# SNR in Digital Cameras in 2020

There are significant number of misconceptions about noise in digital cameras and how this depends on variables like the sensor size or the pixel size. In this short post I will try to explain in clear terms the relationship between Signal Noise Ratio (SNR) and sensor size.

Signal (S) is the number of photons captured by the lens and arriving on the sensor, this will be converted in electric signal by the sensor and digitised later on by an Analog Digital Converter (ADC) and further processed by Digital Signal Processors (DSP). Signal depending on light is not affected by pixel size but by sensor size. There are many readings on this subject and you can google it yourself using sentences like ‘does pixel size matter’. Look out for scientific evidence backed up by data and formulas and not YouTube videos.

S = P * e where P is the photon arrival rate that is directly proportional to the surface area of the sensor, through physical aperture of the lens and solid angle of view, and e is the exposure time.

This equation also means that once we equalise lens aperture there is no difference in performance between sensors. Example two lenses with equivalent field of view 24mm and 12mm on full frame and MFT with crop 2x when the lens aperture is equalised produce the same SNR. Considering a full frame at f/2.8 and the MFT at f/1.4 gives the same result as 24/2.8=12/1.4 this is called constrained depth of field. And until there is sufficient light ensures SNR is identical between formats.

Noise is made of three components:

1. Photon Noise (PN) is the inherent noise in the light, that is made of particles even though is approximated in optics with linear beams
2. Read Noise (RN) is the combined read noise of the sensor and the downstream electronic noise
3. Dark Current Noise (DN) is the thermal noise generated by long exposure heating up the sensor

I have discovered wordpress has no equation editor so forgive if the formulas appear rough.

Photo Noise is well mapped by Poisson distribution and the average level can be approximated with SQRT(S).

The ‘apparent’ read noise is generally constant and does not depend on the signal intensity.

While 3 is fundamental to Astrophotography it can be neglected for majority of photographic applications as long as the sensor does not heat up so we will ignore it for this discussion.

If we write down the Noise equation we obtain the following:

Noise=sqrt({PN}^2+{RN}^2+{DN}^2)

Ignoring DN in our application we have two scenarios, the first one is where the signal is strong enough that the Read Noise is considerably smaller than Photon Noise. This is the typical scenario in standard working conditions of a camera. If PN >> RN the signal to noise ratio becomes:

SNR =sqrt S

S is unrelated to pixel size but is affected by sensor size. If we take a camera with a full frame and one with a 2x crop factor at high signal rate the full frame camera and identical f/number it has double the SNR of the smaller 2x crop. Because the signal is high enough this benefit is almost not visible in normal conditions. If we operate at constrained depth of field the larger sensor camera has no benefit on the smaller sensor.

When the number of photons collected drops the Read Noise becomes more important than the photon noise. The trigger point will change depending on the size of the sensor and smaller sensor will become subject to Read Noise sooner than larger sensors but broadly the SNR benefit will remain double. If we look at DxOMark measurements of the Panasonic S1 full frame vs the GH5 micro four thirds we see that the benefit is around 6 dB at the same ISO value, so almost spot on with the theory.

Due to the way the curve of SNR drops the larger sensor camera will have a benefit or two stops also on ISO and this is the reason why DxOMark Sport Score for the GH5 is 807 while the S1 has a sport score of 3333 a total difference of 2.046 stops. The values of 807 and 3333 are measured and correspond to 1250 and 5000 on the actual GH5 and S1 cameras.

If we consider two Nikon camera the D850 full frame and the D7500 APSC we should find the difference to be one stop ISO and the SNR to drop at the same 3 dB per ISO increment.

The graphic from DxoMark confirms the theory.

If the SNR does not depend on pixel size, why do professional video cameras and, some high end SLR, have smaller pixel count? This is due to a feature called dual native ISO. It is obvious that a sensor has only one sensitivity and this cannot change, so what is happening then? We have seen that when signal drops, the SNR becomes dominated by the Read Noise of the sensor so what manufacturers do is to cap the full well capacity of the sensor and therefore cap the maximum dynamic range and apply a much stronger amplification through a low signal amplifier stage. In order to have enough signal to be effective the cameras have large pixel pitch so that the maximum signal per pixel is sufficiently high that even clipped is high enough to benefit from the amplification. This has the effect of pushing the SNR up two stops on average. Graphic of the read noise of the GH5s and S1 show a similar pattern.

Sone manufacturers like Sony appear to use dual gain systematically even with smaller pixel pitch in those cases the benefit is reduced from 2 stops to sometimes 1 or less. Look carefully for the read noise charts on sites like photonsforphotos to understand the kind of circuit in your camera and make the most of the SNR.

Because most of the low light situation have limited dynamic range, and the viewer is more sensitive to noise than DR, when the noise goes above a certain floor the limitation of the DR is seen as acceptable. The actual DR is falling well below values that would be considered acceptable for photography, but with photos you can intervene on noise in post processing but not DR, so highest DR is always the priority. This does not mean however that one should artificially inflate requirements introducing incorrect concepts like Useable DR especially when the dual gain circuit reduce maximum DR. Many cameras from Sony and Panasonic and other manufacturers have a dual gain amplifier, sometimes advertised other times not. A SNR of 1 or 0 dB is the standard to define useable signal because you can still see an image when noise and signal are comparable.

It is important to understand that once depth of field is equalised all performance indicators flatten and the benefit of one format on the other is at the edges of the ISO range, at very low ISO values and very high ISO and in both cases is the ability of the sensor to collect more photons that makes the difference, net of other structural issues in the camera.

As majority of users do not work at the boundaries of the ISO range or in low light and the differences in the more usual values get equalised, we can understand why many users prefer smaller sensor formats, that make not just the camera bodies smaller, but also the lenses.

In conclusion a larger sensor will always be superior to a smaller sensor camera regardless all additional improvement made by dual gain circuits. A full frame camera will be able to offer sustained dynamic range together with acceptable SNR value until higher ISO levels. Looking for example at the Panasonic video orientated S1H the trade off point of ISO 4000 is sufficient on a full frame camera to cover most real-life situation while the 2500 of the GH5s leaves out a large chunk of night scenes where in addition to good SNR, some dynamic range may still be required.