1. Introduction

Imaging extrasolar planets is a technically challenging but crucial step in the study of planet formation and planetary science. Imaging young Jupiter-like planets still glowing with the heat of formation will require contrasts of between 10^-6 and 10^-7. High-contrast imaging requires suppressing diffraction and controlling wavefront errors. Laboratory tests investigating the experimental limits to contrast are ongoing at several institutions including the Extreme Adaptive Optics (ExAO) Testbed at the Laboratory for Adaptive Optics (LAO) located at the University of California, Santa Cruz, which supports the Gemini Planet Imager (GPI) [1]. This instrument, which has expected first light in 2011, will be deployed at Gemini Observatory to conduct a survey of giant planets. The Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) project also has a ground-based imager under development planned for first light in the same year [2] for the European Southern Observatory (ESO) Very Large Telescope (VLT). There is also interest in imaging planets fromspace. The Terrestrial Planet Finder (TPF) is a space-based instrument with more stringent contrast requirements for imaging earth-like planets. Testbed experiments in support of TPF are on-going on the High Contrast Imaging Testbed (HCIT)[3] at the Jet Propulsion Laboratory (JPL). On the ExAO testbed we continue to investigate diffraction suppression and wavefront control, but here we focus on PSF stability, particularly the effect of small heat sources on that stability.

Most optical systems have heat sources and these sources can introduce optical errors that will reduce performance, particularly of a high-contrast adaptive optics system. Heat sources can introduce additional speckles, which directly limit contrast, or more likely will reduce the efficiency of cornographic techniques by introducing image motion. In a testbed environment the system is usually spread out enough to avoid having heat sources directly under the beam, and generally the small sources associated with a CCD or servo-motor are ignored. Instrument design has many more constraints than testbed design and it is particularly challenging for a telescope with a cassegrain focus, because of the space, weight and temperature constraints on an instrument attached to the telescope, rather than the comparatively flexible conditions on a nasmyth platform. These conditions may lead to small heat sources being in less than desirable locations. Here we use the ExAO testbed to examine upper bounds for the effect of a small heat source on PSF stability, which would ultimately limit contrast in an ExAO instrument. Both the magnitude and the location of the heat source are investigated. These effects are not expected to be large, but as small errors are important in high-contrast imaging it is important to quantify the upper bounds. We find that heat sources up to 20 watts can be accommodated near a beamline in instrument design provided that standard testbed precautions, such as baffling of fans and system enclosures, are used to control air turbulence. Without controlling air turbulence smaller heat sources can introducemeasurable imagemotion, but speckles in the region of high contrast will remain relatively stable. Heat sources near the focal plane have significantly less effect than those near a pupil plane and are preferred when possible in instrument design.

2. Experimental method

The ExAO testbed is well suited to high-contrast experiments. High-contrast measurements have been recorded with a flat mirror and a MEMS deformablemirror (DM) [4, 5]. The testbed can also operate in interferometry, or phase shifting diffraction interferometer (PSDI), mode. A 1024 MEMS DM [6] was installed and closed loop performance was characterized with the PSDI as the wavefront sensor (WFS) [7]. The precision wavefront correction of <1 nm over controllable spatial frequencies has yielded contrast of ~10^-6 [5], while contrast with the flat is ~10^-7[4], with a shaped pupil coronagraph. Contrast on the testbed is generally limited by a combination of phase and amplitude. While the testbed is simpler optically then the GPI instrument (and many AO systems) the layout is still relevant for testing components such as the deformable mirror or concepts like the effect of a heat source near a pupil or focal plane. Certainly these components and concepts become more complicated in a more realistic layout, but those complications impede rather than facilitate understanding of the fundamental limits to performance. One difference between the instrument and the testbed, which should be addressed is the lack of collimated beam space. The pupil plane and the MEMS are not conjugate but are separated by 18 cm. This separation can introduce amplitude effects, however for these experiments a flat mirror is used in place of the MEMS as no active correction is needed, eliminating amplitude concerns. The slow beamline and lack of additional optics simulates the effect of a collimated beam for the purpose of these tests. The original layout for the ExAO testbed is described in several publications [4, 7]. The system was later upgraded to include a spatially filtered wavefront sensor (not shown in Fig. 1) [8]. In 2006 Phase II of the testbed was completed. In brief, the Phase I system was extended with two spherical mirrors (M1 and M2 in Fig.1) to add an additional pupil and focal plane, allowing a more sophisticated lyot-style coronagraph for diffraction suppression. The second focal plane also makes far-field imaging with shaped pupils easier as the core of the PSF still needs to be blocked to increase dynamic range. Figure 1 is a simplified schematic of the Phase II testbed. In the top left corner is the PSDI front end which feeds both the reference and the measurement (or test) beams. The two spherical mirrors used to re-image the pupil introduce astigmatism, and the far-field camera is placed out-of-plane to correct that error. For the results presented here the MEMS mirror was replaced with a flat. The systemgenerally uses 1024 - actuatorMEMS deformablemirror (DM), produced by Boston Micromachines Corp. (BMC). The first engineering grade 4096-actuator MEMS devices have been delivered and will eventually replace the 1024-actuator device in the system.

In imaging mode, the testbed consists of a laser source (532 nm) passed through an optical fiber and a high-quality lens (<1 nm rms over a 50-mm beam size). The beam passes through a pupil stop, reflects off the DM (or a flat mirror), is brought to focus where the focal plane mask for the shaped pupil (or an occulter for a Lyot-style coronagraph) blocks the PSF core and then is re-imaged onto the CCD. The CCD is sampled at ~5 times the Nyquist limit. Diffraction is suppressed with a shaped pupil coronagraph [9]. Previous high-contrast measurements were taken with simple single-opening prolate shaped pupil [4], but the multi-opening mask used here produces a much larger region of interest (ROI) (See Fig. 2). This larger ROI is particularly helpful for stability measurements as more of the speckle pattern is visible in each image. It should be noted that this more sophisticated design does not improve contrast, as contrast in our system is limited by a combination of phase and amplitude errors. Experiments are also underway with the apodized pupil lyot coronagraph [12, 13] that will be used for GPI. Preliminary contrast measurements with the APLC are quite promising[14] and the APLC will likely replace shaped pupils for most new measurements.

 

Fig. 1. Schematic of the Phase II ExAO testbed. The PSDI front end located at the top left feeds the test (measurement) and reference fibers for the system. The far-field camera is out-of-plane to reduce astigmatism introduced by the spherical mirrors (M1 and M2). Focus 1 is the first focal plane of the system and can be used for the coronagraph occulter or a simple focal plane mask for shaped pupil high-contrast imaging. The far-field Camera is replaced with the PSDI reference source for interferometry mode (not used for this work).

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Fig. 2. The shaped pupil coronagraph made by Princeton University [10, 11] is shown on the left with a simulation of the corresponding high-contrast PSF on the right.

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Imaging mode is used to directly measure contrast, defined as the ratio of the intensity in the ROI to the core intensity. High-contrast imaging on the ExAO testbed is typically done with two images, an unsaturated image of the core of the PSF and a saturated image with the core blocked by a focal plane mask to avoid saturating the CCD. The saturated image is normalized by the unsaturated peak value and the known scale factor produced by ND filters or integration time between the two images.

PSF stability on the ExAO testbed was assessed using a series of measurements over time of both unsaturated (un-occulted) far-field images and saturated images with a focal plane mask (to avoid CCD saturation). Often for convenience the unsaturated images used a circular pupil instead of the shaped pupil. Neutral density filters were used to decrease power by 5 orders of magnitude between occulted images of the PSF wings and un-occulted images of the PSF core. Typically each measurement consists of 100 frames of 0.01s integration time. The total time for a 100 frame measurement is about 30s because of the CCD readout time. This is the shortest shutter time of the far-field CCD. In early measurements sets of only 25 frames were used [15], but longer datasets improved repeatability of image motion data. The datasets of 25 frames were taken over a similar time scale as a larger portion of the CCD was read out for each frame. Stability of the region of high contrast was assessed from these earlier sets of 25, and as the effect of the heat source was small the saturated images used for high contrast were not repeated when the longer 100 frame measurements were taken. After systematic stability was measured (and improved) an additional variable heat source was introduced to the system. The heat source is a 25 watt resistor powered by a variable voltage supply. The resistor is mounted four inches below the beamline of the testbed (See Fig. 1). The most common position for the source is 10 cm in front of the pupil plane. Some measurements were also taken with the source moved 50 mm away from its initial position (away from the beamline of the system), directly in front of the MEMS DM plane (flat mirror in this case) and between the input and output beams on the MEMS. We carried out short experiments with the source located near the focal plane, but as expected the effects on image motion were negligible so these were not extensively repeated. Some changes were made to the system between earlier less repeatable measurements and themeasurements presented here including adjustments to the baffling of the far-field CCD fan and the addition of a beam block between the incoming and outgoing beams off the flat mirror next to the heat source. As is discussed later the baffling of the far-field CCD fan is important and the beam block is probably not.

The heat source varied to introduce between 0 and 20 watts of energy, which corresponds to a temperature change (of the resistor not the surrounding air) of 152°C. The system was given 20 minutes to stabilize with each new heat setting. No measurements were taken to determine the stability of the voltage source used to power the heat source, however as only small optical effects were measured the effect of such an instability, if it exists must be small as well. While systematic PSF stability was assessed without an additional heat source, the same time scales were used. In addition systematic stability wasmeasured over longer time scales. Measurements were taken over several hours and over night.

3. Results and discussion

We are interested in PSF stability in the high-contrast regime. Figures 3 and 4 are typical of high-contrast measurements on the ExAO testbed. These measurements were made with the new more sophisticated shaped pupil. Figure 3 contains a high-contrast images measured with the new shaped pupil coronagraph on the ExAO testbed with a MEMS mirror (top) and the flat mirror (bottom). The radial average over 60 degrees of these images is shown in Fig. 4. Contrast with the flat mirror is better primarily because of amplitude errors introduced by the MEMS mirror. Also, theMEMS contrast measurements are slightly worse than previousmeasurements and the predicted contrast from the PSDI measured phase and amplitude. This could be caused by scattered light off of the pupil itself or the window on this particularMEMS device.

 

Fig. 3. Log-scale far-field images with the MEMS (top) and the flat (bottom) using the new shaped pupil coronagraph, with increased ROI over previous results. The core of the PSF is blocked at focus position 1 to avoid saturating the CCD. In the MEMS image the bright replications of the PSF on the right and left side are caused by the ripple on the MEMS device. The triangles indicate the typical angle for ROI and the spatial frequencies controllable by the MEMS device. The radial averages of both images are shown in Fig. 4.

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3.1. PSF image motion

High-contrast imaging will typically involve long exposures; image motion during these exposures will degrade strehl ratio and resolution. In practice the motions measured here are small enough to have very little effect on strehl, however when using an advanced coronagraph such as the APLC performance will degrade if image motion mis-aligns the various components of the coronagraph, in particular the occulter. Based on the GPI error budget [1] we require image motion of less than 0.1 λ/D. Image motion was assessed by calculating the center of the PSF (using center of mass) for a series of high-contrast measurements. In previous works [4], 10 images of the PSF are averaged to generate the high-contrast image, but these are not sufficient to assess stability. Initially for stability a series of 25 frames was measured, however when the heat source was introduced these measurements lacked the desired repeatability. Instead 3 trials about a minute apart of 100 frames are used. The need for longer repeated measurements is apparent in Fig. 5, where the centroid position (relative to the average center) is plotted for several examples. There is less variation in systematic measurements without the additional heat source, although some larger scale motion is visible causing some variation in rms image motion. Typical values for the system are 0.01 λ/D rms. Small vibration problems in the system and inadequate baffling of the fan on the far-field camera can lead to an increase in systematic image motion to values as high as 0.8 λ/D rms. Over the 10 frames recorded for previously published high-contrast measurements image motion is typically 0.01 λ/D. Systematic image motion remains stable across several days. When image motion is dramatically increased the most common source is a loose optical mount introducing vibration.

 

Fig. 4. Radial average over 60 degrees of the MEMS and flat mirror high-contrast image. The contrast achieved with the MEMS mirror is slightly worse than predicted by the phase and amplitude measured by the PSDI, possibly caused by increased scatter off of the new mask or reflections off the window of this particular MEMS device.

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When the heat source is added to the system (in Fig. 5 the source is placed in front of the pupil plane) image motion increases only in the horizontal axis, the vertical axis remains basically the same as in the no heat case. Two trials of 100 frames each are shown for the heat source at 20 watts. In both cases there are large slow variations and smaller faster scale variations in the horizontal centroid position. The rms values for measurements of only 25 frames can vary depending on where along the large scale variations the measurement is taken. The heat source was placed in front of the pupil plane and 3 trials of 100 frames each weremeasured for heat levels between 0 and 20 watts. The average standard deviation of the image position (i.e. rms image motion) for each heat level is plotted in Fig. 6. In this dataset the introduction of heat does increase image motion, but even at 20 watts the rms motion is still significantly less than the 0.1 λ/D GPI limit. In previous measurements [15] a linear trend was observed of 0.02 λ/D per watt in the pupil plane leading to a cutoff of 5 watts for heat sources near the pupil plane. Those results also indicated some difference between placing the heat source in different locations. Based on these longer measurements those differences are probably within the error bars of the shorter 25 frame measurements. Attempts to improve the repeatability of stability measurements on the testbed also lead to reduced overall image motion with heat. The main adjustment to the system was the baffling of the far-field CCD fan. In general we were also quite careful of sources of vibration, additional sources of heat (small stepper motors are used to control the position of the occulter) and sources of air turbulence (when the doors of the enclosure have been opened the system must be allowed to stabilize). To examine the effect of some of these changes in the system the heat source was set to 20 watts and 3 trials of 100 frames each were recorded for several scenarios. The average of each trial (for the horizontal centroid only) are shown in Fig. 7. Trial 0 is the last measurement as the heat source was increased from 0 to 20 watts (the last point in Fig. 6). In trial 1 the heat source was moved 50 mm away from the beam (and the block between the beams was left in place). In trial 2 the heat source was returned to its original position. Measurements from trial 2 should be similar to trial 0. In trial 3 the block between the beamlines is removed. In trial 4 the heat source is moved between the MEMS and pupil planes and in trail 5 the heat source is placed between the two beamlines (input and output beam on the MEMS). There is an increase in both average image motion and the variation between the three trials as the measurements progressed, however it seems more related to opening and closing the enclosure to adjust the system then to a particular position of the heat source. It also appears that the baffle between the beamlines is not necessary. This is consistent with our observations in trying to improve repeatability of stability measurements that the combination of air currents and heat is much more of a problem than heat alone. The baffling of the far-field camera fan, for example, is critical (it is difficult to get both low systematic image motion and consistent measurements of image motion with heat when the CCD is not draped sufficiently). When image motion increases it is likely not cause by an individual problem but the combination of small problems. For example a heat source and increased air turbulence because of moving part or open enclosure door. One possible explanation is that when the heat source is present in otherwise still air a relatively laminar convection plume is set up and there is no time-varying displacement of the beam. This convection plume could also explain why only horizontal motion is observed. Columns of relatively stable heat rise off of the individual fins of the resistor producing variations in the index of refraction primarily horizontally across the beam and not vertically. The horizontal motion is increased when additional air motion is introduced by the fan or open doors as the packets of hot air (with corresponding index of refraction variations) are moved in and out of the beam. In previous measurements the heat source was placed near the focal plane and stability appeared comparable to systematic variation even at 15 watts [15], suggesting that heat sources near a focal plane introduce less error than those near the pupil.

 

Fig. 5. The relative centroid position for two trials with 0 and 20 watts of heat introduced to the system (in front of the pupil plane) is plotted here to illustrate the variation over 100 frames and between trials. Each 100 frame trial (0.1 s integration time for each frame) takes about 30s. A measurement of only 25 frames will return inconsistent rms values because of the large scale variation occurring on the 100 frame time scale.

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Fig. 6. The heat source was placed in front of the pupil plane and 3 trials of 100 frames each were measured for heat levels between 0 and 20 watts. The average standard deviation of the image position (i.e. rms image motion) for each heat level is plotted above.

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Fig. 7. To assess the effect of the position of the heat source and effectiveness of baffling several trials were completed with the heat source set at 20 watts. The standard deviation of image position was plotted for each trial. Trial 0: last point in Fig. 6, Trial 1: Heat source is moved 50 mm away from the beamline, Trial 2: Heat source is returned to original position, Trial 3: Block between beamlines is removed, Trial 4: Heat source is moved between the MEMS and pupil planes, Trial 5: Heat source is moved between the two beamlines. It appears that the opening and closing of the system enclosure to adjust the system has more effect on increase image motion than a particular location of the heat source.

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In all of these measurements (and most high-contrastmeasurements on the testbed) the apertures size is 10 mm (at the pupil plane not the MEMS plane). To test if heat-induced turbulence could cause different imagemotion for different size apertures a 5, 10 and 15 mm aperture were tested with the heat source in front of the pupil plane. The results for heat versus image motion for the three aperture sizes are shown in Fig. 8. The difference between the apertures is within the error bars of these types of measurements.

 

Fig. 8. To test if heat-induced turbulence could cause different image motion for different size apertures a 5, 10 and 15 mm aperture were tested with the heat source in front of the pupil plane. The results for heat versus rms image motion for the three aperture sizes are shown here. The difference between the apertures is within the error bars of these types of measurements.

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3.2. Stability in the region of high contrast

Detecting a companion in a high-contrast image is not merely a question of contrast, but also of the stability of the ROI of the PSF. Experiments on the JPL HCIT have shown the ability to detect companions a factor of 10 below the average PSF halo contrast [3]. One way to detect such variations is by doing PSF subtraction; we chose instead to look at the time variations in intensity at a given location in the PSF, expressed as a standard deviation. We also examine the raw contrast in the image, which we would expect to only be affected by very strong heat-induced turbulence. The average contrast and the standard deviation of the region of high contrast were both calculated over a ROI from 10 to 25 λ/D over an angle of 30 degrees on both sides of the PSF core. As expected average contrast was not affected by the heat source, but the standard deviation versus heat is more interesting. One difficulty in analyzing the standard deviation is removing image motion. Image motion was measured in the un-occulted images and we would like to decouple the effect of motion from the evolution of the speckle pattern in the ROI. When no heat is introduced there is very little image motion, and very few changes to the speckle pattern, however in these measurements when heat was introduced image motion was significant and needed to be removed in software. The images are registered by calculating the correlation between frames over a small rectangular region of the PSF and shifting the images the corresponding amount. Image distortion and changes in the speckle pattern that we might see as a result of the additional heat source could limit the robustness of this technique. This is particularly true close to the core of the image where image motion can produce more significant changes with increased light scatter around the focal planemask. The region used to register the image is from 10 to 25 λ/D in order to avoid the region close to the core. Figure 9 is a movie of the images in the focal plane taken over a total time period of approximately 30 seconds (25 frames separated by about a second) with the heat source, set at 15 watts, in the beam near the pupil plane. This is a typical example of the experiments we performed and is perhaps the one most sensitive to the heat. Individual frames are registered to each other through correlation of their speckle patterns, which normalizes out most of the heat induced image motion (the dominant effect) and accentuates the changes in the speckle pattern itself, i.e. shows how the heat convection changes the wavefront. The changes are evident but small (the scale is logarithmic, ranging from 1×10^-9 to 1×10^-6 of peak intensity), suggesting that the heat source is not a significant contributor to wavefront error other than through image motion.

 

Fig. 9. A 25 frame movie (Media 1) of the images in the focal plane taken over a total time period of approximately 30 seconds (25 frames separated by about a second) with the heat source, set at 15 watts, in the beam near the pupil plane. This is a typical example of the experiments we performed and is perhaps the one most sensitive to the heat. Individual frames are registered to each other through correlation of their speckle patterns, which normalizes out most of the heat induced image motion (the dominant effect) and accentuates the changes in the speckle pattern itself, i.e. shows how the heat convection changes the wavefront. The changes are evident but small (the scale is logarithmic, ranging from 1×10^-9 to 1×10^-6 of peak intensity), suggesting that the heat source is not a significant contributor to wavefront error other than through image motion.

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One way to quantify the speckle variation is to take the standard deviation of each pixel over time in the registered images. To reduce noise we have averaged the standard deviation in time over the same ROI used to calculate the average contrast (10–25 λ/D over 30 degrees on both sides of the PSF). The average standard deviation over this region is plotted versus the heat for each location of the heat source (See Fig. 10). If the increase in standard deviation is only a result of the corresponding increase in image motion caused by the heat source then some correlation between the image motion of the un-occulted images and the standard deviation of the high-contrast region would be expected, but no such correlation is observed. Based on these measurements we conclude that the increase in speckle standard deviation with heat is mostly de-coupled from image motion after image registration.

In Fig. 10 the line labeled no-heat was taken over the same timescale as the heat source measurements, but without a heat source. Some of the measurements taken with a heat source, including all of the measurements with the heat source placed outside the optical beam, have less variation then the no heat case. This is a reflection of the measurement error of the system. In typical far-field measurements, the noise floor is a few times 10^-8 so it is not surprising that measurements below 2×10^-8 standard deviation over time in the high-contrast regime is not robust. The limitation of these measurements implies that there is not a big difference in the standard deviation of the cases with the heat source in the pupil plane, the MEMS plane or the re-imaged Lyot plane. Increased heat in these planes does lead to an increase in the variation of the high-contrast region, but the level of variation should be lower than other error sources in the GPI instrument and does not significantly effect high-contrast measurements on the bench.

 

Fig. 10. The temporal standard deviation of each pixels intensity over the 25 frames taken at each heat level, averaged over the a 30 degree region from 10 to 25 λ/D on both sides of the PSF is plotted versus heat for each location of the source. The images were registered prior to the calculation of standard deviation which should mostly remove the effect of image motion.

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4. Conclusions

We have assessed PSF stability on the ExAO testbed in the presence of additional heat sources to inform the design of the GPI. The introduction of the heat source introduces a small effect in the speckle pattern of the region of high contrast. Primarily it causes image motion. On the ExAO testbed systematic image motion is 0.01 λ/D rms, well below the 0.1 λ/D rms requirement for GPI. Introducing a heat source of 20 watts near the pupil plane increases image motion slightly to 0.02 λ/D rms, which is still well below the GPI requirement. Image motion is only perpendicular to the location of the heat source itself (only horizontal image motion is introduced in this case). It appears that the location of the heat source and the size of the aperture do not significantly change the amount of image motion introduced by the heat source, although some preliminary data indicates that heat introduced near the focal plane has less of an effect than other locations in the beam. In general image motion is introduced by a combination of heat and air turbulence that can be introduced by changes to the system enclosure or fans from system components. Controlling these effects also improves the repeatability of stability measurements. While these tests were conducted in support of GPI, the simple optical layout of the ExAO testbed makes them more broadly applicable. In general heat sources of 20 watts can be accommodated in the beamline of an AO system, even a high-contrast AO system provided that relatively standard precautions regarding air turbulence are taken. In systems where baffling of fans or a system enclosure are not feasible heat sources, could be a problem. It appears that placing heat sources near the focal plane rather than the pupil plane is advantageous. We conclude that the typical level of care used in reducing air turbulence and vibration on the GPI instrument will also reduce the effects of heat sources less than 20 watts in the instrument and special precautions in the design phase are not needed.