Information limits of photonic lantern wavefront sensing: a Fisher- and quantum-Fisher-information framework and its relation to Fourier-filtering sensitivity limits
Abstract
The photonic lantern is an all-photonic wavefront sensor native to single-mode-fibre-fed instruments, but its performance is almost always quoted through a specific reconstruction algorithm, obscuring how much wavefront information the device itself encodes. We develop, from first principles, the Fisher-information and Cramer-Rao theory of the photonic-lantern wavefront sensor, benchmark it against the quantum Cramer-Rao bound via an explicit multi-parameter quantum-Fisher-information calculation, and relate it to two established frameworks: the Fourier-filtering noise-propagation model of Chambouleyron et al (2023) and the classical/quantum sensitivity limit of Haffert et al (2023). Treating the lantern as a deterministic map from aberration coefficients to N output intensities, we derive the Poisson and read-noise Fisher information matrices (FIM), the per-mode CRLB, the per- photon Fisher-Rao geometry on the intensity simplex, and a flux- and estimator-independent sensitivity metric beta with quantum ceiling beta = 2. The lantern CRLB scales as N_ph^(-1/2) and is bounded, mode by mode, by the quantum limit of 1/2 rad rms per photon. That multi-parameter bound is jointly saturable: the phase generators are real and commuting, so the mean Uhlmann curvature vanishes and wavefront sensing carries no quantum incompatibility between simultaneously estimated modes, extending Haffert et al's single-mode ceiling to all low-order modes at once. We further show that the photon-noise sensitivity s_gamma of Chambouleyron et al is exactly the diagonal of our per- photon FIM, whereas the CRLB uses the diagonal of its inverse; the two coincide only for a diagonal FIM, so s_gamma is optimistic for a mode-mixing lantern. The framework is device-agnostic: it returns estimator-independent sensitivities comparable on a common beta <= 2 scale with pyramid, Zernike and PIAA-ZWFS sensors.
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BibTeX
@misc{madhav2026information,
title = {{Information limits of photonic lantern wavefront sensing: a Fisher- and quantum-Fisher-information framework and its relation to Fourier-filtering sensitivity limits}},
author = {Kalaga Madhav},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.29342},
eprint = {2607.29342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.29342},
}
RIS
TY - UNPB
TI - Information limits of photonic lantern wavefront sensing: a Fisher- and quantum-Fisher-information framework and its relation to Fourier-filtering sensitivity limits
AU - Kalaga Madhav
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2607.29342
UR - https://arxiv.org/abs/2607.29342
AB - The photonic lantern is an all-photonic wavefront sensor native to single-mode-fibre-fed instruments, but its performance is almost always quoted through a specific reconstruction algorithm, obscuring how much wavefront information the device itself encodes. We develop, from first principles, the Fisher-information and Cramer-Rao theory of the photonic-lantern wavefront sensor, benchmark it against the quantum Cramer-Rao bound via an explicit multi-parameter quantum-Fisher-information calculation, and relate it to two established frameworks: the Fourier-filtering noise-propagation model of Chambouleyron et al (2023) and the classical/quantum sensitivity limit of Haffert et al (2023). Treating the lantern as a deterministic map from aberration coefficients to N output intensities, we derive the Poisson and read-noise Fisher information matrices (FIM), the per-mode CRLB, the per- photon Fisher-Rao geometry on the intensity simplex, and a flux- and estimator-independent sensitivity metric beta with quantum ceiling beta = 2. The lantern CRLB scales as N_ph^(-1/2) and is bounded, mode by mode, by the quantum limit of 1/2 rad rms per photon. That multi-parameter bound is jointly saturable: the phase generators are real and commuting, so the mean Uhlmann curvature vanishes and wavefront sensing carries no quantum incompatibility between simultaneously estimated modes, extending Haffert et al's single-mode ceiling to all low-order modes at once. We further show that the photon-noise sensitivity s_gamma of Chambouleyron et al is exactly the diagonal of our per- photon FIM, whereas the CRLB uses the diagonal of its inverse; the two coincide only for a diagonal FIM, so s_gamma is optimistic for a mode-mixing lantern. The framework is device-agnostic: it returns estimator-independent sensitivities comparable on a common beta <= 2 scale with pyramid, Zernike and PIAA-ZWFS sensors.
ER -