Core Array Interferometry: Methods & Trade-offs

• Core Array Interferometry is a technique that uses a concentrated group of antennas or telescopes to enhance sensitivity, stabilize calibration, and capture coherent measurements over short baselines.
• It employs measurement operators such as visibility functions, coherence metrics, and delay-and-sum beamforming to reconstruct high-fidelity images in diverse scientific regimes.
• Architectural trade-offs are key, balancing factors like angular resolution, brightness sensitivity, and computational complexity in radio, optical, and transient imaging systems.

Core array interferometry denotes, across the literature surveyed here, a family of interferometric architectures in which a dense central array, a short-baseline operational subset, or a central beam-combination stage provides the dominant measurements for imaging, calibration, or coherent beamforming. In radio synthesis arrays, the “core” is typically a compact cluster that densely samples short baselines and stabilizes calibration; in optical stellar intensity interferometry it is the electronically synchronized network of telescopes that measures second-order coherence; in transient arrays it appears as a coherently delayed and summed aperture for real-time direction finding; and in some photonic implementations it is literally a central optical processor. The common objective is to exploit correlated measurements over many baselines while balancing sensitivity, angular resolution, calibratability, and algorithmic tractability (Dillon et al., 2016, Gonzalez et al., 2023, Kieda et al., 2017, Jiang et al., 2024).

1. Domain-specific meanings of the “core”

In radio aperture synthesis, a dense central core increases the weight of short baselines, improving sensitivity to extended emission and lowering image noise for large-scale structures. It also produces dense uv-coverage near the origin, which stabilizes deconvolution and self-calibration, although it limits instantaneous angular resolution unless longer baselines are added. This formulation is explicit in the Multipurpose Interferometer Array Pathfinder, where a staged build from a three-antenna pathfinder to a 16-element array is presented as a natural implementation of “core array interferometry” (Gonzalez et al., 2023).

In 21 cm cosmology, the core is more specifically a compact, densely packed, highly redundant array. The Hydrogen Epoch of Reionization Array is analyzed in exactly these terms: multiple antenna pairs share the same baseline vector, so the same Fourier mode is sampled many times, boosting sensitivity and enabling calibration that does not rely on detailed sky models. The same compactness that improves sensitivity to low-$k_\perp$ modes also makes foreground control, calibratability, and point-spread-function design central design variables rather than secondary engineering details (Dillon et al., 2016).

A different usage appears in hybrid facilities such as the FAST Core Array, where the “core” is a named array concept: FAST is combined with 24 secondary 40-m antennas, and FAST itself functions both as an interferometric element and as a phased-array beamformer. In that case, the core is neither purely compact nor purely redundant; it is a heterogeneous architecture optimized to combine very high sensitivity with arcsecond-scale angular resolution (Jiang et al., 2024).

Optical and photonic literature adds two further meanings. In stellar intensity interferometry with Imaging Atmospheric Cherenkov Telescopes, the array core is the electronically synchronized ensemble of telescopes and correlators that measures $|\Gamma(u,v)|^2$ over many baselines (Kieda et al., 2017). In integrated discrete-optics interferometry, the “core optical processor” is a two-dimensional coupled-waveguide array that maps input-field coherences to output intensities, serving as the beam-combination nucleus of the interferometer (Minardi et al., 2010).

2. Measurement operators, coherence functions, and invariants

The common mathematical language of core array interferometry is the visibility function. In radio form, the sky brightness distribution $I(l,m)$ and the measured visibility $V(u,v)$ are related by

$$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$

with the primary beam $A(l,m)$ modulating the sky response. Each antenna pair samples one point in the uv-plane, and Earth rotation synthesis fills additional Fourier modes over time (Gonzalez et al., 2023).

Optical stellar intensity interferometry replaces first-order field interference by second-order intensity correlations. For chaotic light,

$$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$

and the measured quantity is the squared visibility,

$$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$

The Van Cittert–Zernike theorem then links $\Gamma(u,v)$ to the Fourier transform of the sky brightness distribution, so populating the uv-plane with $|\Gamma(u,v)|^2$ samples permits image reconstruction even though the Fourier phase is not directly measured (Kieda et al., 2017).

Transient interferometry often uses time-domain coherent summation rather than accumulated visibilities. In the Auger Engineering Radio Array, the beamformed signal for hypothesized delays $|\Gamma(u,v)|^2$0 is

$|\Gamma(u,v)|^2$1

and the best-fit geometry maximizes a coherence or intensity metric on grids perpendicular to the shower axis. ANITA uses an analogous delay-and-sum logic for ultra-wideband impulsive signals, together with normalized pairwise cross-correlations and coherence maps over trial directions (Dillen, 5 Sep 2025, Romero-Wolf et al., 2013).

A further layer is provided by closure quantities. For co-polar interferometry with local complex gains $|\Gamma(u,v)|^2$2,

$|\Gamma(u,v)|^2$3

The gauge-theoretic treatment of this equation identifies closure phases and closure amplitudes as invariants of the array graph. For an $|\Gamma(u,v)|^2$4-element array, the complete independent set comprises

$|\Gamma(u,v)|^2$5

closure phases and

$|\Gamma(u,v)|^2$6

closure amplitudes when auto-correlations are not required. This places the familiar triangular and quadrilateral closure observables inside a unified $|\Gamma(u,v)|^2$7 framework (Thyagarajan et al., 2021).

3. Representative architectures and implemented systems

The architectural diversity of core array interferometry is unusually broad. Some systems are compact and redundant, some are sparse but heavily synchronized, and some are explicitly heterogeneous.

System	Core configuration	Stated capability
VERITAS/CTA SII	IACT arrays with $|\Gamma(u,v)|^2$8 m separations; extension to $|\Gamma(u,v)|^2$9 km via White Rabbit	Sub-milliarcsecond to $I(l,m)$0 U/V imaging (Kieda et al., 2017)
ASTRI Mini-Array	Nine Cherenkov telescopes	36 simultaneous baselines; sub-milliarcsecond images of the brightest nearby stars (Vercellone, 2023)
MIA	16 planned 5 m antennas; three-antenna pathfinder	Dual polarization, $I(l,m)$1 MHz bandwidth centered at $I(l,m)$2 MHz (Gonzalez et al., 2023)
HERA-like core	331 hexagonally packed 14 m dishes, 14.6 m minimum spacing	630 unique baseline vectors with redundant calibration emphasis (Dillon et al., 2016)
FAST Core Array	FAST plus 24 additional 40 m antennas	300 baselines; $I(l,m)$3 at $I(l,m)$4 GHz (Jiang et al., 2024)

In stellar intensity interferometry, current and planned Cherenkov arrays are used as sparse optical interferometers. VERITAS employs four 12 m telescopes with $I(l,m)$5 m separations, giving six instantaneous baselines, while CTA adds many more telescopes and baselines over $I(l,m)$6 km scales. The instrumental concept couples narrowband U/V optics, high-speed digitizers, sub-nanosecond timing, and offline or FPGA-based correlation. The ASTRI Mini-Array extends the same logic to nine Cherenkov telescopes at the Observatorio del Teide, yielding 36 simultaneous pairwise baselines and an explicitly stated sub-milliarcsecond stellar-imaging objective (Kieda et al., 2017, Vercellone, 2023).

Radio implementations emphasize either dense-core redundancy or heterogeneous sensitivity. MIA is a compact L-band array based on 16 antennas of 5 m diameter, dual polarization, and a processed bandwidth of 250 MHz centered at 1325 MHz, with an FX correlator built from CASPER SNAP boards. Its three-antenna pathfinder is explicitly designed to validate closure phase, bandpass calibration, and dual-polarization correlation before scaling to the 120-baseline 16-element configuration (Gonzalez et al., 2023). HERA, by contrast, is analyzed as a deliberately redundant short-baseline core of 331 hexagonally packed 14 m dishes. Off-grid antennas and outriggers are treated as controlled perturbations of that core, intended to improve imaging and foreground mitigation without destroying redundant calibratability (Dillon et al., 2016).

The FAST Core Array is a hybrid rather than a purely compact core. FAST is combined with 24 individual 40 m dishes, and the resulting 25-element system supports standard correlation, phased-array beamforming, and VLBI export. The final specification targets a maximum interferometric baseline of $I(l,m)$7 km, with a quoted angular resolution of $I(l,m)$8 at $I(l,m)$9 GHz and tied-array sensitivity $V(u,v)$0 (Jiang et al., 2024).

A useful limiting case is KaVA at 44 GHz, where the array functioned effectively as a short-baseline core because compact maser emission was detected only on baselines shorter than approximately 100 M$V(u,v)$1, corresponding to $V(u,v)$2 km. In that regime, the “core” is operational rather than geometric: the detectable information resides on the short-baseline subset, while longer baselines resolve out most of the flux (Matsumoto et al., 2014).

4. Synchronization, calibration, and image formation

Core array interferometry depends on calibration regimes that are strongly architecture-specific. In stellar intensity interferometry, precise timing is the dominant requirement. VERITAS/CTA designs use a GPS-locked central timecode generator and White Rabbit distribution, with timing resolution $V(u,v)$3 ps RMS and clock synchronization across up to 80 km better than 1 ns RMS. Thirty-minute runs are started simultaneously by 1-PPS signals, gain equalization is applied with IACT optical flasher systems, noise is characterized in $V(u,v)$4-minute subchunks, and the resulting $V(u,v)$5 measurements are associated with uv-track segments before amplitude-only inversion with a modified MIRA package (Kieda et al., 2017).

In compact radio cores, calibration is more often gain-centric. MIA distributes PPS and a 10 MHz reference for ADC alignment and calibration, injects internal noise through a directional coupler for amplitude and bandpass calibration, and uses closure phase on the three-antenna pathfinder as a direct test of non-closing errors. Its correlator chain is FX: polyphase filter bank, FFT, multiply-accumulate, packetization, and 10 GbE export (Gonzalez et al., 2023).

Highly redundant arrays admit a further simplification: calibration by internal consistency. In HERA-like layouts, the redundant calibration model

$V(u,v)$6

can be solved with logcal and lincal, leaving one overall amplitude degeneracy and three phase degeneracies. The rank criterion is explicit: $V(u,v)$7 must have exactly four zero eigenvalues for full redundant solvability. Additional zero modes indicate disconnected redundant subgraphs (Dillon et al., 2016).

Wide-field compact arrays require correspondingly explicit imaging operators. The brute-force mapmaking formalism for MITEoR writes the measurement equation as

$V(u,v)$8

with the minimum-variance regularized estimator

$V(u,v)$9

The associated point-spread matrix

$$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$0

makes the position-dependent PSF explicit and quantifies how Earth rotation and dense short-baseline coverage fill otherwise missing modes (Zheng et al., 2016).

Phase recovery remains the major methodological divide. Radio interferometry can use closure phases and closure amplitudes directly, whereas stellar intensity interferometry does not directly measure Fourier phase. Its reconstructions therefore rely on regularization and prior constraints such as positivity, compactness, and smoothness, or on higher-order correlations that supply closure-phase-like information (Thyagarajan et al., 2021, Kieda et al., 2017).

5. Resolution, sensitivity, and design trade-offs

Angular resolution is baseline-limited across all domains, approximately as

$$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$1

The numerical implications are strongly wavelength-dependent. In U/V-band stellar intensity interferometry, $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$2 and $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$3 give $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$4 mas, while $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$5 and $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$6 give $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$7, and $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$8 gives $$V(u,v) = \iint A(l,m)\,I(l,m)\,e^{-2\pi i (u l + v m)}\,\mathrm{d}l\,\mathrm{d}m,$$9. The same paper emphasizes that fiber-based sub-nanosecond synchronization enables baselines greater than 10 km and therefore U/V-band imaging well below $A(l,m)$0 (Kieda et al., 2017).

Sensitivity scaling is equally architecture-dependent. For stellar intensity interferometry, the paper adopts

$A(l,m)$1

and translates this into practical observing limits: for arrays of 10–12 m IACTs, stars as faint as $A(l,m)$2 are observable, approximately 1000 stars in the JMMC catalog are observable by VERITAS SII in 1-hour exposures, and $A(l,m)$3 are detectable with 10-hour exposures. With 5-hour observations on VERITAS, the zenith PSF approaches $A(l,m)$4 mas, while CTA gains an additional factor of $A(l,m)$5 in S/N over VERITAS plus a further factor of $A(l,m)$6 from 10× higher sampling speed in MST-SCT optics (Kieda et al., 2017).

Dense radio cores exhibit the opposite trade-off: they deliberately sacrifice maximum instantaneous resolution to improve surface-brightness sensitivity, uv-filling near the origin, and calibration robustness. HERA’s configuration studies show that modest off-grid sampling and outriggers can improve imaging without major loss of raw 21 cm sensitivity; the cumulative detection significances remain close, at $A(l,m)$7, $A(l,m)$8, and $A(l,m)$9 for the moderate foreground scenario and $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$0, $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$1, and $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$2 for the optimistic scenario across the compared layouts (Dillon et al., 2016).

The same trade-off appears in compact-source work. KaVA recovered only $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$3 of the single-dish 44 GHz maser flux in VLBI images, with $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$4 resolved out, because most of the emission resided on scales larger than the longest detected short baselines could preserve. This is a direct counterexample to the common assumption that longer baselines are always preferable: in that experiment, the short-baseline “core array” was the only subset that matched the source structure (Matsumoto et al., 2014).

Transient arrays add a computational trade-off. In the Tianlai study, cross-correlation beamforming is more general than electric-voltage beamforming because it can synthesize beams not realizable by a rank-1 voltage-weight matrix, but for $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$5, $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$6, and $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$7 it requires about 10 times more beamforming computation. The same study finds that cross-coupling has relatively small impact on normalized beam profiles, so the more expensive formalism does not automatically imply better practical performance (Liu et al., 11 Oct 2025).

Survey optimization in the FAST Core Array literature shows an analogous balance between area and depth. FAST single-dish mode performs well at low redshift, $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$8, but becomes shot-noise limited at higher redshift, whereas the Core Array maintains sufficient number density for power-spectrum measurements and BAO constraints up to $$g^{(2)}(\tau) \equiv \frac{\langle I(t)\, I(t+\tau)\rangle}{\langle I(t)\rangle^2}, \qquad g^{(2)}(0)=1+|g^{(1)}(0)|^2,$$9. At $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$0, increasing survey area has little impact on single-dish observations because shot noise dominates, while the interferometric mode continues to benefit from higher sensitivity and angular resolution (Li et al., 22 Aug 2025).

6. Scientific regimes, methodological limits, and research directions

The scientific reach of core array interferometry is unusually broad because different core architectures expose different parts of the measurement problem. In optical stellar work, Cherenkov-array intensity interferometry targets rotational deformation, gravity darkening, Be/B[e] decretion disks, Wolf–Rayet winds, interacting binaries such as Spica and Algol, and starspots, all in the U/V bands where contrast is favorable and kilometer-scale baselines yield sub-milliarcsecond to tens-of-microarcsecond resolution. The ASTRI Mini-Array places stellar intensity interferometry inside a formal core science program, with the goal of obtaining sub-milliarcsecond images of the brightest nearby stars and their environments (Kieda et al., 2017, Vercellone, 2023).

Long-baseline optical amplitude interferometry provides a different scientific role. CHARA Array measurements combined with asteroseismology have been used to derive near model-independent radii, temperatures, and luminosities for dwarfs, subgiants, and red giants, and to test stellar evolution models. For the ten-star CHARA/Kepler/CoRoT sample, simple asteroseismic radii for main-sequence stars were empirically shown to be accurate to $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$1 (Huber et al., 2012). For the core-helium-burning red giant $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$2 Cyg, CHARA+PAVO and TESS yielded $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$3, $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$4, and $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$5, while models that matched the envelope-dominated oscillation frequencies still overestimated the radius and under-predicted the observed $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$6, implying deficiencies in current treatments of convective boundary mixing (Chowhan et al., 15 Apr 2026).

In radio cosmology and sky mapping, the core-array approach underpins both calibration and diffuse imaging. MITEoR’s compact redundant core enabled brute-force mapmaking of the northern sky from 128 MHz to 175 MHz at about $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$7 resolution and yielded an overall spectral index of $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$8. The same methodology is presented as directly relevant to HERA-like arrays, where short baselines, wide fields of view, and redundancy make core-array imaging and calibration tightly coupled problems (Zheng et al., 2016).

Transient science extends the concept into real-time coherent processing. AERA’s delay-and-sum interferometry on several thousand inclined air-shower observations produced geometry reconstructions comparable to or better than conventional timing/amplitude fits, recovered low-energy signals so that interferometric reconstruction succeeded for 57 of 194 events versus 17 for standard radio reconstruction in a $$|\gamma|^2 \propto \frac{\langle \Delta I_1(t)\,\Delta I_2(t+\tau)\rangle}{\langle I_1\rangle\,\langle I_2\rangle}, \quad \tau \approx 0.$$9 EeV high-zenith subset, and measured event-level polarization centered near the expected $\Gamma(u,v)$0 direction (Dillen, 5 Sep 2025). The FAST Core Array is designed to exploit a related synergy among real-time correlation, phased-array beamforming, and wide-field feeds for fast radio bursts, gravitational-wave counterparts, resolved HI studies, pulsars, and exoplanetary radio emission (Jiang et al., 2024).

Several methodological limits recur across these domains. A dense core improves calibratability and brightness sensitivity but does not by itself guarantee high angular resolution. Intensity interferometry is largely immune to atmospheric phase fluctuations, but it does not directly measure Fourier phase and therefore shifts complexity into inversion and higher-order statistics. More general beamformers can be mathematically attractive without being computationally or statistically optimal. A plausible implication is that “core array interferometry” is best understood not as a single instrument class but as a design principle: concentrate the architecture, baseline distribution, or beam-combination logic where the dominant uncertainty actually resides, whether that uncertainty is photon statistics, gain degeneracy, wide-field mode coupling, delay tracking, or phase corruption.