See what each exposure adds to the stack.

Combine the full imaging train with measured or estimated electron rates to compare signal, sky, dark current and read noise.

Purpose and method

What this calculator does

What SNR will this imaging plan produce? Estimate calibrated signal-to-noise for a stack.

In words: Signal is divided by the quadrature sum of photon, dark and read noise.

The saved optical train supplies image scale. Source, sky, dark-current and read-noise rates must describe the actual target, site and camera operating mode.

Working geometry

Signal and noise accumulation

Source electrons add linearly while independent noise terms combine in quadrature.

Inputs

Train, rates and stack

Effective focal length

Unit: mm

Camera pixel pitch

Unit: µm

Binning

Unit: ×

Source signal rate

Unit: e⁻/s/arcsec²

Sky background rate

Unit: e⁻/s/arcsec²

Dark current

Unit: e⁻/s/px

Read noise

Unit: e⁻

Sub-exposure

Unit: s

Frame count

Unit: frames

Calculated now

Stack estimate

Stack SNR: 26.83
Single-frame SNR: 4.90
Total integration: 1.00 h
Image scale: 1.108″ / px
Source electrons: 2,210 e⁻
Sky / read variance: 36.8×

Equation

Signal to noise ratio for a calibrated stack

SNR = \frac{N S}{\sqrt{N (S + B + D + R^{2})}}

S, B and D are electrons per sub-exposure in one binned pixel; R is read noise and N is frame count.

Use rates measured from calibrated linear data where possible. This ideal model excludes flat-field error, gradients, clipping, registration loss, correlated noise, rejection losses and target structure within a pixel.

Optics & framing

Image quality

Acquisition

Mount & guiding

Sky & environment

Session planning

Formula

Where to find the inputs