Wavefront-Conditioned Photon Measurements for Exoplanet Spectroscopy: Contrast Limits and Conditional Gains

Abstract

A wavefront-sensor (WFS) prediction can select the photon measurement before detection or condition its likelihood afterward. This matters for reflected-light spectra requiring hundreds of hours, because subtracting residual starlight cannot remove its photon noise. In a two-mode, low-occupation model, isotropically distributed leakage makes planet-mode projection---ideal single-mode injection matched to the planet---the optimal fixed single-photon measurement, including unequal aligned backgrounds and equal Poisson detector-event rates per output. For nonzero leakage, an attainable two-output conditioned measurement is optimal and strictly more informative before differential loss. For an isotropic background, a contrast bound holds for any distribution of recorded leakage directions: relative transmission $0.80$ and relative admitted-time duty $0.90$ limit the Fisher information per scheduled time to $0.81$ of the fixed optimum at equal predictable-leakage and planet contrasts. Haar averaging sharpens this ceiling to $0.78$. The necessary leakage-to-planet ratios for gain are approximately $2.25$ for any direction law and $3.26$ for Haar directions. A concentration-model certificate identifies directional diversity sufficient to beat recalibrated fixed measurements. Independently gated fixed-basis fallback guarantees no loss of continuum-profiled spectral information when rates and costs are known. For the Habitable Worlds Observatory, the candidate regime is predictable, directionally diverse, leakage-dominated residuals, not a general sensitivity improvement.

18 pages, 5 figures, and 5 tables