### Gion Kunz

Let's create together.

SNR = P_{signal} / P_{noise}

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\%

- 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*

- Dark current noise,
- 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*

- Photon shot noise / Poisson noise,

DSNU

Hot/Cold-Pixels

Sensor Glow

PRNU

Obstructions

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

DSNU

Hot/Cold-Pixels

Sensor Glow

PRNU

Obstructions

**Bias or Darkframe**

**Darkframe**

**Darkframe**

**Flatframe**

**Flatframe**

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.

Sensor

Photons

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

30s

30s

30s

30s

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).

For expected 8 electrons

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!

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

10 Frames with DSNU and read noise

10 Frames simple average stack

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

n

= Sub-frame count

SNR_{Enhancement} = \sqrt{n}

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

D

= Dark current (e-/pixel/seconds)

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

s

= Sub-exposure length (seconds)

P

= Light pollution (e-/pixel/seconds)

R

= Read-noise (e-/pixel)

Light-pollution

Read Noise

Dark current

Total

By Gion Kunz

SAIG workshop about noise in digital imaging

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