Learning objectives
- calculate fringe phase and resolution scales, visualize uv coverage, and demonstrate missing short-spacing sensitivity.
- Propagate a statistical or calibration uncertainty and report a limitation.
- Preserve a reproducible record of inputs, transformations, and outputs.
Preparation, materials, and setup
Use Python 3 with the standard library (or a spreadsheet capable of regression and plotting), the supplied ../data/uv_samples.csv, and the relevant lecture notes. Record file name, row count, columns, units, and provenance level before editing. No facility observing time is assumed.
Dataset status: the supplied compact record is synthetic/instructor-provided (level 3), not an archived observation. Compare its analysis workflow with the real survey or observatory source cited in ../reference-log.md.
Computed check: synthesized FWHM scale = 0.03942 arcsec; largest-scale estimate = 24.73 arcsec.
Apparatus and procedure
- The supplied u_lambda and v_lambda columns are already spatial frequencies in wavelengths. Verify the scale by converting a 3-km baseline at 1.4 GHz to wavelengths, then identify each sample's radius and position angle in the uv plane.
- For each source offset, calculate complex point-source visibility amplitude and phase from the flat-sky measurement equation.
- Plot uv samples with equal axis scale and identify the largest gap in position angle and radial spacing.
- Construct a one-dimensional dirty beam from the supplied sampling coordinates using a discrete inverse Fourier sum.
- Compare a compact source and a broad Gaussian after applying the same uv sampling; quantify recovered integrated-flux fraction.
Measurement record and uncertainty
| Record | Required entry |
|---|---|
| Input | File, release/source, units, masks or flags, and provenance level. |
| Model | Equation, parameter values, convention, and approximation. |
| Statistics | Fit covariance or counting error plus one calibration/selection/systematic term. |
| Validation | Independent recomputation, residual plot, and limiting-case check. |
Submit the uv plot, dirty-beam plot, recovered-flux table, and a paragraph distinguishing resolution from largest recoverable scale.
Deliverables and criteria
- Reproducible code or spreadsheet with inputs and units documented.
- One publication-quality labeled plot and a short interpretation (400-700 words).
- Uncertainty budget that separates random, common-mode, and model terms where relevant.
- Credit requires correct method, units, interpretation, provenance, and a limitation; a copied numeric result without an audit trail earns at most half credit.
Interpretive boundary
Long baselines supply fine angular scales; absent short baselines suppress smooth emission even when the synthesized beam is narrow. State explicitly which parts of your result are facts about this prepared teaching record and which are transferable inference methods.
References and provenance
Course teaching record: ../data/uv_samples.csv, level 3. Real facility/survey context: reference log. No external image is used.