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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. 

Abstract Resolving fine details of astronomical objects provides critical insights into their underlying physical processes. This drives in part the desire to construct ever-larger telescopes and interferometer arrays and to observe at shorter wavelengths to lower the diffraction limit of angular resolution. Alternatively, one can aim to overcome the diffraction limit by extracting more information from a single telescope’s aperture. A promising way to do this is spatial-mode-based imaging, which projects a focal-plane field onto a set of spatial modes before detection, retaining focal-plane phase information that is crucial at small angular scales but typically lost in intensity imaging. However, the practical implementation of mode-based imaging in astronomy from the ground has been challenged by atmospheric turbulence. Here, we present the first on-sky demonstration of a subdiffraction-limited mode-based measurement, using a photonic-lantern-fed spectrometer installed on the Subaru Coronagraphic Extreme Adaptive Optics instrument at the Subaru Telescope. We introduce a novel calibration strategy that mitigates time-varying wave-front error and misalignment effects, leveraging simultaneously recorded focal-plane images and using a spectral-differential technique that self-calibrates the data. Observing the classical Be starβCMi, we detect spectral-differential spatial signals and reconstruct images of its Hα-emitting disk. We achieve an unprecedented Hαphotocenter precision of ∼50μas in about 10 minutes of observation with a single telescope, measuring the disk’s nearside–farside asymmetry for the first time. This work demonstrates the high precision, efficiency, and practicality of photonic mode-based imaging techniques in recovering subdiffraction-limited information, opening new avenues for high-angular-resolution spectroscopic studies in astronomy. 

Abstract This paper presents a proof of concept for a new analogue-based framework for the detection and attribution of hurricane-related hazards. This framework addresses two important limitations of existing analogue-based methodologies: the lack of observed similar events, and the unsuitability of the distance metrics for hurricanes. To do so, we use a track-based metric, and we make use of synthetic tracks catalogues. We show that our method allows for selecting a sufficient number of suitable analogues, and we apply it to nine hurricane cases. Our analysis does not reveal any robust changes in wind hazards, translation speed, seasonality, or frequency over recent decades, consistent with current literature. This framework provides a reliable alternative to traditional analogue-based methods in the case of hurricanes, complementing and potentially enhancing efforts in addressing extreme weather event attribution. 

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. 

Observational data have long suggested that in the tropics, when the troposphere locally warms, the lower stratosphere locally cools. Here, the observed anti-correlation between tropospheric and lower stratospheric temperature is confirmed—the lower stratosphere cools by approximately 2 degrees per degree of warming in the mid-troposphere. This anti-correlation is explained through a recently proposed theory holding that there is a quasi-balanced response of the stratosphere to tropospheric heating [J. Lin, K. Emanuel, Tropospheric thermal forcing of the stratosphere through quasi-balanced dynamics.J. Atmos. Sci.(2024).]. The local-scale anti-correlation between tropospheric and lower stratospheric temperature also holds when considering climate change—where the troposphere has been anomalously warming relative to the zonal mean, the lower stratosphere has been anomalously cooling, and vice versa. This suggests that zonally asymmetries in tropospheric temperature trends will be reflected in that of the lower stratospheric temperature trends. The zonally asymmetric trends are also found to be comparable in magnitude to the mean temperature trends in the lower stratosphere, highlighting the importance of the pattern of warming. The results and proposed theory suggest that in addition to forcing via wave-dissipation, the lower stratosphere can also be subject to direct forcing by the troposphere, through quasi-steady, quasi-balanced dynamics.