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Physica Scripta

Multi-baseline interferometric angular estimation under baseline imperfections

Yi-Xin Shen, Zhou‐Kai Cao, Jian Leng, Xiang-Bin Wang

Published Apr 24, 2026• 0 citations
Publisher

Abstract

Abstract Precise angular estimation of remote targets is a fundamental task in optical interferometry, particularly in the weak-light regime where photon resources are limited. Interferometric schemes employing multiple telescopes can overcome the diffraction limit of a single aperture but are often highly sensitive to experimental imperfections. In this work, we study a piecemeal interferometric approach that jointly exploits measurement data from multiple baselines for angular estimation, and we relax the constraints on baseline configurations. The proposed scheme remains effective even with a reduced number of baselines, highlighting its practical applicability. Focusing on realistic experimental conditions, we analyze the impact of baseline length and orientation errors on the estimation performance. We show that both the original and generalized piecemeal protocols exhibit strong robustness against these imperfections and achieve higher angular estimation precision than existing single-baseline weak-light interferometric schemes under identical practical conditions.

DOI
10.1088/1402-4896/ae648d

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Abstract Precise angular estimation of remote targets is a fundamental task in optical interferometry, particularly in the weak-light regime where photon resources are limited. Interferometric schemes employing multiple telescopes can overcome the diffraction limit of a single aperture but are often highly sensitive to experimental imperfections. In this work, we study a piecemeal interferometric approach that jointly exploits measurement data from multiple baselines for angular estimation, and we relax the constraints on baseline configurations. The proposed scheme remains effective even with a reduced number of baselines, highlighting its practical applicability. Focusing on realistic experimental conditions, we analyze the impact of baseline length and orientation errors on the estimation performance. We show that both the original and generalized piecemeal protocols exhibit strong robustness against these imperfections and achieve higher angular estimation precision than existing single-baseline weak-light interferometric schemes under identical practical conditions.
Angular localization of remote optical objects is a fundamental challenge in fields such as remote sensing and astrometry. We propose the piecemeal method for a telescope array, with explicit formulas showing its key advantages strictly: higher precision, efficiency, and robustness, which are further confirmed by numerical simulations. Specifically, our method achieves a 10 4 precision improvement with 10 5 photon number reduction compared to existing telescope arrays, and achieves precision improvements of 10 3 and 10 2 over the Gaia telescope and the ultimate quantum limit for incoherent imaging, respectively, under comparable photon numbers. We have also presented a reference-object-based implementation framework for our method that seamlessly integrates with existing optical interferometric systems.
periodicity of phase readout introduces a wrap-around ambiguity, which confines the unambiguous measurement range to a single period and leads to a structural trade-off between precision and measurement range in high-sensitivity settings. To address this problem, we propose a robust Chinese remainder theorem-based multi-baseline measurement scheme: we choose a set of pairwise coprime scale factors and recover the wrap-around number from congruence relations among the reduced phases. In the setting of optical-interferometric quantum telescopes, we construct a telescope array based on the Chinese remainder theorem using fractional baselines, which substantially enlarges the unambiguous angular range (effective field of view) while retaining the high precision enabled by long baselines. Numerical simulations show that, under the same constraint on the shortest achievable baseline, our scheme achieves an exponential improvement in detection range over existing methods and attains a better range-precision trade-off with fewer probing resources. This framework supports practical multi-baseline quantum-interferometric observations and can be generalized to other phase-sensitive quantum precision-measurement tasks.
Observations using interferometers provide sensitivity to features of images on angular scales much smaller than any single telescope, on the order of Δθ ∼ λ/b where b is the interferometric baseline. Present-day optical interferometers are essentially classical, interfering single photons with themselves. However, there is a new wave of interest in interferometry using multiple photons, whose mechanisms are inherently quantum mechanical, which offer the prospects of increased baselines and finer resolutions among other advantages. We will discuss recent ideas and results for quantum-assisted interferometry using the resource of entangled pairs, and specifically a two-photon amplitude technique aimed at improved precision in astrometry.
Telescope systems with distributed apertures are a well-established approach for boosting resolution in astronomical imaging. However, theoretical limits on quantitative imaging precision, and the fundamentally best possible mode-sorting, beam-combining, and detection schemes to use with such arrays, remain largely unexplored. Using mathematical tools of the quantum and classical Crámer-Rao bounds, we perform analyses showing the fundamental origins of the enhancement provided by distributed imaging systems, over and above a single monolithic telescope, and consider the precision with which one can estimate any desired parameter embedded in a scene's incoherent radiation with a multi-aperture imaging system. We show how quantum-optimal measurements can be realized via beam-combination strategies of two classes: (1) , where light from different apertures is directed to a common focal plane, e.g., of a segmented-aperture telescope; and (2) , where light collected at each aperture, e.g., telescope sites of a long-baseline array, is routed to an optical interferometer. As an example, we show an explicit calculation of the quantum Fisher information (QFI) for estimating the angular separation between two-point emitters using two identical apertures separated by a baseline distance. We show that this QFI splits instructively into additive contributions from the single apertures and from the baseline. We quantify the relative benefits of intratelescope (e.g., spatial-mode) optical processing and intertelescope beam combination. We show how both receiver designs can be used to capture both sources of information and discuss how similar methods could be extended to more general imaging tasks. We discuss translating QFI-attaining measurements to explicit receiver designs, and the use of preshared entanglement to achieve the QFI when it is impractical to colocate and combine light collected by the apertures. Published by the American Physical Society 2024
A quantum-enhanced telescope (interferometer) can have significant advantages in precisely measuring the angular position of remote objects through sending out ancillary quantum entanglement pairs alongside the large baselines of telescopes. In principle, the larger the baseline, the higher the expected measurement resolution. However, the well-known major problem of photon transmission loss would drastically undermine the practical application of all quantum-enhanced telescopes and optical interferometers that transmit photons along the baseline, especially for the large baselines required for high angular resolution. Here, we propose a photon-transmission-loss-independent quantum-enhanced interferometer that is robust to the transmission loss and keeps its advantages unchanged given whatever large baseline. This removes the well-known barrier to the practical application of quantum-enhanced telescopes. Moreover, in contrast to the previous results of quantum-entanglement-enhanced telescopes requesting sophisticated resources—perfect single-photon entanglement, photon-number-resolving detectors, or quantum memories—our method requires only threshold detectors and tunable coherent-state or two-mode squeezed-state sources, which are mature technologies nowadays, and it does not need any quantum memory. We demonstrate the high performance of our method using Fisher information. For the phase difference of weak light from a remote star, the high-quality result of Fisher information remains constant under arbitrarily large transmission loss, and hence all the advantageous results and the performance of our method are actually independent of transmission loss.