ASTR 340 Problem Set 02: Plate Scale and Nyquist Sampling for a New Instrument

Problem set for lecture unit 2.

Problems

1. Plate scale for a new focal length 20 points

A proposed new Keck instrument uses a re-imaging focal length of f=25.0 m (different from Keck's native 17.5 m Cassegrain focus). Compute its plate scale in arcsec/mm.

2. Pixel scale for a 12 µm detector 15 points

Using your Problem 1 plate scale and a 12 µm pixel detector, compute the pixel scale in arcsec/pixel.

3. Nyquist check against Keck AO 15 points

Keck's AO-corrected K-band diffraction-limited FWHM is 46.7 mas (Lecture 11). Determine whether your Problem 2 pixel scale adequately Nyquist-samples this FWHM, or whether it under- or oversamples it.

4. Design trade-off 20 points

If the Problem 2 pixel scale underscamples Keck's AO-corrected diffraction limit, propose one specific design change (to focal length, pixel size, or both) that would bring the instrument to adequate Nyquist sampling, and show the resulting pixel scale numerically.

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