TECHNICAL
REPORT
Title: Simulations of MIRI coronagraphic Doc #:
JWST-STScI-001952, SM-12
images
Date:
December 31, 2009
Rev:
-
Authors: Rémi Soummer, Phone: 410 Russell Makidon
338-4737
1.0
Release Date: March 9, 2010
Abstract
This report provides an introduction to the MIRI Four Quadrant Phase Masks (FQPM)
coronagraphs, with a description of their theoretical principle and implementation. The
purpose of the document is to describe a new simulation software package, which was
developed from the JWPSF software (Cox & Hodge 2006). The goal is to provide a tool
for the simulation of coronagraphic images for operations studies at the Science and
Operations Center. The software includes a number of features to simulate the effects of
target acquisition on the coronagraph performance (effect of various misalignments due
to imperfect target acquisition, reference star subtraction, roll-subtractions).
2.0
Introduction
The field of high contrast imaging has expanded rapidly in the past few years, especially
with new discoveries of extra-solar planets and faint circumstellar disks. Although
indirect methods are still producing most of the exoplanet discoveries, a few planets have
been imaged directly using high-contrast coronagraphic techniques (Kalas et al. 2008,
Marois et al. 2008).
The classical Lyot coronagraph (Lyot 1939) was initially invented for the study of the
solar corona outside of eclipses. However, it does not provide sufficient contrast to obtain
direct images and spectra of extrasolar planets. Several coronagraphic techniques have
been developed in the past decade to reach higher contrast levels for this application. The
James Webb Space Telescope (JWST) will include coronagraphs in the instruments
NIRCam, TFI, and MIRI. In this report, we discuss the Four Quadrant Phase Mask
(FQPM) coronagraph in the MIRI Camera.
The FPQM idea (Rouan et al. 2000) was proposed to improve the classical Lyot
coronagraph and the Phase Mask (PM) coronagraph (Roddier & Roddier 1997). In
theory, the PM coronagraph can achieve total starlight extinction (Aime et al. 2002), but
it is severely limited by chromatic effects in broadband. The FQPM was introduced to
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Aeronautics and Space Administration under Contract NAS5-03127
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solve some of the chromatic problems of the PM, namely, the size dependence of the
point-spread function with wavelength. The FQPM was selected for the MIRI instrument
in JWST.
3.0
Four Quadrant Phase Mask Coronagraph
3.1
Coronagraph principle
Lyot-type coronagraphs consist of a set of masks placed in successive optical planes to
achieve optical Fourier filtering. The classical Lyot coronagraph (Figure 1) uses a small
occulting spot on the image of the star in a focal plane (plane B). In a classical Lyot
coronagraph, the diameter of this occulting spot is somewhat larger than the FWHM of
the point-spread function (PSF) and therefore it blocks most of the direct starlight. This
occulting spot diffracts starlight in the following pupil plane (plane C), according to the
Babinet theorem, and in particular outside of the geometric image of the aperture. The
coronagraph produces a destructive interference between light diffracted by the mask and
wave corresponding to the un-occulted star. Therefore, in this pupil plane the image
appears dark inside the geometric image of the telescope aperture and bright outside (see
Figure 5 and Figure 6). The coronagraph is complete with the use of a second mask,
called “Lyot stop”, which blocks the bright diffracted starlight in this pupil plane.
Figure 1: Schematic layout for the classical Lyot and Phase Mask coronagraphs. The layout enables
optical filtering in two successive planes, a focal plane and a pupil plane. The classical Lyot
coronagraph uses a small occulting spot in the focal plane (plane B), replaced by a π-phase shifting
spot for the PM coronagraph. In both cases, the coronagraph produces a destructive interference in
the following pupil plane, and the light diffracted outside the geometric image of the telescope
aperture is blocked by a second mask, called “Lyot stop”.
In first approximation, the focal plane mask will not affect the light from an off-axis
source (e.g. a planet), as long as the core of the planet PSF is well outside the occulting
mask. This defines the notion of inner working angle (IWA), which is the smallest
angular separation at which a planet can be detected from its parent star. In order to
detect planets close to their star, or to enable observations of more distant stars, small
IWA are highly desirable. A coronagraph generally presents a tradeoff between starlight
suppression and IWA.
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The Roddier PM principle is to replace the opaque occulting spot of the classical Lyot
coronagraph by a phase mask to produce a more efficient destructive interference and
therefore better coronagraphic starlight suppression. The phase shifting region has the
shape of a small disk, of diameter comparable to the core of the PSF, with the advantage
of a small IWA. However, the size of the PSF is a function of the wavelength and the
PM diameter is optimal at a single wavelength. In addition, it is challenging to produce
an achromatic π phase shift.
The FQPM was introduced to solve the size chromaticity issue of the PSF. However, the
chromaticity of the phase shift itself remains a challenge. The layout of the FQPM
coronagraph is identical to all Lyot-type coronagraphs (Figure 2).
Figure 2: The FQPM coronagraph relies on a similar principle as the classical Lyot or PM
coronagraphs. The focal plane occulting spot is replaced by the four-quadrant mask (plane B), and a
Lyot stop is also used in the pupil plane (plane C).
3.2
Four Quadrant Phase Mask
The FQPM introduces a π phase shift in two opposite quadrants of the focal plane (Figure
3). Because of the geometry of the FQPM, this coronagraph is insensitive to the size of
the PSF. A remaining challenge is to produce an achromatic π phase shift for best
performance. Several solutions have been investigated using multi-layer deposits, or
polarization. However, in the case of the MIRI coronagraph, a monochromatic FQPM is
sufficient and the phase shift is not achromatic (Figure 4) because the overall
performance is limited by other parameters (segments, wavefront errors, alignment).
Figure 3: The FQPM introduces a π phase shift in two opposite quadrants of the focal plane (the
other two quadrants do not introduce any phase shift). Right: image of an actual FQPM mask
obtained using reactive ion etching on Germanium (image credit: Boccaletti et al.). Manufacturing
challenges include the transition regions between quadrants and at the center, and the thickness of
the deposit (or recess) creating the phase shift.
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Figure 4: Chromaticity of the phase shift in the case of a simple optical path difference (e.g. a small
step on an optical surface): the π phase shift is only obtained at a single wavelength (here 10.65
micron). This corresponds to the case of the MIRI coronagraph.
3.3
Lyot stop
In the Lyot plane, the Lyot stop must be optimized to block the starlight diffracted by the
focal plane mask. Since the aperture is uniformly illuminated for an off-axis source, the
optimization of the Lyot stop involves a minimization of the residual diffracted starlight,
while maintaining sufficient off-axis throughput and image resolution for the planet.
Figure 5 shows the Lyot plane intensity (without Lyot Stop) in the case of a perfect
circular aperture and in the case of circular aperture with central obstruction. Note how
the diffracted light around the central obstruction is similar to the pupil without
obstruction. This illustrates the sensitivity of the FQPM coronagraph to structures inside
the aperture.
Figure 5: Illustration of the Lyot plane intensity before application of the Lyot stop for a FQPM.
Left: case of a perfect circular aperture. Right: case of a perfect circular aperture with central
obstruction. The square structures correspond to the light diffracted by the FQPM that must be
blocked by the Lyot stop.
With a more complex pupil geometry as in JWST, the diffracted light in the Lyot plane
has a more complex structure illustrated in Figure 6. Note that the simulation does not
include primary mirror segments, which also add features in the Lyot plane. This image
can be used for the optimization of the Lyot stop: a simple method is to define the Lyot
stop to block the region where the intensity is above a given threshold. The result is
shown in Figure 7, and a manufacturable Lyot stop can be defined by simplifying the
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contours of this mask. The result is very similar to the actual Lyot stop used in MIRI.
This is intended to illustrate why the Lyot stop has such a particular shape. The Lyot stop
used in the simulation is the actual shape provided by the MIRI team.
Figure 6: Illustration of the Lyot plane intensity before application of the Lyot stop for a FQPM and
the particular geometry of JWST. Similarities exist with the simplest case presented in Figure 5, but
in this case the light diffracted by the FQPM has a complex geometry. The Lyot stop geometry must
be optimized to block the bright areas inside the aperture of the telescope.
Figure 7:Left: a Lyot stop can be obtained by applying a threshold to the image shown in Figure 6, in
order to block the brightest areas. A manufacturable Lyot stop can be obtained from this
intermediate image (center). The actual lyot stop was designed using a similar approach (right).
3.4
Sensitivity of the FQPM coronagraph
The coronagraph is sensitive to a number of parameters that degrade its performance, and
are included in the simulation software described in this report. The most significant
degradation comes from the wavefront aberrations (Figure 8), which produce speckle in
the final image. Chromaticity of the FQPM phase shift is also a noticeable effect and is
illustrated in Figure 9 in the absence of wavefront errors. In practice, for JWST the
overall performance is dominated by the wavefront errors and aperture geometry, which
justifies the use of monochromatic FQPM in the simulation software. Finally, the size of
the FQPM is not infinite and the limitation of the field of view can reduce the
performance (Figure 10). The multiplication by a field mask in the focal plane
corresponds to a convolution in the Lyot plane, therefore adding leakage inside the Lyot
plane aperture from the diffracted starlight outside the pupil. The summary of the features
included in the software is given in Table 1.
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Figure 8: Wavefront errors propagate through the coronagraph and produce light that is not
blocked by the Lyot stop in the pupil plane, even if the FQPM itself is perfect. The final result is the
presence of speckle (right).
Figure 9: Images with a narrow band filter (right) have a reduced performance with more speckle
than the monochromatic case (left). This is due to the imperfect phase shift, which is optimal at a
single wavelength. The MIRI coronagraph is mainly dominated by the geometry of the aperture and
the wavefront errors leaking through he coronagraph, and not by the chromaticity of the FQPM
itself.
Figure 10: the finite size of the FQPM is included in the simulation. In the monochromatic case
without wavefront error this limitation has an appreciable effect. Left: infinite size FQPM. Right:
actual size.
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Effect
Wavefront aberrations
Bandpass
Alignment
Finite field of view
Lyot stop misalignment
FQPM errors
Included in the software
yes
yes
yes
yes
yes
no
Comment
Using Ball’s RevT OPD maps
Using top hat filter transmissions
User defined offset from FQPM center
Field mask size accurate, but orientation not included
Used defined offset for the Lyot stop
FQPM is assumed perfect
Table 1: Features included in the software package
4.0
Simulations of FQPM coronagraphic images
4.1
Principle
The principle of the simulation is to propagate the electric field from plane to plane and
apply the successive masks. An illustration of each simulation step is given in Figure 11
in the perfect monochromatic case without wavefront aberrations. Starting with a
representation of the JWST aperture, the field in the focal plane is obtained by calculating
a fast Fourier transform (FFT). The FQPM transmission is then multiplied by the electric
field. Note that the π phase shift corresponds to a simple multiplication by -1 at the
design wavelength, and corresponds to another phase shift at other wavelengths. The field
is then propagated to the next pupil plane using an FFT, and the Lyot stop is applied to
the field. Finally the field is propagated to the final focal plane, and the intensity is
exported as a FITS file for further analysis.
Figure 11: Illustration of the successive steps involved in the simulation of the FQPM coronagraph,
starting from a representation of the telescope aperture, to the final coronagraphic PSF.
4.2
Specific features of the software package
In order to study and define the target acquisition with MIRI coronagraphs, the software
package includes a number of dedicated features:
- The three available FQPM masks are available. Each of them corresponds to a
different narrow band filter, and specific field mask. The code selects
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automatically these parameters from the selection of the coronagraphic mask. The
number of wavelengths used in the simulation is optional.
Target positioning: the FQPM mask is fixed in the simulation and the target star
can be moved with respect to the center of the mask. The user can input the
location of the star in polar coordinates (arcsec, degrees).
Lyot stop positioning: the filter wheel holding the Lyot stop limits its positioning
accuracy to about 4% of the aperture diameter. The code enables simulations with
slightly misaligned Lyot stop in x and y coordinates.
Reference off-axis source. For calibration purposes, it can be necessary to
simulate the PSF of an off-axis source (e.g. a planet, or the star itself before target
acquisition is complete). Indeed the off-axis source is not affected by the FQPM
in first approximation, but the PSF corresponds to the Lyot stop aperture, which is
very different from the original JWST pupil.
Flux calibration: the calibration preserves the convention chosen in JWPSF for
non-coronagraphic image, where the total flux in a PSF is normalized to 1. With
the coronagraph, the total flux in the coronagraphic PSF is a small number
(~0.001), which reflects the residual starlight leaking through the coronagraph.
Note that in the case of a coronagraphic off-axis image, the PSF is affected by the
Lyot stop and the total flux is ~0.6 (this corresponds mostly to the Lyot Stop
throughput). Simulated images should be used to evaluate exposure time during
target acquisition.
Because of the small IWA of the FQPM, the coronagraphic PSF depends strongly
on the alignment of the target with the center of the FQPM. This not only affects
contrast but also exposure times: the exposure time is a function of the position of
the target with respect to the FQPM. Note that the “off-axis” mode merely
removes the FQPM mask. In the case where the target falls on one of the axis of
the FQPM, partial coronagraphic suppression is achieved and the actual PSF
should be simulated using the ‘on-axis’ mode with appropriate positioning of the
source.
4.3
Running simulations with the software package
The software package can be easily operated in batch mode for example using the file
“example.py” (Figure 12). The command to run the program is:
./example.py
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Figure 12: example of the batch mode
The batch file includes the following parameters:
- Path and name of the pupil file (this does not need to be modified)
- Path and name of the optical path difference (OPD) file (this can be modified to
select from several OPD maps in the JWPSF library.
- FQPM and Lyot Stop path and files (this does not need to be modified). For now
the code only operates with a single Lyot Stop file. It will be possible to add the
options for the various Lyot stops available in MIRI.
- Output file path and name (FITS format). The result of the simulation will be
written to this specified file
The function call includes the following parameters:
- instrument = ‘MIRI’ (do not edit)
- pupil_file=pupil (do not edit)
- phase_file=opd_file (do not edit)
- FQPM_file=FQPM_file (do not edit)
- lyot_file=lyot_file (do not edit)
- coro_type=’FQPM1065’ (input here the coronagraph chosen for the simulation.
Possible entries are FQPM1065, FQPM1140, and FQPM1550
- image_type=’OnAxis’ (input OnAxis for occulted coronagraphic images, possibly
with target misalignment, or OffAxis to assume no effect from the FQPM
- output=output (do not edit, this defines the output file name and path)
- diameter =6.5 (do not edit)
- oversample=4 (This defines the oversampling with respect to the specified pixel
size. For example 4 means that the PSF pixels are 4 times smaller than the
specified detector pixels (therefore 16 PSF pixels in one physical pixel). Do not
edit, this is a feature of the code. It is possible to upgrade the code to enable
different oversampling values if necessary.
- output_size: this specifies the size of the final array exported to the FITS file
- pixel_size: physical detector pixel size in arcsec
- offset_r: radial offset of the target given in arcsec (only for the OnAxis mode)
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offset_r: clocking offset in degrees.
lyotstop_xshift: horizontal shift in fraction of the diameter (e.g. 0.01 means a
translation of 1% of the telescope diameter)
lyotstop_yshift: vertical shift
nb_lambda: number of wavelengths used in the simulation. Use 1 for
monochromatic simulations. Use preferably an odd number for broadband. The
wavelengths used in the simulation are calculated automatically based on the
coronagraph selected by ‘coro_type’
verbose: print comments while the code is running
4.4
Application: study of target acquisition
The FQPM has a very small IWA by design. As a consequence, the coronagraph is very
sensitive to alignment with respect to the mask. In normal operations the observer will
most likely want to perform a reference star subtraction or a roll-subtraction. However,
because a new target acquisition is required for a new star, or for the same star after a
roll, it is not guaranteed that the star will be located exactly at the same place behind the
coronagraph. The software package enables Monte-Carlo simulations of the target
acquisition to simulate the effect of reference star subtraction with various alignment
accuracies. Figure 13 shows an example where two coronagraphic images are subtracted
from each other. In the first image the star is 10mas off the center of the FQPM, and the
second image 15 mas off.
Figure 13: example of the subtraction between two imperfectly centered coronagraphic images,
producing an appreciable residual. Here the alignment difference between the two targets is 5 mas.
5.0
Conclusions
This report presents an introduction to the Four Quadrant Phase Mask coronagraph in
MIRI, and describes a new software package to simulate this instrument. The package
includes all necessary features to study target acquisition, operations and science
performance of the MIRI coronagraph.
The software package is available from R. Soummer (soummer@stsci.edu)
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6.0
References
Aime, C., Soummer, R., Ferrari, A. (2002). Total coronographic extinction of rectangular
apertures using linear prolate apodizations. Astronomy and Astrophysics 389,
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Cavarroc, C., Boccaletti, A., Baudoz, P., Amiaux, J., Regan, M. (2008) Target
Acquisition for MIRICoronagraphs. Publications of the Astronomical Society of
the Pacific 120, 1016-1027.
Cavarroc, C., and 11 colleagues (2008). First tests of the coronagraphic device of
MIRI/JWST.Society of Photo-Optical Instrumentation Engineers (SPIE)
Conference Series 7010
C. Cox and P. Hodge (2006) “Point spread function modeling for James Webb Space
Telescope,” SPIE http://www.stsci.edu/jwst/software/jwpsf
Kalas, P., Graham, J.R., Chiang, E., Fitzgerald, M.P., Clampin, M., Kite, E.S.,
Stapelfeldt, K.,
Marois, C., Krist, J. (2008). Optical Images of an Exosolar Planet 25 Light-Years from
Earth. Science 322, 1345.
Lyot, B., (1939). The study of the solar corona and prominences without eclipses (george
darwin lecture, 1939). Monthly Notices of the Royal Astronomical Society 99,
580.
Marois, C., Macintosh, B., Barman, T., Zuckerman, B., Song, I., Patience, J., Lafrenière,
D.,
Doyon, R. (2008). Direct Imaging of Multiple Planets Orbiting the Star HR 8799.
Science 322, 1348.
Roddier, F., Roddier, C., (1997). Stellar coronagraph with phase mask. Astronomical
Society of the Pacific 109, 815–820.
Rouan, D., Riaud, P., Boccaletti, A., Clénet, Y., Labeyrie, A. (2000). The four-quadrant
phase- mask coronagraph I. principle. Publication of the Astronomical Society of
the Pacific 112, 1479– 1486.
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Appendix: Acronym list
FFT
FQPM
FWHM
IWA
JWST
MIRI
NIRCam
OPD
PM
PSF
STScI
TFI
Fast Fourier Transform
Four Quadrant Phase Mask
Full Width Half Maximum
Inner Working Angle
James Webb Space Telescope
Mid Infrared Instrument
Near Infrared Camera
Optical Path Difference
Phase Mask
Point Spread Function
Space Telescope Science Institute
Tunable Filter Imager
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