ASTR 340 Problem Set 06: Strehl Ratio Trade-offs for a New AO System

Problem set for lecture unit 6.

Problems

1. Strehl ratio at K and J band 20 points

A proposed upgraded Keck AO system achieves σ=100 nm residual wavefront error. Compute its Strehl ratio at K band (2200 nm) and at J band (1250 nm).

2. Comparison to the current system 15 points

Compare your K-band Problem 1 result to the current representative Keck AO Strehl ratio at σ=160 nm (0.812, Lecture 11/Lab 06), and state the improvement factor.

3. Wavefront-error budget for the improvement 15 points

The wavefront-error improvement from 160 nm to 100 nm might come from several independent upgrades (better wavefront sensing, faster deformable-mirror control, brighter guide stars). If three independent upgrades each contribute equally in root-sum-square to reduce the total from 160 nm to 100 nm, estimate the wavefront-error contribution of each individual upgrade.

4. Science case justification 20 points

Using your Problem 1-2 results, write a two-to-three sentence technical justification (in the style of Lecture 14's capstone) for why a science case requiring high-contrast J-band imaging would specifically benefit from this proposed AO upgrade.

Due and Scope

Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.

OpenStax Companion Reading

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.

References and Data Sources