Kalman Filter Estimation for Focal Plane Wavefront Correction

Space-based coronagraphs for future earth-like planet detection will require focal plane wavefront control techniques to achieve the necessary contrast levels. These correction algorithms are iterative and the control methods require an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field. In addition to a significant reduction in exposures, we discuss the relative merit of this algorithm to other estimation schemes, particularly in regard to estimate error and covariance. As part of the reduction in exposures we also discuss a novel approach to generating the diversity required for estimating the field in the image plane. This uses the stroke minimization control algorithm to choose the probe shapes on the deformable mirrors, adding a degree of optimality to the problem and once again reducing the total number of exposures required for correction. Choosing probe shapes has been largely unexplored up to this point and is critical to producing a well posed set of measurements for the estimate. Ultimately the filter will lead to an adaptive algorithm which can estimate physical parameters in the laboratory and optimize estimation.Comment: 14 pages, 9 figures, SPIE Astronomical Telescopes and Instrumentation 2012 conference proceedings. Journal version at arXiv:1301.382

Rectangular-Mask Coronagraphs for High-Contrast Imaging

We present yet another new family of masks for high-contrast imaging as required for the to-be-built terrestrial planet finder space telescope. The ``best'' design involves a square entrance pupil having a 4-vane spider, a square image-plane mask containing a plus-sign shaped occulter to block the starlight inside 0.6 lambda/D, and a Lyot-plane mask consisting of a rectangular array of rectangular opennings. Using Fraunhofer analysis, we show that the optical system can image a planet 10^{-10} times as bright as an on-axis star in four rectangular regions given by {(xi,zeta): 1.4 < | xi | < 20, 1.4 < | zeta | < 20}. Since the design involves an image plane mask, pointing error is an issue. We show that the design can tolerate pointing errors of about 0.05 lambda/D. The inclusion of a 4-vane spider in the entrance pupil provides the possibility to build a mirror-only on-axis system thereby greatly reducing the negative effects of polarization. Each of the masks can be realized as two masks consisting of stripes of opaque material with the stripes oriented at right angles to each other. We call these striped masks barcode masks. We show that it is sufficient for the barcode masks by themselves to provide 10^{-5} contrast. This then guarantees that the full system will provide the required 10^{-10} contrast.Comment: 12 pages, 5 figure

Identification and adaptive control of a high-contrast focal plane wavefront correction system

All coronagraphic instruments for exoplanet high-contrast imaging need wavefront correction systems to reject optical aberrations and create sufficiently dark holes. Since the most efficient wavefront correction algorithms (controllers and estimators) are usually model-based, the modeling accuracy of the system influences the ultimate wavefront correction performance. Currently, wavefront correction systems are typically approximated as linear systems using Fourier optics. However, the Fourier optics model is usually biased due to inaccuracies in the layout measurements, the imperfect diagnoses of inherent optical aberrations, and a lack of knowledge of the deformable mirrors (actuator gains and influence functions). Moreover, the telescope optical system varies over time because of instrument instabilities and environmental effects. In this paper, we present an expectation-maximization (E-M) approach for identifying and real-time adapting the linear telescope model from data. By iterating between the E-step (a Kalman filter and a Rauch smoother) and the M-step (analytical or gradient-based optimization), the algorithm is able to recover the system even if the model depends on the electric fields, which are unmeasurable hidden variables. Simulations and experiments in Princeton's High Contrast Imaging Lab demonstrate that this algorithm improves the model accuracy and increases the efficiency and speed of the wavefront correction

Shaped pupil design for the Gemini Planet Imager

The Gemini Planet Imager (GPI) is an instrument designed for the Gemini South telescope to image young Jupiter-mass planets in the infrared. To achieve the high contrast needed for this, it employs an apodized pupil Lyot coronagraph (APLC) to remove most of the starlight. Current designs use a partially-transmitting apodizer in the pupil; we examine the use of binary apodizations in the form of starshaped shaped pupils, and present a design that could achieve comparable performance, along with a series of design guidelines for creating shaped pupil versions of APLCs in other systems.Comment: 20 pages, 7 figures, accepted for publication in Ap

Spiderweb Masks for High-Contrast Imaging

Motivated by the desire to image exosolar planets, recent work by us and others has shown that high-contrast imaging can be achieved using specially shaped pupil masks. To date, the masks we have designed have been symmetric with respect to a cartesian coordinate system but were not rotationally invariant, thus requiring that one take multiple images at different angles of rotation about the central point in order to obtain high-contrast in all directions. In this paper, we present a new class of masks that have rotational symmetry and provide high-contrast in all directions with just one image. These masks provide the required 10^{-10} level of contrast to within 4 lambda/D, and in some cases 3 lambda/D, of the central point, which is deemed necessary for exosolar planet finding/imaging. They are also well-suited for use on ground-based telescopes, and perhaps NGST too, since they can accommodate central obstructions and associated support spiders.Comment: 20 pages, 9 figures, to appear in Ap