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arXiv · 2609.32023

An Analytic Error-Budget Model for the Habitable Worlds Observatory Coronagraph: From Optical Disturbances to Flux-Ratio Noise

Slava G. Turyshev
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Abstract

A coronagraph stability allocation must protect a planet measurement, not merely satisfy a contrast target. Residual starlight both generates photon noise and interferes with small field perturbations, coupling optical stability to detection reliability. We develop a modular analytic model for the Habitable Worlds Observatory (HWO), using a reduced two-roll angular-differential-imaging realization of its OS-1 scenario. Complex-field sensitivities, wavefront sensing/control, finite observing windows, polarization, detector calibration are propagated to flux-ratio noise (FRN) and detection probabilities. Joint-visit Gaussian quadratic moments retain differential bias, cross covariance; spatial overlap/field phase determine which disturbances resemble a planet. A 6-m, 500-nm benchmark shows why the science test must precede category allocation. For a 115.46-parts-per-trillion (ppt) quadrature planet, 30,000 independent Gaussian search statistics, and a $10^{-3}$ family-wise false-alarm objective, 20-ppt FRN gives 64.55% conditional detection power; 99% requires 14.94 ppt. Photon and calibration noise exhaust the optical remainder at 8.11 pc in 100 h under the fixed response, so tighter stability alone cannot restore feasibility. An unrecognized 1% high-variance component carrying twenty percent of the variance tightens the modal allowance by a factor of 2.88; an ideal, exactly known state label reduces that penalty to 1.29 under equal conditional false-alarm limits and the same average-power objective. Thus, requirements depend on both the optical response and the information retained by the observing protocol. The framework identifies when suppression, stability, calibration, or state monitoring addresses the limiting mechanism. Numerical tolerances are controlled model results; flight allocation requires architecture-specific responses and calibrated disturbance state-estimation laws.

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Slava G. Turyshev. 2026-09-25. An Analytic Error-Budget Model for the Habitable Worlds Observatory Coronagraph: From Optical Disturbances to Flux-Ratio Noise. https://arxiv.org/abs/2609.32023

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