Estimate the integration time needed to detect an exoplanet transit at a chosen signal-to-noise ratio under a simplified detector-noise model.
Instead of asking what SNR a fixed exposure delivers, this page solves the same photon-counting relationship for time. It is useful for comparing target brightness, transit depth, detector read noise, and background when planning a transit sequence.
1. Enter the detected stellar rate
Use electrons per second at the detector.
2. Specify the expected depth
Enter the transit depth in ppm.
3. Choose the target SNR
Set the detection strength you want the simplified model to reach.
4. Describe the noise terms
Enter background electron rate, read noise, and exposure length.
5. Compare time with transit duration
If required integration exceeds the available in-transit window, additional transits or a different observing setup may be needed.
Variance rate = S + B + RN² / texposure
Required time = SNR² × variance rate / (S² × d²)
S and B are electron rates, RN is read noise per exposure, texposure is exposure length, and d is transit depth as a fraction.
The result is the statistical integration time required by this simplified independent-noise model.
Visibility, stellar variability, systematics, and scheduling overhead are outside the calculation.
Given: S = 80,000 e−/s, depth = 300 ppm, target SNR = 7, B = 4,000 e−/s, RN = 7 e−, exposure = 60 s.
Calculation: Variance rate = 80,000 + 4,000 + 49/60 = 84,000.82 e−²/s. Required time = 7² × 84,000.82 / (80,000² × 0.0003²) ≈ 7,146 s = 1.99 h.
Result: About 2.0 hours of integration are required under the stated assumptions.
For a single-transit detection, yes. If the required time is longer than the usable in-transit duration, observations can be combined across multiple comparable transits.
Transit signals are often small fractions of stellar brightness, and ppm is convenient for expressing those shallow depths.
The RN²/exposure term approaches zero, leaving source and background shot noise as the dominant modeled terms.
No. Add slew, acquisition, calibration, readout dead time, and baseline observations separately when scheduling.
Yes, if you consistently translate each instrument concept into detected source rate, background rate, read noise, and exposure length.