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Exoplanet Transit Signal Budget Planner

Build a simplified photon-counting signal budget for an exoplanet transit and estimate the resulting signal-to-noise ratio.

The calculation treats the transit as a small deficit in stellar electrons and combines source shot noise, background shot noise, and detector read noise. It is most useful for early instrument trades where an electron-rate estimate is available but a full detector simulator is not yet justified.

Inputs

e−/s
ppm
h
e−/s
e−
s
Result
—
Estimated transit SNR
Transit deficit signal—
Total noise—
Exposure count—

1. Enter the detected stellar rate
Use the electron rate after throughput and detector efficiency, not the incident photon rate unless those are already included.

2. Enter the transit depth
Provide the fractional transit depth in ppm.

3. Set integration and exposure timing
Integration time is the total on-target time; exposure length controls how many read-noise contributions occur.

4. Add background and read noise
Use rates and per-exposure values in electrons.

5. Review the SNR
A higher value indicates a more statistically distinct transit deficit under this independent-noise model.

Transit signal = S × d × t
Noise = √[(S + B) × t + Nexp × RN²]
SNR = transit signal / noise

S is the stellar electron rate, d is transit depth as a fraction, B is background electron rate, t is integration time in seconds, RN is read noise per exposure, and Nexp is the number of exposures.

What the result means

The SNR shows how strongly the expected transit deficit stands above the modeled statistical noise.

Systematic and time-correlated noise can make real performance worse than this estimate.

Given: S = 100,000 e−/s, depth = 500 ppm, t = 2 h, B = 5,000 e−/s, RN = 8 e−, exposure = 60 s.

Calculation: t = 7,200 s and Nexp = 120. Signal = 100,000 × 0.0005 × 7,200 = 360,000 e−. Noise = √[(105,000 × 7,200) + (120 × 8²)] ≈ 27,495 e−. SNR ≈ 13.09.

Result: The simplified transit signal budget produces an SNR of about 13.1.

Should source rate include telescope throughput?

Yes. For this model, use the electron rate actually reaching the detector after aperture, throughput, quantum efficiency, and bandpass effects.

Why does shorter exposure time sometimes reduce SNR?

With fixed total integration time, shorter exposures create more detector reads, so read-noise variance is added more times.

Does the model include scintillation or correlated noise?

No. It includes only independent source, background, and read-noise terms.

Can the background rate be zero?

Yes. Set it to zero when background is negligible or already included elsewhere in your source-rate model.

How is this different from the observation-time estimator?

This planner computes SNR for a chosen time, while the observation-time estimator solves for the time needed to reach a chosen SNR.