Efficient Exoplanet Imaging Simulations of the Habitable Worlds Observatory

Abstract

Direct imaging simulations of starshades and other proposed mission concepts are needed to characterize planet detection performance and inform mission design trades. In order to assess the complementary role of a 60 m starshade for the Habitable Worlds Observatory (HWO), we develop the optical model of a starshade and simulate solar system imaging at 0 degrees and 60 degrees inclinations. The optical core throughput of a direct-imaging system is a key metric that governs exposure time and the potential exoplanetary yield of a mission. We use our optical model to evaluate core throughput, incorporating 6 m segmented and obscured telescope apertures, over the visible to near-infrared wavelength band (500-1000 nm). Accurate diffractive optical simulations of this form require many large Fourier transforms, with prohibitive run-times, as both the starshade mask and telescope aperture require fine-scale spatial sampling. We introduce a Fourier sampling technique, the Bluestein Fast Fourier Transform (BFFT), to efficiently simulate diffractive optics and enable high-fidelity simulations of core throughput. By characterizing sampling requirements and comparing BFFT's computational complexity to standard Fourier methods (for example, DFT and FFT), we demonstrate its efficiency in our optical pipeline. These methods are implemented in PyStarshade (Taaki 2025), an open-source Python package offering flexible diffraction tools and imaging simulations for starshades. Our results show the HWO starshade used with a segmented off-axis telescope aperture achieves an optimal core throughput measured within a photometric aperture of radius 0.7 lambda/D of 68 percent. With an additionally obscured aperture, a 66 percent core throughput is achieved.

Figures (12)

• Figure 1: The optical model of a starshade is illustrated. The input function $f_{\lambda}(x, y)$ describes the flux density of a star-planet scene, as viewed from a fixed angle, and as a function of wavelength. This input function propagates past the starshade $s(x,y)$, onto a telescope aperture mask $P(x, y)$ at distance $d$, and onto a CCD in the image plane at a distance $d_f$. The IWA is the angular separation from the star where an exoplanet can be imaged. In the output image $I_\lambda(x,y)$, the light from the host-star has been suppressed revealing the faint exoplanetary system.
• Figure 2: Suppression in logarithmic units (diffraction intensity at the telescope aperture $\|f_P^{\parallel}\|^2$) is shown for the HWO 60 m starshade with 16 petals at a wavelength of 500 nm, with a spatial sampling of $\Delta P=2$ cm, $N_P = 6000$. The central dark shadow is masked by the telescope and produces the on-axis stellar PSF. The dark shadow must therefore be as large as the aperture. To maintain the dark shadow (contrast), the Fresnel number should remain constant $\mathcal{f} = \frac{R_{ss}^2}{\lambda z} \sim 10-20$. This can be maintained at wavelengths outside of the band by changing the lateral flight distance of the starshade $z$. The dark shadow is approximately the size of the starshade in diameter (60m).
• Figure 3: Illustration of the starshade and pupil plane sampling (not to scale). The pupil radius is approximately $\frac{1}{10}$ the starshade radius. The starshade grid is of size $N_s \cdot N_s$ with sampling $\Delta s$. The zero-padding of the starshade $N_s \cdot \gamma_{ss}$ necessary to achieve a $\Delta P$ sampling in the telescope plane with an FFT computation is illustrated. In the telescope plane, the telescope aperture of size $N_P \cdot N_P$ is shown, as is the slightly larger computed field of size $N_P^\parallel \cdot N_P^\parallel$.
• Figure 4: The relative complexity in real FLOPs among 2D Fourier transform computations described in Table \ref{['tab:comparison']} is shown for varying the ratio of non-zero input samples $N$ to output samples $M$ (x-axis) with complexity on a log scale (y-axis). Figures left to right show increasing the overall size of $N$ and $M$. For the (starshade $\to$ telescope) propagation $N/M = N_s/N_P^\parallel = 20$, for the (telescope $\to$ focal plane) $N/M = N_P/N_f = 1$. When a smaller number of output samples $M < 50$ are needed, the BDW and DFT method are optimal over the B-FFT. On the right, for larger input/output sizes $N, M \geq 200$ as used in this work, the B-FFT is generally optimal.
• Figure 5: Suppression (diffraction intensity at the telescope aperture) of a point source is shown for the NI2 Roman starshade (16 petals) at $\mathcal{f} = 9.1$ corresponding to $\lambda = 500$ nm, with different starshade pixel sizes $\Delta s$. No change is seen increasing the discretization past $\Delta s =$ 1 mm.