Incorporating Wavefront Error, Wavefront Sensing and Control, and Sensitivities into Exposure Time Calculations for Future Space Missions with the Error Budget Software (EBS)

A primary goal of NASA's Habitable Worlds Observatory (HWO) concept is to explore with high completeness the Habitable Zones (HZ) of $\sim$ 100 stellar systems and potentially acquire spectra of $\sim$ 25 terrestrial-type planets in the habitable zones of sun-like stars (implying planet/star flux ratios on the order of $10^{-10}$), which places tight constraints on the performance of observatory systems. In particular, coronagraph instrumentation needs to be matured for higher throughput, deeper contrasts, and better broadband performance, while also taking into account their sensitivity and ability to mitigate the impact of telescope instability and wavefront error (WFE), which can have a profound impact on exo-Earth imaging. Due to the specific focus on the quantity of observed/characterized exo-Earths, the success of various proposed HWO mission architectures is often represented by the estimated exo-Earth candidate yield. Computation of the minimum exposure time to achieve the required signal-to-noise on a given target, using an exposure time calculator (ETC), is a key part of yield estimation. Moreover, one relies on ETCs not only for yields, but also to identify key observatory parameters that have large effects on expected exposure, and might warrant dedicated technology development. The impacts of coronagraph sensitivity, WFE, and wavefront sensing and control (WFS\&C) have been well studied in the context of developing error budgets for missions and instruments such as the Roman Coronagraph Instrument. Noneteless, there is currently no easily accessible and open-source way to directly incorporate the effects of these key parameters into calculating exposure times to perform trade studies for HWO. To address this gap, we developed the Error Budget Software (EBS) \textemdash an open-source tool that synthesizes sensitivity, WFE, and WFS\&C information for a variety of temporal and spatial scales, and directly interfaces with the open-source yield code EXOSIMS to produce exposure times. We also demonstrate how EBS can be used for mission error budgeting using the example of the Ultrastable Observatory Roadmap Team (USORT) observatory design. This includes a series of both single and multi-variate parameter explorations using EBS where we identify trends between raw contrast and wavefront error, and detector noise and energy resolution. We also highlight the existence of bifurcation points \textemdash points at which mission performance dramatically changes for only a moderate variation of the observatory/instrument parameter considered. This code has been becnhmarked against other ETCs \cite{2025ETCCrossCal}