Mobile Intensity Interferometry for Stellar Observations

• Mobile intensity interferometry is a technique that measures the normalized second-order correlation function to extract spatial coherence and stellar diameters at sub-mas precision.
• It employs deployable optical telescopes equipped with high-speed photon-counting detectors and precise timing electronics to build real-time delay histograms and extract stellar visibility functions.
• Its modular design and flexible baseline configuration enable scalable and rapid field deployment for detailed imaging of stellar surfaces and circumstellar environments.

A mobile intensity interferometer for stellar observations is a deployable, electronically connected array of optical telescopes equipped with high-speed photon-counting detectors and precision timing electronics. The primary purpose is to measure the normalized second-order (intensity) correlation function, $g^{(2)}(\mathbf{b},\tau)$, across configurable baselines to infer spatial coherence and visibility functions of stellar targets with milliarcsecond (mas) or sub-mas angular resolution. Modern mobile implementations leverage compact optics, portable structures, low-cost acquisition, and real-time data pipelines to enable field deployment, modular scaling, and u–v plane coverage optimized for high-resolution measurements of stellar surfaces, envelopes, and circumstellar environments.

1. Instrumental Architecture and Photometric Design

The essential structure comprises opto-mechanical telescope units, photon-counting detectors, and correlated digital backend. For example, the I2C system used a 1.54 m Ritchey–Chrétien (MéO) and a portable 1 m Newtonian (T1M), both fitted with a custom Coupling Assembly (CA) featuring beam stabilization (automated tip-tilt, $\gtrsim10$ Hz correction), focal reduction (e.g., f/20.1 to f/2 via relay optics), dichroic and narrow-band H$\alpha$ splitting, polarization selection (PBS + linear polarizer), and graded-index fiber injection. Downstream, signal paths are split and directed onto single-photon avalanche diodes (SPADs), with four independent zero-baseline or cross-baseline correlation channels per telescope. Outputs are registered via a Time-to-Digital Converter (TDC) providing $\lesssim100$ ps timing, building $g^{(2)}$ histograms in real time (Matthews et al., 2023).

Other systems, such as MI$^2$SO, utilize lightweight 1 m-diameter acrylic Fresnel lenses, manual $z$-translation stages for wavelength-dependent focus adjustments, and Hamamatsu photomultiplier tubes with sub-nanosecond transit-time spread, processed by GHz-range digitizers (Ingenhütt et al., 16 Jan 2026). Notably, scalability is addressed by using modular, low-mass optics and electronics, enabling rapid deployment and baseline reconfiguration.

2. Theoretical Foundations and Correlational Signal Concepts

Intensity interferometry measures the normalized second-order correlation function,

$$g^{(2)}(\mathbf{b},\tau) = \frac{\langle I_1(\mathbf{r},t) I_2(\mathbf{r}+\mathbf{b}, t+\tau)\rangle}{\langle I_1\rangle \langle I_2\rangle}$$

which, for chaotic sources, relates to the Siegert relation: $$g^{(2)}(\mathbf{b},\tau) = 1 + |g^{(1)}(\mathbf{b},\tau)|^2$$ with $g^{(1)}$ the mutual degree of coherence, determined via the van Cittert–Zernike theorem as the normalized Fourier transform of the brightness distribution. For a uniform disk of angular diameter $\theta$, the spatial coherence is

$$g^{(1)}(b) = \frac{2J_1(\pi b \theta / \lambda)}{\pi b \theta / \lambda}$$

allowing direct extraction of stellar diameters by fitting the baseline dependence of $|V(b)|^2$ (Ingenhütt et al., 16 Jan 2026, Matthews et al., 2023). H$\alpha$-specific systems employ narrow filters (e.g., $\Delta\lambda \approx 1$ nm) to exploit the increase in temporal coherence time $T_c$, with spectral line profiles characterized to predict $T_c$ via

$T_c = \int |s(\nu)|^2 d\nu$

where $s(\nu)$ is the normalized line spectrum.

3. Baseline Configuration, Synchronization, and Deployment

Deployment schemes are designed for flexible baseline selection. T1M-type units are positioned on calibrated footings with differential GPS, allowing baseline vectors $\mathbf{r}$ to be known to $\lesssim$1.5 cm. Field campaigns reconfigure telescope positions within hours, covering both intermediate ($\sim$13–21 m) and long ($\sim$32–38 m) baselines, achieving mas-scale fringe spacings appropriate to main-sequence disks (e.g., $\theta_{\text{FWHM}} \approx 3.5$ mas for $\gamma$ Cas at H$\alpha$) (Matthews et al., 2023). Systems such as the Southern Connecticut Stellar Interferometer employ portable 0.6 m Dobsonians (mass $<30$ kg) on rapid-setup platforms, guaranteeing sub-mm placement repeatability and software-tunable baseline orientation (Horch et al., 2021).

Timing calibration is critical; cable delays and detector offsets are continuously monitored, with timing drift kept well below the intrinsic electronic jitter ($<$500 ps for I2C; $\leq$48 ps for SPAD systems) (Matthews et al., 2023, Horch et al., 2021). Modern designs increasingly use GPS/PPS-discipline or White Rabbit synchronization to support sub-ns timing accuracy across arrays.

4. Sensitivity, Signal-to-Noise, and Data Reduction Pipeline

The raw sensitivity of an intensity interferometer is given by

$$\text{SNR} \propto A\,\eta\,n\,|V|^2\sqrt{\Delta f\,T/2}$$

where $A$ is the collecting area, $\eta$ quantum efficiency, $n$ photon flux, $\Delta f$ electronic bandwidth, and $T$ integration time (Matthews et al., 2023, Dravins et al., 2012, Ingenhütt et al., 16 Jan 2026). For narrow-band operation, reduction in photon flux is compensated by proportionally increased $T_c$, keeping SNR invariant for flat spectra.

Photon-counting rates per channel reach $10^5$–$10^6$ s$^{-1}$ (zero-baseline SPAD), with H$\alpha$ contrast $g^{(2)}(0)-1 \approx 1.43\times 10^{-3}$ and FWHM $\sim$885 ps at Calern (Matthews et al., 2023). Data processing pipelines produce delay histograms (typ. $\Delta\tau = 50$ ps), with cross-correlation peaks Gaussian fitted to extract $|V(r)|^2$. Calibration procedures include zero-baseline normalization and validation of system coherence times against spectrometric predictions (Matthews et al., 2023).

For multi-baseline systems, the data rate is managed via FPGA-based correlators or GPU pipelines (as in MAGIC-SII), outputting $g^{(2)}(\tau)$ arrays per baseline at up to 1 Hz with real-time feedback (Collaboration et al., 2024).

5. Scientific Performance, Benchmark Results, and Comparison

In operational campaigns, intensity interferometry using mobile platforms has demonstrated quantitative agreement with amplitude-based long-baseline interferometry. The full range of measured $|V(r)|^2$ at various baselines precisely traces the expected Airy pattern for uniform/limb-darkened disks:

• $\gamma$ Cas: $|V|^2$ transitions from $\sim$1.0 (unresolved, $r<13$ m) to $\sim$0.05 (fully resolved, $r>32$ m), yielding disk diameters consistent within $1\sigma$ of established values (FWHM $\approx 3.5$ mas) (Matthews et al., 2023).
• Arcturus (MI$^2$SO): $10.8$ h integration at baselines $2.5$–$4.85$ m, derived $\theta=19.7\pm1.7$ mas by template fitting, matching the literature (Ingenhütt et al., 16 Jan 2026).
• MAGIC-SII: Routine resolution of diameters $0.5$–$0.8$ mas in 20–100 h on a range of early-type stars, percent-level agreement with amplitude interferometric measures (Collaboration et al., 2024).

Sensitivity is currently limited by collecting area, quantum efficiency, bandwidth, and photon background. 1 m-class units with PMTs/SPADs typically access mag $\lesssim$2–3 stars for $<$10 h integration at mas-scale precision; large Cherenkov telescopes (17 m) extend to $B$ mag $\sim$3, with sub-mas detection thresholds for $\sim$100 m baselines (Collaboration et al., 2024).

6. Scalability, Modular Expansion, and Prospects

Mobile intensity interferometers are designed for modularity—e.g., the I2C architecture can be extended to four 1 m-class telescopes, generating up to six baselines, enhancing u–v coverage and enabling two-dimensional synthesis (Matthews et al., 2023). MI$^2$SO demonstrates that arrays of 100 low-mass units could, in aggregate, measure 1% diameters on $m=2$ stars in $<20$ h (Ingenhütt et al., 16 Jan 2026). The use of multi-channel spectral slicing (dispersive optics, APD arrays) increases $\Delta f$ and overall SNR, with modern designs projecting limiting magnitudes $m_\mathrm{R}\simeq 14$ for km-scale aperture arrays (Trippe et al., 2014).

Rapid reconfiguration (baseline, orientation, filter set), compatibility with varied telescope types (Newtonian, Ritchey–Chrétien, Cherenkov, or Fresnel lens), and the use of portable infrastructure (trailers, lightweight housings, GPS timing) facilitate both dedicated deployments and opportunistic retrofits to existing large-aperture arrays (Matthews et al., 2023, Ingenhütt et al., 16 Jan 2026, Dravins et al., 2012, Collaboration et al., 2024).

Upgrades under consideration include real-time FPGA/GPU correlators, sub-500 ps time-resolution detectors, automated baseline calibration, and scalable White Rabbit timing for sub-50 ps synchronization across km-scale arrays (Ingenhütt et al., 16 Jan 2026, Collaboration et al., 2024).

7. Applications and Future Science Directions

Mobile stellar intensity interferometry enables high-resolution studies of:

• Circumstellar envelopes (e.g., H$\alpha$ disks around Be stars; $\gamma$ Cas FWHM $\sim$3–4 mas)
• Limb, gravity, and temperature darkening in rapid rotators
• Binary star separations ($\sim$100–500 $\mu$as) and pre-main-sequence disks
• Mass-radius relationships, rotation, convection, and surface/spot mapping for early-type stars (Matthews et al., 2023, Trippe et al., 2014, Ingenhütt et al., 16 Jan 2026)

Potential future directions include multi-color and polarimetric II, direct imaging of fainter or more distant targets by scale-up (N $\gg$ 10 telescopes, km-scale baselines), and the exploitation of Cherenkov telescope infrastructure for observing O/B-type stars at microarcsecond resolutions (Trippe et al., 2014, Dravins et al., 2012, Dravins, 2016, Collaboration et al., 2024). Mobile interferometric platforms are uniquely positioned for flexible science campaigns, pathfinder missions, and technology development toward the next generation of high-precision optical stellar imaging.