Interferometry Baseline Lab

Interactive synthesis-interferometry laboratory for ENU array geometry, projected baselines, Earth-rotation uvw coverage, complex binary visibility, and the response from incomplete Fourier sampling.

Author: Biswajit Jana

Purpose

The laboratory makes the source-projected nature of angular resolution explicit. A fixed ground array samples different Fourier coordinates as the source hour angle changes. It is an educational, narrow-field model, not a calibrated imaging pipeline.

Array model

Choose among three idealised local ENU layouts:

• two-collector east-west pair;
• three-collector L layout;
• four-collector Y layout.

They are synthetic teaching geometries, not reproductions of an observatory configuration. For an antenna-pair vector (B_E, B_N, B_U), hour angle H, declination delta, and wavelength lambda, the code uses

u = [B_E sin(H) + B_N cos(H)] / lambda
v = [-B_E sin(delta) cos(H) + B_N sin(delta) sin(H) + B_U cos(delta)] / lambda
w = [B_E cos(delta) cos(H) - B_N cos(delta) sin(H) + B_U sin(delta)] / lambda

Every pair contributes an Earth-rotation track and Hermitian counterpart to the coverage display. The pair with the largest projected baseline supplies the single fringe and binary-visibility readout.

For a binary source with flux ratio r and angular separation vector (dx, dy), the complex visibility is

V(u, v) = [1 + r exp(-2 pi i (u dx + v dy))] / (1 + r)

The sampling-response panel is a naturally weighted real Fourier sum over all selected tracks. It is an instrumental response function, not a reconstructed sky image.

Features

• Idealised two, three, and four-collector array presets.
• Local east-north array-layout diagram.
• ENU to uvw projection for every baseline pair.
• Adjustable hour-angle synthesis span.
• uv coverage and Hermitian counterparts.
• Projected resolution, spatial frequency, complex binary visibility, and phase.
• Correlated fringe signal from the selected longest projected baseline.
• Natural-weighted sampling response from all selected tracks.
• Clearly labelled synthetic ALMA-scale scenario.

Run and validate

Open index.html in a modern browser.

node tools/validate_arrays.js

The check verifies ENU projection limits and the expected pair counts: 2 collectors give 1 baseline, 3 give 3, and 4 give 6.

Model boundaries

• No primary beam, thermal noise, calibration/gain errors, atmospheric phase error, delay tracking, gridding kernel, bandwidth synthesis, or deconvolution.
• The response panel is not a dirty image or a CLEAN reconstruction.
• The w coordinate is calculated and reported but no wide-field w correction is applied.
• The binary source and all layouts are synthetic.
• The ALMA scale preset is a documented scale comparison only; it is not an ALMA archive-data client.

References

• Thompson, Moran and Swenson, Interferometry and Synthesis in Radio Astronomy.
• Monnier, 2003, Optical interferometry in astronomy.
• Taylor, Carilli and Perley, Synthesis Imaging in Radio Astronomy II.

Topics

interferometry, radio-astronomy, instrumentation, uv-coverage, angular-resolution, scientific-visualisation, javascript