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We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of the linear phase retrieval scheme to higher order; the resulting Taylor polynomial can then be solved using the method of successive approximations, though we discuss alternate methods such as homotopy continuation. In the second class of techniques, a model of the WFS intensity response is created using radial basis function interpolation. We consider both forward models, which map phase to intensity and can be solved with nonlinear least-squares methods such as the Levenberg-Marquardt algorithm, as well as backwards models, which directly map intensity to phase and do not require a solver. We provide demonstrations for both types of techniques in simulation using a quad-cell sensor and a photonic lantern wavefront sensor as examples. Next, we demonstrate how the nonlinearity of an arbitrary sensor may be studied using the method of numerical continuation, and apply this technique both to the quad-cell sensor and a photonic lantern sensor. Finally, we briefly consider the extension of nonlinear techniques to polychromatic sensors. 

Adaptive optics (AO) systems are critical in any application where highly resolved imaging or beam control must be performed through a dynamic medium. Such applications include astronomy and free-space optical communications, where light propagates through the atmosphere, as well as medical microscopy and vision science, where light propagates through biological tissues. Recent works have demonstrated common-path wavefront sensors (WFSs) for adaptive optics using the photonic lantern (PL), a slowly varying waveguide that can efficiently couple multi-moded light into single-mode fibers (SMFs). We use the SCExAO astrophotonics platform at the 8 m Subaru Telescope to show that spectral dispersion of lantern outputs can improve correction fidelity, culminating with an on-sky demonstration of real-time wavefront control. This is the first, to the best of our knowledge, result for either a spectrally dispersed or a photonic lantern wavefront sensor. Combined with the benefits offered by lanterns in precision spectroscopy, our results suggest the future possibility of a unified wavefront sensing spectrograph using compact photonic devices. 

We present numerical characterizations of the wavefront sensing performance for few-mode photonic lantern wavefront sensors (PLWFSs). These characterizations include calculations of the throughput, control space, sensor linearity, and an estimate of the maximum linear reconstruction range for standard and hybrid lanterns with between 3 and 19 ports, atλ=1550nm. We additionally consider the impact of beam-shaping optics and a charge-1 vortex mask placed in the pupil plane. The former is motivated by the application of PLs to high-resolution spectroscopy, which could enable efficient injection into the spectrometer along with simultaneous focal-plane wavefront sensing; similarly, the latter is motivated by the application of PLs to vortex fiber nulling (VFN), which can simultaneously enable wavefront sensing and the nulling of on-axis starlight. Overall, we find that the PLWFS setups tested in this work exhibit good linearity out to ∼0.25−0.5 radians of RMS wavefront error (WFE). Meanwhile, we estimate the maximum amount of WFE that can be handled by these sensors to be around ∼1−2 radians RMS before the sensor response becomes degenerate. In the future, we expect these limits can be pushed further by increasing the number of degrees of freedom, either by adopting higher mode-count lanterns, dispersing lantern outputs, or separating polarizations. Finally, we consider optimization strategies for the design of the PLWFS, which involve both modification of the lantern itself and the use of pre- and post-lantern optics like phase masks and interferometric beam recombiners. 

Abstract The ~5 Myr PDS 70 is the only known system with protoplanets residing in the cavity of the circumstellar disk from which they formed, ideal for studying exoplanet formation and evolution within its natal environment. Here, we report the first spin constraint and C/O measurement of PDS 70b from Keck/KPIC high-resolution spectroscopy. We detected CO (3.8σ) and H₂O (3.5σ) molecules in the PDS 70b atmosphere via cross correlation, with a combined CO and H₂O template detection significance of 4.2σ. Our forward-model fits, using BT-Settl model grids, provide an upper limit for the spin rate of PDS 70b (<29 km s⁻¹). The atmospheric retrievals constrain the PDS 70b C/O ratio to ${0.28}_{-0.12}^{+0.20}$(<0.63 under 95% confidence level) and a metallicity [C/H] of ${-0.2}_{-0.5}^{+0.8}$dex, consistent with that of its host star. The following scenarios can explain our measured C/O of PDS 70b in contrast with that of the gas-rich outer disk (for which C/O ≳ 1). First, the bulk composition of PDS 70b might be dominated by dust+ice aggregates rather than disk gas. Another possible explanation is that the disk became carbon enrichedafterPDS 70b was formed, as predicted in models of disk chemical evolution and as observed in both very low-mass stars and older disk systems with JWST/MIRI. Because PDS 70b continues to accrete and its chemical evolution is not yet complete, more sophisticated modeling of the planet and the disk, and higher-quality observations of PDS 70b (and possibly PDS 70c), are necessary to validate these scenarios. 

Abstract We used the Keck Planet Imager and Characterizer to obtain high-resolution (R∼ 35,000)K-band spectra ofκAndromedae b, a planetary-mass companion orbiting the B9V star,κAndromedae A. We characterized its spin, radial velocity, and bulk atmospheric parameters through use of a forward-modeling framework to jointly fit planetary spectra and residual starlight speckles, obtaining likelihood-based posterior probabilities. We also detected H₂O and CO in its atmosphere via cross correlation. We measured a $v\sin \left(i\right)$value forκAndromedae b of 38.42 ± 0.05 km s⁻¹, allowing us to extend our understanding of the population of close-in bound companions at higher rotation rates. This rotation rate is one of the highest spins relative to breakup velocity measured to date, at close to 50% of breakup velocity. We identify a radial velocity $-{17.35}_{-0.09}^{+0.05}$km s⁻¹, which we use with existing astrometry and radial velocity measurements to update the orbital fit. We also measure an effective temperature of 1700 ± 100 K and a $\log \left(g\right)$of 4.7 ± 0.5 cgs dex. 

Abstract We present the projected rotational velocity and molecular abundances for HD 33632 Ab obtained via Keck Planet Imager and Characterizer (KPIC) high-resolution spectroscopy. HD 33632 Ab is a nearby benchmark brown dwarf companion at a separation of ∼20 au that straddles the L–T transition. Using a forward-modeling framework with on-axis host star spectra, which provides self-consistent substellar atmospheric and retrieval models for HD 33632 Ab, we derive a projected rotational velocity of 53 ± 3 km s⁻¹and carbon monoxide and water mass fractions of logCO = −2.3 ± 0.3 and logH₂O = −2.7 ± 0.2, respectively. The inferred carbon-to-oxygen ratio (C/O = 0.58 ± 0.14), molecular abundances, and metallicity ([C/H] = 0.0 ± 0.2 dex) of HD 33632 Ab are consistent with its host star. Although detectable methane opacities are expected in L–T transition objects, we did not recover methane in our KPIC spectra, partly due to the highvsiniand to disequilibrium chemistry at the pressures to which we are sensitive. We parameterize the spin as the ratio of rotation to the breakup velocity, and compare HD 33632 Ab to a compilation of >200 very low-mass objects (M≲ 0.1M_⊙) that have spin measurements in the literature. There appears to be no clear trend for the isolated low-mass field objects versus mass, but a tentative trend is identified for low-mass companions and directly imaged exoplanets, similar to previous findings. A larger sample of close-in gas giant exoplanets and brown dwarfs will critically examine our understanding of their formation and evolution through rotation and chemical abundance measurements. 

The photonic lantern (PL) is a tapered waveguide that can efficiently couple light into multiple single-mode optical fibers. Such devices are currently being considered for a number of tasks, including the coupling of telescopes and high-resolution, fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling. In conjunction with these use cases, PLs can simultaneously perform low-order focal-plane wavefront sensing. In this work, we provide a mathematical framework for the analysis of a PL wavefront sensor (PLWFS), deriving linear and higher-order reconstruction models as well as metrics through which sensing performance—in both the linear and nonlinear regimes—can be quantified. This framework can be extended to account for additional optics such as beam-shaping optics and vortex masks, and can be generalized for other wavefront sensing architectures. Finally, we provide initial numerical verification of our mathematical models by simulating a six-port PLWFS. In a forthcoming companion paper (Lin and Fitzgerald), we provide a more comprehensive numerical characterization of few-port PLWFSs, and consider how the sensing properties of these devices can be controlled and optimized. 

Abstract GQ Lup B is one of the few substellar companions with a detected cicumplanetary disk (CPD). Observations of the CPD suggest the presence of a cavity, possibly formed by an exosatellite. Using the Keck Planet Imager and Characterizer (KPIC), a high-contrast imaging suite that feeds a high-resolution spectrograph (1.9–2.5µm,R∼35,000), we present the first dedicated radial velocity (RV) observations around a high-contrast, directly imaged substellar companion, GQ Lup B, to search for exosatellites. Over 11 epochs, we find a best and median RV error of 400–1000 m s⁻¹, most likely limited by systematic fringing in the spectra due to transmissive optics within KPIC. With this RV precision, KPIC is sensitive to exomoons 0.6%–2.8% the mass of GQ Lup B (∼30M_Jup) at separations between the Roche limit and 65R_Jup, or the extent of the cavity inferred within the CPD detected around GQ Lup B. Using simulations of HISPEC, a high resolution infrared spectrograph planned to debut at W.M. Keck Observatory in 2026, we estimate future exomoon sensitivity to increase by over an order of magnitude, providing sensitivity to less massive satellites potentially formed within the CPD itself. Additionally, we run simulations to estimate the amount of material that different masses of satellites could clear in a CPD to create the observed cavity. We find satellite-to-planet mass ratios ofq> 2 × 10⁻⁴can create observable cavities and report a maximum cavity size of ∼51R_Jupcarved from a satellite. 

Abstract Using Keck Planet Imager and Characterizer high-resolution (R∼ 35,000) spectroscopy from 2.29 to 2.49μm, we present uniform atmospheric retrievals for eight young substellar companions with masses of ∼10–30M_Jup, orbital separations spanning ∼50–360 au, andT_effbetween ∼1500 and 2600 K. We find that all companions have solar C/O ratios and metallicities to within the 1σ–2σlevel, with the measurements clustered around solar composition. Stars in the same stellar associations as our systems have near-solar abundances, so these results indicate that this population of companions is consistent with formation via direct gravitational collapse. Alternatively, core accretion outside the CO snowline would be compatible with our measurements, though the high mass ratios of most systems would require rapid core assembly and gas accretion in massive disks. On a population level, our findings can be contrasted with abundance measurements for directly imaged planets withm< 10M_Jup, which show tentative atmospheric metal enrichment compared to their host stars. In addition, the atmospheric compositions of our sample of companions are distinct from those of hot Jupiters, which most likely form via core accretion. For two companions withT_eff∼ 1700–2000 K (κAnd b and GSC 6214–210 b), our best-fit models prefer a nongray cloud model with >3σsignificance. The cloudy models yield 2σ−3σlowerT_efffor these companions, though the C/O and [C/H] still agree between cloudy and clear models at the 1σlevel. Finally, we constrain¹²CO/¹³CO for three companions with the highest signal-to-noise ratio data (GQ Lup b, HIP 79098b, and DH Tau b) and report $v\sin i$and radial velocities for all companions. 

Abstract The 1RXS J034231.8+121622 system consists of an M dwarf primary and a directly imaged low-mass stellar companion. We use high-resolution spectroscopic data from Keck/KPIC to estimate the objects' atmospheric parameters and radial velocities (RVs). Using PHOENIX stellar models, we find that the primary has a temperature of 3460 ± 50 K and a metallicity of 0.16 ± 0.04, while the secondary has a temperature of 2510 ± 50 K and a metallicity of ${0.13}_{-0.11}^{+0.12}$. Recent work suggests this system is associated with the Hyades, giving it an older age than previous estimates. Both metallicities agree with current Hyades [Fe/H] measurements (0.11–0.21). Using stellar evolutionary models, we obtain significantly higher masses for the objects, 0.30 ± 0.15M_⊙and 0.08 ± 0.01M_⊙(84 ± 11M_Jup), respectively. Using the RVs and a new astrometry point from Keck/NIRC2, we find that the system is likely an edge-on, moderately eccentric ( ${0.41}_{-0.08}^{+0.27}$) configuration. We also estimate the C/O ratio of both objects using custom grid models, obtaining 0.42 ± 0.10 (primary) and 0.55 ± 0.10 (companion). From these results, we confirm that this system most likely went through a binary star formation process in the Hyades. The significant changes in this system's parameters since its discovery highlight the importance of high-resolution spectroscopy for both orbital and atmospheric characterization of directly imaged companions.