Apparatus and Setup
This lab applies the Maréchal approximation (Lecture 11) to representative Keck natural-guide-star adaptive optics residual wavefront errors, computing Strehl ratios at K band and V band.
Materials and Data
| Residual wavefront error σ (nm) | Strehl ratio at K band (2200 nm) |
|---|---|
| 80 | 0.949 |
| 120 | 0.889 |
| 160 | 0.812 |
| 200 | 0.722 |
| 260 | 0.576 |
| 320 | 0.434 |
| 400 | 0.271 |
Values are representative published Keck natural-guide-star AO performance figures (Wizinowich et al. 2000), not independently re-verified this session.
Procedure
- Using S = exp[-(2πσ/λ)²], independently reproduce the Strehl ratio at K band for σ=160 nm, and confirm your value against 0.812.
- Recompute the Strehl ratio for the same σ=160 nm at V band (551 nm) instead of K band, and confirm your value against 0.0358.
- Using Keck's aperture and the diffraction-limited FWHM relation (FWHM≈1.03λ/D), compute Keck's diffraction-limited K-band FWHM, and compare it qualitatively to the AO-corrected image expected at Strehl=0.81.
- Using your two Strehl-ratio results (steps 1-2), explain quantitatively why natural-guide-star adaptive optics historically targets near-infrared science cases rather than visible-light imaging, for the same physical AO correction hardware.
Analysis and Uncertainty
State explicitly that a Strehl ratio below 1.0, even at K band, means the AO-corrected image still contains a broader residual halo in addition to a sharper diffraction-limited core, and that this course's single representative σ value does not capture how AO performance varies with atmospheric conditions, guide-star brightness, and target elevation on a real night.
Deliverables
- Both independently reproduced Strehl-ratio calculations (K band and V band).
- The diffraction-limited K-band FWHM calculation.
- A written explanation of the near-infrared AO preference, quantitatively grounded in the two Strehl-ratio results.
Assessment Criteria
- Correct Maréchal-approximation arithmetic at both wavelengths.
- Correct diffraction-limited FWHM arithmetic.
- Correct, quantitatively grounded explanation of the near-infrared AO preference.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 6 (astronomical instruments), descriptive only; this course exceeds that introductory treatment throughout.
- Keck AO residual wavefront-error/Strehl-ratio figures: standard published values (Wizinowich et al. 2000), not independently re-verified this session; Keck aperture live-verified this session; see
materials/ASTR340/reference-log.md. - Generated by
materials/ASTR340/src/generate_astr340_content.py.