Noise is defined as random variations in the recorded image that are not repeatable. Noise can arise from many different sources.

Photon Noise

Because of the quantum nature of light, a light source of uniform intensity produces photons at an average rate that can vary somewhat. This deviation from uniform intensity, over time, follows a Poisson distribution. The actual intensity of the source can be known only to the square root of the total number of photons that are measured. In reality, we are not counting photons, we are really counting photo-electrons released in the sensor by the impact of photons. The statistics of these photo-electrons are Poissonian, just like the photons themselves.

This variation leads to a statistical uncertainty that is random. This random variation is defined as noise. Because it is random, it cannot be reproduced, and it can never be removed from the signal. This type of noise is called photon noise or shot noise.

The mathematical description of the variation was developed by French mathematician Simeon-Denis Poisson and is called a Poisson distribution. Photon noise is sometimes also called "Poisson Noise".

Photon noise is proportional to the square root of the signal. If 100 photons hit a pixel in the sensor, we can expect a random variation, or photon noise of 10 photons (10 is the square root of 100... 10 x 10 = 100). In this case, the signal-to-noise ratio is 10 to 1 (100 signal photons divided by 10 noise photons).

Because of the way that Poisson statistics work, we can greatly increase the signal-to-noise ratio by simply gathering more photons. For example, if we gather 100 photons in 1 minute, we have a signal-to-noise ratio of 10 to 1. But if we increase the exposure to 10 minutes and gather 1,000 photons, the noise will then increase to 31 photons (31 is roughly the square root of 1,000), but the signal-to-noise ratio will now be 1,000 to 31, or 31 to 1. This is a three times higher signal-to-noise ratio for a 10 minute exposure compared to a one minute exposure.

Because the solid state detectors in CCD and DSLR cameras are linear, we can also shoot a number of shorter exposures to equal one longer one. Any way we can gather more photons will improve the signal-to-noise ratio.

Photon noise is the largest source of noise for exposures where the signal is much larger than the noise floor of the camera. Photon noise comes from both the object signal and the sky background signal.

The effects of object signal photon noise can be reduced by shooting longer exposures, or by adding or averaging together many shorter exposures together, to improve the signal-to-noise ratio. Sky background photon noise can be reduced by shooting under darker skies or by using filters.

Thermal (Dark) Current Noise

Thermal current is heat-generated signal created by electrons that get counted along with the object signal photo-electrons. These thermal electrons are subject to the exact same Poissonian statistics as the photo-electrons. It is this statistical uncertainty that results in thermal current noise.

Thermal current noise is present in both the light frames and the dark calibration frames. Subtracting a dark frame removes thermal current, but actually adds thermal noise to an image.

Removing thermal current signal is a good thing, but adding thermal current noise in a dark frame is a bad thing. Thermal current noise, being random and non-repeatable, cannot be removed from an image. To reduce the amount of thermal dark current noise added in calibration, many dark frames can be averaged together to create a master dark frame with less noise than a single dark frame.

If you shoot two dark frames with a thermally stabilized camera, at exactly the same exposure and temperature, and then subtract them from each other, you will see the dark current noise.

Random Noise

Random noise can arise from fluctuations in the camera's electronic circuitry, electromagnetic interference and other sources. Random noise is usually very small, especially in today's well-built cameras. It cannot be removed but can be reduced in effect by increasing the signal by adding and averaging techniques.

Readout Noise

Readout noise is noise that is generated by the output amplifier when it cannot determine exactly how many electrons have come from each photosite.

In a given photosite, the amount of charge is too small to be measured without amplification, and because no amplifier is perfect, noise is added to the measurement.

Readout noise can be dealt with by exposing long enough so that the image is photon-noise limited from skyfog instead of read-noise limited. Its amplitude can be reduced by averaging frames.

When many short exposures are added or averaged together in an attempt to equal a longer one, each individual exposure contains readout noise, and this is also added together. This means that an average of 4 four-minute exposures has twice the readout noise as 1 sixteen-minute exposure.

If the individual exposures are background limited, the readout noise is small compared to the photon noise from the sky background. In this case it is better to average many short exposures because one long exposure would result in saturated pixels and clipped data.

Quantization Noise

A CMOS or CCD sensor is an analog device. When photons strike the silicon substrate in the sensor, their energy frees electrons which are then stored in the well. The electrons create a voltage, or charge, that is amplified and sent to an Analog to Digital (A/D) converter. This A/D converter takes the analog output voltage and turns it into analog to digital units, or ADUs.

When electrons don't arrive in exact multiples of the step size, an uncertainty is introduced because the A/D converter must arbitrarily make an assignment to a digital value. This uncertainly results in quantization noise.

Processing Noise

Adding or averaging light frames, and subtracting or dividing support frames, always adds noise to the image. This noise is called processing or calibration noise. We can get away with this because adding or averaging light frames increases the signal faster than it increases the noise, so we end up with a net gain in the signal-to-noise ratio.

Subtracting dark frames also adds random noise to the image. We can reduce the amount of random noise added by averaging a number of dark frames to create a master dark frame which has a better signal-to-noise ratio where the signal is thermal signal and the noise is thermal Poisson noise. Removing the thermal signal by subtracting a good master dark frame should improve the image more than the addition of the calibration noise degrades the image.

Dithering the light frames will also help improve the degradation from subtracting dark frames. Because the master dark frame is subtracted from each individual light frame before the light frames are added or averaged together, the random noise from the master dark is averaged when the light frames are shifted to be aligned. Here again, the noise is not reduced, but the signal-to-noise ratio is increased.

We can reduce processing noise by keeping the noise in the master dark, bias and flat frames as low as possible. This is done by combining as many frames as possible to create the master calibration frames.