A focal plane wavefront sensor offers major advantages to adaptive optics, including removal of non-commonpath error and providing sensitivity to blind modes (such as petalling). But simply using the observed point spread function (PSF) is not sufficient for wavefront correction, as only the intensity, not phase, is measured. Here we demonstrate the use of a multimode fiber mode converter (photonic lantern) to directly measure the wavefront phase and amplitude at the focal plane. Starlight is injected into a multimode fiber at the image plane, with the combination of modes excited within the fiber a function of the phase and amplitude of the incident wavefront. The fiber undergoes an adiabatic transition into a set of multiple, single-mode outputs, such that the distribution of intensities between them encodes the incident wavefront. The mapping (which may be strongly non-linear) between spatial modes in the PSF and the outputs is stable but must be learned. This is done by a deep neural network, trained by applying random combinations of spatial modes to the deformable mirror. Once trained, the neural network can instantaneously predict the incident wavefront for any set of output intensities. We demonstrate the successful reconstruction of wavefronts produced in the laboratory with low-wind-effect, and an on-sky demonstration of reconstruction of low-order modes consistent with those measured by the existing pyramid wavefront sensor, using SCExAO observations at the Subaru Telescope.
Photonic lanterns (PLs) allow the decomposition of highly multimodal light into a simplified modal basis such as single-moded and/or few-moded. They are increasingly finding uses in astronomy, optics, and telecommunications. Calculating propagation through a PL using traditional algorithms takes ∼1 h per simulation on a modern CPU. We demonstrate that neural networks can bridge the disparate opto-electronic systems and, when trained, can achieve a speedup of over five orders of magnitude. We show that this approach can be used to model PLs with manufacturing defects and can be successfully generalized to polychromatic data. We demonstrate two uses of these neural network models: propagating seeing through the PL and performing global optimization for purposes such as PL funnels and PL nullers.
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