Issue:
Method for determining signal-to-noise ratio (SNR) or decibel (dB) value for PGR cameras.

Solution:
This article describes the general methodology used by Point Grey Research for determining the signal-to-noise ration (SNR) or decibel (dB) values for PGR IEEE-1394 digital cameras.

An ideal camera sensor would convert a known amount of light into an exactly predictable output voltage. Unfortunately, ideal sensors (like all other electronic devices) do not exist. Due to temperature conditions, electronic interference, etc., sensors will not convert light 100% precisely. Sometimes the output voltage will be slightly bigger than expected and sometimes it will be slightly smaller. The difference between the ideal signal that you expect and the real-world signal that you actually see is usually called noise. The relationship between signal and noise is called the signal-to-nose ratio (SNR). Signal-to-noise ratio is also frequently stated in decibels (dB). The formula for calculating a signal-to-noise ratio in dB is: SNR = 20 x log (Signal/Noise).

There are a variety of sources of noise in the CCD readout, including the A/D converter (every analog to digital conversion circuit will show a distribution or spread about an ideal conversion value), and the CCDs themselves, which spontaneously generate a small charge. The noise you see when a pixel reads 80% of maximum is not fixed, but depends very strongly on the GAIN of the system, which multiplies noise that is read out of the CCDs.

A large fraction of the low-level noise (e.g. the spontaneous generation of charge in the CCDs) is independent of the amount of light hitting the CCD. So, if you have not very much incoming light, this fixed amount of noise is comparable to the signal, and if you then magnify the signal to 80% of the max, you will get a comparable noise level in your image. If instead you have a large amount of light, this will dwarf any fixed amounts of noise, and even after multiplying by the gain, your signal-to-noise ratio will still be good.

The way PGR measures the SNR is to measure the "dark noise" of the CCDs. This is the noise that is present when there is no external signal, and is a standard measure of camera quality. The gain is set to a low value (ideally zero), since of course the gain will increase the noise level proportionately. We then:

1. Set Gain to minimum.
   
2. Put the camera into a Y16 video mode, at the fastest frame rate available for that mode.
   
3. Make sure that no light is hitting the camera (e.g. put the lens cap on).
   
4. Set Shutter to minimum.
   
5. Set Brightness to a level such that the zero value of the A/D converter is off the floor.
   
6. Take two (2) images (they will be black).
   
7. Convert the images from 16-bit to double. The most-significant byte forms the integral part, while the valid bits from the least-significant byte form the fractional part.
   
8. Take the absolute difference of the images to create a "diff" image.
   
9. Take the standard deviation (S) of the pixels in the "diff" image.
   
10. The SNR is then (255/(S/sqrt(2))) because the max signal we can get (with a large amount of light) is 255 in a pixel and the noise that is present is the std dev divided by sqrt(2) (the noise from two images has been added together).

Related Articles:
1.) Using longer (ribbon) cables for PGR extended head cameras.
2.) Method for converting signal-to-noise ratio (SNR) to/from bits of data.
3.) Increasing dynamic range of PGR cameras.