Use the projected baseline along the source offset, , and . The first bandwidth null occurs at . A worst-case gives . That is a zero of the response, not a good usable bandwidth. A quantitative maximum needs an allowed attenuation.
For example, requiring a response of at least gives at . Hence
for that worst projection. A strictly east-west offset in a sides-aligned square instead samples at most , giving a first null and a ten-percent-loss bandwidth. The original two-antenna geometry supplies an additional projection; these examples use its maximum magnitude. Thus a bandwidth of order is a reasonable conservative estimate with a stated small-loss criterion, rather than a unique geometry-free limit.
Figure 1.
Array baselines and bandwidth decorrelation away from the tracking center
. Original array geometry and rectangular-band sinc calculations for a ten-arcminute offset. The marked ten-percent-loss bandwidth is an illustrative response criterion; the first null is not a usable-bandwidth recommendation. Details.
To use a much wider total band, channelize the signals before correlation or before irreversible frequency averaging. Correlate sufficiently narrow channels, track the reference delay and phase at each frequency, and combine frequency-aware visibilities or images. This preserves sensitivity while avoiding field-dependent averaging losses in radio interferometry. Merely adding a phase correction after a broad channel has decorrelated cannot recover the lost signal; nor can one tracking delay cancel every sky direction simultaneously.[ref]