Complex visibility
Definition: The complex cross-correlation measured by an antenna pair for one projected spatial frequency.
Why it matters here: It is needed to answer A point source moves east by one fringe spacing. What happens to its visibility phase on a fixed baseline? Why does amplitude not change for an ideal point source? and to interpret Correlating voltages preserves phase information that single-dish total-power measurements do not contain.
Relationships: Use it with Fringe phase and Geometric delay; the lecture model is \(V(u,v)=\iint I(l,m)e^{-2\pi i(ul+vm)}\,dl\,dm,\qquad\theta_{\rm fringe}\simeq\lambda/B_{\rm proj}\).
Boundary or common confusion: The flat-sky Fourier relation assumes a narrow field and ignores the w-term; wide-field imaging needs non-coplanar-baseline correction.
Geometric delay
Definition: The path-length difference from a sky direction to two antennas, expressed as a signal arrival-time offset.
Why it matters here: It is needed to answer A point source moves east by one fringe spacing. What happens to its visibility phase on a fixed baseline? Why does amplitude not change for an ideal point source? and to interpret Correlating voltages preserves phase information that single-dish total-power measurements do not contain.
Relationships: Use it with Complex visibility and Baseline; the lecture model is \(V(u,v)=\iint I(l,m)e^{-2\pi i(ul+vm)}\,dl\,dm,\qquad\theta_{\rm fringe}\simeq\lambda/B_{\rm proj}\).
Boundary or common confusion: The flat-sky Fourier relation assumes a narrow field and ignores the w-term; wide-field imaging needs non-coplanar-baseline correction.
Baseline
Definition: The vector separation of two antennas, projected perpendicular to the source direction and measured in wavelengths.
Why it matters here: It is needed to answer A point source moves east by one fringe spacing. What happens to its visibility phase on a fixed baseline? Why does amplitude not change for an ideal point source? and to interpret Correlating voltages preserves phase information that single-dish total-power measurements do not contain.
Relationships: Use it with Geometric delay and uv coordinate; the lecture model is \(V(u,v)=\iint I(l,m)e^{-2\pi i(ul+vm)}\,dl\,dm,\qquad\theta_{\rm fringe}\simeq\lambda/B_{\rm proj}\).
Boundary or common confusion: The flat-sky Fourier relation assumes a narrow field and ignores the w-term; wide-field imaging needs non-coplanar-baseline correction.
uv coordinate
Definition: A projected baseline component that identifies the sampled Fourier mode of sky brightness.
Why it matters here: It is needed to answer A point source moves east by one fringe spacing. What happens to its visibility phase on a fixed baseline? Why does amplitude not change for an ideal point source? and to interpret Correlating voltages preserves phase information that single-dish total-power measurements do not contain.
Relationships: Use it with Baseline and Fringe phase; the lecture model is \(V(u,v)=\iint I(l,m)e^{-2\pi i(ul+vm)}\,dl\,dm,\qquad\theta_{\rm fringe}\simeq\lambda/B_{\rm proj}\).
Boundary or common confusion: The flat-sky Fourier relation assumes a narrow field and ignores the w-term; wide-field imaging needs non-coplanar-baseline correction.
Fringe phase
Definition: The visibility phase accumulated from geometric delay and source position.
Why it matters here: It is needed to answer A point source moves east by one fringe spacing. What happens to its visibility phase on a fixed baseline? Why does amplitude not change for an ideal point source? and to interpret Correlating voltages preserves phase information that single-dish total-power measurements do not contain.
Relationships: Use it with uv coordinate and Complex visibility; the lecture model is \(V(u,v)=\iint I(l,m)e^{-2\pi i(ul+vm)}\,dl\,dm,\qquad\theta_{\rm fringe}\simeq\lambda/B_{\rm proj}\).
Boundary or common confusion: The flat-sky Fourier relation assumes a narrow field and ignores the w-term; wide-field imaging needs non-coplanar-baseline correction.