How sensorgen figures are calculated

Sensorgen extracts figures for read noise, saturation capacity and quantum efficiency from measurements of a camera's signal to noise ratio. One source, the one which is used for the data on this site is DxOmark.com. DxOmark provides a number of measurements on is site. The ones used for this analysis are the 'ISO sensitivity' figures and the 'FullSNR curves'. The method used here is based on one demonstrated in discussion on the Digital Photography Review forums by 'DSPographer'. [1]. This method was subsequently presented again by another member, Chrisk99, who extended it to also provide a figure for quantum efficiency.[2]

Curve fitting

The concept behind the analysis is to fit a curve of the theoretical SNR function for a sensor against the actual curves SNR curves. When a fit is found the size of the variables representing the various noise sources in that function gives the magnitude of those noise sources for the camera being analysed.

The theoretical noise function is

where:

SNR is the signal to noise ratio in decibels (y axis on the DxO plot).

G is the charge/grey scale conversion factor or 'gain'. This is the nuber of photoelectrons representing 1% grey scale level. In other words, 100G is the number of photoelectrons representing 'white' or 'full scale'. This is an unconventional scaling of this measure, but allows direct use of data from DxO plots.

g is the grey scale level in percent of white, from the DxO plot.

r is the read noise , measured in electrons.

p is a coefficient for the pixel response non-uniformity (PRNU)

An excellent discussion of these noise sources has been given by Emil Martinec [3]. The formula above is simply the decibel expression of the ratio of the number of photoelectrons counted, given by G times G, and the noise which is the quadrature summation of the three noise sources where the read noise is a constant value, the photon shot noise (second term) is the square root of the number of photoelectrons, and the PRNU is proportional to the number of photoelectrons collected.

The curve fitting process finds values for G, r and p which best fit the measured curve.

The read noise figure is given directly by r. The saturation capacity is simply the number of photoelectrons at 100% grey (aka white), so is 100G.

The quantum efficiency is calculated using a formula derived by Chrisk99 [4]. Using the DxO measure ISO figure, a calculation is made of the number of photons incident on a pixel. The actual number collected at saturation, divided by this number gives the quantum efficiency.

Generating the data.

The HTML pages shown here are generated directly by a program starting from tables taken from DxO data. There is no human intervention or editing of the figures produced by the program, and the figures are presented without comment, for the reader to interpret as he/she sees fit.

The source of the curve fitting part of the program is given here.