Apparatus and Setup
This lab computes the plate scale and pixel scale of several real telescope/instrument combinations (Lecture 03) and checks each against the Nyquist sampling criterion using the resolution limits derived in Lab 01.
Materials and Data
| Telescope | Focal length (m) | Plate scale (arcsec/mm) |
|---|---|---|
| Keck | 17.5 | 11.787 |
| HST | 57.6 | 3.581 |
| JWST | 131.4 | 1.570 |
| DECam host (Blanco 4m) | 11.28 | 18.286 |
DECam's published pixel size is 15 µm; the camera is a 570-megapixel, 62-CCD mosaic (standard published facility specification, level 2).
Procedure
- Using s = 206265″/f[mm], independently reproduce the plate scale for all four telescopes in the data table.
- Compute DECam's pixel scale (arcsec/pixel) from its plate scale and 15 µm pixel size, and confirm it against the published value of 0.274 arcsec/pixel.
- The Blanco 4m telescope (DECam's host) is a seeing-limited, ground-based facility with typical seeing of about 1.0″. Apply the Nyquist criterion (pixel scale ≤ FWHM/2) to determine whether DECam's pixel scale adequately samples this typical seeing disk.
- Suppose DECam's pixel scale were instead used on Keck (an entirely hypothetical combination). Using Keck's much finer diffraction-limited resolution from Lab 01, determine whether this pixel scale would undersample, adequately sample, or oversample Keck's diffraction limit, and explain why an instrument built for Keck would need substantially smaller pixels (or a longer focal length) than DECam's.
Analysis and Uncertainty
State explicitly why plate scale depends only on focal length, not aperture, and why this means two telescopes of very different aperture (e.g., Keck and the Blanco 4m) can in principle share very similar plate scales if their focal lengths happen to be similar, even though their light-gathering power and diffraction limits differ enormously.
Deliverables
- Independently reproduced plate-scale table.
- DECam pixel-scale derivation and confirmation.
- Both Nyquist-sampling checks (DECam on its own host telescope, and the hypothetical DECam-on-Keck combination) with explicit conclusions.
Assessment Criteria
- Correct plate-scale arithmetic for all four telescopes.
- Correct pixel-scale derivation matching the published DECam value.
- Correct Nyquist-criterion application and conclusion in both sampling checks.
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.
- DECam pixel size, CCD count, and megapixel count: standard published facility specifications (NOIRLab/CTIO), not independently re-verified this session; Keck, HST, JWST focal lengths: standard published mission/facility specifications; see
materials/ASTR340/reference-log.md. - Generated by
materials/ASTR340/src/generate_astr340_content.py.