Swiss Astro Imaging Group

Digital Imaging Noise theory and analysis

What is Noise?

SNR (Signal to noise ratio)

SNR = P_{signal} / P_{noise}

Measuring SNR

P_{noise}

P_{signal}

Simplification on uniform image

= Mean value of image

= Standard deviation of image

SNR = P_{signal} / P_{noise} = \frac{13105}{3273} \approx 4 \approx 25\%

Sources of noise

Dark Noise (when taking pictures in the complete absence of light)
- Dark current noise, random temporal noise
- Read-noise, random 1-time noise
- Hot-/Cold-Pixels, fixed-pattern noise
- Dark signal non-uniformity noise (DSNU), fixed-pattern noise
- Sensor Glow, fixed-pattern temporal signal
Lit Noise (when exposing under light)
- Photon shot noise / Poisson noise, random temporal noise
- Photo response non-uniformity (PRNU), fixed-pattern noise
- Obstruction based patterns (Dust in the optical system, Vignetting etc.), fixed-pattern unwanted signal reduction

Fixed Pattern Noise

DSNU

Hot/Cold-Pixels

Sensor Glow

PRNU

Obstructions

Calibration to remove FPN

Fixed-pattern noise can be removed completely by using proper calibration frames.

DSNU

Hot/Cold-Pixels

Sensor Glow

PRNU

Obstructions

Bias or Darkframe

Darkframe

Flatframe

Random Noise

After eliminating fixed-pattern noise, we're left only with random noise. We can reduce random noise by using statics to average it out. This is only a reduction and never an elimination.

10 Frames with DSNU and read noise

10 Frames simple average stack

After stacking 10 frames with FPN and random read noise, we can see the random noise disappear slowly.

Light is noisy

Sensor

Photons

Photon shot noise or Poisson noise as a result of the statistical nature of light.

30s

2e-

3e-

2e-

1e-

3e-

Each sub-frame will contain a different amount of photons due to the statistical nature of light (Poisson distribution).

Poisson distribution of light

For expected 8 electrons

Gaussian and Poisson SNR

The amount of shot noise in photography is always the square root of the signal.

P_{Noise} = \sqrt{P_{Signal}}

If You have 4 signal, your noise will be 2. That's 50% noise!

If You have 10000 signal, your noise will be 100. That's only 1% noise!

Example without units

The light itself is not the problem but the inherent photon noise is!

Light Pollution

Noise reduction by stacking

10 Frames with DSNU and read noise

10 Frames simple average stack

After stacking 10 frames with FPN and random read noise, we can see the random noise disappear slowly.

N_{Reduction} = \frac{1}{ \sqrt{n} }

= Sub-frame count

SNR_{Enhancement} = \sqrt{n}

Putting random noise into perspective

It's important to know what random noise sources you have and how large they are relative to each other.

Light-pollution

Read Noise

Dark current

Noise adds in quadrature

= Dark current (e-/pixel/seconds)

N_{total}=\sqrt{R^{2}+D\cdot s+P\cdot s}

= Sub-exposure length (seconds)

= Light pollution (e-/pixel/seconds)

= Read-noise (e-/pixel)