ExEp: Demonstration of Spectral Linear Dark Field Control on NASA’s High Contrast Imaging Testbeds

In order to directly image Earth like exoplanets (exo-Earths) orbiting sun-like stars, a space-based coronagraph will be required to suppress the starlight by a factor of 10−10. Coronagraphs use active methods of wavefront sensing and control (WFSC) such as pairwise probing (PWP) and electric field conjugation (EFC) to create regions of high contrast in the science camera image, called dark holes. Due to the low flux of these exo-Earths, long exposure times are required to spectrally characterize them. During these long exposures, the optical system tends to drift degrading the contrast. Unfortunately one cannot simply reuse PWP as it modulates the intensity in the image plane, interrupting the science acquisition. A wavefront sensing and control loop could be running in parallel during the science acquisition without modifying the dark hole to prevent the contrast from drifting. Spectral linear dark field control (LDFC) takes advantage of the linear relationship between the change in intensity of the out-of-band light, called the sensing band, and small changes in wavefront to stabilize the dark hole region during science exposures. The advantage of the linear relationship simplifies the WFSC algorithms required to maintain the dark hole contrast. We are able to use an extension of the singular value decomposition (SVD) psuedoinverse to perform iterative modal control. This control algorithm allows us to place loop gains and leaks on the eigenmodes themselves. In this paper, we show experimental results which demonstrate spectral LDFC can be used to stabilize contrast levels of approximately 10−9 on a Lyot coronagraph testbed which is housed in a vacuum chamber. Promising results show that spectral LDFC can be used to correct for disturbances that degrade the contrast by more than 100x. To our knowledge, this is the first experimental demonstration of spectral LDFC and the first demonstration spatial or spectral LDFC on a vacuum coronagraph testbed and at contrast levels less than 1 × 10^−8.