This simulator models a radio interferometer array as a set of point-like dishes placed along a 1-D ground track. A plane wave from a distant source at angle θ reaches each dish with a phase 2π/λ·x·sinθ set by its position x and the wavelength λ = c/f. The array's combined response is computed by summing exp(i·2π/λ·x·sinθ) over every dish, squaring the magnitude of that complex sum, and multiplying by a single-dish diffraction envelope sin(u)/u squared — the same physics behind real arrays like the VLA and VLBI networks. The angular resolution is θ≈λ/B, set entirely by the longest baseline B between any two dishes, so combining widely spaced small dishes synthesises the resolving power of one enormous aperture without needing to build it.
Incoming plane wavefronts sweep down onto a row of dishes on the ground, and a live plot below traces the array's combined response — the synthesised beam — as a function of sky angle, with fringes narrowing into a sharp peak as more dishes and longer baselines are added.
Drag the baseline, dish count, frequency, and source-angle sliders, or pick a layout (Linear, Y-shape, Random) and a preset (Single dish, Two-element, VLA, VLBI) to jump to a known configuration. Watch the stats panel for live angular resolution, wavelength, fringe spacing, and the resolution gain over a single dish.
The Event Horizon Telescope linked radio dishes on different continents into a single VLBI network with a baseline as wide as Earth itself, giving it the angular resolution needed to image the shadow of the supermassive black hole in galaxy M87 — a feat no single dish, however large, could ever match.
What sets an interferometer's angular resolution?
The resolution is θ≈λ/B, where B is the longest baseline (the maximum separation between any two dishes) and λ is the observing wavelength, computed in this simulator as c/f from your frequency slider. Doubling the baseline halves the smallest resolvable angle, which is why the simulator lets you push B out to 100 km (VLBI-like) for far sharper resolution than any single dish diameter could achieve.
How does the simulator compute the fringe pattern and synthesised beam?
For every sky angle θ near the source, the code sums exp(i·2π/λ·x·sinθ) over every dish position x, takes the squared magnitude of that complex sum, and normalises by the number of dishes squared — this is the array's interference response. It is then multiplied by a single-dish primary beam envelope, sin(u)/u squared with u = πD/λ·sinθ, so the plotted curve is the true product of array fringes and single-aperture diffraction.
Why do two dishes produce a simple sinusoidal fringe but many dishes a sharp single peak?
With only two dishes the response sum has just one pair separation, so |sum|² reduces to a plain cosine-squared fringe with period λ/B. Adding more dishes at different spacings introduces many more terms with different periods that add constructively only very close to the true source direction and destructively almost everywhere else, collapsing the broad fringe into a narrow synthesised beam — exactly how real arrays like the VLA turn many small apertures into one sharp effective aperture.
Linear places all dishes evenly along a single line from −B/2 to +B/2, giving good resolution along one direction only. Y-shape (modelled on the real Karl G. Jansky VLA) distributes dishes across three arms at 120° spacings projected onto the ground track, sampling many different baseline lengths and orientations for a cleaner beam with fewer sidelobes. Random scatters dishes irregularly across the array extent, which is closer to how VLBI networks of independently sited telescopes are actually distributed.
Single dish sets N=1 with a tiny 50 m baseline, so resolution falls back to λ/D for one 25 m dish. Two-element uses two dishes on a 1 km baseline to show a clean fringe pattern. VLA (Y) sets 27 dishes in a Y-layout on a 36 km baseline at 5 GHz, matching the real VLA's configuration. VLBI uses 10 randomly sited dishes on a 100 km baseline at 8 GHz, illustrating the very long baselines that let networks like the Event Horizon Telescope achieve micro-arcsecond resolution.
Every real dish has finite diameter D and so diffracts incoming light with its own beam pattern, sin(u)/u squared with u = πD/λ·sinθ, which falls off away from boresight regardless of how the dishes are arrayed. Multiplying the array's fringe pattern by this envelope reflects the fact that an interferometer cannot see further off-axis than any one of its dishes can — the fine fringes from the baseline live inside a broader single-dish envelope that limits the field of view.
The source-angle slider sets θ in the incoming plane wave, which shifts both the visual wavefront lines in the sky panel and the location of the response peak in the beam plot — the code always centres its synthesised-beam window on the current source angle. This mirrors how a real interferometer must be steered (or its data phase-corrected) to point at the direction it is trying to image, since the fringe phase B·sinθ depends directly on that pointing angle.