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Gain and read-out noise of Canon EOS 450D

In this page, the performance of the Canon EOS 450D are calculated. The methodology is largely inspired from the tutorials given by C. Buil.

The Canon EOS 450D uses a CMOS sensor, and delivers frames coded on 14 bits. The following sensitivities are available : 100 ISO, 200 ISO, 400 ISO, 800 ISO and 1600 ISO. I have made a characterization of the noise and gain properties for 100 ISO, 400 ISO and 1600 ISO.

Analysis of offset frames

In the table below I give the offset value and the read-out noise. The offset value is a median value (there are lower and higher pixel values in the frame). The read-out noise is calculated by substracting two offset frames, and dividing the noise of the obtained picture by sqrt(2) ~1,41. The same offset values and read-out noises are found on the 4 different color planes of the Bayer matrix. I also observed that the maximum value of 16384 ADU is never reached. The highest value I could find was 15848. I suspect that the level of the image is lowered to get the value 1024 for the offset so that the dynamics is slightly reduced.

Sensitivity Offset (ADU) Read-out noise (ADU)
100 ISO 1024 9.3
400 ISO 1024 10.9
1600 ISO 1024 22.0


Calculation of gain

To calculate the gain, I took pictures with a uniform illumination of the sensor. For each color plane I found a different signal, since the illumination source is not exactly white (or, more precisly, does not match the responses of the 4 pixels types in the Bayer matrix). So I performed a separate calculation for the 4 color planes. If the sensor is illuminated by I [photons] and has an offset O [ADU], its signal will be

where g is the gain [ADU/electrons] and QE the quantum efficiency [electrons/photons]. On another hand, its noise will be

From the offset analysis, I already know O and sRO2. From the characterization the 4 color planes of a frame with uniform illumination, I can get S and sTOT2. The gain is calculated with

The results are reported in the table below. The fact that I find similar gain values for the 4 color planes is a good indicator that the method is working.

  Signal S [ADU] Total noise sTOT2 [ADU] Gain g [ADU/electrons]
100 ISO - color plane 1 10987 75.5 0.55
100 ISO - color plane 2 6508 57 0.56
100 ISO - color plane 3 7780 61 0.52
100 ISO - color plane 4 10920 76 0.57
400 ISO - color plane 1 5268 91 1.90
400 ISO - color plane 2 2610 54 1.69
400 ISO - color plane 3 4594 80 1.73
400 ISO - color plane 4 5258 89 1.81
1600 ISO - color plane 1 10662 261 6.97
1600 ISO - color plane 2 4667 161 6.85
1600 ISO - color plane 3 9029 234 6.72
1600 ISO - color plane 4 10674 261 6.96


Noise model, optimal gain

The read-out noise is varying with the detector gain. It can be expressed as the combination of a fixed noise (noise after amplifier) and an amplified noise (noise before amplifier). The read-out noise is then


fitting the measured points, we find


The variations of gain and read-out noise with the sensitivity as summarized on the graphs below.

Canon EOS 450D : Gain wrt sensitivity
Canon EOS 450D : Read-out noise variations with gain


Signal to noise ratio

The SNR can be calculated from the number of collected photons F



In astronomy we are usually interested in the detection of very small photon fluxes F. A first order developpement with respect to F gives



So that, as expected, the slope of the SNR at very small fluxes increases with the gain. So the best situation will always be achieved by setting the maximum gain. In our case, this means that we must use 1600 ISO for the sensitivity. On the other hand, the slope of the SNR at very small fluxes, at very high gains, tends to saturate



The gain where the saturation tends to be significant is given by



which corresponds to a sensitivity of 1060 ISO. The SNR slope at very small fluxes is depicted on the graph below as a function of the gain.


Canon EOS 450D : SNR slope at very small fluxes, showing saturation at high gains