Solve for the exposure time needed to reach a target signal-to-noise ratio under a simplified telescope photon budget. Source rate, background rate, throughput, and read noise are combined analytically so observers can estimate cadence and the number of targets that fit into a session.
Let S and B be detected source and background rates. Solve SNR = S·t ÷ √((S+B)·t + read noise²). The positive quadratic root gives the required exposure time.
Treat the main result as an engineering estimate based on the stated inputs. Compare it with the applicable mission requirement and retain enough traceability to update the result when assumptions change.
This calculator supports early trade studies and does not replace mission-specific simulation, environmental analysis, or professional engineering review.
For 120 source photons/s, 35 background photons/s, 65% throughput, 6 electrons read noise, and target SNR 100, the required exposure is about 165.95 seconds.
It uses the values shown in the input panel and the formula stated on this page. It does not add hidden operational or environmental allowances.
Yes. Decimal values are accepted within each field’s displayed range, and calculations retain precision until the result is formatted.
Use a value justified by your project’s maturity, uncertainty policy, and verification plan rather than treating the default as a universal recommendation.
No. It is a first-pass estimate for trade studies. Verify the design with subsystem models, test data, and mission-specific constraints.
Zero is accepted where it represents a physically meaningful absence of load, loss, background, duty, or maneuver demand. Inputs used as divisors must remain above zero.
| Item | Use |
|---|---|
| Primary inputs | Enter values in the units printed beside each field. |
| Margin or reserve | Applied only where stated in the formula. |
| Displayed result | Rounded for readability; internal math keeps full precision. |