# The vector-apodizing phase plate coronagraph: design, current performance,
and future development

D. S. Doelman  1* *  | F. Snik  1 *  | E. H. Por  1,2 *  | S. P. Bos  1 G.P.P.L. Otten  1,3 *  | M. Kenworthy  1 *  | S. Y. Haffert  1,4 *  | M. Wilby  1 A. J. Bohn  1 *  | B. J. Sutlieff  5,1 *  | K. Miller  1 *  | M. Ouellet  1,6 J. de Boer  1 C. U. Keller  1 *  | M. J. Escuti  7 *  | S. Shi  7 N.Z. Warriner  7 K. J. Hornburg  7 J. L. Birkby  8,5,9 *  | J. Males  4 K. M. Morzinski  4 L.M. Close  4 J. Codona  4 J. Long  4 L. Schatz  4 J. Lumbres  4,10 A. Rodack  4 K. Van Gorkom  4 A Hedglen  4 O. Guyon  4,10,11,12 J. Lozi  11 T. Groff  13 J. Chilcote  14 N. Jovanovic  15 *  | S. Thibault  6 C. de Jonge  16 G. Allain  6 C. Vallée  6 D. Patel  6 O. Côté  6 C. Marois  17,18 P. Hinz  4,19 J. Stone  4,20 A. Skemer  19 *  | Z. Briesemeister  19 A. Boehle  21 *  | A. M. Glauser  21 W. Taylor  22 P. Baudoz  23 E. Huby  23 O. Absil  24 *  | B. Carlomagno  24 and C. Delacroix24 *  | 1 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands
2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
3 Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
4 Steward Observatory, 933 North Cherry Avenue, University of Arizona, Tucson,
AZ 85721, USA
5 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, 1098 XH Amsterdam, The Netherlands
6 COPL, Département de physique, génie physique et optique, Université Laval,
2375, rue de la Terrasse, Quebec,G1V 0A6, Canada.
7 Department of Electrical and Computer Engineering, North Carolina State
University, Raleigh, NC 27695, USA
8 Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson
Building, Keble Road, Oxford, OX1 3RH, United Kingdom
9 Harvard & Smithsonian | Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA
10 College of Optical Sciences, University of Arizona, 1630 E University Blvd,
Tucson, AZ 85719, USA
11 Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences (NINS), 650 North A‘ohōkū Place, Hilo, HI,
96720, U.S.A.
12 Astrobiology Center of NINS, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan
13 NASA-Goddard Space Flight Center, Greenbelt, MD, USA
14 Department of Physics, University of Notre Dame, South Bend, IN, USA
15 Department of Astronomy, California Institute of Technology, 1200 East
California Blvd., Pasadena, CA, 91125, U.S.A.
16 SRON Netherlands Institute for Space Research, Landleven 12, 9747AD
Groningen, The Netherlands
17 National Research Council of Canada Herzberg, 5071 West Saanich Road,
Victoria, BC V9E 2E7, Canada
18 Department of Physics and Astronomy, University of Victoria, 3800 Finnerty
Road, Victoria, BC V8P 5C2, Canada
19 Department of Astronomy and Astrophysics, University of California, Santa
Cruz, 1156 High Street, Santa Cruz, CA, 95064, U.S.A
20 Naval Research Laboratory, Remote Sensing Division, 4555 Overlook Ave. SW,
Washington, DC 20375, USA
21 Institute for Particle Physics and Astrophysics, ETH Zurich, Wolfgang-
Paulistr. 27, 8093 Zurich, Switzerland
22 UK Astronomy Technology Centre, STFC, Blackford Hill, Edinburgh EH9 3HJ, UK
23 LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université,
Université de Paris, 5 place Jules Janssen, 92195 Meudon, France
24 STAR Institute, Université de Liège, Allée du Six Août 19c, B-4000 Liège,
Belgium<EMAIL_ADDRESS>
###### Abstract

Over the last decade, the vector-apodizing phase plate (vAPP) coronagraph has
been developed from concept to on-sky application in many high-contrast
imaging systems on 8-m class telescopes. The vAPP is an geometric-phase
patterned coronagraph that is inherently broadband, and its manufacturing is
enabled only by direct-write technology for liquid-crystal patterns. The vAPP
generates two coronagraphic PSFs that cancel starlight on opposite sides of
the point spread function (PSF) and have opposite circular polarization
states. The efficiency, that is the amount of light in these PSFs, depends on
the retardance offset from half-wave of the liquid-crystal retarder. Using
different liquid-crystal recipes to tune the retardance, different vAPPs
operate with high efficiencies ($>96\%$) in the visible and thermal infrared
(0.55 µm to 5 µm). Since 2015, seven vAPPs have been installed in a total of
six different instruments, including Magellan/MagAO, Magellan/MagAO-X,
Subaru/SCExAO, and LBT/LMIRcam. Using two integral field spectrographs
installed on the latter two instruments, these vAPPs can provide low-
resolution spectra (R$\sim$30) between 1 $\mu$m and 5 $\mu$m. We review the
design process, development, commissioning, on-sky performance, and first
scientific results of all commissioned vAPPs. We report on the lessons learned
and conclude with perspectives for future developments and applications.

††journal: osac††articletype: Research Article

##  1 Introduction

Many different coronagraphs have been proposed since the creation of the first
solar coronagraph in 1939 by Bernard Lyot [1]. Originally, the existing
coronagraph concepts could be organized in a family tree [2]. However, this
tree was cut down in the Lorentz Center workshop paper [3], because new
developments in coronagraph design lead to the merging of various branches.
Due to its simplicity, an adapted version of the Lyot coronagraph is still the
most used coronagraph for ground-based high-contrast imaging systems. The use
of Lyot coronagraphs resulted in many scientific breakthroughs in
understanding exoplanets and circumstellar disks. Preliminary results of the
two largest exoplanet surveys are presented by Nielsen et al. (2019) [4]
(GPIES) and Vigan et al. (2020) [5] (SHINE), and a summary paper on
circumstellar disks was presented by Avenhaus et al. (2018) [6].
The Lyot coronagraph and other focal-plane coronagraphs require accurate
centering of the star on their focal-plane masks. Pupil-plane coronagraphs do
not have this disadvantage, as the coronagraphic PSF does not change
significantly with position in the field of view. The Apodizing Phase Plate
(APP) coronagraph is a single-optic pupil-plane coronagraph [7, 8]. An APP
modifies the phase in the pupil plane to create regions in the PSF where the
star light is suppressed, so-called dark zones. A pupil-plane coronagraph has
some distinct advantages over a focal-plane coronagraph. First, the
coronagraph is simple because it consists of only a single optic, making it
easy to install in any high-contrast imaging instrument. Second, the
coronagraphic performance is insensitive to tip-tilt errors caused by
vibrations or residual wavefront from the adaptive optics (AO) system.
Moreover, tip-tilt insensitivity is good for the near-infrared (3-5 $\mu$m)
where nodding is required to remove the background. With nodding the PSF moves
over a large distance ($\gg\lambda/D$) on the detector and alignment with a
focal plane mask afterwards takes time and the final position is not always
the same, resulting in PSF differences. For a pupil-plane coronagraph no
realignment is required after nodding, increasing the on-axis time. Third, the
coronagraph design can easily be adapted to include complex pupil shapes (e.g.
segments/spiders). Fourth, all objects have the coronagraphic PSF, enabling
high-contrast imaging of binary systems. These advantages contributed to
success of the APP, having imaged multiple substellar companions (e.g. $\beta$
Pictoris b, discovering HD100546 b and HD 984, [9, 10, 11]). Disadvantages of
pupil-plane coronagraphs are the high intensity of the stellar PSF often
resulting in saturation, the lower planet throughput due to the reshaping of
the PSF, and the larger inner working angle with respect to the current best
focal-plane coronagraphs. More specifically for the APP, the properties of the
diamond-turned phase plate limited the exoplanet yield. As the APP applies
dynamic (chromatic) phase, the APP performance is only optimal for a single
wavelength, and the dark zone contrast is degraded for broadband light. More
importantly, the diamond turning requires smooth phase transitions, which
limited the APP designs to an outer working angle of 9 $\lambda/D$ and
restricted dark zones to a single side of the PSF.
The vector-Apodizing Phase Plate (vAPP) coronagraph is an upgraded version of
the APP coronagraph. The vAPP induces geometric (or Pancharatnam-Berry) phase
[12, 13] for circularly polarized light [14, 15]. The vAPP generates two
coronagraphic PSFs that have dark zones on opposite sides of the point spread
function and have opposite circular polarization states, see Fig. 1. The vAPP
is a patterned half-wave retarder where the fast-axis orientation changes as a
function of position. The induced phase, $\phi$, is equal to plus/minus twice
the fast-axis orientation $\theta$: $\phi=\pm 2\theta$, with opposite sign for
the opposite circular polarization states. Geometric phase is by definition
achromatic, and the efficiency, the percentage of light that acquires this
phase, depends on the retardance offset from half-wave. The fraction of the
light that does not acquire the phase is called the “polarization leakage”.
The broadband performance of the vAPP is therefore determined by the
retardance as a function of wavelength.
The vAPP is manufactured with liquid-crystal technology. A direct-write system
is used to print the desired fast-axis orientation pattern in a liquid-crystal
photo-alignment layer that has been deposited on a substrate [16]. The induced
orientation depends on the linear polarization of the incoming light of the
direct-write system. Multiple layers of self-aligning birefringent liquid-
crystals are deposited on top with varying thickness and twist, carefully
designed to generate the required half-wave retardance [17, 18]. The stack is
referred to as a multi-layered twisted retarder (MTR). By tuning the twist and
thickness of layers in the MTR, very high efficiencies ($>96$%) can be
achieved for large wavelength ranges, e.g. $2-5\mu$m [15].
Both unpolarized light and linearly-polarized light contain equal amounts of
left- and right-circularly polarized light. As opposite circular polarization
states create a PSF with a dark hole on opposite sides, the vAPP implements
circular polarization splitting to separate two complementary dark holes. The
relative intensity of the two coronagraphic PSFs depends on the circular
polarization state of the incoming light.

Figure 1: Schematic of two different vAPP implementations. Top: The vAPP,
where PSFs with dark zones on opposite sides and opposite polarization states
are separated using a quarter-wave plate and a polarizing beam-splitter.
Bottom: The gvAPP where polarization states are separated by adding a phase
ramp (= polarization grating) to the vAPP phase pattern, which generates
opposite tilt for light with left- and right-circular polarization, adapted
from [19].

A vAPP for broadband imaging is obtained in combination with a polarizing
beamsplitter (e.g. a Wollaston prism) and a quarter-wave plate, but the non-
coronagraphic PSFs corresponding to various polarization leakage terms degrade
the contrast in the dark holes [14, 15, 19]. The polarization leakage can be
separated from the coronagraphic PSFs by adding a grating pattern (= phase
tilt) to the phase pattern, i.e. the “grating-vAPP” (gvAPP) [20]. The gvAPP
has the same advantages as all pupil-plane coronagraphs, and also overcomes
three limitations of the vAPP. First, no polarization splitting or filtering
optics are required due to the grating. The result is that the gvAPP is also
unaffected by polarization crosstalk which could arise in the instrument
between the vAPP and the polarization splitting. Second, the polarization
leakage of the gvAPP is physically separated from the coronagraphic PSFs. The
performance of the gvAPP is therefore largely unaffected by the leakage term.
For the vAPP, the leakage term of the vAPP for unpolarized light would present
a low-intensity ($\sim 1\%$) non-coronagraphic PSF at the location of the
coronagraphic PSF. Moreover, for linearly polarized light this PSF would even
be coherent with the coronagraphic PSF. Both reduce the contrast at the
smallest separations. Third, the gvAPP has two dark holes on opposite side,
increasing the search space by a factor two. This comes at the cost of a
factor of two in exoplanet throughput, with half of the light being imaged at
the bright side of one of the two coronagraphic PSFs. We note that for unknown
companions this factor is the same when using an APP, having to rotate the APP
to image both sides. Advantages of the two vAPP dark holes are that they have
the same AO performance, such that one PSF can be used as a reference for post
processing [21], and that the antisymmetric PSF is beneficiary for wavefront
sensing [22]. Moreover, the direct-write system is capable of writing much
finer structures ($\sim 1\mu$m) compared to diamond turning ($\sim 50\mu$m)
and has the ability to write discontinuous phase steps. These properties
enable a tremendously increased phase pattern complexity that can be used for
holography [23] and manufacture more optimal phase patterns [24].
A third kind of vAPP is the double-grating vAPP (dgvAPP). The dgvAPP combines
a gvAPP with a second polarization grating on a separate substrate [24]. This
second grating is identical to the gvAPP grating and has the opposite effect,
diffracting both the main beams back on axis. Polarization leakage of the
liquid-crystal film on the first substrate is diffracted outside the dark zone
by the second grating, reducing the total on-axis polarization leakage by
multiple orders of magnitude. Because both beams are recombined, the phase
pattern needs to produce a 360∘ dark zone, which requires more extreme
patterns, increases the inner boundary of the dark zone, and generally reduces
the PSF-core throughput. However, the planet light is also recombined in the
dark zone, so the throughput is a factor 2 higher. A common property is that
all vAPP implementations is that they operate over 100% bandwidth with
extremely high efficiency ($>96$%).
The development of multiple types of vAPP coronagraphs coincided with progress
in many other areas of the vAPP coronagraph, including vAPP design, the
improvement of the focal-plane wavefront capabilities, and the manufacturing
of gvAPPs for multiple high-contrast imaging instruments. In this paper we
review this progress. In section 2, we detail the design considerations and we
provide the first complete step-by-step description of the vAPP design
process, including adding holograms, or wavelength selective behavior. We
describe the impact of a standard gvAPP design on observation and data
reduction in section 3, followed by an overview of the manufactured and
planned vAPPs in section 4. This includes their properties, details of the
commissioning, performance, and for some, their first scientific results. In
section 5 we discuss the current status and provide suggestions for future
upgrades.

##  2 Design of a gvAPP

The design of a gvAPP starts with the optimization of an APP phase pattern.
The goal of the optimization is to null the stellar PSF in the dark zone to by
orders of magnitude with respect to the PSF core, e.g $10^{5}$. We define the
contrast as this ratio of flux in the dark zone divided by the flux in the PSF
core and it depends on the focal plane coordinates, see Fig. 2. Light has to
be diffracted from the stellar PSF core to null the dark zone, reducing the
intrinsic Strehl ratio of the star. We define the Strehl ratio as the summed
flux of the non-coronagraphic stellar PSF core in an aperture divided by the
summed flux of energy in the coronagraphic stellar PSF core using the same
aperture. In simulation without noise this aperture has a diameter of one
pixel, and for all other applications it is common to use a diameter of $\sim
1.4\lambda/D$[3]. Destructively interfering the star light in the dark zone
results in constructive interference of the light on the opposite side of the
PSF. A reduction of the stellar Strehl ratio is unwanted, as the Strehl ratio
of the companion PSF is affected in the same way. Therefore, the optimization
simultaneously maximizes the Strehl ratio of the stellar PSF, while minimizing
the flux inside the dark zone. This optimization problem is highly non-linear
in the complex phase exponential. Consequently, first attempts at calculating
APP patterns did not aim to find the optimal solution, their aim was to find
solutions that are close. These attempts used phase iteration techniques [25,
7] or a modified Gerchberg-Saxton (GS) algorithm [26] and were moderately
successful. They have shown that these methods can produce a dark zone of any
shape with extreme contrasts ($<10^{-10}$) [27], yet their Strehl ratios are
low for small inner working angles. Another set of solutions were generated by
adapting the global optimization algorithms for shaped-pupil coronagraphs to
include phase [28]. This algorithm produces APPs with regions containing
several discrete phases and sharp transitions in between these regions. This
algorithm was improved to yield _globally_ optimal solutions with unity
amplitude across the pupil, smooth phase patterns for $180^{\circ}$ and
D-shaped dark zones, and 0-$\pi$ solutions for $360^{\circ}$ dark zones [29].
As this last algorithm allows both phase and amplitude modulation in the
pupil, this proves empirically that APPs are the globally optimal solutions
for pupil-plane coronagraphs.

###  2.1 Dark zone considerations

The globally optimal solutions are critical to ensure a high exoplanet yield.
However, it is not the full story. As shown in [29], there is a trade-off
between inner working angle (IWA), outer working angle (OWA), contrast, and
Strehl. The definitions of the four properties can be found in Fig. 2.

Figure 2: Definitions of the dark zone properties. Top left: The pupil of the
telescope. Top middle: A D-shaped dark zone (log10 scale). Top right: An
annular dark zone (log10 scale). Bottom: PSF slice of a non-coronagraphic and
coronagraphic design (annular). Adapted from Por 2017 [29].

For focal-plane coronagraphs, the IWA is defined as the smallest angular
separation at which the total energy throughput of an off-axis source reaches
50% of the maximum throughput [3]. For pupil-plane coronagraphs this can be
adapted to the smallest angular separation where the planet throughput reaches
50% of the maximum throughput in the region where the contrast reaches the
target contrast. Equivalently, the OWA is defined as the largest angular
separation where the planet throughput still reaches 50% of the maximum
throughput in the region where the contrast reaches the target contrast. A
good choice of these parameters can be different for every planetary system,
observing conditions, wavelength, telescope design and instrument performance.
This becomes clear by using a metric that defines a planet detection given
instrument limits. In Ruane et al. 2018 [3], the integration time $\Delta t$
that is required for a $1\sigma$ detection is given by

$\Delta
t\propto\left[\frac{\eta_{s}+\sum_{n}a_{n}}{\eta_{p}^{2}-b^{2}/\epsilon^{2}}\right],$
(1)

where $\eta_{s}$ fraction of available star light detected at the planet
location, $\eta_{p}$ fraction of available planet light detected, and
$\epsilon$ is the planet-to-star flux ratio. The factor $a_{n}$ represents
noise factors like the background or detector noise such that
$\sigma^{2}_{n}=a_{n}N_{\star}$, with $N_{\star}$ the total signal from star
in photo-electrons. In the same way $\sigma_{\text{speck}}=bN_{\star}$, which
represents the speckle noise. In this framework, $\eta_{p}$ is directly
proportional to the vAPP Strehl and the contrast is given by
$\eta_{s}/\eta_{p}$. We do not minimize $\Delta t$ with vAPP optimization due
to several complicating factors. However, we can use this equation to explore
the impact of design choices. Here we outline some of the considerations when
choosing these parameters.
_1\. Strehl:_ The Strehl ratio of a vAPP design impacts the planet throughput
for the full field of view. In the case of the photon noise limit, Eq. 1
becomes $\Delta t=\eta_{s}/\eta_{p}^{2}$, demonstrating that Strehl greatly
impacts the integration time that results in a 1$\sigma$ detection. The gvAPP
already has the disadvantage of reducing the planet throughput by a factor of
2, so keeping the Strehl high is crucial for good performance. The definition
of a high Strehl is somewhat arbitrary given the impact of the shape of the
telescope pupil, AO performance and presence of other noise sources.
Therefore, we use the Strehl mostly for a trade-off between the other dark
zone properties.
_2\. Contrast:_ For ground-based high-contrast imaging systems, the intrinsic
contrast of a coronagraph is almost never reached. AO residuals and non-common
path errors result in quasi-static speckles that limit the performance. In
addition, atmospheric jet streams create a wind-driven halo, as the temporal
lag between the application of the wavefront correction and the evolving
turbulence [30]. Designing a gvAPP with an intrinsic contrast much lower than
the expected raw contrast does not yield the optimal performance. This is
clear from Eq. 1, where planet is not detected in the presence of speckle
noise if $\eta_{p}<b/\epsilon$ (negative integration time), independent of
$\eta_{s}$. Yet, removing bright PSF structures by creating a dark zone
reduces speckle pinning, i.e. speckles that are spatially confined to
secondary maxima in the diffraction limited PSF [31]. Taking into account
speckle pinning, it can be argued that a design contrast lower than the
expected AO-limited contrast does result in an improved performance, although
that has not been studied in detail. For inner working angles $>2.0\lambda/D$
and a central obscuration lower than 30%, a design contrast of 10-4 results in
Strehl ratios higher than 70% [29]. This design contrast is already
significantly lower than the raw contrast of extreme AO systems. Another
consideration is that constant contrast in the dark zone will yield the
highest Strehl, although the changes in Strehl are minor for lower contrasts
further out. These considerations lead to the conclusion that a more optimal
gvAPP design has a contrast that decreases gradually with the estimated AO
residuals and becomes constant at a point where other noise factors take over,
such as detector noise or background noise ($\sim 10^{-6}$). An example of
such a design contrast is shown in Fig. 2. In this case, the vAPP design
contrast can be determined by AO simulations and verified with end-to-end
simulations of the performance.
_3\. IWA:_ All indirect detection methods for exoplanets (e.g. transit,
radial-velocity, astrometry), show that there is a huge fraction of planets
that is currently out of reach for direct imaging. While these methods are
biased to find these close-in planets, it shows that a small IWA is a critical
to find new worlds with direct imaging. However, the Strehl ratio is also very
dependent on the IWA. For $10^{-6}$ contrast, an OWA of 8 $\lambda/D$, and a
central obscuration of 10% changing the IWA from 2.05 to 1.75 $\lambda/D$
reduces the Strehl from 60% to 20% [29]. Furthermore, the gain of a smaller
inner working angle is usually limited. Uncorrected low-order aberrations,
both atmospheric or non-common path, reduce the performance at the smallest
separations for ground-based telescopes.
_4\. OWA:_ The outer working angle has limited impact on the Strehl of APP
designs, while the dark zone area increases with the OWA squared. The non-
coronagraphic PSF contains only a small fraction of the energy at larger
separations, so increasing the contrast in this region results in a small
decrease in Strehl as well. In these regions the SNR of the exoplanets is not
dominated by the contrast, however. Further out, techniques like ADI are more
effective in removing speckles, the wind-driven halo and PSF structures.
Thermal background in the near- and mid-infrared ($\lambda>2$ µm) or detector
noise start to dominate the SNR, e.g. [32]. It is therefore unnecessary for
most applications to create a gvAPP with a OWA $>20\lambda/D$.
There is no general design that works for any telescope or wavelength range.
All gvAPP designs are different because the optimal phase pattern depends on
the telescope aperture and properties like the AO performance and background
noise. It is therefore advisable to perform a grid search to find the trade-
offs between IWA, OWA, contrast at the IWA and the slope of the contrast as
function of radius. An example grid could be the IWA between 1.8 and 2.3
$\lambda/D$ in steps of 0.1, the OWA between 12 and 20 $\lambda/D$ in steps of
1, the $\log($contrast$)$ between $10^{-3.5}$ and $10^{-5}$ in steps of 0.5,
and a slope between 0.25 and 0.5 $\log($contrast$)$ per $\lambda/D$ in steps
of 0.05.
Another consideration is the dark zone shape itself. A gvAPP with D-shaped
dark zones provides phase solutions with higher Strehl ratios compared to 180
degree dark zones with identical inner working angles [29]. This difference in
Strehl increases for smaller inner working angles ($<2.5\lambda/D$), which is
why the D-shape is used in most gvAPPs. The impact of the D-shape on observing
is discussed in section 3.1. An interesting trade-off exists for planet
detection at larger IWAs ($>3\lambda/D$). Beyond this IWA threshold, the
designs with an annular dark zone will have a Strehl ratio that can be
competitive with D-shaped dark zones. While the Strehl ratio of designs with
annular dark zones are still significantly lower, dgvAPPs with annular dark
zones have twice the planet throughput compared to a gvAPP. The origin of this
factor two is that half of the planet light is imaged on the bright side of
the coronagraphic PSF for a gvAPP. The trade-off between D-shaped and annular
dark zones is highly dependent on the telescope pupil, as a central
obscuration size and spider thickness greatly impact the Strehl of annular
dark zone designs. We note that comparing Strehl ratios with a factor two
correction factor for planet throughput and the same contrast levels does not
necessarily select the best of the two. There are other factors that are more
difficult to add to this trade-off. For example, a dgvAPP will not have
wavelength smearing due to grating diffraction, companions will be inside the
dark zone for all parallactic angles, post-processing is different, and a
gvAPP requires a larger field of view. Because factors like these are
difficult to quantify, we did not attempt a general trade-off study. So far,
only one dgvAPP has been installed on the large binocular telescope (LBT). The
pupil of the LBT is favourable with a central obscuration ratio of $\sim 11\%$
and thin spiders that were not included in the design. Moreover, a vAPP with
an annular dark zone was installed on the William Herschel Telescope (WHT),
which was designed for an off-axis 1-m pupil without central obscuration and
spiders.

###  2.2 Optimization of the APP design

The optimization of the APP starts with a pupil definition. Existing HCI
instruments usually have a pupil camera where the pupil can be measured or
have their own mask to define the pupil. Extreme caution is warranted when
defining the pupil, as the maxima and minima of the phase pattern will be
located near the pupil edges. An error in pupil definition leads to a stark
reduction in vAPP performance. For this reason we define an APP pupil, which
is the undersized version of the true pupil to accommodate alignment errors,
definition errors, and pupil movement. Drastic undersizing increases the IWA,
negatively impacts Strehl with thicker spiders and a larger central
obscuration ratio, and reduces throughput by removing effective telescope
area. Therefore, this balance results in an undersizing of the instrument
pupil by 2-5%, depending on the amplitude of the expected pupil movement and
the alignment tolerances, and in coordination with the instrument team. In
addition, it can be beneficial to change the orientation of the dark zones
depending on the pupil shape. Spiders add narrow diffraction structures that
locally enhance the PSF intensity. A D-shaped dark zone can, depending on the
orientation with respect to the pupil, overlap with one or more spider
diffraction structures. Removing these structures leads to a decrease in
Strehl, so if there is freedom to choose the dark zone orientation the
straight edge should be oriented parallel to two spiders. Residual atmospheric
dispersion, detector ghosting effects, the FOV of an IFS or the orientation of
a slit or image slicer can limit this design freedom.
For a given set of APP parameters and a pupil definition, we use the
optimization solver, Gurobi Optimizer [33], to calculate the optimal solution.
Computer memory and run time limitations limit the APP phase pattern to
$100\times 100$ pixels and a dark zone up to 14 $\lambda/D$.

Figure 3: Optimization of an APP pattern, showing the phase pattern (left) and
corresponding PSF (right). a) The low-resolution input pupil for the global
optimizer and the corresponding PSF. b) Output of the global optimizer for a
lower contrast ($10^{-3}$) and a smaller dark zone, indicated by the white
lines. c) High-resolution APP design created using the Gerchberg-Saxton
algorithm on the Fourier-scaled global optimal APP design. Additional dark
zones have been added for the opposite coronagraphic PSF, the leakage PSF and
additional holograms.

For N pixels in the pupil plane, the optimization problem scales as N2 in
computer memory and N3.5 in run time. These scaling laws also hold true for
pixels in the focal plane for the OWA. Hence, it is not possible to calculate
the APP design at the full resolution that is used in the direct-write system,
which is on the order of a 1000$\times$1000 pixels. We therefore adopt a two-
stage approach for finding the vAPP phase pattern. First we find the optimal
APP phase pattern for a downscaled version of the APP pupil. If necessary we
decrease the OWA to the 14 $\lambda/D$ limit set by the computer memory. This
downscaled version also does not contain additional dark zones for the
coronagraphic PSF with opposite circular polarization or dark zones that
minimize crosstalk with the leakage term or additional holograms. In section
2.3 the use of these additional dark zones and holograms is explained.
Secondly, we upscale this low-resolution APP phase pattern design with Fourier
upsampling [34] and use this solution as a prior for the second stage. This
second stage adds all dark zones and corrects any errors made during the
upsampling of the low-resolution phase pattern. We use a modified Gerchberg-
Saxton (GS) algorithm [35] for this stage. This algorithm does not guarantee
an optimal solution like the global optimizer does. However, with the starting
point already quite close the optimal solution, the GS algorithm is likely to
converge before unacceptable Strehl losses occur.
An example for resulting phase patterns after the first and second stage are
shown in Fig. 3. In practice, we find that limiting the design contrast during
the first stage of optimization often increases the Strehl of the final
design. Typically, for a final design contrast $<10^{-4}$ the design contrast
during the first stage should be between $10^{-2}$ and $10^{-3.5}$ to recover
a new solution with the highest Strehl. Both optimization stages are
implemented in HCIPy [36] and an example of vAPP optimization using only GS
can be found in its documentation111https://docs.hcipy.org.

###  2.3 Adding functionality with holograms

Enabled only by the accurate and high-resolution of the direct-write process
and the liquid-crystal properties, it is possible to add capabilities to all
types of vAPPs. Here we will discuss two capabilities, focal-plane wavefront
sensing (FPWFS) and reference spots for astrometry and photometry. Both
capabilities have solutions based on holograms. We define holograms as PSF
copies imaged off-axis, which can be biased with a wavefront aberration. In
essence, the vAPP PSFs are also holograms. Combining multiple holograms into a
single phase screen is possible through multiplexing wavefronts into a single
phase screen, as described in [37, 38, 39]. A multiplexed phase screen directs
light to multiple holograms, each with a different PSF. These holograms can be
added anywhere in the focal plane up to the Nyquist limit, with any bias, and
with any amplitude mixing ratio. Due to circular-polarization splitting,
adding a holographic copy at a certain position in the focal plane will
necessarily also add a hologram with opposite bias at the location mirrored in
the optical axis. These properties of holograms make them very diverse and
easily adapted for FPWFS and reference spots. A natural extension is to
generate multiple coronagraphic PSFs per polarization state. For example, it
is possible to position two coronagraphic PSFs for one polarization such that
they precisely overlap with the two coronagraphic PSFs of the opposite
polarization state. The advantage is that the otherwise polarized
coronagraphic PSFs now become unpolarized [40]. This has benefits for
including polarimetry and/or focal-plane wavefront sensing with the vAPP. One
important downside is that multiplexing many holograms results in significant
crosstalk. Crosstalk adds PSFs at locations that are the vector-addition of
the individual gratings and multiples thereof.

####  2.3.1 Photometric and astrometric reference spots

For accurate photometry of a companion the vAPP already has an advantage
compared to focal-plane coronagraphs. The coronagraphic PSFs themselves
provide a photometric reference, given that the two PSFs are not saturated.
Otherwise the leakage PSF can serve as photometric reference if it is not too
affected by speckles. However, it does have a different spectrum due to the
wavelength dependence of the diffraction efficiency. A solution is an unbiased
reference spot, which is a copy of the non-coronagraphic PSF. Multiplexing
unbiased wavefronts with the vAPP results in reference PSFs that can be used
both for photometry and astrometry. For other coronagraphs, such spots have
been generated using the deformable mirror or static phase screen. A full
summary of these efforts can be found in Bos (2020) [41] and references
therein. Moreover, the vector speckle grid that is proposed in Bos (2020) [41]
produces speckles that are effectively incoherent with the underlying halo,
which greatly improve the photometric and astrometric accuracy. By
multiplexing the vAPP with two holograms with opposite phase modulation on the
opposite polarization states, this vector speckle grid is easily implemented
in the vAPP coronagraph. Astrometry with a vector speckle grid could provide
astrometric solutions with a precision of $<0.01\lambda/D$ [41], however this
has not yet been tested on-sky.

####  2.3.2 Focal-plane wavefront sensing

Adding a bias wavefront to holograms changes their sensitivity to the incoming
wavefront. Holographic modal focal-plane wavefront sensing is possible because
of these variations [27]. FPWFS is critical to remove non-common path
aberrations (NCPA), aberrations from optics after the AO system, which are
therefore unseen by the AO wavefront sensor. An example of a focal-plane
wavefront sensor is the coronagraphic modal wavefront sensor (cMWS) [38, 23],
which provides simultaneous coronagraphic imaging and focal-plane wavefront
sensing with the science point-spread function. The cMWS creates multiple
holograms, each biased with a different wavefront mode drawn from a suitable
basis set. The normalized difference between the PSF copies with opposite
circular-polarization state responds linearly to the corresponding aberration
mode present in the input wavefront. The main advantage of this wavefront
sensor is that the monitoring the Strehl ratios of the holograms and the
wavefront reconstruction are straightforward and can be done at high speeds
and with the actual science camera, independent from the dark hole(s).
Moreover, no modulation of the wavefront is required. Multiplexing holograms
removes light from the coronagraphic PSF, and for efficient wavefront sensing
each mode takes away $\sim 1\%$ of Strehl, on top of the already lower vAPP
Strehl. The trade-off between modal coverage, sensitivity and Strehl is
difficult to optimize, as it is a priori unclear how much the selected
wavefront modes contribute to speckles. The cMWS has successfully been tested
with the Leiden exoplanet instrument (LEXI) [23], and in lab demonstrations of
Magellan/MagAO-X [42].
Another method for FPWFS is an adaptation of phase diversity (PD) [43]. Where
classical PD requires an in-focus and out-of-focus image, phase diversity
holograms are biased with defocus of opposite amplitude, similar to the cMWS
with a larger bias. This larger bias results in an increase in modes that can
be reconstructed, while decreasing the average intensity of the hologram. So
compared to the cMWS, a larger fraction of the incoming light is diffracted to
the PD holograms, e.g. 10% instead of 1%. This FPWFS method was implemented in
the Subaru/SCExAO[44], Magellan/MagAO-X[45] and HiCIBaS instruments.

Figure 4: Updates of the holographic phase patterns to minimize crosstalk and
light scattering into the dark zones. a) An unaltered phase diversity hologram
with a defocus of 0.87 radian RMS. b) The updated PD hologram with suppressed
diffraction structures in all dark zones, calculated using the Gerchberg-
Saxton (GS) algorithm. c) Same as b), only without defocus to create a
photometric or astrometric reference hologram. Each hologram has displaced
dark zones. This displacement corresponds to the relative location of the
hologram with respect to the dark zones of the coronagraphic PSF after
multiplexing the phase patterns. Figure 5: Creation of a gvAPP phase pattern
by multiplexing the APP design (1) with the three holograms. Hologram 2 is
defocused and could be used for focal-plane wavefront sensing. Hologram 3 and
4 are unaberrated and are located in a square grid at the grating frequency
for astrometric referencing. Additional iterations with GS have cleared the
dark zone of second order effects caused by multiplexing. The PSF is
calculated assuming unpolarized light and a polarization leakage of 1%.

A different implementation of PD is described in Por (2016) [46], directly
reconstructing the focal-plane electric field in the dark zone. Coronagraphic
PSF copies are created with each a unique probe in the dark zone, making use
of the pairwise nature of the holograms [27]. The unaltered science PSF is
still available, providing the same advantages as the cMWS, but adding the
capability to sense all modes corresponding to the dark zone.
Interestingly, the coronagraphic PSFs themselves can also be designed to
encode wavefront information in the bright field by including a pupil-plane
amplitude asymmetry. The added advantage of the vAPP is that there are two
coronagraphic PSFs, with opposite bright fields that cover all of the spatial
frequencies. This reduces the number of modes that can otherwise not be
measured by one coronagraphic PSF [47]. We refer to such vAPP designs as
Asymmetric Pupil vAPPs (APvAPPs), and was successfully implemented by Bos et
al. (2019) [22]. They show that if the pupil is asymmetric, both odd and even
modes can be recovered from the coronagraphic PSFs only. Earlier versions of
an asymmetric pupil wavefront sensor [48] could not be combined with a
coronagraph. A non-linear model-based wavefront sensing algorithm was proposed
by [22] and is limited, due to computational considerations, to the first
$\sim 100$ Zernike modes, yet it showed nearly an order of magnitude
improvement in contrast between 2 and 4 $\lambda/D$ with the internal source,
and on-sky the gain was a factor of 2. Spatial linear dark field control
(LDFC) [49, 42] is also a very powerful combination with the APvAPP. LDFC
empirically derives a linear relationship between DM actuation and focal-plane
intensity response in the bright field, allowing it to control a larger number
of modes. As LDFC can only drive back the wavefront to a reference state, it
requires an initial calibration by non-linear model-based wavefront sensing
algorithm, making both methods complimentary. LDFC uses the linear response to
wavefront aberrations in the bright side of the vAPP PSF to reconstruct the
wavefront. For Magellan/MagAO-X, simulations have shown that LDFC is capable
of correcting the full dark zone using 400 modes [42]. Recently, LDFC in
combination with an APvAPP was installed and tested using Subaru/SCExAO [50].
An on-sky demonstration followed soon after [51]. By multiplexing two
coronagraphic PSFs per polarization state, each of these PSFs designed with a
different pupil-plane amplitude asymmetry, it is also possible to design
APvAPPs that can measure both pupil-plane phase and amplitude modes
simultaneously [40]. The possibility of adding photometric, astrometric, and
wavefront sensing capabilities to the vAPP make it a unique and diverse
coronagraph. Exploring these techniques for a more integrated approach to
building high-contrast imaging systems shall lead to a better performance at
the systems level.

####  2.3.3 Implementation into vAPP designs

Adding holograms by multiplexing phase patterns does not result in an optimal
combination. Crosstalk between modes and the vAPP PSF will decrease the
contrast in the vAPP coronagraphic dark zones. Moreover, the crosstalk will
change the response of the holograms. Minimizing this crosstalk is implemented
by changing the vAPP PSF, the modes and optimizing after multiplexing. First,
the coronagraphic PSF can be suppressed at the locations of the holograms,
such that interference is minimized. Additional dark zones can be added during
the upscaling of the APP design. Second, the modes can be adapted to also have
a reduced intensity at the location of the APP dark zone. These dark zones can
be added using the GS algorithm, as is shown in Fig. 4. All modified
holograms, including the coronagraphic vAPP hologram, can then be combined by
multiplexing. Third, the crosstalk in the vAPP dark zones caused by the
multiplexing can be removed by applying an additional round of GS. The
combined result is shown in Fig. 5. Every time GS is applied, it has a minor
impact on the Strehl of the coronagraphic PSF. The final cleaning of the dark
zone could impact the performance of holographic wavefront sensors, though we
estimate that this effect is minimal, as no significant deviation from
expected performance was found in [42]

###  2.4 Additional design choices

So far we have focused on the design of the vAPP phase pattern. However, there
are additional choices regarding the vAPP optic that are independent of the
phase pattern. We will highlight two design choices that impact the
manufacturing complexity and the wavelength dependent performance of the vAPP.

Figure 6:  Top left: Phase of a grating-vAPP for an undersized pupil of the
Subaru Telescope. An amplitude mask for the pupil is shown in black. Bottom
left: Logarithmic plot of the PSF of the grating-vAPP, showing two
coronagraphic PSFs for opposite handedness of circularly polarized light. The
grating-vAPP was simulated to be a perfect half-wave retarder, so no leakage
is present. Center: The grating mask (top) and resulting PSF (bottom) that
will be used as an amplitude mask. The grating has 90 periods across the
diameter of the pupil. Right: The phase and PSF of the grating-vAPP combined
with the grating mask. The incoming light has a pupil of radius 0.45 (black)
and the light is separated in a grating mask component and a grating-vAPP
component. A small misalignment of the pupil does not affect the coronagraphic
PSF, relaxing alignment tolerances. Adapted from Doelman et al. 2017 [44].

####  2.4.1 The grating mask

As discussed in section 2.2, the pupil definition is critical for the
performance of the vAPP. During manufacturing it is therefore standard to add
a physical binary amplitude mask to the assembly that is aligned with sub-
micron accuracy with the phase pattern. These amplitude masks and their
alignment add significant complexity and cost to the vAPP optic. Especially
for lab demonstration projects that often require multiple phase patterns, it
is not cost effective to use these amplitude masks. Separate metal laser-cut
masks can provide a cheap solution at the cost of reduced alignment accuracy.
We note that it is not necessary to absorb or reflect the light at the pupil
plane. A different solution is to diffract the light outside of the field of
view of the coronagraphic PSFs. Diffracting the light that is not falling onto
the coronagraphic phase pattern to outside the FOV requires a patterned high-
frequency polarization grating outside of the pupil, e.g. beyond the outer
diameter, inside the spiders, and within the central obscuration. This grating
should have a different orientation and frequency than the grating of the
gvAPP. A simple spatial filter in an intermediate focal plane can remove the
light outside the pupil. We call this concept the “grating mask”. This concept
is described in detail in Doelman et al. 2017 [44], and a reworded version is
added here for clarity. An example of the gvAPP with a grating mask is shown
in Fig. 6. Critical for the workings of a PG as amplitude mask is that the
tilt is applied _locally_ , as the phase is accumulated inside the liquid-
crystal layer [52]. This is unlike a regular grating where the interference
between the _full_ grating results in the diffraction orders. Adding a mask
only outside the pupil does not significantly alter the coronagraphic PSF. It
does, however, change the leakage term from the PSF of the undersized vAPP
pupil to the PSF of the telescope or instrument pupil.
How the grating mask reduces the complexity of the vAPP optic can be seen in
Fig. 7.

Figure 7: Various substrate designs for vAPP manufacturing.

With a grating mask the first substrate is no longer necessary, removing a
glue layer as well. Moreover, the lab demo vAPPs can be manufactured without
any additional substrates. While their phase patterns and pupils can be
extremely complex, only homogeneous illumination is necessary for them to work
as expected. We note that an end cap would make them more durable and less
easy to damage.

Figure 8:  a) Photograph of the vAPP with a simplified RST pupil between
crossed polarizers, manufactured for testing the grating mask. The zoomed in
microscope image shows the high-frequency grating used for the grating mask
that is not captured by the normal camera. b) Reimaged pupil with a field stop
inserted in the focal plane. The field stop removes the diffracted light from
outside the pupil defined by the grating mask. Even spiders with a width of a
few times the grating period are removed extremely well.

For lab testing a 1 cm grating mask was produced with 8 pixels of 8.75 micron
per period. The pupil is a simplified version of the Nancy Grace Roman Space
Telescope and was chosen for the thin spiders and complex pupil design. The
full mask between crossed polarizers is shown on the left in Fig. 8 in
addition to a microscopic image which shows a spider with the grating pattern.
The width of the spider is a few times the grating period, yet this does not
affect the performance of the grating mask. The right panel of Fig. 8 shows
the reimaged pupil when a field stop is added to the focal plane. The light
outside the simplified RST pupil, which is diffracted by the grating, is
blocked and does not appear in the reimaged pupil.
When applied in a real high-contrast imaging system, two things need to be
considered. First, one has to be careful where the diffracted light from
outside the pupil is directed to. The diffracted light can scatter back onto
the detector by reflections inside the instrument if not blocked. Because the
direction of the PG is a free design parameter, the reflections can be
directed to non-reflective parts with prior knowledge of the instrument
layout. Second, a few percent of the light that would be normally blocked by
an amplitude mask would end up on the science camera due to polarization
leakage. This polarization leakage is always non-zero for a deviation in
retardance from half-wave. The influence of the polarization leakage will be
small when the coronagraphic PSFs are have enough spatial separation from the
leakage. This separation is also a free parameter and is set by the frequency
of the grating of the coronagraphic phase pattern. In addition, the pupil
defined by the grating mask will be undersized a few % compared to the
telescope pupil, so the amount of light that is diffracted by the grating mask
is limited.
Overall, the grating mask is a cheap alternative for amplitude masks and
alleviates the problems that come with aligning an amplitude mask with the
phase pattern.

####  2.4.2 Wavelength selective multi-twist retarders

Another option for the vAPP involves the tuning of the retardance in a non-
standard way. For most applications the retardance is tuned to be close to
half-wave over the full bandwidth of an instrument [18, 21] to maximize the
efficiency. However, by changing the liquid-crystal recipe one can, in
principle, make the retardance follow any continuous curve as function of
wavelength [53]. We note that this is possible because the fast-axis
orientation and retardance of the devices are decoupled.

---
Figure 9:  Top: Simulated retardance (blue) and first order leakage (orange)
as a function of wavelength for a 3-layered MTR. The total thickness is 20.7
micron and it was optimized to have 0 retardance everywhere except for a 10 nm
band around H$\alpha$ wavelength (656.28 nm), where the retardance is close to
180 degrees. Bottom: The simulated PSFs of a grating-vAPP with the retardance
profile shown above. The green lines in the top figure correspond to the
wavelengths of the bottom panel. At wavelengths shorter than H$\alpha$ the
leakage term dominates and almost no coronagraphic PSF can be seen (a). This
is the same for wavelengths larger than 750 nm (c). Around H$\alpha$ the
leakage term disappears and the gvAPP operates as normal (b).

One specific application of a liquid-crystal recipe is the “wavelength-
selective coronagraph” [44]. Here we include a short summary of this work. A
wavelength-selective coronagraph has rapidly changing efficiencies, where the
retardance switches between intervals of 180 degrees as function of
wavelength. A retardance of zero or a full wave results in a zero efficiency,
such that the light traveling through the coronagraph does not acquire
geometric phase. The coronagraph is effectively switched off at those
wavelengths, while it is switched on in the range where the retardance is
close to half-wave. This technology has been demonstrated for RGB lenses [54].
An example for the vAPP coronagraph is shown in Fig. 9. The retardance is
close to 180 degrees for H$\alpha$ and close to zero for smaller than 600 nm
and larger than 750 nm. The light outside the H$\alpha$ spectral band can be
used by a wavefront sensor, enabling wavefront sensing close to the science
bandwidth with optimal efficiency. In addition, the wavefront sensor can be
placed after the coronagraph to minimize non-common path aberrations. This
requires a simple focal plane mask that separates the central term from the
coronagraphic PSFs, aided by some spectral filters to minimize spectral cross-
talk.

##  3 Observing and data reduction

The gvAPP can be described as a simple coronagraph, as it is only a single
pupil-plane optic that suppresses the diffraction halo. However, there are two
differences between other coronagraphs that make both observing and data
reduction much less straightforward, i.e. the D-shaped dark zone and the
grating. For the D-shape dark zone of a gvAPP the dark zones do not cover 360
degrees, which takes away a larger fraction for closer-in orbits caused by
sky-rotation. This has to taken into account for planning observations and in
the data reduction process. In addition, the grating can smear the planet PSF
over multiple pixels in the grating direction, reducing signal-to-noise and
the effectiveness of observing techniques like angular differential imaging
(ADI) [55].

###  3.1 Influence of the D-shaped dark zone

The D-shaped dark zone provides phase solutions that have much higher Strehl
ratios for similar smaller inner working angles than a 180 degree dark zone,
while providing a similar total area. We note that the term inner working
angle is somewhat misleading here. It is correct that the D-shaped and 180
degree dark zone designs can detect a planet down to the same separation, yet
the _amount of time_ it is in the dark zone for pupil tracking mode is very
different. For a 180 degree dark zone the coverage is a full 360 degrees,
while a bar is missing for the D-shaped dark zone, which takes away a larger
fraction for closer-in orbits. The fraction of a circle, $F_{DH}$, with radius
$r$ that is inside a dark zone with an inner working angle IWA is given by

$F_{DH}=\frac{\pi-2\arcsin{(\text{IWA}/r)}}{\pi}.$ (2)

This fraction is also shown in Fig. 10 for a typical gvAPP design.

Figure 10: Planets rotating in the dark zone in pupil-stabilized mode are not
always in the dark zone. Left: Fraction of a circle (white) that is in the
dark zone (red). Right: The same fraction as function of separation for an
inner working angle of 2$\lambda/D$.

On-sky the rotation speed can change dramatically near Zenith, and the
position in the dark zone depends on the local sidereal time at the
observatory. Therefore, observations with the gvAPP should be carefully
planned if a known target is observed. Planning does not help with detecting
unknown objects where certain areas around the star will have more noise due
to the sky-rotation placing objects in the bar between dark zones.
For known objects the blind spots created by the incomplete coverage of the
D-shaped dark zones can be predicted. To this end, we created a preliminary
version of an observation preparation tool in python, which can be found on
Github 222https://github.com/18alex96/vAPP_preparation. The goal of this tool
is to predict the locations of known companions and provide information on
when it is in the dark zone to help determine observation strategies. The
current version has an internal library that contains the information of a few
operational gvAPPs, such that a simple query returns the predicted locations
of companions in a PSF image. The code needs the instrument name, target name,
the companion position angle and separation, and the observation times.
Wavelength scaling has not been implemented yet. The core of the observation
tool is based on Astropy [56], which is used to retrieve object information
and coordinate transformations.

###  3.2 Influence of wavelength smearing

The grating of the gvAPP is an elegant solution to separate the polarization
leakage from the coronagraphic PSFs. It does, however, represent a challenge
for the data reduction. For narrow-band data it displaces the two
coronagraphic PSFs which need to be recombined after centering them
separately. This is similar for data taken with an integral field spectrograph
(IFS), except the instrument provides simultaneous multi-wavelength
observations. For each wavelength, the stellar PSF and companion PSF will have
shifted and also needs to be recombined. This can be characterized, especially
if there are no optical distortions in the IFS such that the displacement from
the grating is linear. Wavelength smearing is likely to reduce the astrometric
accuracy in addition to make object spectra more sensitive to the lenslet
flat. For larger bandwidths the wavelength smearing introduces more problems.
The light of the planet is smeared over many pixels, resulting in an increase
in camera noise and a larger sensitivity to speckle noise. In addition, the
planet PSF rotates around the stellar PSF for every wavelength, which is a
different location on the detector for every wavelength. In the derotated rest
frame of the stellar PSF the orientation of the elongation changes in time,
such that ADI techniques are less effective. Collapsing the PSF in the grating
direction before derotation might solve this problem, but this does not remove
the sensitivity to speckle and camera noise.
The classical vAPP, which separates the two polarization states with a
Wollaston prism, would not have these issues caused by the grating [14].
However, they would be limited by polarization leakage at the smallest
separations for large bandwidths. A double-grating vAPP is also not affected
by the grating, it is not limited by polarization leakage, and does have full
360 degree FOV at the cost of a larger inner working angle. Combining these
two techniques creates a solution for the wavelength smearing and large inner
working angle. This combination then requires a polarizing beam splitter, like
a Wollaston prism, to separate the two polarization states of a double-grating
vAPP with D-shaped dark zones [19].

###  3.3 Data reduction

Figure 11: Method of recombining both coronagraphic PSFs such that the data
can be processed using conventional data reduction techniques.

From the complications of data reduction caused by the D-shape of the dark
zone and the grating, it is clear that gvAPP data can not simply be reduced
with commonly-used data reduction pipelines like the Vortex Image Processing
package [57] or PynPoint [58, 59]. These pipelines include different data
reduction algorithms that have been developed for data taken without
coronagraphs or with focal-plane coronagraphs. In both situations the stellar
PSF is not separated and the search space is 360 degrees. However, with a
relatively simple adaptation it is possible reshape gvAPP data in a way that
these pipelines can be used. We create a window for each coronagraphic PSF and
combine them into a single new data frame that is centered on both PSF cores.
An example is shown in Fig. 11. This method also works for IFS data if the
windows change location with wavelength, but does not solve the wavelength
smearing for large bandwidths. In addition, it does not make use of the fact
that both coronagraphic PSFs are aberrated by the same wavefront aberration.
The rotate subtract algorithm, suggested by [21], provides an additional
contrast gain by using this symmetry. An improved version of this algorithm
does not simply subtract the average PSF but uses principal component analysis
[60] to create a PSF library using one coronagraphic PSF and optimally
removing these components from the other PSF. Another technique that is likely
well suited for gvAPP data is the Temporal Reference Analysis for Exoplanets
(TRAP) algorithm [61]. TRAP creates a data driven model of the temporal
behavior of the systematics using reference pixels, which can also be the
pixels at the other coronagraphic PSF. Moreover, this algorithm assumes a PSF
model that can include wavelength smearing, which is a significant problem for
the gvAPP. Therefore, TRAP presents an exciting opportunity to improve the
gvAPP data reduction.

##  4 The world of vAPP

Over the last decade the vAPP has been installed in 7 instruments on 6
telescopes, and will be installed in two instruments on the Extremely Large
Telescope (ELT). The success of the vAPP can be explained by two of its
properties: simplicity and adaptability. Each vAPP is unique and fully
optimized for the system it is implemented in, both in wavelength coverage as
phase design, while only a single optic needs to be installed. The vAPPs cover
almost an order of magnitude in bandwidth, i.e. 0.55-5 $\mu$m, provide
multiple ways of focal-plane wavefront sensing, and provide
photometric/astrometric capabilities. First, we will provide an overview of
the different properties and locations of the vAPPs. Then, we will shortly
describe the unique capabilities of each vAPP.

###  4.1 The vAPP: a global view

High-contrast imaging systems are now part of most 8m-class telescopes. The
vAPP has benefited from the enormous growth in the number of high-contrast
imaging systems. A global view of the vAPP coronagraphs is shown in Fig. 12.

Figure 12: Overview and status of the vAPP coronagraphs around the world.

The vAPPs are operational in both the Northern and Southern hemisphere. For
each vAPP, we show the phase pattern and the simulated PSF. In addition, we
display the project status, indicated by the color of the marker on the map.
As of 2020, the vAPP has been tested in two former instruments, is operational
in four instruments and will be installed on three more instruments. A summary
of most properties of all vAPPs are presented in Table 1.

Table 1: Properties of the vAPP coronagraphs. FPWFS techniques: 1 = AP-WFS [22], 2 = cMWS [27, 38, 42], 3 = PD [43, 45].  Telescope | Instrument | Type | Inst. | $\lambda$ | MTR | Contrast | IWA | OWA | Strehl | FPWFS
---|---|---|---|---|---|---|---|---|---|---
|  |  |  | [$\mu$m] |  |  | [$\lambda/D$] | [$\lambda/D$] | [%] |
Magellan | MagAO/Clio | gvAPP 2x180 | 2015 | 2-5 | 3 | $10^{-5}$ | 2.0 | 7 | 39.8 | -
WHT | LEXI | vAPP 360 | 2017 | 0.6-0.8 | 1 | $10^{-4}$ | 2.5 | 6 | 57.2 | 2
Subaru | SCExAO/ | gvAPP 2x180 | 2018 | 1-2.5 | 3 | $10^{-5}$ | 2.1 | 11 | 49.2 | 1+3
| CHARIS |  |  |  |  |  |  |  |  |
FC | HiCIBaS | gvAPP 2x180 | 2018 | 0.83-0.88 | 1 | $10^{-6}$ | 2.1 | 8.5 | 28.8 | 2+3
Magellan | MagAO-X | gvAPP 2x180 | 2018 | 0.55-0.9 | 3 | $10^{-5}$ | 2.1 | 15 | 40.7 | 1+2+3
LBT | LMIRcam | gvAPP 2x180 | 2018 | 2-5 | 3 | $10^{-5}$ | 1.8 | 15 | 52.6 | 3
LBT | LMIRcam/ | dgvAPP 360 | 2018 | 2-5 | 3 | $10^{-5}$ | 2.7 | 15 | 42.0 | -
| ALES |  |  |  |  |  |  |  |  |
VLT | ERIS | gvAPP 2x180 | 2022 | 2-5 | 3 | $10^{-5}$ | 2.2 | 15 | 50.9 | 1
ELT | METIS | gvAPP 2x180 | 2028 | 2.9-5.3 | 3 | $10^{-5}$ | 2.5 | 20 | 63.8 | 1
ELT | MICADO | gvAPP 2x180 | 2026 | 1-2.5 | 3 | $10^{-5}$ | 2.6 | 20 | 68.8 | -

Another important property of the vAPP is the polarization leakage as function
of wavelength. The design of the liquid-crystal recipes aims to minimize
polarization leakage over the full bandwidth and are given in Table 1. For
small bandwidths ($<15$%), the liquid-crystal design can be kept simple with
only single layer with zero twist. Larger bandwidths require multiple layers,
each with different thickness and twist, to form a multi-twist retarder (MTR).
In general, if the bandwidth is between $15-40$%, a double-layered recipe,
i.e. a 2TR, can have a polarization leakage $<3\%$ for the full bandwidth.
Similar performance can be reached with a 3TR for bandwidths up to 100%.
When a specific design is chosen, the manufacturing process is tuned to
generate a liquid-crystal film with a measured retardance and polarization
leakage that mimics the theoretical as closely as possible. The manufactured
test films are polarization gratings (PGs), such that it is easy to measure
the zero-order leakage using transmission measurements. When a recipe is
perfected, the vAPP is manufactured using this recipe. Measuring the zero-
order leakage of the final optic can be cumbersome with the small angular
separations between the main beams and the leakage, caused by the large
grating periods of a gvAPP. Therefore, the leakage measurement of a
representative PG is used. These polarization leakages of five different
recipes, representative of 5 different instruments and wavelength ranges, is
shown in Fig. 13. All presented recipes have $<6\%$ leakage over their
required bandwidth.

Figure 13: Zero-order leakage as a function of wavelength for different
liquid-crystal recipes, colored by instrument. Figure 14: Same as Fig. 13, but
on log-scale and an additional estimate of the LBT double-grating vAPP.

Together, they span the almost the full visible and near-infrared (0.55-5
$\mu$m). Interestingly, we currently cover this range with three standardized
recipes that have good performance in their respective bandwidths. The same
data is presented in log-scale in Fig. 14. We added the estimated performance
of the double-grating vAPP that is installed in the LBT, by multiplying the
single-grating curve with itself. We note that no direct measurement of its
performance exists.
While the leakage measurements are representative, the actual vAPPs can have
different performances. Lab conditions during manufacturing, like temperature
and humidity, can generate differences between liquid-crystal films for
identical recipes. Characterizing the actual polarization leakage of a vAPP
can then be done after installation or in a high-contrast imaging setup.
Moreover, all vAPPs with identical wavelength coverage will have different
polarization leakages as function of wavelength. These differences can be up
to 2% for a specific wavelength, but the impact on the average is minimal.
Most likely, it is merely a shift of the maxima and minima as function of
wavelength.

###  4.2 The vAPP: individual properties

A large diversity exists between vAPPs, in designs, design goals, additional
functionality, and the instruments that use them. We will provide a summary of
design trade-offs, unique properties, historical details, notable results, and
references to more detailed papers of each vAPP.

####  4.2.1 Magellan/MagAO/Clio

The first operational broadband gvAPP was installed in 2015 in the MagAO/Clio
instrument [62, 63] at the 6.5-m Magellan Clay telescope. The gvAPP has a dark
zone between 2-7 $\lambda$/D and operates between 2 to 5 micron, with a
polarization leakage less than 3% over this bandwidth. A detailed description
of the design, manufacturing and on-sky performance can be found in Otten et
al. (2017) [21]. Being the first gvAPP to be commissioned, it was a technology
demonstrator with the additional goal to use it as a science-grade component.
To demonstrate the performance, Otten et al. observed a bright A-type star
with an $L^{\prime}$-band magnitude between 0 and 1. Characterization of the
leakage term and the PSF showed that the gvAPP was performing as expected. A
new method of data reduction, subtracting the opposite rotated coronagraphic
PSF, yielded an improvement in contrast of 1.46 magnitudes, i.e. a factor 3.8,
at 3.5$\lambda$/D. The performance of the gvAPP for this observation was
better than the best reported performance in literature of coronagraphs at
other systems at this small angle. We note that the method of calculating the
noise is necessarily different between the contrast curves reported in
literature, as noted in Jensen-Clem et al. (2017) [64]. The method of noise
calculation in Otten et al. (2017) [21] does not take into account azimuthally
correlated speckle noise caused by non-common path aberrations, pointing
jitter, and thermal variations. For a gvAPP it is especially difficult to
properly estimate the speckle noise at the smallest separations due to the
limited amount of photometric apertures that fit in the D-shaped dark zones. A
better comparison between this gvAPP and other coronagraphs would be to use
the same detection limit methods that are commonly used, e.g. fake planet
injection.
So far, the scientific yield of the MagAO/Clio gvAPP is limited, with only a
marginal detection of a brown dwarf companion of HR 2562 [65, 66]. This can be
explained by the total awarded observing time ($<$10 nights), which is
insignificant in comparison to the SPHERE and GPI surveys ($>$300 nights) that
detected on the order of 10 sub-stellar companions [4, 5]. Moreover, observing
with a gvAPP can be challenging, especially when using broadband filters, see
section 3.

####  4.2.2 WHT/LEXI

The Leiden Exoplanet Instrument (LEXI) was a visiting instrument at the
William Herschel Telescope (WHT) [67, 23]. The goal of the LEXI instrument was
to develop and test new technology for new high-contrast imaging techniques,
e.g. the cMWS and high-contrast, high-dispersion integral field spectroscopy
[68, 38, 23]. The instrument changed between different visits, changing the
pupil (4m on-axis, 1m off-axis), the wavefront sensor, imaging modes,
spectrographs and vAPP designs. The first observation run in 2016 employed a
spatial light modulator with an APP + cMWS design. This test succeeded, making
it the first demonstration the focal plane wavefront sensing capabilities of
the cMWS on-sky. A second run in 2017 used a simplified instrument, replacing
the SLM for a vAPP. Two instrument properties were taken into account for the
design of the vAPP. First, the ALPAO deformable mirror with 97 actuators,
which has a limited control radius. Second, the AO-loop speed was limited at
800 Hz by the camera frame rate. Thus, the vAPP designs were optimized for
$10^{-4}$ contrast between 2.5-6 $\lambda/D$, resulting in a phase pattern
0-$\pi$ concentric rings. A grating mask used to define the aperture with the
vAPP. With a narrow science band between 600 nm and 800 nm, the vAPP is a 1TR,
resulting in a polarization leakage less than 6%. The intensity of the leakage
at the IWA is lower than the design contrast, which enabled the use of a 360
vAPP without gratings. The vAPP was multiplexed with 20 Disk Harmonic
holograms, resulting in an improved wavefront correction [23].

####  4.2.3 Subaru/SCExAO/CHARIS

The Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) [69] instrument is
an ever-evolving high-contrast imaging system at the 8.2-m Subaru Telescope,
with the aim of providing a platform for technology demonstration for next
generation telescopes. A more recent, and already outdated, overview of the
instrument can be found in [70]. The gvAPP in SCExAO was installed in 2017 in
the near-infrared arm (0.9-2.5 $\mu$m) [44]. The design of the gvAPP has a
reduced grating frequency compared to previous designs to make the PSF fit in
the SCExAO/CHARIS field of view (FOV) for the full bandwidth [44]. CHARIS is
an integral field spectrograph with a resolution of $R\sim 18.4$ for a
bandwidth spanning the $J$, $H$, and $K$ bands (1.13-2.39 $\mu$m) and a FOV of
$2"\times 2"$ [71]. To fit these instrument specifications, the gvAPP was
manufactured with a new liquid-crystal recipe with a diffraction efficiency
greater than 97% between 1-2.5 $\mu$m. Two additional features of this gvAPP
are the grating mask that is undersized with respect to the amplitude mask of
SCExAO and defines the gvAPP pupil, and the first implementation of phase
diversity spots. At the inner working angle of 2.1 $\lambda/D$, the design
contrast is $10^{-5}$, and the outer working angle is 11 $\lambda/D$, which is
limited by the CHARIS FOV in K-band.
The gvAPP was installed together with a patterned ND-filter in the focal
plane, which reduces the coronagraphic and leakage PSF intensity by a factor
10-50, depending on wavelength. An image of the PSF with the patterned ND-
filter is shown in Fig. 15. Such a focal plane mask enables longer integration
times and reduces the risk of saturation and resulting persistence of the
sensitive NIR cameras. The PD holograms are not blocked and can also be used
as a photometric reference. After installation, the first-light images of the
gvAPP with CHARIS showed a PSF shift by $\sim 1$ arcsecond caused by the wedge
of the optic. A second wedged optic that is identical to the one used in the
gvAPP was installed in a filter wheel downstream to successfully correct this
shift.
Testing with the internal source showed promising results with a raw contrast
$<10^{-3}$ at the inner working angle, and $<10^{-4}$ beyond 4.5 $\lambda/D$
[22], demonstrating that the delivered gvAPP is within specifications and
commensurate with the performance of the system and other coronagraphs.
However, on-sky testing resulted in raw-contrasts that were a factor 5-10
worse, caused by prominent diffraction structures present in the dark zones.
These structures are visible in Fig. 15 as bright lines of speckles orthogonal
to the flat side of the dark zone. These structures are not present when using
any other coronagraph present in SCExAO. Inspection of pupil images with and
without the gvAPP showed that these structures are not caused by pupil
misalignment. In addition, the absence of these structures in the internal
source data suggests that they are caused by optics upstream of SCExAO, e.g.
the telescope mirrors or AO188, an upstream adaptive optics instrument.
Simulations show that annular phase offsets at the pupil edges can reproduce
similar dark zone structures, which would not be noticed by other coronagraphs
when a Lyot stop is used. An annular phase structure can be seen in the on-sky
wavefront reconstruction in [22] and it also has been observed with the
pyramid wavefront sensor, but so far any attempt to correct these phase
offsets did not result in a significant improvement of the dark zone contrast.
Despite the lower-than-expected raw-contrast, on-sky observations have been
carried out with both the imager SCExAO/Chuckcam and the IFU SCExAO/CHARIS.
One of the first tests of the gvAPP was the observation of HD 91312 with
CHARIS on 7 February 2018, for a total of integration time of 5 minutes 29
seconds. HD 91312 is a good candidate as it is a binary system, with a
companion at a separation of 150 mas ($\sim$ 5 AU), which has a minimal mass
of 80 MJup [72], and therefore is most likely a M-dwarf. Because HD 91312 A is
an A-star, the relative contrast to HD 91312 b in the near infrared is already
favourable and becomes lower towards longer wavelengths. The companion was
detected in the raw frames, even with the diffraction structures present.
Post-processing with spectral differential imaging (SDI) [73] and rotate
subtract [21] removed the diffraction structures. The extracted PSF at
$\lambda=1.57\mu$m and the final post-processed image are shown in Fig. 15.

Figure 15: Observations of HD 91312 with the gvAPP with CHARIS. Left: Image
slice from the extracted data cube showing the raw PSF. Right: Final image of
HD 91312, showing the companion clearly. The bright streak is a result of
post-processing. The scale of both images is different.

While the on-sky raw contrast is limited by the uncorrected diffraction
structures, the SCExAO gvAPP is still valuable as a technology demonstration
of focal-plane wavefront sensing. The phase diversity between both
coronagraphic PSFs, combined with the asymmetric pupil of SCExAO, resulted in
the first demonstration of FPWFS with only the coronagraphic PSFs [22]. The
improvement of a factor two in raw contrast between 2-4 $\lambda/D$ is similar
to other FPWFS techniques [74]. An additional improvement can be realised by
implementing LDFC [42, 50, 51]. However, it is unclear if the combination of
both FPWFS techniques will resolve the issue with diffraction structures in
the on-sky PSF. A future upgrade of AO188 could resolve the issue and enhance
the gvAPP performance.

####  4.2.4 FAST-CARMEN/HiCIBaS

As is mentioned in the name, the High-Contrast Imaging Balloon System
(HiCIBaS) is a balloon-borne telescope and is installed on the FAST-CARMEN
gondola [75].

Figure 16: Measurements of the HiCIBaS gvAPP PSF (log10 scale) before, during,
and after the flight using the internal source of the HiCIBaS instrument. No
optical component of HiCIBaS sustained major damage during the landing. The
system was realigned after the flight.

The main goals of this mission were to test new high-contrast imaging
technology in a space-like environment and the training of five master
students of Laval university [76]. The scientific goal was to measure and
characterize the wavefront distortions from high-altitude ($>$40km)
turbulence, using low-order wavefront sensors (LOWFS) [77]. The balloon
launched August 25 2018 at 11:18 pm local time from the Timmins Stratospheric
Balloon Base in Ontario, Canada. The flight plan was to ascend to 40 km, and
stay there for the duration of $\sim$ 12 hours. A separate arm was created for
high-contrast imaging. This arm would benefit from the pointing stabilization
necessary for the LOWFS measurements. The 37-element IRIS AO MEMS deformable
mirror was installed to correct wavefront aberrations, however, it was not
connected to the LOWFS to reduce complexity. The gvAPP was selected because
the coronagraph is stable against residual pointing inaccuracies. The design
has a small dark zone from 2.1 to 8.5 $\lambda/D$ and a contrast of $10^{-6}$,
delivering more extreme performance in the low-turbulance regime. With a
limited bandwidth between 0.83 and 0.88 $\mu$m, a 1TR gvAPP was sufficient.
Also, the gvAPP was designed to provide complementary wavefront sensor
information using a 12-mode Zernike basis cMWS or PD holograms. The
performance of the LOWFS and the gvAPP FPWFS were successfully tested close-
loop in the system before the flight. The PSF before the flight is shown in
Fig. 16. An internal laser source was used to show that both the cMWS and the
PD holograms worked.
While the launch and flight happened according to the flight plan, an
unfortunate mechanical failure resulted in the inability to operate the
telescope. As a result, the telescope never pointed at a celestial source. An
internal source was present in the flight instrument case of such a failure,
which was used to record the gvAPP PSFs. It was also discovered that the
deformable mirror did not respond to commands in flight and was stuck in a
random, non-flattened state. Extreme noise from electronic crosstalk resulted
in low-quality images of the PSF. The resulting images are not useful to
characterize the gvAPP performance during flight, see Fig. 16. The balloon and
payload were recovered after the flight. The high-contrast imaging system,
including the gvAPP, were still operational. Post-launch images of the gvAPP
PSF do not show any significant deviation from pre-launch performance, and the
flight PSF is similar to the after-flight PSF with the DM off. We note that
both comparisons are qualitative, and have not been fully characterized. We
conclude that the gvAPP or similar LC coronagraph can operate in a space-like
environment.

####  4.2.5 Magellan/MagAO-X

The MagAO-X instrument is a completely different instrument than MagAO,
operating in the visible and near-infrared with an extreme AO (ExAO) system
[78]. The key science goal of MagAO-X is high-contrast imaging of accreting
protoplanets at H$\alpha$ (656.28 nm). To achieve this goal, MagAO-X will
deliver high Strehls ($>$70% at H$\alpha$), and high contrasts ($<10^{-4}$)
from $\sim$ 1 to 10 $\lambda/D$. In addition, MagAO-X implements many of the
lessons-learned from SCExAO, including the real-time controller
CACAO333https://github.com/cacao-org. The first phase (Phase I) aims to fully
characterize and calibrate the instrument while obtaining the first science
results. With non-optimal wavefront correction in phase I, the gvAPP was
chosen as a robust coronagraph. To accommodate wavefront sensing and good
coronagraphic performance, the Strehl ratio of the design is lower than most
other coronagraphs (40.7%). The coronagraph design creates a dark zone from
2.1-15 $\lambda/D$, with $10^{-5}$ contrast at the IWA, and the dark zones are
elongated in the grating direction. Therefore, wavelength smearing up to 20%
does not compromise the dark zone towards the edges.
The gvAPP pupil was specifically altered with a thicker spider to be
asymmetric with the goal of enabling focal-plane WFS using the coronagraphic
PSFs. As a result, the gvAPP design employs three ways of wavefront sensing,
i.e. PD, cMWS, and AP-WFS, in addition to LDFC for wavefront control. Each of
these wavefront sensing modes have been tested separately using a test plate
with different gvAPP designs [45, 42]. The wavefront sensing capabilities
enable better instrument calibration by accurately measuring non-common path
aberrations (NCPA), which are more severe in the visible. MagAO-X employs a
separate DM that is dedicated to correct NCPA, which will be fed directly by
the focal-plane wavefront sensors of the gvAPP. FPWFS can be done at much
greater speeds with MagAO-X because a laser-cut mask in the intermediate focal
plane separates the dark zones from the bright field. This mask transmits the
dark holes to the EMCCD science camera and reflects the stellar bright field
back to a second EMCCD that will act as the dedicated FPWFS. The cMWS was
especially useful for alignment of the off-axis paraboloids, providing direct
visual feedback on the first 9 low-order Zernike modes. For on-sky operations,
a likely strategy would be to use PD, cMWS and AP-WFS to minimize the non-
common path aberrations before observing and use LDFC to remove any drifts.
MagAO-X had first light in 2019, where it demonstrated a Strehl ratio of 46%,
and a 5$\sigma$ post-processed gvAPP contrast of $10^{-4}$ at 3 $\lambda/D$ at
900 nm (z’) [79]. These results are promising for discovering exoplanets
during formation through direct detection of $H\alpha$ from accretion of
hydrogen onto these protoplanets. Applying the Massive Accreting Gap (MAG)
protoplanet model[80] to the observed first light MagAO-X contrasts results in
a predicted maximum yield of 46$\pm$7 planets from 19 stars[81].

####  4.2.6 LBT/LMIRcam/ALES

The Large Binocular Telescope Mid-Infrared camera (LMIRcam) is an
imager/spectrograph that operates behind the Large Binocular Telescope
Interferometer (LBTI) [82]. The LBT is a unique telescope with two 8.4-m
primary mirrors mounted next to each other. Both apertures can be combined
with LBTI and create fringes on LMIRcam, resulting in a 22.8-m baseline. The
LBT and LMIRcam are ideal for $L$ and $M$ band observations with a minimal
number of warm optics and a deformable secondary mirror. This makes
LBTI/LMIRCAM the most sensitive infrared instrument in the Northern
hemisphere.

Figure 17: Detection of Kepler 21B using the gvAPP at LBT/LMIRcam ($\Delta
m=3.9$ and the inner three HR 8799 planets ($\Delta m=\sim 10$) using the
dgvAPP at LMIRcam/ALES.

We take advantage of this opportunity with two different vAPPs, a grating vAPP
(1.8-15 $\lambda/D$) and a double-grating vAPP (2.7-15 $\lambda/D$). The
designs are pushing the limits in inner working angle, and the gvAPP also
incorporates focal-plane wavefront sensing with PD holograms and
photometric/astrometric reference spots. Their more extreme designs are
enabled by the small secondary and the extremely thin secondary support
structure. The optic contains two vAPPs, one for each aperture. Their beams
can be imaged separately, partially combined with overlapping fringing
holograms, or completely overlapped to produce fringes for nulling.
LMIRCam was augmented in 2015 with the Arizona Lenslets for Exoplanet
Spectroscopy (ALES) [83], an integral field spectrometer (IFS). After a recent
upgrade, ALES facilitates 2 to 5 $\mu$m low-resolution (R$\sim$35)
spectroscopy of directly imaged gas-giant exoplanets [84]. Currently, it is
the only IFS operating in the $L$ and $M$ bands, containing broad molecular
features (CO, CH4), and also covers the 3.1 $\mu$m ice feature, 3.3 $\mu$m PAH
feature, and 4.1 $\mu$m Br-alpha emission line. Therefore, low-resolution
spectroscopy can provide a unique window for gas giants in the L-T transition,
where their atmospheres transition from CO-rich and cloudy (L-type), to
CH4-rich and relatively cloud free (T-type).
Both vAPPs installed in LMIRcam are available for ALES, and, together with the
annular groove phase mask (AGPM) coronagraph, they are the only coronagraphs
installed in LMIRcam/ALES that cover the full wavelength range. Both vAPPs do
have significant absorption (up to 100%) between 3.15 and 3.45 $\mu$m from
glue and the liquid-crystals. The outer working angle of both coronagraphs is
larger than the FOV of ALES for wavelengths larger than $\sim 3$ $\mu$m. For
the gvAPP only one of the two coronagraphic PSFs can be fitted inside the FOV,
and the wavelength smearing moves it across the detector. While this is not
ideal, the gvAPP provides a much smaller inner working angle compared to the
dgvAPP. The dgvAPP provides a stable central PSF and is more sensitive than
the gvAPP due to the recombination of both coronagraphic PSFs. Moreover, as it
provides a 360 degree dark zone it is much more user friendly and intuitive.
Tests with the internal source show that both vAPPs are operating as expected.
Only a few observations have been carried out, but already show the great
promise of these vAPPs, see Fig. 17. The results on the HR 8799 system will be
discussed in more detail in a future paper. The unique feature of the vAPPs is
the presence of the stellar PSF on the detector. This is particularly
interesting for photometric monitoring of exoplanets. For example, monitoring
the stellar PSF can be used to reduce the impact of variability in AO
performance during the observing run. In addition, an upgraded data reduction
technique has been developed to remove the thermal background with great
accuracy using the science frames themselves. Nodding the telescope to
characterize the thermal background with off-source measurements is still
necessary, however at much lower cadence, increasing the on-source time. To
summarize, there are still many opportunities with the vAPPs in LMIRcam/ALES.

####  4.2.7 VLT/ERIS

The Enhanced Resolution Imager and Spectrograph (ERIS) will be installed in
the Cassegrain focus of UT4 at the Very Large Telescope in the near future
[85, 86]. ERIS is a 1-5 $\mu$m instrument with an imager (NIX) operating from
$J$-$M_{p}$ band and an IFS (SPIFFIER) in $J$-$K$ band with R$\sim$8000\.
ERIS/NIX will have a vortex coronagraph and a gvAPP, while ERIS/SPIFFIER is
non-coronagraphic. The ERIS gvAPP has a dark zone from 2.2-15 $\lambda/D$,
which has been widened to accommodate wavelength smearing, and the APP phase
is multiplexed with two photometric/astrometric reference spots [87]. The
pupil has an asymmetric central obscuration because the (warm) tertiary mirror
(M3) will be moved aside to illuminate the Cassegrain focus where ERIS is
residing. While the asymmetry is small, it is still possible to estimate NCPA
with FPWFS [22] if the software is implemented. The gvAPP has been
manufactured in 2018, and was later tested in the near-infrared test bench of
the group for Exoplanet & Habitability at ETH Zurich [88]. The setup imaged
the gvAPP PSF at 3.8 $\mu$m and was limited by background noise to $\sim
10^{-3}$. Since then an updated setup has been realized and the gvAPP was
tested to the $\sim 10^{-5}$ level [89]. These measurements demonstrate the
ERIS/gvAPP operates as expected, within the limits of the test bench.
While ERIS/NIX is an imager, it will have a long-slit spectroscopic mode with
R$\sim$850, covering the full $L$ band. With the gvAPP absorption feature
between 3.15-3.45 $\mu$m, direct detection of methane will be more difficult.
For atmospheres with elevated methane levels, e.g. T-type brown dwarfs, the
spectral slope beyond 3.5 $\mu$m can be used to measure methane levels.
Another unique opportunity of ERIS/NIX is enabled by the combination of a
sensitive wavefront sensor and the powerful (20W) laser guide star. The laser
guide star allows observations of much fainter science targets, which will
greatly increase the number of potential targets accessible to this new
instrument.

####  4.2.8 ELT/METIS and ELT/MICADO

The Extremely Large Telescope (ELT) [90] will revolutionize direct imaging of
exoplanets because of its primary mirror diameter of 39 meters. The supreme
resolution will be fully exploited by first generation instruments. With five
times the resolution of the VLT and 25 times the sensitivity, the ELT will
provide new insights in planet formation, protoplanetary disks, planet-disk
interaction, planetary atmospheres and planet evolution. Both the Mid-infrared
ELT Imager and Spectrograph (METIS) [91] and the Multi-Adaptive Optics Imaging
CamerA for Deep Observations (MICADO) [92] have exoplanet detection and
characterization as one of the main science goals. To this end, both
instruments have a gvAPP as a baseline coronagraph.
METIS covers the science bands between 3-14 $\mu$m, and has a high-resolution
IFS mode with $R\sim 100,000$ in $L$ and $M$ band, in addition to an imaging
mode from $L$ to $N$ band. This high spectral resolution is achieved over a
large FOV of 0.5 by 1.0 arcseconds, which is made possible by an image slicer
that divides the field of view into multiple strips on a slicer mirror.
Simulations show that METIS will detect and characterize multiple planets
found with radial-velocity studies [93]. Two gvAPPs with different dark zone
designs will be installed in the IFS and the imager in $L$ and $M$ band [94].
A specific downside of the gvAPP is that the star light is not blocked,
leading to high intensities in the IFS focal plane. This can be prevented by
changing the position of the star in the field of view using the chopper. Due
to this offset only the dark zone of the gvAPP PSF is imaged onto the image
slicer. The ELT pupil is not favourable for coronagraph design, with the large
central obscuration. The METIS pupil is a cold stop and has additional thick
spiders, complicating the design process further. The METIS gvAPP design
therefore has a larger inner working angle of 2.5 $\lambda$/D to keep the
Strehl above 65%. Moreover, the gvAPP has a more moderate contrast towards the
inner working angle, going down from a few times $10^{-4}$ at 3 $\lambda/D$ to
$10^{-6}$ beyond 6 $\lambda/D$. Simulations show that this does not affect the
performance of the coronagraph compared to other baselined coronagraphs like
the AGPM, as NCPA, residual wavefront aberrations, and missing mirror segments
of the primary will limit the performance at the smallest separations. In
addition, the AGPM is quite sensitive to tip-tilt which can be significant for
nodding and high frequency structural vibrations [95].
MICADO, the European ELT first-light imager [96], covers the science bands
between 0.8-2.4 $\mu$m and will benefit from both the M4 single-conjugate AO
system [97] and the dedicated multi-conjugate AO system instrument (MAORY)
[98]. With diffraction limited performance, MICADO will deliver extremely
high-resolution imagery to study the inner regions of planetary systems [99].
The high contrast imaging modes will comprise two classical Lyot coronagraphs
[100], one gvAPP and two non redundant masks [101]. One challenge in designing
the high contrast imaging modes of MICADO comes from the fact that they have
to be limited to one focal plane upstream the atmospheric dispersion
corrector, and one downstream pupil plane. While the atmospheric dispersion
might have an impact on the performance of the smallest Lyot coronagraph in
broadband, gvAPP is not sensitive to this effect and will thus offer high
performance even at high airmass. The MICADO gvAPP design is optimized between
2.5 $\lambda/D$ and 20 $\lambda/D$ with a square shape. On-sky expected
contrast performance reaches $2\times 10^{-5}$ at 3.5 $\lambda/D$ in K band
with a Strehl ratio of 70%. For bright nearby stars, the starlight could
saturate the detector for the shortest exposure time, and the use of a neutral
density filter might be necessary.

##  5 Current status and future developments

With the vAPP successfully installed in many different telescopes, the focus
for the vAPP developments is now transitioning from testing and commissioning
the technology, to science observations. Much of the time spent on vAPPs so
far has been oriented towards technology development and design optimization.
However, the on-sky technology demonstration, observation planning, and data
reduction are critical to achieve competitive science results.
The majority of the current on-sky data with a vAPP have been taken with the
MagAO, LEXI and SCExAO instruments. Bright targets were selected to provide
optimal AO correction for technology demonstration of the vAPP and FPWFS.
While the technology demonstration was often successful and benefited from
test observations and consequent understanding and iterations, time awarded to
science observations has been limited, and conditions for these observations
have been sub-optimal. Attempts on more challenging targets, e.g. HD 206893
with SCExAO, resulted in non-detections. Due to the sub-optimal circumstances,
limited available data and sub-optimal data reduction methods, it is difficult
to gauge the performance with respect to other coronagraphs. We tried bridging
this gap by pursuing targets with intermediate contrast by looking into
stellar multiplicity and to understand the detection limits. This science case
was awarded a few nights at the LBT and Subaru, most of which were lost due to
bad weather. Currently the vAPPs of the LBT have yielded the best results,
recovering HR 8799 c,d,e.
To fully exploit the opportunities of the ERIS, MICADO and METIS gvAPPs,
getting more experience with on-sky observations is paramount. We note that
these instruments have had a gvAPP baselined in the instrument design, and
have dedicated engineering time planned to resolve any issues. Moreover, of
all the vAPPs that are currently installed, only the SCExAO gvAPP did not
reach the expected performance on-sky. The diffraction structures in the
SCExAO dark zones are not caused by the gvAPP itself because the lab results
do not show these structures. So, it is likely caused by uncorrected
aberrations from the optics upstream of the internal source injection, which
is unlikely for the ERIS instrument that is installed in the Cassegrain focus.
For METIS and MICADO the vAPPs will be tested extensively and problems should
be identified during this process. We conclude that future efforts should
focus on observation planning and a standardized vAPP data reduction pipeline.
For both observation planning and a data reduction pipeline a preliminary
version already exists, as discussed in Section 3. The vAPP observation
preparation tool does include most vAPPs that are currently available,
however, it does not provide a proper indication whether a companion will be
in the dark zone. In future upgrades we will add this functionality, in
addition to showing the field rotation of the companion in the dark zones of
on-sky PSFs. Ultimately, this could be used to calculate which days of a
semester are optimal for observations of known objects to help proposal
writing.
The data reduction pipelines are currently all custom for each vAPP. A
unification of these pipelines would centralize all efforts on vAPP data
reduction and provide a standardized pipeline that can be used by anyone with
vAPP data. In addition, it would increase efficiency of implementing new
algorithms like rotate-subtract or TRAP. To minimize duplication of previous
efforts, it is essential that the pipeline can also port to existing post-
processing pipelines like the Vortex Image Processing package [57] or PynPoint
[59]. Lastly, these pipelines should include methods to use capitalize on the
astrometric and photometric holographic PSFs.
Future technical developments should be towards enabling broadband imaging
with the vAPP. The main challenge to overcome is a (super)achromatic QWP that
adds minimal wavefront aberration and ghosts to the system [19]. By adding
another QWP before the vAPP, it is also possible to combine the vAPP with
imaging polarimetry [102, 19], another powerful tool to distinguish
astronomical signals from speckle noise [103]. Adding multiple coronagraphic
PSFs per polarization state can then simplify more advanced polarimetric vAPP
designs [40]. Another potential interesting avenue to explore is the
combination of the vAPP with multi-color holography [104], as that would
completely eliminate leakage problems [40]. However, this implementation is
more difficult to implement in an instrument and puts strong requirements on
the shape of the pupil.

##  6 Conclusion

The vector-apodizing phase plate coronagraph is a versatile single-optic
pupil-plane coronagraph that is easily adapted to any telescope aperture. It
delivers good contrast (<10-4, limited by AO performance) at small inner
working angles ($\sim 2\lambda/D$), it can host many different focal-plane
wavefront sensing techniques, and can include astrometric and photometric
reference PSFs. The manufacturing using direct-write for liquid-crystal
technology enables extreme and accurate patterning and the mult-twist retarder
technology provides excellent efficiencies ($>96\%$) for bandwidths up to 100%
between 0.55 $\mu$m and 5 $\mu$m. Because of these properties, the vAPP has
now been installed in 6 different instruments. Measurements with the internal
source of these instruments demonstrate that the vAPPs are operating as
expected. The grating of gvAPPs and their D-shaped dark zone make observing
and data reduction more complicated compared to focal-plane coronagraphs.
Future efforts should focus on software for observation planning and data
reduction to fully exploit the opportunities provided by future instruments
that have the vAPP baselined, i.e. VLT/ERIS, ELT/METIS, and ELT/MICADO.

##  7 Acknowledgements

The research of David Doelman, Steven Bos, and Frans Snik leading to these
results has received funding from the European Research Council under ERC
Starting Grant agreement 678194 (FALCONER). Ben Sutlieff is fully supported by
the Netherlands Research School for Astronomy (NOVA). MagAO-X was funded by
NSF MRI Award #1625441. KMM’s work is supported by the NASA Exoplanets
Research Program (XRP) by cooperative agreement NNX16AD44G. This research made
use of HCIPy, an open-source object-oriented framework written in Python for
performing end-to-end simulations of high-contrast imaging instruments [36].

##  8 Disclosures

The authors declare no conflicts of interest.

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