In photography the higher the ratio of Signal to Noise, the less grainy the final image normally looks.  The Signal-to-Noise-ratio SNR is therefore a key component of Image Quality.  Let’s take a closer look at it.

We know that for a given mean number of impinging photons during exposure our cameras’ digital sensors produce a proportional mean output signal () in units of photoelectrons () according to the simple relationship:

(1)  

where EQE is Effective Quantum Efficiency.  We can model three macro ‘random’ noise components present at the sensor’s output together with the signal, the relative strength of each indicated by its own standard deviation ():

1. ‘Shot Noise’ inherently present in the incoming light and photoelectric conversion process ()
2. ‘Read Noise’ introduced by the sensor and downstream electronics ()
3. ‘Pixel Response Non Uniformities’ (), unpredictable per-pixel gain variations proportional to signal

all in units of .   Since the three components are independent, Total Random Noise is then obtained by summing the three standard deviations in quadrature

(2)  

(or more precisely by adding their variances).  This discussion ignores Pattern and other types of noise which these days is seldom an issue in normal photography, you can learn more about modeling noise in digital cameras from these excellent pages by Emil Martinec.

If we plot the signal, the three noise components and their total in units of photoelectrons this is the graph that results when using average values for the parameters above from a Nikon D610 at base ISO:

The horizontal axis is interchangeable with the number of arriving photons which are directly related to the output signal by per equation (1).  Note that the Total Noise curve (solid black line) has three very distinct areas, depending on the relative values of the three components of noise: at very low signals it is mainly made up of  shot and read noise; at 5 or 6 stops below saturation it is mainly shot noise; and approaching saturation it is mainly shot noise and PRNU.  If we define total SNR as the ratio of  mean signal to total noise

(3)  

and plot the two variables on a log-log plot this is what they look like

The red curve is the measured SNR curve, what DxOMark.com calls a Full SNR Curve. They present their x-axis as a relative percentage of signal full scale while the graph above has an absolute scale in units of lx-s, which will come in handy in future posts.

SNR curves are a good way to characterize a sensor’s IQ by showing at a glance its noise performance  throughout the operating range – from deep shadows, to mid-tones to highlights.   Note how the measured SNR curve dips from the ideal at low signal levels because of the increasing contribution of the read noise ‘floor’; and near saturation, although less dramatically, because of PRNU.

The ‘engineering’ Dynamic Range of the sensor can be read off the x-axis by simply counting the number of stops between saturation Exposure and when the SNR is equal to 1 (zero as a logarithm above), in this case from 0.06 to -13.5, for a total of 13.6 stops of pixel level DR.  This threshold is relevant when pixel peeping, higher SNR thresholds may be appropriate depending on the application, see for instance Photographic Dynamic Range.

Also note that SNR is highest near saturation and it continues to decreases monotonically until it hits eDR’s lower limit .  Therefore in order to maximize SNR (hence IQ) if a photographer can they should always use the full dynamic range at their disposal by exposing the image so that the brightest desirable highlights are recorded just below saturation, a strategy sometimes descibed as Exposing To The Right (ETTR).

In clean sensors at low ISOs (for instance Exmor class sensors) there is usually an area where the SNR curve is approximately all due to shot noise, in this example 5 or 6 stops below saturation.  This area is significant because it allows us to estimate the signal in by simply squaring the ratio of the mean () and standard deviation () of the values of a uniform patch in the raw file, measured in Data Numbers with a program like RawDigger.    This bit of magic allows us to jump straight from output raw file in DN to input signal in (photons if we know EQE) bypassing all the complicated steps and parameters that we would need to know otherwise.  It is called Photon Transfer and it works because shot noise follows Poisson statistics where

(4)  

So in a shot noise dominated area of the picture signal in units of .  Since gain falls out of the equation can be calculated in DN from the raw file and the estimated mean signal is in at the output of the relative photodiodes.

Next, how to use SNR curves to compare cameras.