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Telescope Resolution Signal Budget Planner

The Telescope Resolution Signal Budget Planner estimates signal-to-noise ratio for a telescope observation using source photoelectrons, background photoelectrons, detector read noise, exposure time, and number of exposures. It is intended for first-order observing trades where image quality depends on collecting enough signal relative to photon and detector noise.

The result can be used to compare exposure strategies or determine whether a proposed observation has adequate statistical signal quality. It is deliberately compact: detailed observatory models may also include dark current, flat-field error, cosmic rays, saturation, scintillation, correlated noise, and throughput that varies with wavelength.

Calculator inputs

e⁻/s
e⁻/s
e⁻ rms
s
exp
Result
—
Estimated combined SNR
Total source electrons—
Total noise—
Single-exposure SNR—

1. Enter source rate
Use the expected detected source-electron rate inside the chosen measurement aperture.

2. Enter background rate
Include sky, thermal, or other background electrons accumulated in the same measurement aperture.

3. Set detector read noise
Enter the effective read-noise contribution per exposure for the measurement.

4. Enter exposure plan
Specify exposure duration and the number of exposures to combine.

5. Review SNR
Compare the combined SNR with the science or detection requirement for the observation.

Signal = source rate × exposure time × number of exposures
Noise = sqrt(signal + background rate × exposure time × number of exposures + read noise² × number of exposures)
SNR = signal / noise

The model assumes Poisson shot noise for source and background and independent Gaussian read noise for each exposure. The source rate and background rate should already reflect aperture size, throughput, and detector efficiency. Additional systematic or correlated noise is not included.

What the result means

The result is the ratio of total detected source electrons to the combined photon and read noise across all entered exposures.

It is a statistical detector-noise estimate and does not include systematic calibration errors or image-quality losses.

Given

  • Source rate = 120 e⁻/s
  • Background rate = 65 e⁻/s
  • Read noise = 4 e⁻ rms/exposure
  • Exposure = 30 s
  • 10 exposures

Calculation
Signal = 120×30×10 = 36,000 e⁻. Background = 65×30×10 = 19,500 e⁻. Read variance = 4²×10 = 160. Noise = √(36,000+19,500+160) = 235.9 e⁻. SNR = 36,000/235.9 = 152.6.

Result
Combined SNR ≈ 152.6.

This observation is strongly source-detected under the simplified shot-noise and read-noise model.

Why does splitting time into more exposures increase read-noise contribution?

Read noise is incurred each time the detector is read. For the same total integration time, more exposures therefore add more read-noise variance.

Should background rate be measured per pixel?

Use the total background rate that contributes to the same photometric or extraction aperture as the source signal. If you start from a per-pixel rate, multiply by the effective number of pixels.

Does this calculator include dark current?

Not as a separate field. You can add dark-current electrons to the background rate if that is appropriate for your detector model.

Can high SNR guarantee the required angular resolution?

No. SNR and angular resolution are different constraints. A high-SNR image can still be blurred by diffraction, sampling, aberrations, atmosphere, or pointing jitter.

What if the source rate is zero?

The computed SNR is zero because there is no source signal, even though background and read noise may still be present.