The predicted performance of the ACS coronagraph

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1 Instrument Science Report ACS The predicted performance of the ACS coronagraph John Krist March 30, 2000 ABSTRACT The Aberrated Beam Coronagraph (ABC) on the Advanced Camera for Surveys (ACS) has the potential to significantly suppress diffracted light in the wings of the point-spread function (PSF). How well it can do this depends on its on-orbit alignment and how accurately an object can be positioned behind the occulting spot. Optimal contrast improvement can only be achieved with subtraction of the coronagraphic PSF, either by using a coronagraphic image of a reference star or by rolling the telescope between observations and subtracting the object from itself. Detailed PSF modeling has been performed to determine what the coronagraph can do and how to get the most out of it. Introduction The Advanced Camera for Surveys (ACS) provides a coronagraphic mode in the High Resolution Camera (HRC), which has a field of about and a resolution of arcsec pixel -1. The Aberrated Beam Coronagraph (ABC), as the name implies, functions on the spherically aberrated wavefront from HST, before it is corrected by the ACS optics. While not as efficient as a corrected-beam coronagraph, the ABC can provide a significant reduction in the diffracted light in the wings of the point spread function (PSF). It does this by means of occulting spots (which reduce saturation effects and internal scatter) and a Lyot stop (which suppresses the power in the wings and diffraction spikes). The ABC The ABC is a selectable mode of the HRC. The occulting spots and Lyot stop are on a flip-down mechanism that is placed in the beam when required. There are two spots: a 0.9 radius spot at the center of the field and a 1.5 radius one near a corner. Both are hard-edged (non-apodized). The spots are located in the plane of the circle of least confusion. At this position, defocus and spherical aberration are balanced to provide the 1

2 most compact concentration of light. Given the amount of spherical aberration in HST, this circle is fairly large, requiring spot diameters greater than would be required for a corrected-beam coronagraph. Figure 1 shows the defocused, aberrated PSFs at the plane of the occulting spots. The 0.9 and 1.5 spots block about 88% and 95% of the light, respectively. The spots help in multiple ways. They block light from the target so that it will not saturate the detector and cause column bleeding, which could cover a portion of the surrounding field and could possibly create electronic artifacts. This also helps reduce scattering by the internal ACS optics. And by masking the central region of the PSF, a spot acts as a high-pass filter, concentrating the remaining diffracted light from the target towards the edges of the pupil. When a point source is not behind a spot, the Lyot stop cannot suppress the diffraction structure (wings, spikes). The Lyot stop is placed at the exit pupil of the camera. In the ACS HRC, this is located at the M2 mirror, where the M1 mirror forms an image of the entrance pupil and the spherical aberration from the telescope is corrected. The Lyot stop masks the images of obscurations in the telescope that diffract light; specifically, the outer edge of the primary mirror, the secondary mirror baffle, the spider vanes, and the primary support pads. Light is concentrated at these locations in the exit pupil by the high-pass filtering effect of the occulting spot. The stop is oversized to ensure that most of the diffracted light is blocked; it reduces throughput by 48%. It also acts as the diffracting obscuration pattern for objects that are not behind the occulting spot, creating a slightly broader PSF than in the non-coronagraphic mode, with significantly more light in the Airy rings near the core. In the ABC, the Lyot stop is placed a few millimeters in front of the M2 mirror and is aligned between the incident and reflected rays. Thus, the stop is not exactly at the exit pupil and encounters a slightly defocused beam twice, one that is spherically aberrated on the way in, and is corrected on the way out. Also, because of the ~8 angular separation between the incident and reflected rays, the Lyot stop, when projected into the exit pupil, will appear shifted in opposite directions by about 3.5% of the pupil radius. This will have little effect on the coronagraphic performance, but will create slightly elliptical offspot PSFs that have asymmetric banding patterns in the diffraction spikes. In addition to the occulting spots, there is a 0.8 wide occulting finger that is always in place in either the direct or coronagraphic modes. It is oriented to block the central portion of the 1.5 spot. It does not provide any coronagraphic effects like the spots since it is positioned near the detector; however, it can prevent saturation of bright targets when used for direct imaging. Since it is not exactly in the image plane, there is some vignetting around the edges of the finger. 2

3 F435W F814W Figure 1. Model PSFs at the location of the ACS occulting spots (i.e. in the plane of the circle of least confusion). The sizes of the 0.9 and 1.5 radius spots are indicated. The crosses at the centers of the PSFs and the ellipticities of the circles of least confusion are due to off-axis astigmatism from the HST, which is later corrected by the ACS optics. Simulating ACS Coronagraphic PSFs and Images It is relatively easy to generate PSF models for the case of direct (non-coronagraphic) imaging: the PSF is simply the square of the modulus of the Fourier transform of the pupil function. This is how Tiny Tim creates PSFs. However, there are some additional steps required to simulate coronagraphic PSFs and images, with some particular modifications necessary for the ABC. The first step is to compute the complex-valued amplitude spread function at the position of the occulting spot, by taking the Fourier transform of the pupil function. In the case of the ABC, the pupil function consists of the obscuration pattern (A) defined by the HST obscurations and the wavefront errors (σ) in the plane of the spot, including the uncorrected spherical aberration, defocus, off-axis astigmatism, and zonal errors: ASF spot = FFT[ Aexp(2πiσ / The ASF is then multiplied by the spot mask and inverse-transformed to a conjugate pupil (i.e. the exit pupil, P exit ): P exit = FFT 1 [ ASF@ spot ] 3

4 At this point we assume that the Lyot stop is placed exactly in the exit pupil. As discussed previously, this is not actually the case, but it is much easier computationally and should provide results that are close to reality. To account for the angled reflection at the M2 mirror, the Lyot stop pattern is shifted in opposite directions by an appropriate amount to represent its projection onto the exit pupil. The exit pupil is multiplied by the Lyot stop pattern, and then the aberrations corrected by the ACS optics (spherical and astigmatism), along with the initial defocus, are subtracted. The result is then Fourier-transformed and the modulus-squared taken to produce the PSF at the detector: PSF = FFT ( P exit 2 ) Care must be taken in all of these steps to ensure the proper normalization of the PSF. Misalignment of the Lyot stop can be simply modeled by shifting the stop relative to the exit pupil. Adjusting the tilt in the wavefront can simulate mispositioning of the object behind the mask. The procedure described above produces a coronagraphic PSF for a point source centered behind the occulting spot. Objects outside of the spot must be convolved with an off-spot PSF computed using the Lyot stop, rather than the telescope entrance pupil, as the obscuration function. Because the stop is not located exactly in a pupil, its projected pattern will shift depending on the field position of the object, creating a slightly fielddependent PSF. Objects that extend from behind the mask, such as galaxies, are multiplied by the occulting spot convolved with the normal ACS PSF (to represent the spot as it is reimaged by the corrective ACS optics). The image is then convolved with the off-spot PSF. Polychromatic PSFs are simulated by generating multiple PSFs at different wavelengths and adding them together with weights corresponding to the instrumental bandpass and source spectrum. The size of the pupil function is adjusted at each wavelength to produce the same specified pixel scale at all wavelengths. The Nominal ABC PSF Figures 2 and 3 show the model ABC PSFs for a perfectly aligned system with the star precisely centered behind the occulting spot. A significant portion of the light in the wings and diffraction spikes has been suppressed: in F435W, 1.0% and 0.2% of the light remains with the 0.9 and 1.5 spots, respectively; in F814W, 1.0% and 0.5% remains. Figure 4 shows that the surface brightness of the PSF wings is reduced by at least an order of magnitude and up to almost two. There appears to be little difference in the PSF at longer wavelengths with respect to the spot size; beyond 2.5, there is no significant advantage to using the larger spot. At shorter wavelengths there does appear to be a greater reduction in scattered light when using the 1.5 spot. 4

5 There is a peak in the center of the image of the spot that may cause problems with very bright targets. It exists because the spot does not completely mask all of the low-spatialfrequency components of the aberrated beam, as evidenced by the broad halo outside of the spot in Figure 1. These unmasked regions are eventually assembled by the ACS corrective optics into a diminished PSF core. In the case of the 0.9 spot, the central peak is the brightest part of the coronagraphic PSF at all wavelengths. Its maximum pixel intensity is ~10-5 in both filters, relative to the unobscured (no spot or Lyot stop) total stellar flux. At these levels, an I=0 star in F814W would begin saturation bleeding in the center in about two seconds. Because the 1.5 spot masks a greater portion of the aberrated PSF, the central peak is considerably reduced. In both filters, its relative peak pixel intensity is ~ If the ABC components remain in proper alignment on-orbit, then the occulting finger will always block the peak in the 1.5 spot. Inside and around the spot there is residual light, again caused by the incomplete masking of the low-spatial-frequency components. Coronagraph users should pay particularly close attention to the plots in Figure 4 to ensure that their targets do not begin to saturate in the region of the spot. 5

6 F435W 0.9" Spot 1.5" Spot Log Linear Figure 2. Simulated ACS coronagraphic PSFs for filter F435W. Each image is 17.5 on a side. All images are scaled between the same minimum & maximum intensity values. 6

7 F814W 0.9" Spot 1.5" Spot Log Linear Figure 3. Simulated ACS coronagraphic PSFs for filter F814W. Each image is 17.5 on a side. All images are scaled between the same minimum & maximum intensity values. 7

8 10-5 F435W 10-6 Flux / Pixel / Stellar Flux HRC PSF Arcsec 10-5 F814W 10-6 Flux / Pixel / Stellar Flux HRC PSF Arcsec Figure 4. Azimuthal median profiles of simulated ACS HRC and coronagraphic PSFs. In each plot, the top line is the normal HRC PSF, and the lower lines are the 0.9 spot (solid) and 1.5 spot (dashed) PSFs. The normalizations are set so that the normal HRC PSF has a total flux of 1.0. Over most the plotted range, the azimuthal maximum and minimum pixel value profiles would be about 5 above and 5 below the median line. The Off-Spot PSF Objects that are observed in the coronagraphic mode but that are not placed behind the spot have a PSF that is defined by the Lyot stop. Because the stop effectively reduces the diameter of the telescope and introduces larger obscurations, this PSF is wider than 8

9 normal, with more power in the wings and diffraction spikes (Figure 5). In addition, the stop reduces the throughput by about 48%. In F814W, this PSF has a peak pixel containing 4.3% of the total (reduced) flux and a sharpness (including CCD charge diffusion effects) of (compare these to 7.7% and 0.026, respectively, for the normal HRC PSF). In F435W the peak is 11% and the sharpness is (compared to 17% and for the normal F435W PSF). Observers need to take into account the reduced throughput and sharpness when determining detection limits for planned observations HRC PSF Off-Spot PSF F435W Flux / Pixel / Peak Arcsec 1.0 F814W 0.8 Flux / Pixel / Peak Arcsec Figure 5. Cross-sectional plots of simulated PSFs. The solid line is the normal HRC PSF, and the dashed one is the PSF for an object observed in the coronagraph but not behind a spot. 9

10 PSF Subtraction & Optimizing Coronagraphic Observations The coronagraph reduces but does not completely remove diffracted light. Thus, the remaining PSF must be subtracted for programs that require the highest possible contrast. Under the best circumstances, coronagraphic PSF subtraction can reduce the remaining light by an additional 500. There are two ways to do this. In the first, the object is imaged at different orientations of the telescope; the telescope is either rolled between orbits or the object is observed again in a later visit with the telescope in a different orientation. The PSF from one roll is then subtracted from the other. The second method is to simply observe a different star with the coronagraph and use its image as the reference PSF. The first method, which is sometimes called roll deconvolution, has some advantages. Because it uses the same object, there are no worries about subtraction residuals caused by differences in the colors of the target and reference PSFs. Also, having observations at different roll angles can help distinguish between subtraction artifacts and real sources. And in the case of programs where the telescope is rolled between orbits in the same visit, the observations occur under similar thermal conditions. This improves the chances that there will not be large discrepancies in focus that would cause PSF mismatches (this does not apply to observations taken in different visits). Of course, the primary disadvantage of roll deconvolution is that it cannot be used when the target is surrounded by an extended source such as a galaxy or circumstellar disk (unless the disk is very close to edge-on, like Beta Pictoris). It is, however, the best solution for observing stellar companions. The telescope can be rolled by 5-30 between orbits during the same visit, depending on the location of the object and the time of year. A coronagraphic image acquisition must be performed after each roll. Using the PSF of a different star is less optimal for subtraction but is the only practical solution for many objects, like extended targets such as QSO hosts or inclined circumstellar disks. One PSF can also be used for multiple targets. However, significant subtraction residuals may result from PSF mismatches caused by color and focus differences. While nothing can be done about matching focus, the observer should take care in matching the colors of the PSFs. Coronagraphic PSFs were computed with varying parameters to determine the level of residuals that can be expected from PSF subtraction. Models were generated in the F435W and F814W filters for both spot sizes. Except for the analysis of the effects of color differences, all PSFs assumed an A0V spectrum. All of the subtractions were idealized; that is, the target and reference PSFs were perfectly registered and matched in intensity, with no noise. In real observations, interpolation errors resulting from the registration of the images will introduce some residuals. Also, real observations will include a number of different errors, not just one. It is important that unsaturated images of the target and reference PSFs be obtained in order to accurately match the intensities. 10

11 Focus Differences Thermal variations alter the separation between the telescope s primary and secondary mirrors, causing focus changes on suborbital timescales. This effect, called breathing, appears to be driven primarily by heating of the secondary mirror assembly during occultations by the relatively warm Earth. The system expands and contracts by about 3 µm during an orbit, with a fairly periodic trend over a number of orbits. Additional factors, such as the orientation of the telescope with respect to the sun, can create larger focus offsets (up to ~8 µm) that may steadily decay over a few orbits. The dominant effect of breathing-level focus changes is a redistribution of light over the diffraction structure, rather than variations in the size of the PSF. While these changes may not be evident just by looking at the image, they can be readily seen in subtractions. Coronagraphic PSFs, which consist mostly of high-spatial-frequency diffraction patterns, are especially sensitive to focus. ABC PSF models were generated with secondary mirror defocus amounts of 0, 0.75, and 2.5 µm. The 0µm-0.75µm subtraction is probably representative of what one could expect from roll deconvolution using back-to-back orbits with an intervening roll. In this case, the observer would hope that the breathing pattern remains constant and the observations are taken at the same breathing phase. However, there is currently no knowledge of how rolling the telescope might change the focus. If the target is bright enough, it may be wise to take a number of exposures in each orbit and then try to find the best matches. The 0µm-2.5µm subtraction shown in Figures 6 and 7 indicates an order of magnitude increase in residual flux compared to the 0µm-0.75µm case. It is what one might expect from using another star as the reference PSF, ignoring any color differences. In fact, the chances are probably about even that the focus difference will be greater. Color Differences ABC PSFs were simulated for A0V, A3V, G2V, and K0V spectral types. The subtraction results are shown in Figures 7 and 8 for the F435W 0.9 spot (they are practically the same for the larger spot and for F814W). Even when the stars are fairly close types (e.g. A0V vs. A3V), the residuals are nearly equivalent to a 2.5 µm focus mismatch and about an order of magnitude greater than a 0.75 µm mismatch. These illustrate the importance of having PSFs of similar colors, and the advantage offered by the roll deconvolution method. 11

12 10-6 F435W Flux / Pixel / Stellar Flux µm µm Arcsec Figure 6. Azimuthal median profiles of the absolute residuals from the subtraction of ABC coronagraphic PSFs with different amounts of defocus due to breathing (F435W with the 0.9 spot). The top line is a perfectly focused PSF subtracted by one with 2.5 µm of breathing, and the bottom is perfect-0.75 µm. The maximum and minimum residual profiles would be about 10 above and 1000 below the median profile, respectively. In these units, a Jupiter at 5 AU from the star would have a peak pixel value of Figure 7. Absolute residuals from the subtraction of simulated ABC coronagraphic PSFs in F435W with the 0.9 spot, displayed with identical logarithmic stretches. A0V - A3V 0 µm µm Focus 12

13 10-6 F435W 10-7 Flux / Pixel / Stellar Flux A0V - K0V A0V - G2V A0V - A3V Arcsec Figure 8. Azimuthal median profiles of the absolute residuals from the subtraction of ABC coronagraphic PSFs of different colors in F435W with the 0.9 spot. The Occulting Spot & PSF Centering A 0.1 mm shift in the occulting spot is 0.36 arcsec in image space, or about 14 pixels at the detector. However, the position of the spot is unimportant as long as it remains constant; once its location is determined (by its shadow in a flat field), the telescope can always target the object of interest behind it. If the location is not constant, then the center will always be uncertain except when a flat field or image of a very extended object is taken. Since the spots and Lyot stop are located on the calibration door mechanism, internal flats cannot be used to determine the spot location automatically prior to an observation (as is done for NICMOS). An error in the positioning of the target behind the spot produces the same effect as a spot misalignment. At the start of a coronagraphic imaging sequence, an acquisition frame is taken with the target located outside of the spot. The ACS computer determines the centroid of the target and the necessary offset required to place it behind the designated occulting spot. The telescope is then automatically commanded to that location. If there is an error in the centroiding or the slew, the target will not be precisely placed. 13

14 A spot shift or centering error of 56 mas or less does not affect the unsubtracted coronagraphic PSF in any significant way, except for in and immediately around the spot. The error does show up in PSF subtracted images, where the residuals increase by about 5 between 7 mas and 56 mas decenters (Figure 9). Until on-orbit images are obtained, we cannot predict what the typical centering error is likely to be or if the spot positions will be constant. In either case, nothing can be done to fix the problem directly. For optimal subtractions, the only solution would be to use a dither pattern while the target is behind the spot to improve the chances of getting a good match. If back-to-back orbit roll deconvolution is possible, then that could get around the problem of spot shifting, as long as the calibration door that holds the spots remains in place between orbits F435W 10-8 Flux / Pixel / Stellar Flux mas mas 0-56 mas Arcsec Figure 9. Azimuthal median profiles of the absolute residuals from the subtraction of ABC coronagraphic PSFs with different offsets from the spot center, in F435W with the 0.9 spot. 14

15 The Lyot Stop The results presented so far have assumed that the Lyot stop is perfectly aligned and the target star is precisely centered behind the occulting spot. However, given the tight requirements for positioning and the lack of mechanisms for on-orbit alignment of the stop, it seems that some deviations from these ideal cases are likely. A 1% shift in the ACS Lyot stop (relative to the pupil radius) corresponds to a ~0.1 mm offset. Simulations show that stop misalignments of <5% do not greatly impact coronagraphic performance (before PSF subtraction, that is). The average PSF differences between a 1% and 5% shift are ~30% within 2.5 and ~10% beyond. However, a 5% shift does show an increase in the diffraction spike intensity as the mask begins to uncover the spiders. A 10% shift increases the average wing intensity by about 70%. At such large misalignments, the mask no longer covers the spiders and actually contributes its own spiders to the system obscuration pattern, resulting in bright and wide diffraction spikes. Direct Imaging with PSF Subtraction vs. the Coronagraph The ACS coronagraph is not ideal for some programs. The relatively large occulting spots are similar in size to many objects that require high-contrast imaging, notably circumstellar disks around young stars or distant galaxies with active, bright nuclei. In these cases, the only option is to directly observe the target and subtract the PSF by using an image of a reference star. This will require saturating the images, but if a series of short, medium, and long exposures are taken, then saturated pixels can be replaced by scaled values from shorter exposures. Just as with coronagraphic PSFs, the quality of the subtraction of directly imaged PSFs depends on breathing and object colors. However, one does not need to worry about occulting spot misalignments. Also, throughput is improved by a factor of two since there is no Lyot stop. Observers can use the Tiny Tim PSF modeling program to explore the sensitivities to color and focus when using direct imaging. 15

16 An Example Coronagraphic Observation Figure 10. Simulated observations (noiseless) of M51 at z=0.5 with PSF-like cores with fluxes equal to 1, 10, and 100 the integrated flux of the rest of the galaxy. The simulations do not include saturation effects, which would significantly affect the direct imaging cases. In the 100 case, the PSF-like core was assumed to have an A0V spectrum and was in perfect focus, and the reference PSF used for subtraction had a G2V spectrum with 2 µm of breathing. F814W with 0.9 spot, square-root stretches. Coronagraph Direct 100x - PSF 100x 10x 1x 16