thoughts on noise and related issues, since I hear a lot of complaining, explaining that CANON is not capable of making good sensors etc.

One can make now some simple calculations on what has Canon achieved and why finally this camera is not so bad, but indeed could be better.

But in order to do so, we need some maths and physics.

If you do not like the proof, jump at the end

In a detector there are 2 kind of noise.

1) Quantum noise due to the particle behavior of light. From poissonian statistics, this noise is equal to the square root of the number of photons

2) Thermal noise on the detector, meaning how many extra electrons can be collected but when no photon hit the pixel.

So the noise is equal to sqrt[n]+thermal

and signal is equal to n, where n is the number of photons.

I use the dynamic range posted on this page

http://forums.dpreview.com/forums/readflat.asp?forum=1019&thread=32904610

At 100 ISO, we have a dynamic range of 11 ev = 2^11 = 2048

at 12800 ISO we have a dynamic range of 7 eV (128) for the 7D and almost 6.2 (73) for the 50D.

The dynamic range can be seen as the following : when the number of photons is equal to noise, then we see only noise. When the signal to noise ratio is equal to the dynamic range, it gives the maximal photons the pixels can collect.

Let's calculate S/N ratio

N/(sqrt(N)+thermal)=2048 (at 100ISO)

(N/128) ( sqrt(N/128)+thermal) = 128 (7D) or = 73 (50D) at 12800 ISO. At 12800 ISO one has 128 times less photons than at 100 ISO

Solving the equations gives us

The maximal number of photons each pixel can see is

7D = 4.5 Million

50D = 5.7 Million

the number of thermal electrons is

7D = 90

50D = 400

What do we learn

First, in fact the 7D pixels are smaller than the 50D pixels, and can only accept 1.26 times less photons. Since the 50D is a 15Mpx camera and 7d is 18Mpx the area ration is 1.44 so Canon has changed as claimed their spacing between pixels and the 7D pixels are wider than expected

Second : The thermal noise of the 7D is 8 times less than for the 50D, which is in accordance with the claim that the 7D has a new version that heats up less

Final conclusion :

YES it is possible to put more pixels on an APS-C camera if you diminish the thermal noise, since the system is not yet limited by quantum physics.

So please, before complaining on the fact that it is not the right direction to go, think of the detector as a physical instrument, and look what are the limits.

Also take in account that I did not include any electronic issues related with the ADC (analog-digital converter)

Alex