Demonstrations of adjoint electric field conjugation for a vortex coronagraph

Focal plane wavefront sensing and control (FPWFSC) will be required for coronagraph instruments attempting to reach the high contrasts needed to discover and characterize exoplanets. The most commonly implemented method of FPWFSC has been electric field conjugation (EFC), which uses a precomputed model-based Jacobian. This can require extensive computation times and memory resources, particularly for coronagraphs utilizing a large number of actuators and a focal plane mask (FPM) needing a combination of large spatial extent and high resolution to model. However, the more recent adjoint EFC (aEFC) approach demonstrated on the High-contrast Imager for Complex Aperture Telescopes used algorithmic differentiation and nonlinear optimization to solve for the actuator commands without the use of a Jacobian. We derive the adjoint model for a vortex coronagraph and demonstrate aEFC both with simulations and with a laboratory experiment using the Space Coronagraph Optical Bench (SCoOB). The simulations use an independent Fresnel model of a vortex coronagraph instrument, which captures the Talbot effect between propagations from optic to optic. These simulations include the first demonstration of broadband aEFC where a contrast below 10⁻¹⁰ is achieved between 3 λ∕D − 36 λ∕D and over a 10% bandpass. An additional broadband simulation with the presence of model errors is performed to demonstrate that model errors can be overcome with aEFC using a regularization bumping scheme similar to that of EFC. Finally, we experimentally test this aEFC method on the SCoOB where a contrast of 8.1 × 10⁻⁹ is achieved between 3 λ∕D and 10 λ∕D with a 632.8-nm laser source.