The number of planets discovered orbiting other stars has soared over the past decade, exciting astronomers and the general public alike. While the science obtained has been extremely important, it is still limited by the inability to directly image companion planets. This is because the halo created from diffracted stellar light is many orders of magnitude brighter than the planet (for instance, an Earth-sized planet located one astronomical unit from its parent star is expected to be 10 billion times dimmer). Future plans for both large ground telescopes—e.g., Gemini, the Very Large Telescope array, and Subaru—and forthcoming space observatories include provisions for techniques to create high-contrast regions in the image close enough to the star where very dim companions can be seen with sufficient fidelity.
Figure 1. Aberrated field with a shaped pupil coronagraph. λ0/D: Spatial dimensions are in units of wavelength over telescope diameter.
One such method is known as a coronagraph. This technique consists of a series of field stops and relay optics to suppress the starlight leakage due to diffraction into the planet detection area of the image. While many coronagraphs have been proposed and are currently being studied, all suffer from the same limitation. Coronagraphic imaging is highly sensitive to aberrations created by small manufacturing errors on the optics, requiring wavefront control techniques to recover regions of high contrast. Figure 1 shows a laboratory image taken with a shaped pupil coronagraph at Princeton University.1 A mask is used to block the central star, and the openings are the regions of high contrast. Aberrations result in ‘speckles’ that limit the achievable contrast to no better than one part in 104.
Like adaptive optics systems currently employed on most large telescopes, all proposed coronagraphic systems use deformable mirrors (DMs) to modify the phase of the wavefront, thus correcting the aberrations before creating an image. However, unlike traditional adaptive optics, the extreme sensitivity and desire for very high contrast requires correcting both the amplitude and phase of the aberrated wavefront using only measurements from the science camera (to eliminate non-common path error in the sensing path). It has been shown that using two DMs in series can correct both amplitude and phase over a reasonably broad band of wavelengths.2, 3 At the High Contrast Imaging Lab (HCIL) at Princeton, we have developed algorithms for efficiently estimating the wavefront from multiple images and for optimally determining the DM settings to create what are often called ‘dark holes’ in the image where planets can be detected. Here we describe our recent laboratory results using these algorithms with two Boston Micromachines MEMS (microelectromechanical systems) DMs to create broadband high contrast on both sides of the stellar image.
Focal plane estimation and control
Various algorithms have been proposed or are in use for determining the settings of the DM to create high contrast.4 All require estimates of the real and imaginary parts of the electric field at the science camera. Wavefront estimation using the science detector requires taking multiple exposures while systematically modulating the DMs. The most mature algorithm to date is called DM diversity,5, 6 which provides an estimate with minimal error by solving for the field through a least-squares minimization on three or more pairs of images. In an effort to reduce the number of exposures, we applied a Kalman filter formalism to create a closed loop estimator that optimally uses prior information and dramatically reduces the number of required images.7
Figure 2. Corrected field having two 3×4λ/D dark holes with an average contrast of 2.3×10−7.
Applying estimates from the Kalman filter with the optimal stroke minimization control algorithm4 developed at the HCIL, we achieved a contrast level of 2.3×10−7 on both sides of the image plane (see Figure 2). This is the same contrast as with previous estimation approaches and the only example of correcting both amplitude and phase on both sides of the stellar image using two DMs. Moreover, the Kalman filter estimator requires half the number of measurements. For a space observatory, with exposure times on the order of hours to days, this represents an enormous boost in efficiency.
To perform broadband detection and spectral characterization, we also wish for this control to apply over a bandwidth rather than to a single wavelength. We can extend the monochromatic performance already demonstrated to other wavelengths by augmenting our stroke minimization algorithm4 with multiple wavelengths. In order to avoid taking measurements at multiple wavelengths, we estimate the field over the band. To do this, we extrapolate a monochromatic estimate to other wavelengths by modeling the field with amplitude aberrations that are independent of wavelength and phase aberrations that are inversely proportional to wavelength.
Figure 3. Corrected contrast in a dark hole as a function of wavelength using measurements at a central wavelength and extrapolating to others. AVG: Average.
Figure 4. Corrected broadband field. Achievable contrast is 6.15×10−6 in a 10% band around 635nm.
Figures 3 and 4 show laboratory results creating symmetric dark holes in broadband light using the new control algorithm and extrapolated estimates from the older DM diversity algorithm. We are currently achieving a contrast using extrapolating estimates of 6.15×10−6 over an ∼10% band.8 These results represent the only algorithm to date that has proven symmetric dark holes in broadband light by simultaneously correcting amplitude and phase aberrations at multiple wavelengths.
Our current performance is limited by non-single-mode output from the optical fiber at shorter wavelengths. The laboratory is being upgraded with a new single-mode photonic crystal fiber designed to remedy this, allowing us to more accurately replicate the incident light from a star. At that point we expect to be limited by our models of the DM surface, the limiting factor in our monochromatic results. Future work is directed at modifying the Kalman filter formalism to include parameter adaptive filtering, allowing real-time learning of a parameterized DM surface model. These efforts are intended to continue improving the efficiency and robustness of wavefront control for high-contrast imaging.
This work was funded by NASA grant NNX09AB96G and the NASA Earth and Space Science Fellowship program. We also thank Boston Micromachines and Koheras for their continued technical support.
N. Jeremy Kasdin, Tyler D. Groff
Mechanical and Aerospace Engineering Department
N. Jeremy Kasdin received his BSE from Princeton University (1985) and his PhD in aeronautics and astronautics from Stanford University (1991). He studies exoplanet imaging, space optics, spacecraft design, and astrodynamics. He is currently a professor.
Tyler Groff received his BSc in mechanical engineering and astrophysics from Tufts University (2007). He is currently in his fifth year of graduate study. His research focuses on coronagraph design and wavefront control for ground and space telescopes.
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