Analysis of Angular-Differential Post-Processing Algorithms for Exoplanet Direct Detection with a Photonic Lantern Nuller

TL;DR

This work tackles the challenge of direct exoplanet detection with a Photonic Lantern Nuller (PLN), whose 1D, non-rotationally invariant signals defy standard ADI processing. By reformulating ADI with PCA-based KLIP and introducing an Antiplanet KLIP Subtraction approach, the authors quantify how self-subtraction degrades PLN signals at small inner working angles and demonstrate that injecting an antiplanet before stellar subtraction yields superior detection and localization across multiple sky-rotation regimes. Through extensive Monte Carlo testing, Antiplanet KLIP consistently outperforms Direct Fitting and conventional KLIP in both detection limits and spatial localization of planet parameters ($r$, $\epsilon$, $\Theta$), especially at larger angular coverages ($\Delta\theta = 100^{\circ}, 150^{\circ}$). The findings support PLN as a viable path for imaging faint, close-in exoplanets and provide guidance on data-analysis strategies and observing configurations, including the benefit of maximizing angular diversity. Future work may extend the framework to multi-wavelength data and spectral disentangling to enhance sensitivity further.

Abstract

Exoplanet research is essential for understanding planetary formation and the potential for life beyond our solar system. The direct imaging method captures exoplanet light while minimizing light from the host star. This is conventionally achieved with a coronagraph, which allows detailed characterization of planetary atmospheres and features. The Photonic Lantern Nuller (PLN) is an innovative instrument designed for the direct detection of closely orbiting exoplanets within the inner working angle of standard coronagraphs. Unlike traditional coronagraphs, where the planet's signal is usually rotationally invariant, with the same point-spread-function at different position angles, and which also overlaps minimally with the residual stellar signal, data from a PLN consist of a one-dimensional collection of points that do not have rotational invariance and overlap significantly with the residual starlight arising from wavefront errors. Exploiting angular diversity to subtract these stellar residuals with the PLN thus requires adapting the Angular Differential Imaging (ADI) technique for use with non-rotationally invariant planet signals at close separations, where strong self-subtraction effects occur. We reformulate ADI using principal component analysis to develop a method to extract spatial parameters of exoplanets from simulated one-dimensional PLN data. We test two variations of ADI on simulated data and show that injecting an antiplanet signal before stellar estimation helps localize the planet due to self-subtraction at lower separations.

Figures (12)

• Figure 1: PLN Overview: (a) PLN Selective Nulling: Throughput maps for each port of an ideal six-port mode-selective photonic lantern, spanning from -3 $\lambda/D$ to 3 $\lambda/D$ in each direction.(b) PLN Throughput: Throughput of the Photonic Lantern Nuller. The PLN used throughout this work is depicted by the black curve, which has 4 out of the 6 ports nulled (all except the first and last port), and the throughput is shown peaking around 1 $\lambda/D$, much smaller than the average coronograph throughput peaks. Figure adapted from Xin et al. Xin_2022
• Figure 2: Comparison of instrument data: (a) Simulated 2-Dimensional data from a Charge 6 Vortex Coronagraph containing a bright planet PSF against a field of speckles (the intensity contributed by starlight due to wavefront error), (b) Simulated 1-Dimensional data from the four nulled ports of a PLN. The blue dashed line corresponds to the intensity contributed by a bright planet, while the red solid line corresponds to the combined intensity of the same planet with the intensity contributed by starlight leaked due to wavefront error.
• Figure 3: Comparison of planet PSF correlations across rotation angles : (a) The far off-axis (a separation of $7 \lambda/D$) PSFs of a charge 6 vortex coronagraph are generated, ranging in position angle from 0 to $2\pi$. The 2D images are flattened into a 1D array, normalized, and dotted with each other, showing almost no inter-correlations. (b) The close off-axis (a separation of $1 \lambda/D$) PSFs of a charge 6 vortex coronagraph are generated, ranging in position angle from 0 to $2\pi$ (included for comparison with the PLN, even though this is well within the inner working angle of this coronagraph). The 2D images are flattened, normalized, and dotted with each other to show correlations. (c) Normalized dot products between PSFs generated by the mode-selective PLN at its peak throughput separation of $1,\lambda/D$, for position angles ranging from 0 to $2\pi$. Each PSF’s 1D intensity profile is normalized before computing pairwise dot products, revealing a characteristic angular correlation structure. High correlations occur between PSFs at nearby position angles, with correlation decreasing gradually up to an angular separation of $\pi$. The repeating pattern observed at $\phi_{2} + \pi$ for each pair $(\phi_{1}, \phi_{2})$ indicates the intrinsic $180^{\circ}$ spatial degeneracy of the planet signal captured by the PLN.
• Figure 4: Fraction of a planet's RMS signal intensity retained after median subtraction modelling with itself, characterizing self-subtraction for Charge 2, 4, and 6 coronagraphs and a mode-selective PLN. The retained signal for the PLN drops sharply at $2.5~\lambda/D$, corresponding to a decrease in the instrument's throughput (see Fig. \ref{['fig:PLNInfo']}) and indicating this separation is outside the PLN's effective field-of-view.
• Figure 5: The detection limit plot for the Direct Fit method has 3 histograms, one for each method, and a plot of the ROC curves. The three histograms show the test-statistic distributions for datasets with a planet versus those without. Each histogram is focused on the overlap region (if any) between the two distributions, which is the source of false positives. The bottom-right plot shows the corresponding ROC curves for each method. In the ROC plot, the shaded area highlights the region of poorly-sampled false positive rates, derived from fewer than 30 false detections. The KLIP and Antiplanet KLIP subtraction costs are evaluated with $N_{comp} = 1$, for comparison with Direct Fit at its detection limit.