Measuring masses of long-period planets around F, G, and K stars is necessary to characterize exoplanets and assess their habitability. Imaging stellar astrometry offers a unique opportunity to solve radial velocity system inclination ambiguity and determine exoplanet masses. The main limiting factor in sparse-field astrometry, besides photon noise, is the non-systematic dynamic distortions that arise from perturbations in the optical train. Even space optics suffer from dynamic distortions in the optical system at the sub-μas level. To overcome this limitation we propose a diffractive pupil that uses an array of dots on the primary mirror creating polychromatic diffraction spikes in the focal plane, which are used to calibrate the distortions in the optical system. By combining this technology with a high-performance coronagraph, measurements of planetary systems orbits and masses can be obtained faster and more accurately than by applying traditional techniques separately. In this paper, we present the results of the combined astrometry and and highcontrast imaging experiments performed at NASA Ames Research Center as part of a Technology Development for Exoplanet Missions program. We demonstrated 2.38x10-5 λ/D astrometric accuracy per axis and 1.72x10-7 raw contrast from 1.6 to 4.5 λ/D. In addition, using a simple average subtraction post-processing we demonstrated no contamination of the coronagraph field down to 4.79x10-9 raw contrast.
Differential OTF uses two images taken with a telescope pupil modification between them to measure the complex field over most of the pupil. If the pupil modification involves a non-negligible region of the pupil, the dOTF field is blurred by convolution with the complex conjugate of the pupil field change. In some cases, the convolution kernel, or difference field, can cause significant blurring. We explore using deconvolution to recover a highresolution measurement of the complex pupil field. In particular, by assuming we know something about the area and nature of the difference field, we can construct a Wiener filter that increases the resolution of the complex pupil field estimate in the presence of noise. By introducing a controllable pupil modification, such as actuating a telescope primary mirror segment in piston-tip-tilt to make the measurement, we explain added features to the difference field which can be used to increase the signal-to-noise ratio for information in arbitrary ranges of spatial frequency. We will present theory and numerical simulations to discuss key features of the difference field which lead to its utility for deconvolution of dOTF measurements.
We present an overview of the design of a new testbed for studying coronagraphic imaging and wavefront control using a variety of pupil and coronagraph architectures. The testbed is designed to explore optimal use of starlight (including starlight rejected by the coronagraph) for wavefront control, system self-calibration, and point spread function (PSF) calibration. It is also compatible with coronagraph designs for centrally obscured and segmented apertures, and includes shaped or apodized pupils, a range of focal plane masks and Lyot stops of multiple sizes, and an optional PIAA apodizing stage. Starlight is reflected and imaged from the focal plane mask and Lyot stop for low-order wavefront sensing. Both a segmented and a continuous sheet MEMS DM are included to simulate segmented telescope pupils, apply known test phase patterns, and implement a controllable phase apodization coronagraph. The testbed is adaptable and is currently being used to investigate three different techniques: (1) the differential optical transfer function (dOTF), (2) low-order wavefront sensing (LOWFS) with a hybrid-Lyot coronagraph, and (3) linear dark field control (LDFC).
We demonstrate self-calibration of an adaptive optical system using differential OTF [Codona, JL; Opt. Eng. 0001; 52(9):097105-097105. doi:10.1117/1.OE.52.9.097105]. We use a deformable mirror (DM) along with science camera focal plane images to implement a closed-loop servo that both flattens the DM and corrects for non-common-path aberrations within the telescope. The pupil field modification required for dOTF measurement is introduced by displacing actuators near the edge of the illuminated pupil. Simulations were used to develop methods to retrieve the phase from the complex amplitude dOTF measurements for both segmented and continuous sheet MEMS DMs and tests were performed using a Boston Micromachines continuous sheet DM for verification. We compute the actuator correction updates directly from the phase of the dOTF measurements, reading out displacements and/or slopes at segment and actuator positions. Through simulation, we also explore the effectiveness of these techniques for a variety of photons collected in each dOTF exposure pair.