# Focal-plane wavefront sensing with photonic lanterns I: theoretical framework

**Authors:** Jonathan Lin, Michael Fitzgerald, Yinzi Xin, Olivier Guyon, Sergio Leon-Saval, Barnaby Norris, Nemanja Jovanovic  
**arXiv:** [2208.10563](https://arxiv.org/abs/2208.10563)  
**Date:** 2022-08-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2208.10563v1/

## Key points

- Photonic lantern (PL) is a tapered waveguide that efficiently couples light into multiple single-mode optical fibers
- Suitable for various tasks such as coupling of telescopes and high-resolution fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling (VFN)
- Can perform low-order focal-plane wavefront sensing
- Authors provide a mathematical framework for the analysis of the photonic lantern wavefront sensor (PLWFS), which includes linear and higher-order reconstruction models as well as metrics to quantify sensing performance in both linear and nonlinear regimes
- Framework can be extended to account for additional optics such as beam-shaping optics and vortex masks
- Generalizable to other wavefront sensing architectures
- Numerical simulations show that the mode-selective PL outperforms the standard and hybrid PLs in terms of sensitivity to low order aberrations under even pupil illumination
- Work provides an initial understanding of the capabilities of the PLWFS for low order wavefront sensing
- Lays a foundation for future research on optimizing PLWFS performance for various applications in astronomy and beyond.

## Summary

The photonic lantern (PL) is a tapered waveguide that efficiently couples light into multiple single-mode optical fibers, making it suitable for various tasks such as coupling of telescopes and high-resolution fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling (VFN). In addition to these applications, PLs can also perform low-order focal-plane wavefront sensing. In this work, the authors provide a mathematical framework for the analysis of the photonic lantern wavefront sensor (PLWFS), which includes linear and higher-order reconstruction models as well as metrics to quantify sensing performance in both linear and nonlinear regimes. The framework can be extended to account for additional optics such as beam-shaping optics and vortex masks. It is generalizable to other wavefront sensing architectures. The authors present numerical simulations of a 6-port PLWFS with perfect lanterns and no noise. They compare the wavefront-sensing performance of an idealized standard, hybrid, and mode-selective 6-port PL under even pupil illumination. The results show that the mode-selective PL outperforms the standard and hybrid PLs in terms of sensitivity to low order aberrations. In a companion paper, they extend their simulations to cover a range of PLWFS configurations beyond 6 port geometries considered in this paper. They investigate potential strategies through which PLWFS performance can be further controlled and optimized. This work provides an initial understanding of the capabilities of the PLWFS for low order wavefront sensing. It lays a foundation for future research on optimizing PLWFS performance for various applications in astronomy and beyond.