Astronomy
Telescope Signal-to-Noise Calculator
Estimate stacked source electrons, noise components, modeled total noise, SNR, target margin, and total integration time.
Total stacked source signal-
Total stacked sky signal-
Total stacked dark signal-
Total read-noise variance-
Total modeled noise-
Stacked signal-to-noise ratio-
Stacked SNR minus target-
Total integration time (hours)-
Decision view
Stacked SNR curve with target line
Stacked SNR curve with target lineFrame-count SNR progress is plotted against the entered target while noise components remain visible.
Exact scenario comparisonStacked frame count changes while all other entered assumptions remain constant.
| Stacked frame count | Total stacked source signal | Total stacked sky signal | Total stacked dark signal | Total read-noise variance | Total modeled noise | Stacked signal-to-noise ratio | Stacked SNR minus target | Total integration time (hours) |
|---|
Period-by-period detail
Stacked-frame signal and noise table
How to use Telescope Signal-to-Noise Calculator
- Enter measured source, sky, dark, and read-noise assumptions.
- Enter aperture pixels, subexposure length, frame count, and target SNR.
- Use the SNR curve and noise composition to see which term dominates.
Calculator guide
Understanding Telescope Signal-to-Noise Calculator
Stacked signal-to-noise is a variance problem: source signal accumulates, but sky, dark current, and read noise add to the denominator before the square root.
Calculation method
How the calculation works
Accumulate source, sky, dark, and read-noise variance across frames, then divide total source electrons by the square root of total modeled variance. Multiply each electron rate by exposure duration, aperture pixels, and frame count as appropriate, add variances, take the square root, then divide source signal by noise.
Detailed calculation process
Accumulate stacked signal and noise variance
The default uses 12 source electrons/second, 0.8 sky electrons/second/pixel, 0.02 dark electrons/second/pixel, 3.5 read-noise electrons/pixel/frame, 25 aperture pixels, 180 second subexposures, 40 frames, and target SNR 30.
General formula: S = r_s t nK = r_k t m nD = r_d t m nR = sigma_r^2 m nN = sqrt(S+K+D+R)Z = S/NM = Z-Z_tH = tn/3600 The source term is the desired signal. Sky, dark, and read noise increase the variance. Read noise is squared because it is already a per-frame standard deviation.
What each symbol means
Worked substitution with the default inputs
The default stack reaches SNR 174.111, which is 144.111 above the entered target, with 2.000 hours of integration.
Purpose-built visual
SNR curve with noise composition
The visual combines a frame-count SNR curve with a compact noise-component breakdown.
Worked situations
Practical examples
- The default uses 12 source electrons/second, 0.8 sky electrons/second/pixel, 0.02 dark electrons/second/pixel, 3.5 read-noise electrons/pixel/frame, 25 aperture pixels, 180 second subexposures, 40 frames, and target SNR 30.
- The default stack reaches SNR 174.111, which is 144.111 above the entered target, with 2.000 hours of integration.
Better inputs
Useful tips
- Keep source electrons, sky background, dark current, and read noise on the same per-frame or stacked basis.
- Enter aperture, exposure length, and frame count from one imaging setup so signal and noise assumptions remain comparable.
- Change exposure count separately from exposure duration because stacking improves signal-to-noise through a square-root relationship.
Before relying on the result
Limitations and common mistakes
- Flat-field error, saturation, cosmic rays, resampling, sky gradients, scintillation, rejection, and calibration systematics are excluded.
- The model assumes independent frames and consistent rates.
- Read-noise treatment assumes variance addition.
Reference
Key terms
- Variance
- Noise power terms that are added before taking a square root.
- Aperture pixels
- Pixels included in the measurement region.
- SNR margin
- Modeled SNR minus the entered target SNR.
Important note
Calculated from the entered values using the displayed astronomical model. Use current ephemerides and qualified references for observation or mission decisions.
Frequently asked questions
Why is read noise squared?
The input is a standard deviation, so variance addition uses its square.
Why is sky in the noise term?
Sky background adds shot-noise variance even though it is not target signal.
Does more frames always help?
More integration generally raises SNR, but systematics and saturation can limit real gains.
Is SNR unitless?
Yes. It is signal divided by noise.