Apparatus and Setup
You will evaluate four realistic source/background combinations using the SNR model from Lecture 4: SNR = S / √(S + n_pix·(B_sky + D + R²)). All four scenarios use the same read noise (R = 8 e⁻) so you can isolate the effect of source brightness, aperture size, and sky brightness separately.
Materials and Data
| Scenario | S (e⁻) | n_pix | Sky (e⁻/pix) | Dark (e⁻/pix) | Read (e⁻) | SNR | Classification |
|---|---|---|---|---|---|---|---|
| A (bright source, dark sky) | 2500 | 9 | 150 | 5 | 8 | ||
| B (faint source, dark sky) | 300 | 9 | 150 | 5 | 8 | ||
| C (faint source, large aperture) | 120 | 25 | 150 | 5 | 8 | ||
| D (moderate source, moonlit sky) | 800 | 9 | 400 | 5 | 8 |
Procedure
- For each scenario, compute the noise term n_pix×(B_sky + D + R²), then SNR, showing your arithmetic.
- Classify each scenario as a secure detection (SNR ≥ 5), a marginal detection (3 ≤ SNR < 5), or a non-detection (SNR < 3).
- Compare Scenario A to Scenario B: both use the same aperture and sky, but very different source counts. State the SNR ratio and check it is close to the ratio of the square roots of the source counts (an approximation valid when source-dominated).
- Compare Scenario B to Scenario C: explain, using the noise term, why enlarging the aperture from 9 to 25 pixels can turn a marginal detection into a non-detection even though the source flux captured is similar.
- Compare Scenario A to Scenario D: quantify how much the SNR degrades when sky background rises from 150 to 400 e⁻/pix (a moonlit-night effect), holding the source brightness closer to but not identical to Scenario A.
Analysis and Uncertainty
State explicitly which term dominates the noise budget in each scenario (source shot noise, sky shot noise, dark current, or read noise) and justify your answer with the relative sizes of S, n_pix×B_sky, n_pix×D, and n_pix×R².
Deliverables
- Completed SNR table with arithmetic shown for all four scenarios.
- A short paragraph identifying the dominant noise term in each case.
- A one-paragraph recommendation for how an observer could improve the Scenario C detection (e.g., smaller aperture, longer exposure, better seeing).
Assessment Criteria
- Correct SNR values for all four scenarios (within rounding).
- Correct classification (secure/marginal/non-detection) for each.
- Dominant noise term correctly identified and justified with numbers, not assertion.
- Recommendation is physically reasonable and tied to the noise model.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e.pdf), Chapter 6.3 (detectors) and Chapter 17.1 (brightness of stars).
- Scenario values are instructor-provided synthetic parameters logged in
materials/ASTR210/reference-log.md.