We want to find out how the numbers in the raw file relate to the exposure that the sensor has received. We can also use the same measurements later to calculate the signal to noise ratio.
We photograph a flat target of uniform reflectance that is evenly illuminated. We use a fixed aperture but vary the shutter speed over a wide range so that we have shots that are heavily under-exposed, heavily over-exposed, and also a fair number at intermediate points. We take two shots at each shutter speed so that we can subtract them later to get the noise.
The EF70-200mm f/2.8L IS lens was used set at 200mm focal length and focussed at infinity, although the target was 1.5m away. For further details of the method please see here.
For ISO 100, I ended up with 24 pairs of images, each pair taken at a different exposure. The aperture was f/9 and the shutter speeds varied from 1/8000 to 1.6 seconds. The statistics of a 200 x 200 pixel area in the centre of the image for the green wells are in the table below, and you can scroll it down to see figures for the red and blue:
Looking at the Mean DN column, it is obvious that for the longest five exposures of the green the number in the raw file is the same at 3711, and the standard deviation of that value is zero. This tells us that the firmware is clipping the numbers in the raw file at 3711, which is 385 short of the maximum output of the camera's 12-bit ADC.
The data for the red and blue wells is similar, except that longer exposure is needed to reach the clipping point. All three colours limit at the same value of 3711.
The graph shows the response of all three colours on linear scales, after removing the offset of about 128 that we measaured here.
As already mentioned, the fact that the green curve is steeper than the other two may simply be due to the lighting of the target being more intense in the green than the blue region of the spectrum.
The dashed white line is the best straight line fit to the green points, ignoring the top five (saturated)
and bottom one (a bit wonky) and with the intercept constrained to be zero.
The equation is
DN = 6116.9 * T,
where T is the shutter time in seconds. R² = 0.9993 (Of course, the slope of this line only applies to the
particular target and illumination used. It is done to demonstrate the linearity, see the right-hand two columns of the table above)
Except for the bottom point, the linearity in the green is better than 10% and it is maintained right the way up to saturation. Excluding saturation and the bottom point, the RMS nonlinearity is 3.25%.
Because of the linear exposure time scale, many of the data points are crowded in the bottom left corner. A better view is given by plotting the same data on logarithmic scales:
The horizontal axis is relative exposure in photgraphic stops. The offset has been subtracted from the DN values (not that this matters on a log plot).
This gives a better impression of the linearity of the camera's response. The range of the linear region can be seen to be about 11.7 stops, and over 12 if one includes the slightly wonky lefthand point. It does not follow that that is the camera's dynamic range, as we shall see later, because we also have to consider the noise.
Peter Facey, Winchester, England
20080309 originated