Instrument Science Report ACS 2000-04
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 29” × 29” and a resolution of 0.025
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
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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.
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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, A@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 [ A exp( 2πiσ / λ )]
The ASF is then multiplied by the spot mask and inverse-transformed to a conjugate
pupil (i.e. the exit pupil, Pexit):
Pexit = FFT −1 [ ASF@ spot ]
3
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 ( Pexit )
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.
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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 ~7×10-7. 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.
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F435W
1.5" Spot
Log
Linear
0.9" Spot
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.
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F814W
1.5" Spot
Log
Linear
0.9" Spot
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.
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F435W
10-5
Flux / Pixel / Stellar Flux
10-6
10-7
HRC PSF
10-8
10-9
10-10
10-11
0
2
4
6
8
6
8
Arcsec
F814W
10-5
Flux / Pixel / Stellar Flux
-6
10
-7
10
HRC PSF
-8
10
10-9
10-10
-11
10
0
2
4
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
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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 0.010 (compare these to 7.7% and 0.026, respectively, for the normal
HRC PSF). In F435W the peak is 11% and the sharpness is 0.025 (compared to 17% and
0.051 for the normal F435W PSF). Observers need to take into account the reduced
throughput and sharpness when determining detection limits for planned observations.
F435W
1.0
HRC PSF
Flux / Pixel / Peak
0.8
Off-Spot PSF
0.6
0.4
0.2
0.0
-0.30
-0.20
-0.10
-0.00
Arcsec
0.10
0.20
0.30
0.10
0.20
0.30
F814W
1.0
Flux / Pixel / Peak
0.8
0.6
0.4
0.2
0.0
-0.30
-0.20
-0.10
-0.00
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.
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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.
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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.
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F435W
10-6
Flux / Pixel / Stellar Flux
10-8
0-2.5 µm
10-10
0-0.75 µm
10-12
10-14
0
2
4
6
8
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 5 × 10-11.
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 - 2.5 µm Focus
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F435W
-6
10
Flux / Pixel / Stellar Flux
10-7
-8
10
-9
10
A0V - K0V
10
-10
A0V - G2V
A0V - A3V
10-11
10-12
0
2
4
6
8
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.
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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
10-6
Flux / Pixel / Stellar Flux
10-8
0 - 150 mas
0 - 56 mas
10-10
10-12
10-14
0
0 - 7 mas
2
4
6
8
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.
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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.
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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.
Direct
100x - PSF
100x
10x
1x
Coronagraph
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