EXCEDE Technology Development I: First demonstrations of high contrast at 1.2 λ/d for an Explorer space telescope mission.

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1 EXCEDE Technology Development I: First demonstrations of high contrast at 1.2 λ/d for an Explorer space telescope mission. Ruslan Belikov *a, Eugene Pluzhnik a, Fred C. Witteborn a, Thomas P. Greene a, Dana H. Lynch a, Peter T. Zell a, Glenn Schneider b, Olivier Guyon b, Domenick Tenerelli c. a NASA Ames Research Center, Moffett Field, CA; b University of Arizona, Tucson, AZ; Lockheed Martin Space Systems Company, Palo Alto, CA. ABSTRACT Coronagraph technology is advancing and promises to enable space telescopes capable of seeing debris disks as well as seeing and spectrally characterizing exo-earths. Recently, NASA's explorer program has selected the EXCEDE (EXoplanetary Circumstellar Environments and Disk Explorer) mission concept for technology development. EXCEDE is a 0.7m space telescope concept designed to achieve raw contrasts of 1e-6 at an inner working angle of 1.2 λ/d and 1e- 7 at 2 λ/d. In addition to doing fundamental science on debris disks, EXCEDE will also serve as a technological and scientific precursor for an exo-earth imaging mission. EXCEDE uses a Starlight Suppression System (SSS) based on the Phase Induced Amplitude Apodization (PIAA) coronagraph to provide high throughput and high contrast close to the diffraction limit, enabling aggressive performance on small telescopes. We report on the latest progress in developing the SSS and present coronagraphic performance results from our air testbed at NASA Ames. Our results include a lab demonstration of 1e-5 contrast at 1.2 λ/d, 1.3e-6 contrast at 1.4 λ/d and 2e-8 at 2 λ/d in monochromatic light. In addition, we discuss tip-tilt instabilities, which are believed to be our main limiting factor at present, and ways of characterizing them. Keywords: extrasolar planet, high contrast, coronagraph, PIAA, wavefront control 1. OVERVIEW OF THE EXCEDE MISSION CONCEPT In this paper, we present the first results from a technology development effort to mature the Starlight Suppression System (SSS) for the EXoplanetary Circumstellar Environments and Disk Explorer (EXCEDE) mission concept. We begin by giving a brief overview of EXCEDE in this section to provide context for our progress and results. For a more comprehensive description of EXCEDE, and especially EXCEDE science, see [1]. EXCEDE was proposed to the Explorer AO last year by a team led by Dr. Glenn Schneider of University of Arizona (UofA) and is a partnership between UofA, Lockheed-Martin (LM) Corporation, and the NASA Ames Research Center (ARC). It has been determined to be a Category III investigation by the Explorer program, and was selected for technology development. EXCEDE consists of a 0.7m coronagraphic space telescope (see Figure 1) with an unobscured pupil that images in two 20%-wide bands at 0.4 and 0.8 μm. The key enabling technology for EXCEDE is its Starlight Suppression System (SSS) which suppresses starlight to 10-6 raw contrast between 1.2 and 2.0 λ/d and 10-7 raw contrast between 2 and 22 λ/d, and with speckle subtraction in post-processing, it is capable of seeing targets down to 10-9 augmented contrast per resolution element for sufficiently long integration times. The main EXCEDE mission goals are: 1. To characterize the circumstellar environments in habitable zones and assess the potential for habitable planets. 2. To understand the formation, evolution, and architecture of planetary systems. 3. To develop and demonstrate advanced coronagraphy in space, enabling future exoplanet imaging missions. * Ruslan.belikov@nasa.gov, Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, edited by Mark C. Clampin, Giovanni G. Fazio, Howard A. MacEwen, Jacobus M. Oschmann, Jr., Proc. of SPIE Vol. 8442, SPIE CCC code: /12/$18 doi: / Proc. of SPIE Vol

2 T EXCEDE E telescope concept. c Bottoom: HST opttical images of o Circumstelllar (CS) disk ks, with Figure 1. Top: HST/ACS an nd EXCEDE inner workingg regions com mpared. EXCE EDE will imagge ~1000x fain nter in contrasst and at least 3x closer to their stars and at spattial resolutionss comparable to the best JW WST will delivver EXCED DE Starligh ht Suppresssion System m (SSS) The starlightt suppression system s for EX XCEDE is show wn schematicaally in Figure 2. 2 It consists of o the followinng major elements: a Phase P Induced Amplitude Appodization Lyoot Coronagraphh (PIAALC, [2]) that removes diffracted staarlight in the absence of o wavefront (WF) ( aberratioons; a WF conttrol system bassed on a deform mable mirror (DM) ( made byy Boston Micromachinnes that remov ves static and slowly s varyingg aberrations; a Low Order Wavefront W Sensor (LOWFS, [3]) that senses fast low-order aberrrations such as a tip/tilt and focus; f a fine steering s mirrorr (FSM) for high h precision pointing control; and a two-band Ny yquist sampledd imaging polarrimeter. A sim mulation of the performance of o this system is i shown o Figure 2, wh here the raw coontrast betweenn 1.2 and 2.0 λ/d λ is limited by b coronagraphh design and EXCEDE E at the right of stability erroor budget, and the raw contraast between and 28 λ/d D is limited byy residual chromaticity in thee system after WF corrrection. The region r beyond 28 λ/d is lim mited by the abberrations preseent in the systtem beyond the spatial control bandw width of the DM D (these aberrrations are dom minated by thee measured higgh-order aberraations on the suurface of the DM itselff). Figure 2. Leeft: Schematicc representatiion of EXCED DE's starlight suppression system. s Rightt: Simulated expected e performance of the systeem after wavvefront controol, taking intoo account exp pected chromatic aberratioons, low order instab bilities, and kn nown static errrors. Proc. of SPIE Vol

3 1.2 The Coronagraph The heart of the EXCEDE SSS is the PIAALC coronagraph. It is based on the PIAA concept, which is a highly efficient coronagraph that features close to 100% throughput and an inner working angle (IWA) of 2 λ/d, close to the theoretical limit of any possible high contrast imaging system. Furthermore, PIAA has benefited from a strong technology development effort, both theoretical and experimental, and has demonstrated raw contrasts in monochromatic light well below 10-7 at 2 λ/d and ~10-6 at 1.4 λ/d [4,5,6]. At the heart of the PIAA coronagraph are two highly aspheric optics that reshape the pupil of a telescope from a uniform "top-hat" shape into a special high-contrast apodized-pupil shape (see Figure 3). With this new apodized pupil, the image formed at the detector focal plane is devoid of Airy rings, resulting in an imaging system with a high-performance combination of contrast, inner working angle, and bandwidth. A PIAA coronagraph also benefits from a (high-throughput) shaped pupil apodizer [7,8] as shown in Figure 3 that slightly tapers the edges of the beam, thereby greatly relaxing the otherwise difficult radius of curvature requirements on the edge of the PIAA mirrors, and also the undesirable chromatic diffraction effects that such a sharp surface feature would produce. Figure 3 Left: PIAA apodization principle. The telescope beam is apodized (its edges are made "softer") by geometrical redistribution of the light using a pair of aspheric optics. Right: A schematic (unfolded) diagram showing the PIAA coronagraph with the inverse PIAA add-on, as well as the Lyot pupil mask. This makes the system a hybrid PIAA - APLC coronagraph (PIAALC) that improves the inner working angle of the conventional PIAA to 1.2 λ/d. PIAA systems commonly also employ "inverse PIAA" optics (see Figure 3, right), that remove off-axis aberrations created by the high asphericity of the PIAA optics themselves. This expands the useful (unaberrated) field of view outer limits from ~ 5 λ/d to several hundreds of λ/d. The PIAA optics downstream of the focal plane occulter do not need to be very high quality (with most of the starlight blocked by an occulter at first focus), and in fact it is possible to use small and inexpensive diamond-turned lenses rather than mirrors for the inverse system. A variation of the PIAA concept used by EXCEDE is the PIAALC (PIAA Lyot Coronagraph), which combines PIAA with the APLC (Apodized Pupil Lyot Coronagraph) concept [2,9] as shown on the right of Figure 3. This improves the inner working angle (IWA) of PIAA to 1.2 λ/d. The classical APLC combines classical (prolate spheroidal) apodization with a hard edged focal plane mask and a Lyot stop. In the PIAALC concept, the PIAA essentially acts as the apodizer for the APLC, thus combining the throughput advantage of PIAA with the IWA advantage of the APLC. As a result, the EXCEDE PIAALC design maintains a 90% throughput in addition to its aggressive contrast while improving the IWA. In order to reap the starlight suppression benefits of a high contrast coronagraph, it is essential to accurately sense and control WF phase and amplitude errors. For this purpose, EXCEDE employs two WF sensors for measurement of WF errors, a low-order WF sensor (LOWFS) and the science camera focal plane detector for mid-spatial frequency sensing. WF error correction is performed by a FSM for tip-tilt, and a DM for all other modes. 1.3 Wavefront Control System for slowly-varying mid-spatial frequency errors EXCEDE corrects slowly varying WF aberrations with a Boston Micromachines MEMS DM, and uses the Electric Field Conjugation (EFC) algorithm [10] to measure the aberrations and compute the DM setting. Unlike conventional groundbased adaptive optics where the WF aberrations are typically directly measured by a pupil-plane based sensor (e.g., Proc. of SPIE Vol

4 Shack-Hartmann), EFC employs the science camera itself as the main aberration sensor, thus obviating non-common path errors that otherwise can be significant at high contrasts. The camera provides an indirect focal-plane based measurement of the WF and the EFC algorithm uses a system model combined with phase diversity techniques (taking several images with different DM settings) to efficiently reconstruct wavefront phase and amplitude. EFC then efficiently computes the DM setting that will remove unwanted stellar residual in the focal plane region of interest. 1.4 Fast Low Order Wavefront Sensor Low order aberrations such as tip/tilt and defocus tend to vary too quickly for EFC computation and the science camera, especially considering that most of the information about low order aberrations is contained in the core of the stellar PSF which is blocked. The LOWFS [3] addresses this by using this blocked starlight reflected by the focal plane occulting mask, and a very simple and fast algorithm to measure low order aberrations from this signal (tip/tilt, focus, astigmatism). A defocused image (an in-focus image would suffer from sign ambiguity in measuring focus) is formed from the light picked off by this reflective mask onto a small-format LOWFS CCD detector. Thanks to the large number of available photons typical of EXCEDE science targets (V mag < 10; V mag median ~ 7.0) and since only light in the part of the PSF most sensitive to low order aberrations is used, the LOWFS provides accurate measurement of pointing, focus and astigmatism within a short exposure time; it takes only 3.5 ms to measure pointing at the accuracy of 1% λ/d required for EXCEDE, and 1.2s to focus to a milliradian RMS wavefront phase error with a V=10 star for EXCEDE's 0.7m aperture. These measurements serves two purposes: (1) Pointing and focus error signals are used for closed loop correction to keep these modes small enough to maintain < 10-6 raw PSF contrast; (2) Pointing, focus and astigmatism measurement logging during each science exposure provide knowledge of the PSF seen in the science camera which can then be calibrated and subtracted in post-processing. 2. AMES CORONAGRAPH EXPERIMENT (ACE) TESTBED The work described in this paper was performed at the NASA Ames Coronagraph Experiment (ACE) Testbed (Figure 4) which has been successfully advancing PIAA and related high contrast imaging technologies since 2008 [4]. It is designed for flexible and rapid testing of coronagraph technologies prior to full performance verification in vacuum. It is a successor to Co-I Guyon's first PIAA testbed at Subaru [11] that pioneered PIAA, and is designed with several improvements from lessons learned there, in particular with regard to stability and flexibility. It is operated in a (thermally stabilized) air environment as opposed to vacuum, in order to make accessing and reconfiguring the layout easier and cheaper, complementing vacuum facilities such as the high contrast testing in vacuum at JPL, as well as a new vacuum facility being developed for EXCEDE at Lockheed Martin. The testbed is described in some detail in [12,13] and so in this section we limit ourselves to a brief overview. Our testbed consists of an enclosure in a class 100K clean room on a vibration isolated bench. The enclosure is doublelayered, with the outer layer serving as a passive thermal and acoustic insulator and the inner layer being actively cooled by a PID water control circuit. The experiment in our enclosure is designed to test the coronagraph performance by using a laser to create a beam of light as if it was delivered by a telescope looking at a star, then passing it through a breadboard coronagraph and wavefront control system, and finally forming a coronagraphic image on a CCD. 2.1 Coronagraph hardware and layout The light source for the results presented in this paper was a 655nm laser coupled into a single mode fiber. The singlemode fiber serves as a reasonable approximation to a star image delivered by a telescope. This light then passes through our Starlight Suppression System shown in Figure 4. Specifically, the beam first passes through an aperture stop (not shown), sized as to limit the fiber illumination across PIAA M1 to the 90mm active optical diameter. (In a real telescope, PIAA M1 would be sized to the telescope aperture.) Then, the beam passes through our PIAA mirrors (manufactured by L-3 Tinsley, see [14]). The PIAA mirrors are made from Zerodur and coated with protected Al (Al with an SiO 2 overcoat). They have an optical diameter of 90mm and have a special highly aspheric design necessary for PIAA. These mirrors were designed for exo-earth imaging and consequently the manufacturing requirements on these mirrors were set to provide contrast of 10-9 with an inner working angle of 2 λ/d when operating with an optical bandwidth of Δλ/λ = 0.1 (10% bandwidth) around a central wavelength of 800nm, requirements that are somewhat different from EXCEDE. Nevertheless, these mirrors can be adapted to operate at 1.2 λ/d in a PIAALC configuration with an undersized focal plane occulter and a Lyot stop, which is what we did for our tests. Proc. of SPIE Vol

5 Figure 4. Left: Actively stabilized thermal enclosure of the NASA Ames Coronagraph Testbed. Right: system architecture used for the work described in this paper. Our current layout is (for now) a simpler form of the EXCEDE SSS configuration in order to reduce the number of system variables and parameters and better isolate limiting factors. The key current differences from the schematic in Figure 2 are: (1) The DM is downstream of the PIAA; (2) there is no reverse PIAA system; and (3) there is no LOWFS. Thus, our layout is designed to test the top-priority elements of the EXCEDE SSS (coronagraph and wavefront control) in an integrated configuration, but not yet the entire system Wavefront Control System Our wavefront control system is based on a 32x32 actuator deformable mirror (DM) with no bad actuators made by Boston Micromachines. It is located in a plane that is conjugate to PIAA M2. Two wavefront control algorithms have been in operation at ACE: the Electric Field Conjugation (EFC) [10] and a variation of classical Speckle Nulling [4]. Speckle nulling is a slower algorithm than EFC, but is less sensitive to model errors. Thus, both algorithms are useful depending on the limiting factor. For example, Speckle Nulling is best at diagnosing whether the knowledge of system model is limiting performance, and EFC is best at removing light quicker and thus is less affected by system instabilities. In practice, performance improvements require significant human interaction to select the appropriate wavefront control algorithm and tune its parameters in real time as the operator observes its behavior, depending on the particular choice of the inner working angle and system configuration. Thus, the results in this paper demonstrate the ability to achieve high contrast, but not (yet) the ability to do so with a fully automated wavefront control algorithm. 3. RESULTS In a previous paper [4], we demonstrated average raw contrast of 1.9x10-8 between 2.0 and 3.4 λ/d (reproduced in this paper on the right of Figure 5), which is already better than EXCEDE requirements at those working angles (in monochromatic 655nm light). Therefore, the work described here focused on improvements of the inner working angle. Figure 5 shows our results with tests done at inner working angles of 1.2, 1.4, and 2.0 λ/d, respectively. We define the inner working angle as the separation of an off-axis source where the throughput is 50% of the total system throughput (i.e. about 45%). The inner working angle was calibrated empirically as follows. The fiber was moved off-axis to controlled and known locations in several directions and by various amounts using an accurate and precise xy-stage. The z position of the fiber had been precisely aligned to the upstream focus of PIAA M1, so that the distance between the fiber and PIAA M1 was precisely known (900mm), as was the working diameter of PIAA M1 (varied between 82mm and 90mm, depending on desired inner working angle). This allowed us to displace the fiber at precisely known off-axis angles in units of λ/d. The PSF photocenter in the final focal plane was measured on the CCD for each displacement, thus generating a scaling factor of number of CCD pixels per λ/d. Finally, as a sanity check, this was checked against models of the system, with good agreement. After wavefront control was applied, we measured average raw speckle contrast levels of 1x10-5 between 1.2 and 2.0 λ/d and 1.3x10-6 between 1.4 and 2.5 λ/d in the left and center images of Figure 5, respectively. (Where "raw speckle contrast" is the brightness of the speckles in the image relative to the coronagraphic but unocculted star images. The averaging was performed across pixels in the dark zone outlined by the red line). Proc. of SPIE Vol

6 Figure 5. Contrast results from the Ames Coronagraph Testbed using the PIAALC coronagraph with 2-nd generation PIAA mirrors, in monochromatic light at 655nm. The images are taken with a focal plane camera and a focal plane occulter that attenuates the "blocked" region (including the center of the image) by 10 5 (right image) or 10 6 (left and center). The unblocked region includes the "dark zones" outlined by red and yellow lines. Average raw contrast is measured as the pixel value averaged in the zones outlined by the red line, normalized to the unatennuated intensity of the star. Left: 1x10-5 contrast between 1.2 and 2.0 λ/d. Center: 1.3x10-6 contrast between 1.4 and 2.5 λ/d. Right: 1.9x10-8 contrast between 2.0 and 3.4 λ/d. A smaller region (yellow outline) is selected in each region with even better contrast. The left image was taken using a disk-shaped focal plane occulter while the center and right images were taken with a C- shaped focal plane occulter. For the C-shaped occulters, the transmissive opening is a C-shape similar to the red outline in the image, except the inner edge of the opening is closer to the center than the red outline and the outer edge is outside the image altogether. The rest of the light in the image is attenuated by the occulter with an optical density of 5 (right image) and 6 (center image), which includes essentially everything to the left of the red outline. Thus, the attenuated image of a star can be seen at a contrast level of 10-5 in the center of the right image (and can be used as a convenient means of photometric calibration as well as a redundant check of our original photometry calibration procedures described in [2].) On the left image, the occulter was a simple disk with a radius of about 1.2 λ/d projected on the sky. 4. LIMITING FACTOR: TIP-TILT INSTABILITIES 4.1 Comparing real coronagrap ph performance to theoretical sensitivity to tip-tilt errors Improving performance in a high-contrast imaging system lab is to a large degree an exercise in identifying and eliminating numerous factors that limit performance. As different high contrast imaging labs push the performance envelope and sharing knowledge, the community as a whole is developing an understanding about how different limiting factors are affecting performance and some rough trends are emerging (most of which seem to be independent of coronagraph type). For example, scattering and other CCD artifacts often limit contrast to ~1e-5 this is highly dependent on the between adjacent or close pixels; non-stabilized lab air will often limit contrast to about 1e-6 or -7 (although inner working angle and volume of air in the beam); amplitude errors often start appearing at ~1e-6 or -7 contrast, speckle chromaticity starts to set in approximately 1e-9; etc. As we are learning to control these limiting factors, one that has arguably been emerging as a tall pole for all coronagraphs, especially those operating at small inner working angles, is low order instabilities such as tip-tilt and defocus. In fact, this seemss to be the current limiting factor in our demonstrations. Figure 6 plots our three results (from Figure 5), as well as several other publicly anounced ground-breaking demonstrations by different teams and different coronagraphs. Also plotted are the limits for a theoretically ideal coronagraph (computed using methods similar to ones described in [15]), under the condition of uncorrected tip-tilt errors at different rms levels. Care should be taken when comparing the plotted points to each other between different labs and different coronagraphs because there is no standardized way of computing "contrast" and "IWA". In addition, the sensitivities shown by the theoretical limit curves Proc. of SPIE Vol

7 similarly do not exactly correspond to what is plotted in the measurements. Nevertheless, differences in definitions are unlikely to move these points by more than an order of magnitude, so this is still a useful plot to that level of precision. Even with that caveat in mind, there are still some conclusions and conjectures thatt can be derived from Figure 6. First, from the theoretical curves, gains of 0.2 λ/d in inner working angle are equivalent to losses of a factor of 10 in contrast in a stability-limiteto fall close to the 0.01 λ/dd theoretical curve and the measured instabilities at ACE are indeed close to 0.01 λ/d rms (see regime, which is consistent with the behavior in Figure 5. Furthermore, the points in Figure 5 seem Figure 7), suggesting that these instabilities are our current limiting factor. Moreover, the fact that many other demonstrations in different labs seem to follow a similar trend suggests that they also may be limited by a similar level of instability, irrespective of the type of the coronagraph, and that most of the modern coronagraph types are similar and close to theoretically ideal with respect to sensitivities to tip-tilt errors: such sensitivity is more a functionn of the coronagraphs's IWA rather than the coronagraph type. Figure 6. Results from this paper as well as selected other (monochromatic) demonstrations by different coronagraphs and different teams are plotted on a contrast vs. inner working angle scale, along with theoretical limits. This plot suggests that a ~0.01 λ/d instability is limiting our and potentially other labs. VVC4: Vector Vortex; BLC: Band-limited Lyot. Note: caution should be taken comparing these results to each other or to theoretical limits because they were not all taken or computed under uniform conditions and this is meant as an order of magnitude representation only. Thus, the main current challenge to improving our performance at 1.2 λ/d inner working angle is believed to be the control of low-order instabilities (e.g. tip/tilt and defocus) on the testbed. These instabilities can be classified into two different frequency domains: high-frequency (> ~100Hz, those that are not resolved by the LOWFS and are thus uncorrectable), and low frequency (< ~ 100Hz, those that are resolved by the LOWFS and can therefore be corrected). The 100Hz value is not absolute and depends on the brightness of the target. It is the high frequency instabilities that pose the main challenge to us (both in the lab and in space), because they are uncorrectable and must either be eliminated at the source or calibrated and subtracted in software (leaving only the photon noise of those modes in the science image). Instabilities can be further classified by type: thermally induced instabilities, mechanical vibrations, dust particle motion, as well as laboratory environment-specific effects that will not be present in space such as air turbulence, polarization or other optical instabilities of the artificial illumination source. In all cases, it is critical to characterize these instabilities and especially the high frequency instabilities. Proc. of SPIE Vol

8 4.2 Characterizations of ACE instabilities and the SNAC method In this section we present a method that has been particularly helpful in characterizing the high-frequency instabilities on ACE. Normally, high-frequency instabilities are measured by accelerometers. We have been using accelerometers, but they do not directly measure tip-tilt errors. For example, a rigid translation or tilt of the entire bench does not generate any tip-tilt errors but shows up as a signal on accelerometers (unless one uses more than 3 accelerometers or 2 collinear accelerometers), so a lot of the accelerometer signal can be a false positive, which indeed was the case at ACE. Furthermore, accelerometers measure acceleration and not displacement, and while one can double integrate the accelerometer time signal or divide the power spectral density by the square of frequency to get the corresponding displacement measurements, the noise at lower frequencies can be high. Ideally, one would like to measure high frequency tip-tilt frequency of the CCD frame rate and thus cannot be resolved. However, as errors by directly measuring them on the CCD, but often the vibration frequency is beyond the Nyquist long as the frame rate and exposure time of the CCD can be precisely controlled, it is possible to use aliasing properties of high frequencies to infer their presence and in fact measure their true frequency, using a method we call "Super- paper, Nyquist by Aliasing Control" (SNAC). A detailed technical discussion of the method is beyond the scope of this but we present a brief description and an example of its use. Figure 7. Left: Motion of the PSF in the y direction. Right: its power spectrum. Figure 7 shows the unblocked on-axis PSF photocenter motion (in the y direction) in our lab, taken with 1ms exposure times separated by seconds, along with its power spectral density (PSD). The PSD is dominated by a lowwhen the frequency (0.01 Hz) component and an apparent 0.32Hz component. The low-frequency component remains exposure time is increased to 1s, but the 0.32Hz signal disappears. Therefore, the 0.01Hz component is real but the 0.32Hz component is aliased. One can determine the exact frequency of this component by either varying the CCD exposure time or the sampling rate. An example of the measurement of such a peak by varying the sampling rate is shown in Figure 8, which showss several different aliased PSDs of PSF photocenter displacement taken at varying sampling periods (from 1.000s to 1.032s in 1ms increments). In addition to the low-frequency signal at ~0.01Hz common to all PSDs (also aliased to ~1Hz and all multiples of twice the Nyquist frequency), there is a clear aliased signal that varies between PSDs, betraying its aliased nature. In the case where the sampling periods don't vary much between each other, the amount by which this peak moves between different sampling periods is approximately proportional to its real frequency and thus its real frequency can be directly measured as f ~ Δ f a / (ΔT/T 0 ) where f is the real frequency, T 0 is the mean exposure time between measurements, Δ f a is the difference between the aliased frequencies and ΔT is the difference between the sampling periods. The true frequency of the peak in Figure 8 turns out to be 25Hz. A more comprehensive method is to periodically extend all PSDs to higher frequencies and add them together. All aliased peaks will all add together at their true frequency, generatingg a strong signal. This is shown in Figure 8 (right) where a 25Hz peak clearly emerges, effectively reconstructing the PSD orders of magnitude beyond the Nyquist frequency. (In a formal sense, this procedure generates a likelihood function for a certain prior that a PSD has a peak at a particular location rather than a true PSD reconstruction.) Proc. of SPIE Vol

9 Figure 8. Illustration of the SNAC method. Left: Power Spectral Densities of PSF centroid motion for different sampling rates. Right: a reconstruction of the spectrum (formally a likelihood function of PSD peaks) going orders of magnitude beyond the Nyquist frequency of the CCD frame rate. Using the SNAC method and a 1Hz CCD, we weree able to determine that our high frequency tip-tilt errors are dominated by a 120Hz and a 25Hz vibration. These frequencies are also present and prominent on the accelerometer PSD measurements, but they are one of a dozen accelerometer peaks and do not dominate the accelerometer PSD, indicating that most of our physical vibrations and resonances do not lead to actual tip-tilt errors. The disadvantage of SNAC compared to the accelerometer is that it takes a long time to obtain a measurement. However, once it is known which peaks in the accelerometer PSD are relevant, the accelerometer measurements can be used to quickly trace their source. (In our case, the sources of 120 and 25Hz vibrations were traced to equipment outside our lab which we can now turn off but have not yet conducted contrast measurements.) 5. CONCLUSIONS The Ames Coronagraph Experiment lab is developing technology for EXCEDE, an Explorer mission concept designed to directly image debris disks and capable of seeing down to 10 zodis in the habitable zones of many nearby stars. The new results reported here include 1x10-5 contrast between 1.2 and 2.0 λ/d and 1.3x10-6 between 1.4 and 2.4 λ/d in monochromatic light, which is very close to the EXCEDE IWA and contrast requirements. Our main limiting factor appears to be low-order instabilities, which may also be one of the main tall poles for all space coronagraph developers. The Super-Nyquist by Aliasing Control (SNAC) method proved very useful for instability characterizations. ACKNOWLEDGEMENTS This work was supported in part by the National Aeronautics and Space Administration's Ames Research Center, as well as the NASAA Explorer program and the Technology Development for Exoplanet Missions (TDEM) program through solicitation NNH09ZDA001N-TDEM at NASA's Science Mission Directorate. It was carried out at the NASAA Ames Research Center. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Aeronautics and Space Administration. Proc. of SPIE Vol

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