Eclipses by Artificial Satellites to Measure the Angular Sizes of Stars

Eclipses by artificial satellites can be used to measure the angular sizes of stars, overcoming the optical diffraction limit of telescopes by using time-domain information when stars are eclipsed by foreground objects. The paper analyzes the angular resolution achievable by high-speed photon counting devices when stars are eclipsed for several microseconds by satellites in low or mid-Earth orbit, and builds a full Bayesian statistical treatment for analyzing simulated observations.

The authors show that "eclipses by the moon and satellites deliver < 2 milliarcsecond resolution for ∼10 4 stars every year, with the diameters of ∼10 1 − 10 squared stars constrained to better than 0.5 milliarcseconds." The application of satellites requires an ultra-fast, photon-resolving detector capable of continuous readout with inter-frame delay controlled within ≲ 1 µs. Such a fast rate can be handled by the SPINA instrument, which has demonstrated 8 ns inter-frame delay, and potentially by the Cherenkov Telescope Array.

The paper derives the theory of occultation imaging, focusing on the wave-optics regime where the observer is in the near-field of the mask (DOM/DMS ≪ 1). The mask induces a negative point spread function on the background source, and the observed flux variation follows the Fresnel diffraction integral. The angular Fresnel scale is given by θF = 3.6 milliarcseconds for the average Earth–Moon distance, which is below the diffraction limit of current telescopes.

For a star with angular diameter θ∗ smaller than the Fresnel scale, the total flux is the sum of diffraction patterns from different regions of the stellar disc. The net effect of a star with finite angular size is to suppress the intensity of Fresnel fringes and slightly shift their phases. The paper defines an effective angular resolution θres as the 95th percentile of the posterior in the inferred size of a genuine point source from time series data.

The paper examines three classes of foreground masks: Starlink satellites in Low-Earth Orbit (LEO), GPS-like satellites in Medium-Earth Orbit (MEO), and the Moon. Their parameters include angular speeds of 2.3 × 10−1 mas µs−1 for LEO, 3.5 × 10−2 mas µs−1 for GPS, and 3 × 10−4 mas µs−1 for the Moon, with Fresnel scales of 98, 16, and 3.6 milliarcseconds respectively.

The authors simulate mock observations with Poissonian photon-counting noise and validate a Bayesian inference pipeline. They find that the pipeline can recover injected stellar diameters without bias. Results show that LEO satellites provide only mild improvement over the diffraction limit, while GPS satellites can easily achieve resolution below 10 milliarcseconds, and for bright stars with large telescopes, resolution can reach below 1 milliarcsecond. Lunar occultation outperforms satellite-based occultation for bright stars, achieving resolution of ∼10−1 milliarcseconds, but its resolution degrades rapidly for dimmer stars due to photon shot noise from the Moon.

The occultation event rate analysis shows that LEO satellites dominate the daily occultation event rate, exceeding the Moon by 4 orders of magnitude. However, considering resolution, GPS occultations can provide ∼10 1 measurements per night with resolutions no worse than ∼3 milliarcseconds, while LEO occultations can provide ∼700 measurements per night with ≲4 milliarcsecond resolution if telescope pointing overhead is kept within a minute.

The paper concludes that the Moon and GPS satellites are ideal for studying individual stars with the highest resolution, while LEO satellite occultations provide a compelling case for population-level stellar analysis due to their much higher measurement efficiency. The method is primarily limited by photon shot noise, and light curves from multiple occultation events can be stacked to improve signal-to-noise ratio.

Improvements to AI Systems:

1. Bayesian Inference Pipeline for Occultation Data Analysis

• Implement a hierarchical Bayesian model that jointly infers stellar angular diameter, Fresnel scale, and detector noise parameters from time-series photon counts.

• Use Hamiltonian Monte Carlo (HMC) or No-U-Turn Sampler for efficient posterior sampling, enabling real-time analysis of high-cadence occultation light curves.

• The improved system can automatically classify point sources vs. resolved stars and output credible intervals for stellar diameters without manual tuning.

2. Occultation Event Forecasting and Scheduling

• Train a neural network on orbital mechanics (TLE data) and star catalogs to predict upcoming satellite/Moon occultation events with sub-microsecond timing accuracy.

• Integrate telescope pointing constraints (e.g., overhead time, field-of-view) to optimize multi-night observation schedules.

• The system can autonomously prioritize events based on predicted resolution, star brightness, and photon budget, maximizing scientific yield per night.

3. Signal-to-Noise Enhancement via Multi-Event Stacking

• Develop a deep learning model (e.g., a transformer or convolutional autoencoder) that aligns and co-adds multiple occultation light curves of the same star, accounting for variable Fresnel phase shifts and detector jitter.

• The model learns to suppress correlated noise (e.g., lunar background) and recover sub-milliarcsecond stellar diameters from faint sources that individual events cannot resolve.

• This enables population-level stellar diameter surveys using LEO satellites, which currently suffer from low per-event SNR.

4. Adaptive Detector Control and Noise Filtering

• Create a reinforcement learning agent that controls SPINA-like photon-counting detectors in real time, adjusting inter-frame delay and gain based on predicted Fresnel fringe timing and photon arrival statistics.

• The agent minimizes dead-time losses and readout noise during fast occultation events (e.g., LEO with 98 mas Fresnel scale), improving effective resolution for dimmer stars.

• The system can also flag and reject data corrupted by atmospheric scintillation or satellite attitude jitter.

5. Automated Model Selection for Mask Geometry

• Build a Bayesian model comparison framework that distinguishes between LEO, MEO, and lunar occultation signatures in observed light curves, even when the foreground object is unknown.

• Use a mixture-of-experts neural network to classify the mask type and estimate its angular speed and Fresnel scale directly from the diffraction pattern.

• This allows the AI to autonomously decide whether a given event is suitable for high-resolution stellar diameter measurement or should be discarded.

6. Simulation-to-Reality Transfer for Noise Robustness

• Train a generative adversarial network (GAN) on simulated Poissonian light curves to produce realistic detector artifacts (e.g., afterpulsing, clock jitter, background moonlight).

• Use this GAN to augment training data for the Bayesian pipeline, improving its robustness to unmodeled instrumental effects in real observations.

• The improved system can then be deployed on live telescope feeds without retraining, providing accurate stellar size estimates under varying atmospheric and detector conditions.

Direct measurements of the angular sizes of stars (other than our Sun) are inherently limited by telescopes' optical diffraction limit. The spatial diffraction limit can be overcome by using time-domain information when stars are `eclipsed' by anything moving in the foreground: artificial satellites or the Moon (known as `lunar occultation imaging'). Here we analyse the angular resolution achievable by high-speed photon counting devices, when stars are eclipsed for several microseconds by one of the thousands of satellites now in low or mid-Earth orbit. We also build a full Bayesian statistical treatment for analysing simulated observations. We show that eclipses by the moon and satellites deliver <2 milliarcsecond resolution for about 10 4 stars every year, with the diameters of about 10 1 - 10 squared stars constrained to better than 0.5 milliarcseconds. The application of satellites requires an ultra-fast, photon-resolving detector, capable of continuous readout with inter-frame delay controlled within 1 mu s. Such a fast rate can easily be handled by the SPINA instrument, which has demonstrated 8 ns inter-frame delay, and potentially by the Cherenkov Telescope Array.