text:
\section*{CONCLUSION AND FUTURE WORK}
\label{sec:conclusion}

We have successfully designed a pipeline to leverage NRMs installed on the SCExAO platform as wavefront sensors.
We have characterized, in particular, these sparse aperture sensors to be of excellent linearity, of large dynamic range up to the phase wrapping problem, and of excellent sensitivity, down to a few hundred photons per frame, i.e. just a few photons per pixel per frame. This excellent sensitivity, albeit limited by the necessity of limited spectral coverage and the poor pupil transmission inherent to the use of sparse masks, paves way for the use of SAMS in particular and interferometric WFSs in general as auxiliary sensors of choice to general purpose AO loops.

We have demonstrated for the case of SCExAO that using a SAMS in H-band was a successful strategy to recover from one wavelength petal-locking occuring in the upstream AO188 facility AO system, a natural consequence of LWE that cannot, in the current design of the control systems, be averted in anyway by the SCExAO operators.

Calibration source closed-loop sequences on synthetic aberrations have proven that (1) stable control can be satisfactorily maintained; (2) petal discontinuities of up to 660~nm can be captured; and (3) the resulting petal error lies within 100~nm of peak-to-valley errors, which can then easily be captured without ambiguity by the pyramid WFS.
A few select sequences on-sky have confirmed this, however the sub-median seeing and naturally occuring LWE during the allocated engineering time have made a proper telemetry reduction complex and those experiments ought to be re-executed and their results confirmed with more compelling data.

Future work will be oriented on implementing dual-loop command schemes, so as to define a proper dual-sensor asynchronous AO scheme that would allow both sensors to cooperate optimally, each with their preferred modal sensitivities, to restore PSF quality during poor LWE conditions.
We hope to extend the NRM capabilities of SCExAO, notably for SAMS imaging with two spectral bands at visible wavelengths, so that these can be combined and provide an unambiguous capture range beyond $\lambda/2$. The dual-channel visible SAMS will then be compatible for routine operations with coronagraphic science in the near-infrared.

Finally, we intend the SAMS both as a self-contained concept, but also as a stepping stone for wavefront sensing integrated within pupil-remapping interferometers, to be operated directly at the science plane while are performing science observations. Preliminary efforts are already ongoing for the SCExAO-hosted modules FIRST and GLINT, which will moreover provide a spectrally-dispersed wavefront information
\section{INTRODUCTION}
\label{sec:intro}

\subsection{The Subaru Coronagraphic Extreme Adaptive Optics}
\label{sec:intro_scexao}

	The Subaru Coronagraphic Extreme Adaptive Optics\footnote{%
		\url{http://www.naoj.org/Projects/SCEXAO/index.html}%
	}\cite{Lozi2020SCExAOStatus,Currie2020OnSkySCExAO,Currie2021AcceleratingStars} (SCExAO) instrument is a versatile experimental high contrast imaging platform deployed at Subaru Telescope.
	The core scientific purpose of SCExAO is to implement high-efficiency near-infrared coronagraphy, coupled to an extreme adaptive optics (AO) system, so as to achieve direct imaging of faint stellar companions\cite{Currie2020HD33632, Kuzuhara2022Acceleratingstar}, debris and protoplanetary disks\cite{Lawson2020HD15115,Steiger2021MECHIP109427, Uyama2022RYTau}, and exoplanets, \cite{Currie2022NatureABAur}.

	The \emph{extreme} wavefront correction is powered by a dual stage AO system: first, the Subaru facility AO188\cite{Ono2019SubaruAO} performs a preliminary, high-stroke wavefront correction upstream of SCExAO, using wavelengths short of 600~nm. Then, light in I band (800-950~nm) is sent to a pyramid wavefront sensor (WFS) with linear resolution 50~px across the pupil. The pyramid uses a First Light Imaging OCAM$^2$K camera, allowing framerates up to 3.6~kHz with sub-electron readout noise. The computed correction is applied using SCExAO's internal 2040 actuator Boston MicroMachines MEMS deformable mirror (DM). A Strehl ratio of 80 to 90\% in H band is typically achieved in median seeing conditions at Maunakea observatory, up to 93-94\% in the most favorable situations.

	Beyond the core coronagraphic optical path, SCExAO stands as a cutting-edge development platform for new high-contrast imaging technologies\cite{Walter2020MEConSCExAO}, as a prototyping testbed for future high-contrast spectrographs and imagers on extremely large telescopes, e.g. TMT-PSI\cite{Lozi2020SCExAOStatus}, and finally as a ready-to-use platform for wavefront sensing and control algorithmic prototyping, leveraging the diverse optical devices and features already available on the instrument.
	In this context of wavefront sensing and control prototyping activities, we present in this paper the early developments of a dual-wavelength low-order WFS dedicated to the control of low wind effect.

\subsection{Low wind and petaling}
\label{sec:intro_lwe}

	The performance of AO-assisted astronomical imagers depends on the capability of the AO to deliver a high Strehl beam to the scientific modules.
	Beyond the correction of astronomical turbulence outside the dome, another type of wavefront perturbation is a frequent occurrence: the so-called low wind effect (LWE), which generally arises during nights of good to excellent seeing, and low wind speed.
	It has been extensively analyzed from VLT/SPHERE data\cite{Milli2018LWE}, and arises as well on Subaru/SCExAO.
	Empirically, LWE induces a splitting of the core of the point spread function (PSF) into several secondary lobes.
	In relatively weak instances, this results in asymmetric lobes in the first Airy ring. In stronger cases, the PSF can be entirely split into multiple lobes, sometimes as badly as having equal brightness, as shown on fig.~\ref{fig:LWE}.

	\begin{figure}[h]
		\centering
		\includegraphics[width=.45\textwidth]{lwe_ex.pdf}
		\includegraphics[width=.46\textwidth]{chuck_samples_intro.pdf}\\
		\caption{%
			Left: nominal (saturated) and two sample LWE-affected images of Vega at 650~nm wavelength, with the VAMPIRES instrument.
			Right: Identical, except images are in H-band (1630~nm), on star Delta Vir.
		}
		\label{fig:LWE}
	\end{figure}

	The effect physically originates from thermal dissipation from the secondary mirror support structure arms, or \emph{spiders}, and is of significance when the wind inside the dome is insufficient to flush these pockets of warmer or colder air away from the telescope structure.
	As a result, the temperature difference between opposing sides of a spider arm induces a wavefront aberration, which is exceptional in that in contains a discrete, discontinuous wavefront step across the width of the spider. LWE can typically be decomposed over 11 discontinuous, non-Kolmogorov wavefront modes: petal differential piston, tip and tilt over each of the pupil clear apertures, that we call \emph{petals}.

	By including these 11 modes explicitly into the AO reconstructor, it is theoretically possible to achieve direct correction of LWE with the main WFS of an instrument.
	However, traditional general purpose wavefront sensors fare poorly with discontinuous aberrations.
	While existing AO facilities have been able to work around this issue for years even before LWE was acknowledged, it is now well established\cite{Engler2019Pyramid, BertrouCantou2020Petalometry, BertrouCantou2021Confusion} that the problem of properly compensating for LWE becomes more difficult with the increased thickness of spiders on larger telescopes, in particular in the case of ELTs.

	The physical effect at the origin of LWE induces wavefront steps of any amplitude, yet when coupled with running AO systems, the AO loop sometimes actually worsens the original LWE aberration into what can be referred as petaling. Two cases can be defined, depending on how AO control is implemented:
	\begin{itemize}
		\item Petal piston modes are excluded from the AO control law: the petal component of LWE is then uncorrected and free-floating petal pistons are observed, with slowly drifting values.
		\item Petal piston modes are included in the AO control law: \textbf{piston-locking} may occur; The WFS, due to its weak sensitivity to petals, creates a wavefront where one or two petals pistons are corrected one wavelength off from the flat wavefront.
	\end{itemize}

	This second situation arises often with pyramid WFSs, where there is a faint sensitivity to discontinuities under the spider thanks to some diffractive coupling in the sensor plane.
	There is, however, no telling apart from a true flat wavefront an one 1-$\lambda$ petaling, and the sensors non-linearity and weakened sensitivity on spurious wavefronts may actually promote and further the piston locking effect.
	Tip-tilt components over pupil petals can however be easily detected and corrected if allowed in the command law, leaving only 3 degrees of freedom (4 petal pistons minus the global piston) to account for.

\section{Non-redundant masking and the sparse aperture sensor}
\label{sec:intro_sam}

	In sparse aperture masking (SAM) interferometry\cite{Tuthill2006SparseApAO,Tuthill2013NRMInterf},
	the telescope pupil is reduced to smaller holes (see left of fig.~\ref{fig:What_was_that_for}), thus forming a sparse array of apertures over which wavefront error may be neglected.
	After propagation to the focal plane, an interferogram (IG) is formed in place of the classical PSF, consisting of the superposition of interference fringes between each pair of holes of the pupil mask.

	Under the condition that the mask is non-redundant (NRM), i.e. that no two baselines between holes are of the same length and orientation, the phase difference between holes can be reconstructed from the IG, and simultaneously describe the Fourier transform of the observed astronomical object.
	While the scientific modeling of asymmetries in the observed object can be performed regardless of the wavefront aberrations between the mask holes, this wavefront information is directly available in the images, being the phase of the fringes formed between any given pair of non-redundant holes.
	Such an approach has already been proposed, e.g. for the cophasing of the segmented mirror of spaceborne observatories, including the James Webb Space Telescope\cite{Pope2014SAMcophasing, Subedi2015NRMWFS, Cheetham2014NRMPhasing, Greenbaum2016phaseSAMJWST}.

	In the present paper as well as in previous work\cite{Deo2021SAWFS}, we propose to apply this approach on ground-based facilities, and use a NRM of minimal complexity to supplement the main AO system for petal pistons only, for which its sensitivity is minimal.

	We have explored in previous work\cite{Deo2021SAWFS} the use a single camera, in H-band, with a non-redundant 9 hole mask in order to perform petaling correction.
	This paper present subsequent improvements, using two cameras in the visible (675, 775~nm) so as to increase the capture range of the sensor and to free up H-band photons for scientific use.

	\vdeo{FIX BELOW}

	We have adapted the existing, science-oriented non-redundant masking capabilities of SCExAO towards wavefront sensing, and in this study specifically gear our approach towards LWE elimination in supplement to a running extreme AO control loop.
	In sect.~\ref{sec:formalism}, we propose a brief overview of the mathematics involved in NRM focal plane imaging. In sect.~\ref{sec:preproc_techniques}, we present the hardware capabilities of SCExAO for a SAMS, and the preprocessing pipeline we designed for this purpose. We show in sect.~\ref{sec:experimental} the results of static, daytime characterizations performed with the sensor, and finally, we show in sect.~\ref{sec:cl} preliminary results of closed loop operations over synthetic LWE-like pertubations, in particular simulated petal-lockings, both in daytime and on-sky.
\section{INTRODUCTION}
			\label{sec:intro}

				\subsection{Low wind effect and petaling}
				\label{sec:intro:lwe}

Large telescopes with segmented apertures are prone to the nefarious low wind effect (LWE), also named island effect or petaling, which dramatically affects point spread function (PSF) quality.
LWE has been studied in great detail from VLT/SPHERE data\cite{Milli2018LWE}, and its occurrence is fairly common at Subaru Telescope as well\cite{Vievard2019LWEonSCExAO}.

We show on figure~\ref{fig:LWE} two examples of the imaging quality reduction induced by LWE on Subaru/SCExAO\cite{Currie2020OnSkySCExAO, Lozi2020SCExAOStatus} (more details about the instrument are provided in section~\ref{sec:exp_setup}).
First, we show core splitting in a fast imaging dataset using the VAMPIRES visible imager\cite{Norris2014Vampires, Uyama2020VampiresHAlpha}, where a significant fraction of the frames need to be discarded despite the seeing being an excellent 0.3''.
Second, we show the impact of core splitting on a coronagraphic spectral cube acquired with the CHARIS\cite{Lawson2020HD15115,Currie2021AcceleratingStars} integral field unit.
Just a few second-long bursts of core splitting during the exposure induce a significant brightening of the halo at separations within 0.3''.

\begin{figure}[t]
	\centering
	{\footnotesize\bfseries
	VAMPIRES visible imager examples\\
	\includegraphics[width=.45\textwidth]{lwe_ex.pdf}\\[1em]
	CHARIS integral field unit spectral cube
	}
	\includegraphics[width=.9\textwidth]{charis_lwe.png}
	\caption{%
		Top: three selected on-sky PSFs acquired on Vega during Subaru/SCExAO engineering observations with the VAMPIRES visible imager (750~nm) during a night of excellent seeing (0.3'').
		The left PSF is nominally diffraction limited, while the other two show LWE-induced core splitting.
		Bottom: samples of a CHARIS integral field unit spectral cube showing coronagraphic data from 1.2 to 2.2 \textmu m. Core splitting in the northeast-southwest direction behind the 0.113'' Lyot occulter increases the 0.2-0.3'' residual halo by several orders of magnitude.
		The four speckles in a square pattern within the dark hole area are astrometric calibration spots $15.2~\lambda/D$ from the optical axis.
	}
	\label{fig:LWE}
\end{figure}

The LWE aberration has been shown to be physically induced from thermal dissipation from the secondary support structure (spider) of the telescope, creating an optical path difference (OPD) jump between the sides of a spider arm.
This discontinuous aberration can be described fully, along with atmospheric turbulence, by typically extending a Kolmogorov-compatible wavefront mode basis with piston, tip, and tilt modes restricted to each individual clear subaperture (petal), as are shown on figure~\ref{fig:TT_PTT_modes}.
These additional modes make for 11 more degrees of freedom on a telescope with 4 spider arms.

\begin{figure}[b]
	\centering
	\raisebox{2em}{\includegraphics[width=.15\textwidth, angle=-10]{pupil.png}}
	\hspace*{.5em}
	\includegraphics[width=.7\textwidth]{modes_2rows.pdf}
	\caption{%
		Left: pupil of the Subaru Telescope (transmission map), showing the four petal components of the pupil.
		Right: wavefront maps for global tip-tilt and the 12 modes describing LWE for a 4-petal pupil: piston, tip, and tilt within each petal.
		These make for only 11 additional degrees of freedom since overall piston must be excluded.
	}
	\label{fig:TT_PTT_modes}
\end{figure}

				\subsection{Petal locking}
				\label{sec:intro:petallocking}

Traditional general purpose wavefront sensors (WFS) such as Shack-Hartmanns, Pyramids (PyWFS), or curvature WFSs, fare poorly for sensing a discontinuous wavefront step hidden under the shadow of the spider arm.
Adaptive optics (AO) systems may actually worsen petaling\cite{BertrouCantou2021Confusion} beyond what is physically introduced upstream by either physical LWE, or even just from natural seeing when the spider is larger than $\approx r_0$.
The AO can induce spurious stable wavefront control regimes where one or two of the four petals are stabilized one full wavelength (of the AO sensor) away from an appropriately flattened wavefront. We call this phenomenon petal locking.
As an example, Subaru/SCExAO uses a dual AO cascaded scheme.
The first stage AO188\cite{Minowa2010AO188} uses a 500-600~nm curvature WFS and drives a 188-element bimorph deformable mirror (DM); a wavefront discontinuity of 300~nm can be spuriously amplified and locked to $\approx$550~nm.
The second stage extreme AO within by SCExAO operates a 800-950~nm PyWFS and actuates a 50$\times$50 MEMS DM.
We observe petal steps of 600~nm created by AO188 being amplified to $\approx$900~nm by the extreme AO control loop.

Petal \emph{tip-tilt} modes are in theory not an issue for Shack-Hartmann or PyWFS sensors, which perform somewhat of a wavefront gradient measurement.
Petal pistons, however, show zero gradient across the entire aperture, making their detection by PyWFSs extremely difficult, besides some diffractive effects yielding signal along the spider arms, and so only at lower modulation radii with of the order of 1 rad linear capture range\cite{BertrouCantou2020Petalometry}, while more than a full WFS wavelength of capture range will be necessary to recover from petal-locking situations.
By using an appropriate controller, a conventional AO will easily ``flatten'' the wavefront until only petal piston modes remain; which is why the focus of this paper is only the phasing of the three degrees of freedom of piston petals, and not the full additional 11 as shown on figure~\ref{fig:TT_PTT_modes}.

{\iffalse
We show some sample experimental data on figure~\ref{fig:petal_ramp} acquired on SCExAO on the calibration source, showing the H-band (1\,550~nm) PSF quality as well as the PyWFS response to a petal piston ramp from -2~\textmu m to 2~\textmu m steps of optical path difference (OPD).
We observe that although the PyWFS is showing a response signal from the petal mode, the reconstruction of said signal over the control matrix past $\pm$250~nm of OPD steps is non-monotonic and oscillates back through zero.
The local extrema of the PyWFS response at around $\pm$800~nm are where the petal locking phenomenon occurs, with a WFS response vastly outside of linear behavior for a petal piston mode.
The locking is further reinforced by nonlinear effects proper to the PyWFS, e.g. turbulence-induced optical gain reducing the sensitivity of the sensor in petal-locking moreso than in the properly phased regime\cite{Deo2019Telescope, Chambouleyron2020Convolution, BertrouCantou2020Petalometry}.
\fi}

\iffalse
\begin{figure}
	\centering
	\includegraphics[width=0.66\textwidth]{petal_ramp.png}
	\includegraphics[width=0.33\textwidth]{sr_pywfs.png}\\
	\hspace*{3cm}(a)\hspace*{8cm}(b)
	\caption{%
		(a): DM displacement, H-band PSF, and PyWFS response for a petal piston ramp from -2 to +2~\textmu m of optical path difference.
		(b): Strehl ratio in H-band computed from the PSFs shown on (a), and reconstruction of petal mode response from the PyWFS signal.
	}
	\label{fig:petal_ramp}
\end{figure}
\fi

Broadly speaking, we distinguish three different approaches in the AO community to tackle LWE/petaling at existing and future facilities.
(1) Eliminate discontinuous aberrations from the control space. This avoids petal-locking, but also removes capability to correct true, thermally induced LWE.
(2) Focus on developing petal-focused correction algorithms using signals from the main sensor.
This is a more accessible path for instruments designed with H or K band WFSs, where $r_0$ is larger than in the visible and expected discontinuities at the spider will remain within 1~rad.
And finally (3), develop an auxiliary WFS, with low resolution, dedicated to petaling.
In this paper, we propose to use non-redundant sparse aperture interferometry for petal wavefront sensing.

				\subsection{Sparse aperture non-redundant masking}
				\label{sec:intro:sawfs}

Sparse aperture masking (SAM) interferometry\cite{Tuthill2006SparseApAO,Tuthill2013NRMInterf} has been long used to circumvent the effects of atmospheric seeing, with the pupil shrunk to a sparse array of much smaller holes, over which wavefront error could be neglected. Having low speckle noise within each hole is a fundamental hypothesis of SAM. However, today a flat wavefront can be provided over holes significantly larger than $r_0$ thanks to (extreme) AO systems, allowing masks with a reduced number of larger holes.

After propagation from the SAM pupil to the focal plane, an interferogram (IG) is formed in place of the classical PSF, consisting of the superposition of interference fringes between each pair of holes of the pupil mask.
The Fourier transform of the IG is then the autocorrelation of the electric field in the pupil plane; we call these correlograms (CG).
We show on figure~\ref{fig:mask_ig_cg_example} the 7 hole mask, and typical on-sky interferogram and correlogram; these correspond to the setup used throughout this paper and detailed in section~\ref{sec:exp_setup}.

\begin{figure}[b]
	\centering
	\includegraphics[width=0.8\textwidth]{NRM_example.png}
	\caption{%
		Left: 7 hole non-redundant pupil mask, overlaid with the Subaru telescope pupil. Two of the 21 baselines are highlighted with red arrows.
		Middle: typical corresponding focal plane interferogram obtained on the VAMPIRES instrument at a wavelength of 775~nm.
		Right: complex magnitude of the corresponding correlogram, showing the 42 independent components corresponding two-to-one (each plus its Fourier symmetric) to the baselines of the 7 hole mask.
	}
	\label{fig:mask_ig_cg_example}
\end{figure}

Under the condition that a non-redundant mask (NRM) is used, i.e. that no two baselines between holes are of the same length and orientation, the CG map is composed of disjoint domains distinctively identifying each baseline of the mask.
Within each of these domains, the complex argument of the correlogram depends only upon: (1) the structure of the imaged object, from which stems the scientific use of NRMs; as well as (2) the phase difference in the wavefront between the corresponding pair of holes.
The scientific component to the pair's complex argument is fixed, and equal to zero in the case of a point source.
Reading the complex argument of the correlogram offers a straightforward way to measure OPDs between all holes of the mask, and after reconstruction through a linear reconstructor, a low-order description of the wavefront, which in this case would be the phasing of the four petals of the pupil.

We therefore propose the study of using the sparse aperture masking concept for petal wavefront sensing, thus forming the Sparse Aperture Wavefront Sensor (SAWFS).
In previous work\cite{Deo2021SAWFS}, we explored the deployment of a SAWFS with a 9 hole NRM in the near infrared, and showed preliminary results of closed-loop petal piston control during on-sky engineering.
Several limitations arose from this design: (1) the transmission of the 9-hole NRM could be improved using a reduced number of larger holes. Indeed, only 4 holes are necessary for the petal-piston sensing problem at Subaru Telescope.
And (2), using a single IG in H-band restricted the capture range to half-wavelength steps, i.e. 800~nm, beyond which phase wrapping was unavoidable.
As discussed in section~\ref{sec:intro:petallocking}, 800~nm is an insufficient capture range for petal-locking effect in SCExAO.

In this paper, we expose the design of a SAWFS comprised of two cameras sensing IGs at 675 and 775~nm wavelength, both through the same 7~hole mask.
The transmission of the mask is improved to $15$\% of the full pupil, and the use of two wavelength permits the use of a phase unwrapping algorithm that
extends the capture range well beyond steps of $\pm\lambda/2$, up to $\pm2.3$~\textmu m.
This provides enough range for petal-locking issues with red / near-infrared AO systems.
In section~\ref{sec:exp_setup} we detail the experimental hardware used for this experiment on Subaru/SCExAO; in section~\ref{sec:reduction}, we propose some elements of data reduction for single- and twin-wavelength SAWFS, in particular the phase disambiguation algorithm we use for two wavelengths.
In sect.~\ref{sec:lab}, we show experimental noise propagation results, and finally in \ref{sec:sky_ol}, we show the analysis of open-loop SAWFS measurements during an on-sky run.
The authors hope the readers have a pleasant time browsing through this paper.

			\section{SPARSE APERTURE WFS: EXPERIMENTAL SETUP}
			\label{sec:exp_setup}

The Subaru Coronagraphic extreme Adaptive Optics\footnote{%
	\url{http://www.naoj.org/Projects/SCEXAO/index.html}%
}\cite{Lozi2020SCExAOStatus,Currie2020OnSkySCExAO,Currie2021AcceleratingStars} (SCExAO) instrument is a versatile experimental high contrast imaging platform deployed at Subaru Telescope.
The core scientific purpose of SCExAO is to implement high-efficiency near-infrared coronagraphy, permitted by an extreme adaptive optics system, so as to achieve direct imaging of faint stellar companions\cite{Currie2020HD33632}, debris and protoplanetary disks\cite{Currie2017HD36546,Lawson2020HD15115,Steiger2021MECHIP109427}, and exoplanets\cite{Currie2022NatureABAur}.
A Strehl ratio of 80 to 90\% in H band is typically achieved in median seeing conditions at Maunakea observatories, up to 93-94\% for the best observing nights.

\begin{figure}[ht]
	\centering
	\includegraphics[width=.99\textwidth]{VAMPIRES_SAWFS_layout.png}
	\caption{%
		Optical layout of the VAMPIRES instrument, with the key parts of the dual-band SAWFS, among the visible light bench of the SCExAO instrument.
		Not shown is the near-infrared part of SCExAO, which feeds light from 600 to 950~nm through the periscope (blue, top left), and contains the 50$\times$50 DM, and all scientific and technical modules operating in the 950~nm - 2.2~\textmu m wavelength range.
	}
	\label{fig:experimental_setup}
\end{figure}

Within SCExAO, the VAMPIRES \footnote{%
	Visible Aperture-Masking Polarimetric Interferometer/Imager for Resolving Exoplanetary Signatures
} instrument is a twin imager designed for differential polarimetric and H$\alpha$ imaging\cite{Norris2014Vampires}.
We show on figure~\ref{fig:experimental_setup} the layout of VAMPIRES within the upper bench of the SCExAO instrument.
Light from 600 to 950~nm is fed through the periscope from the lower deck of SCExAO, with the wavefront already corrected by both AO188 and the high resolution 2040~element DM of SCExAO.
I band is reserved for the extreme AO PyWFS, and the 600-800~nm range is fed into VAMPIRES.

VAMPIRES was recently expanded with coronagraphic capability\cite{Lucas2022VAMPIRESCoronagraph}, as well as with dual wavelength capability, using a dichroic splitter and two narrowband 675 and 775~nm filters.
The detectors are Andor Ixon 897 EMCCD cameras, which provide images with virtually no readout noise.
The total field of view is 3''$\times$3''; framerates of up to 360~Hz can be achieved using a reduced field of view of 0.37''$\times$0.37'', as we will use throughout this paper.

In order to enable analysis of stellar and circumstellar features below the diffraction limit, VAMPIRES was equipped with a suite of non-redundant masks, with respectively 7, 9, and 18 holes.
For the purpose of implementing a SAWFS, we focus on using the 7 hole NRM, which has the highest transmission of $\approx$15\% relative to the full pupil, while still having holes within each of the 4 pupil segments (figure~\ref{fig:mask_ig_cg_example}), thus allowing petal piston measurement.
It should be noted that having more holes that the absolute minimum of 4 required for petal sensing and control is both beneficial -- with the capability of simultaneous sensing, and thus discarding, tip-tilt from vibrations --, and suboptimal, since a lower number of holes allows greater overall transmission without overlap of baseline components in the CG plane.

			\section{ELEMENTS OF DATA REDUCTION}
			\label{sec:reduction}

				\subsection{Single camera SAWFS}
				\label{sec:reduction:single}

Briefly put, each component of the correlogram obtained from either camera (see figure~\ref{fig:mask_ig_cg_example}) relates to a single of the 21 baselines $ij$ between holes $i$ and $j$, where $0\leq i,j \leq 7$ are identifying indices of the 7 holes of the NRM.

The formalism and algorithmic process we use to reduce each camera to per-baseline measurements is described in much greater detail in reference~\citenum{Deo2021SAWFS}, with the same formalism as used here.
If $\mu_{ij}$ is the complex coherence over baseline $ij$ (obtained by sampling the CG at the peak of the corresponding sidelobe), the quantity of interest is its complex argument:
\begin{equation}
	\mathrm{Arg(\mu_{ij})} = \phi_i - \phi_j + \psi_{ij} +2k\pi,
\end{equation}
where $\phi_i$ is the value of the wavefront phase, at the sensing wavelength, within hole $i$ of the NRM, and $\psi_{ij}$ is the baseline's biasing phase, comprised both of an instrumental term and a physical component due to the imaged object not being a point source.
$k\in\mathbb{Z}$ represents the number of phase wraps between the actual phase difference and the measurement.

After an object-dependent calibration where reference phases $\psi_{ij}$ are determined, we define the phase measurement of the SAWFS as the collection for the 21 baselines, of the:
\begin{equation}
	m_{ij} = \mathrm{Arg}\left(\mu_{ij}\times\exp\left(-j\psi_{ij}\right)\right),
\end{equation}
which observes the relationship
\begin{equation}
	m_{ij} = \phi_i - \phi_j \text{ if} \left|\phi_i - \phi_j\right| \leq \pi.
\label{eq:m_ij}
\end{equation}
Equation~\ref{eq:m_ij} shows how we measure the wavefront phase difference between each pair of NRM holes, and shows that the capture range is limited to half a wavelength of OPD.
Pending that this condition is complied with on all 21 baselines, the wavefront can be reconstructed onto up to 6 modes using typically using a linear reconstruction:
\begin{equation}
	\label{eq:reconstruction}
	\mathbf{v} = \mathbf{D}^\dagger \bullet \dfrac{\lambda}{2\pi} \left[m_{ij}\right]_{0\leq i < j < 7},
\end{equation}
where $\mathbf{v}$ is the vector of modal command, $\mathbf{D}$ the response matrix from measurements (in units of OPD) to modes, $\bullet$ denotes matrix-vector product, and $\lambda$ the sensing wavelength.

				\subsection{Dual-wavelength recombination}
				\label{sec:reduction:dual}

Naturally, if some baseline phases $\phi_i-\phi_j$ exceed the $\pi$~rad capture range, the reconstruction $\mathbf{v}$ would be significantly wrong, and this could go undetected without additional checks on the SAWFS controller output.
This is why using two identical SAWFS at two different wavelengths $\lambda_0$ (=~775~nm) and $\lambda_1$ (=~675~nm) is essential to provide consistent measurements beyond half-wavelength phase jumps.

\begin{figure}[b]
	\centering
	\includegraphics[width=.99\textwidth]{5_ddw_process_schematic.png}
	\caption{%
		Left: simulated wrapped OPD measurements $d_{ij}^0$ and $d_{ij}^1$ at both SAWFS sensing wavelengths for any baseline $ij$ as a function of the OPD difference between holes $i$ and $j$ of the NRM.
		Right: corresponding difference $\delta d_{ij}$, showing the discretization of the possible values used for retrieving the unwrapped OPD.
	}
	\label{fig:reduction:ddw}
\end{figure}

A fairly direct classification technique, that we call the differential dewrapper, is used to combine wrapped phase measurements from both cameras into a single, consolidated OPD measurement of much greater dynamic range.
Using the wrapped OPD quantity:
\begin{equation}
d_{ij}^{\{0, 1\}} = \dfrac{\lambda^{\{0, 1\}}}{2\pi}m^{\{0, 1\}}_{ij} = \dfrac{\lambda^{\{0, 1\}}}{2\pi} \left(\phi_i - \phi_j\right) + k\lambda^{\{0, 1\}},
\end{equation}
where the exponent $\cdot^{\{0, 1\}}$ denotes the index of the camera, we can compute the difference of wrapped OPDs between both spectral channels of the SAWFS:
\begin{equation}
\delta d_{ij} = d_{ij}^0 - d_{ij}^1,
\end{equation}
which, disregarding noise for now, can only take a discrete set of values.
This is illustrated on figure~\ref{fig:reduction:ddw} and allows applying the differential dewrapper.
The difference $\delta d_{ij}$ is related to the nearest permitted value, which maps to a number of phase wraps $k_0$ and $k^1$ for either wavelengths.
The unwrapped OPD is ultimately obtained by averaging both unwrapped values:
\begin{equation}
D_{ij} = \dfrac{\left(d_{ij}^0 - k^0\lambda^0\right) + \left(d_{ij}^1 - k^0\lambda^1\right)}{2},
\end{equation}
where both quantities on the numerator, if properly unwrapped and disregarding noise and differential biases between cameras, should be equal.

A key point to enable differential dewrapping to work, as can be observed from figure~\ref{fig:reduction:ddw}, is the closeness of the different possible discrete values for the wrapped OPD difference $\delta d_{ij}$.
For our chosen wavelengths of 675 and 775~nm, we observe that up to an input OPD of $\pm$2.36~\textmu m, the possible values for $\delta d_{ij}$ are all at least 100~nm apart from each other.
If we were to extend the capture range beyond 2.36~\textmu m, the next new possible values for $\delta d_{ij}$ are $\pm$375~nm, only at best 75~nm apart from the already allowed values $\pm 300$~nm.

As we will explore in section~\ref{sec:noise}, this specification on the classifier for $\delta d_{ij}$ gives a trade-off between acceptable noise and dynamic range. If we accept values only 75~nm apart, the range is extended to $\pm$2.71~\textmu m, at which point a difference occurs only 25~nm from an already existing one. With a tolerance of 25~nm, the range would be extended to $\pm$10.46~\textmu m, at which point $\delta d_{ij}$ start reoccurring again\footnote{
	Noting that 775 = 31 * 25, 675 = 27 * 25, that 27 and 31 are coprime, and 27 * 31 * 25~nm / 2. = 10462.5~nm, the mathematically expected half-period for re-occuring values $\delta d_{ij}$.
}.

We therefore arbitrarily define that with this dual wavelength configuration, the capture range of the SAWFS is $\pm$2.36~\textmu m, and that the noise specification in this case is for less than 50~nm error on all $\delta d_{ij}$, so as to avoid misclassification between possible values 100~nm apart.
Assuming we would want 50~nm of error to be a 2-sigma limit on $\delta d_{ij}$, this gives a standard deviation of 25~nm RMS, which, coming from both cameras, allows only a restrictive error budget of 18~nm RMS, i.e. $\approx 0.15$~rad per baseline per camera!

While we showed in previous work\cite{Deo2021SAWFS} that a single camera SAWFS could produce measurements will less that 1~rad RMS noise with only a few hundred photons --thanks to the high efficiency of interferometric measurements--, a 1~rad RMS error is excessive to allow the differential dewrapper to work.

In order to validate our actual capability to extend the dynamic range by using combined dewrapping of phases with both cameras,
we study in section~\ref{sec:noise} the noise propagation over a single camera; aftewards, we study in section~\ref{sec:sky_ol:results_noise} the a posteriori data from an on-sky dataset to analyze whether the noise conditions were met.

			\section{Experimental noise sensitivity}
			\label{sec:noise}

				\subsection{Photon-to-noise transfer on each camera, each baseline}

Using the calibration source of the SCExAO bench, we analyze experimentally the noise propagation on the baseline phase measurements $m_{ij}$ against the number of photons reaching the detector.
This analysis was performed on only one SAWFS, at 775~nm.
The results are summarized on figure~\ref{fig:noise_propagation_chart}.
Figure~\ref{fig:noise_propagation_chart} shows photon and readout noise theoretical limits, computed from Fourier simulations, as well as photon noise corrected by a $\sqrt{2}$ factor, as is appropriate for the multiplicative noise of the Andor EMCCDs. It should be noted that quantum efficiency has not been accounted for and that the x-axis should be shifted appropriately depending on the sensor used.
Experimental points are computed, at each flux level, as the statistical average of the measurement error over 1000~consecutive frames.
The RMS error over all 21 baselines are shown, as well as the least and most noisy baselines.

\begin{figure}[htbp]
	\centering
	\includegraphics[width=0.8\textwidth]{noise_propagation_megafigure.pdf}
	\caption{%
		Simulated and experimental noise propagation for a single-wavelength SAWFS using our 7 hole NRM. Propagation is measured from the number of photons per frame onto the phase noise \emph{per baseline}. Corresponding R-band magnitudes are given using the VAMPIRES zero-point of $8.24\ 10^7$ ph.frame\textsuperscript{-1}.second\textsuperscript{-1}.nm\textsuperscript{-1} per camera.
		Shown are the simulated photon noise limit without and with $\sqrt{2}$ excess noise; the ceiling corresponding to a uniform phase distribution over $[-\pi, \pi]$; and the read-out-noise floors for 0.1, 1, 10, and 100 $e^-$/px.
		Blue markers show experimental data: the mean and extrema across the 27 baselines of the NRM at the given photon fluxes, from $1.67\,10^3$ through $1.67\,10^5$ photons/frame.
	}
	\label{fig:noise_propagation_chart}
\end{figure}

We note first that the trend below $2\ 10^4$ ph/frame appropriately follows the -1/2 power law of photon noise, and that the least-noisy baselines are marginally above the photon noise limit.
For all measurements, the spread in RMS error between least and most noise baselines is of a factor $\approx$3, which could possibly be explained by illumination variations in the pupil plane; greater vibrations across long baselines; or slight misalignments of certain NRM holes overlapping with spider arms.

The performance bottoms out at 0.1 rad RMS averaged over baselines for illuminations beyond $2\ 10^4$~ph/frame. The best baseline however maintains a power -1/2 decrease up to almost $10^5$~ph/frame.
We suppose that floor in the error budget corresponds to instrumental vibrations and turbulence internal to the optical bench during the measurements: both as global aberrations, i.e. variations in the $\phi_i - \phi_j$, and as speckle noise from small-scale turbulence.

				\subsection{Noise constraints of the differential dewrapper}

We have shown in section~\ref{sec:reduction:dual} that for a capture range beyond $\pm \lambda^0 / 2$ and up to $\pm 2.36$~\textmu m with the dual band SAWFS, we need to measure $\delta d_{ij}$ to better than 50~nm of error.
This noise constraint is actually very strong -- and probably is, at this stage, one of the weakest points of the current choice of wavelengths.
This can be optimized in the future, possibly using more than just 2 channels.
This would enable finding the group delay using least-square methods, with more robustness to noise than the basic 2-channel method that we're implementing here.

A 50~nm error at 2-$\sigma$ extrapolates to 0.15~rad RMS per baseline per camera.
Looking at the experimental measurements shown on figure~\ref{fig:noise_propagation_chart}, this relates to respectively: $8\ 10^3$ ph/frame for the mean baseline overall, $3\ 10^3$ ph/frame for the mean baseline overall, and $2\ 10^4$ ph/frame for the noisiest baseline!
This last value would relate to a limiting magnitude at about $R=+4.4$ for 7~ms exposures (as used in section~\ref{sec:sky_ol}), considering the throughput of the VAMPIRES instrument.

However, the photon limits listed above stand as flexible bounds.
We interpret from figure~\ref{fig:noise_propagation_chart} that the RMSE floor at high flux comes from local turbulence or vibrations.
In this case, the source is actually physical and is correlated between cameras, thus canceling out when computing the $\delta d_{ij}$.
The eventual unwrapped OPD measurement $D_{ij}$ suffers from these perturbation sources, yet they do not compromise the success of the dewrapping.

Furthermore, we could also relax the 2-$\sigma$ separation constraint decided before. Slightly higher noise would induce a higher fraction of misses by the differential dewrapper.
However, many such misses can be detected, and the frame discarded, e.g. by computing and checking the integrity of closure phases on each frame before sending the resulting command to the DM.
The temporal structure of petal-locking, and the intended use of the SAWFS as a ``rectifier'' control over the high-speed AO loop, should permit a slow cadence, and thus it shouldn't be critical to discard identified dubious frames.
Moreover, the noise propagation through the linear reconstructor (eq.~\ref{eq:reconstruction}) is such that a 1~$\lambda$ error on any single baseline propagates into at worst 0.2~$\lambda$ peak-to-valley error on the reconstructed petal map.
This means that as long as dewrapper errors are occasional occurences, this additional error budget could be easily absorbed by the main AO loop, or by the SAWFS control law itself.

We will get back to differential dewrapper failure rate in section~\ref{sec:sky_ol:results_noise}, as we explore the statistics of the OPD difference $\delta d_{ij}$ in an on-sky dataset.

			\section{Open-loop measurements on-sky}
			\label{sec:sky_ol}

				\subsection{Observation conditions}
				\label{sec:sky_ol:conditions}

We performed on-sky engineering for the dual-band SAWFS on Subaru/SCExAO on the night of 2022/03/24, on Delta Virginis (R = +1.86, H = -1.05).
The VAMPIRES cameras were configured using the 7 hole NRM, with the narrowband configuration (675-25~nm and 775-25~nm filters respectively, after a 700~nm dichroïc), i.e. identically to the setup used during daytime tests detailed in the previous sections.
The cameras operate at 142.8~Hz in CCD frame transfer mode, with a 7~ms exposure time.
Camera shutters are synchronized by means of a hardware trigger.
In parallel, the fast imaging camera of SCExAO was acquiring focal plane images in H-band (1630~nm) with an exposure time of 400~\textmu s.
Seeing conditions were sub-median and unstable, with a baseline value of 0.8 - 1.0'' but with frequent bursts in the 1.5 - 2.0'' range, causing both AO loops to struggle to maintain consistent correction or even diffraction limited imaging in H-band.
Unfortunately, due to the AO correction instability, only a fraction of the 20 minutes of data acquired with the SAWFS could be analyzed at this point.
We present in this section some results of this analysis, focusing on a 11~second portion starting on 2022/03/24 11:30:56.7 AM UTC, comprised of 1500 frames for the SAWFS.

A few key results are analyzed through the following subsections: an a posteriori noise regime determination, temporal analysis of reconstructed petal piston statistics, and finally tentative H-band PSF reconstruction.

				\subsection{Results: noise regime for the dewrapper}
				\label{sec:sky_ol:results_noise}

The key requirement on noise for the differential dewrapper that arose throughout sections~\ref{sec:reduction:dual} and~\ref{sec:noise} can be further explored with the baseline phase statistics during our on-sky sequence, so as to assess a posteriori what the success rate of our dewrapping algorithm would have been.
We show on figure~\ref{fig:onsky_apost_histograms} the distribution of the differential OPD $\delta d_{ij}$ prior to differential unwrapping, on each of the 21 baselines of the NRM.

The central component of each $\delta d_{ij}$ histogram is for each baseline higher than the $\pm$100 sidelobes by at least an order of magnitude, allowing us to adjust a distribution for the structure of the peaks.
Empirically, we find the peak is well described by an hyperbolic secant distribution (pdf($x$) $\propto \mathrm{sech}\left(\frac{\pi}{2}\frac{x}{\sigma}\right)$) -- with this distribution fitting significantly better than either a Gaussian or Lorentzian.

\begin{figure}[b]
	\centering
	\includegraphics[width=.99\textwidth]{5_sky_dataset_histograms.pdf}\\[.5em]
	\caption{%
		In blue, histograms of the differential OPD distribution \emph{prior to differential dewrapping} on each of the 21 SAM baselines during the on-sky sequence.
		Histograms are normalized to the height of the main peak.
		Histogram displays are trimmed to $\pm$200~nm, thus not showing the sidelobes at $\pm$675~nm.
		The half-width-at-half-maximum of the central peak is shown on each insert, ranging from 7 (baseline 15) to 35~nm (baseline 3).
		Dashed orange lines show a hyperbolic distribution with the same width as the central peak.
		Solid green lines show hyperbolic distributions with the same width as the central peak and same height as the histogram at the $\pm100$~nm sidelobes.
		Baselines 13, 14, 15 and 20 show no sidelobes as these baselines are internal to a single petal.
	}
	\label{fig:onsky_apost_histograms}
\end{figure}

Having an analytical distribution fitted to the $\delta d_{ij}$ allows us analyze noise statistics and to compute the failure rate of the differential dewrapper for the amount of $\delta d_{ij}$ spread observed on each baseline.
With HWHMs ranging from 7 to 35 nm, the differential dewrapper failure rate --i.e. the fraction of the surface area of each peak falling beyond $\pm50$~nm from its center-- ranges from $1.1\ 10^{-4}$ up to 0.19.
Interestingly, assuming independent processes on all 21 baselines, the dewrapper success rate on all baselines for a given frame would only be 1.3\%.
Even though a proper metric is lacking at this stage of the study, we can assess from petal values and PSF reconstructions (sections~\ref{sec:sky_ol:results_temporal} and~\ref{sec:sky_ol:results_psf}) that the success rate is significantly higher than 50\%, thus hinting that high noise occurences are highly correlated across baselines.
A likely candidate for such a process would be a large amount of high-order wavefront residuals from the AO, resulting in large speckle noise over all NRM holes.

Table~\ref{tab:failure_rates} briefly summarizes the relationship between peak standard deviation, HWHM, dewrapper failure rate, and per-camera noise across a general range of values, based on the analytical distribution fitted on the histograms of figure~\ref{sec:sky_ol:results_noise}.

\begin{table}[h!]
	\centering
	\caption{%
		Computed single-baseline differential dewrapper failure rates, i.e. probabilistic occurrences of  $|\delta d_{ij}| > 50$~nm, based on an empirical hyperbolic distribution of the differential OPD $\delta d$.
		Table shows half-width-half-maximum and standard deviation (std) of the $\delta d$ distribution, as well as the noise in rad RMS on each baseline per camera that maps to the resulting $\delta d$.
	}
	\label{tab:failure_rates}
	\vspace*{0.5em}
	\resizebox{\textwidth}{!}{%
		\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}
			\hline
			HWHM of $\delta d_{ij}$ (nm)& 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 50 & 60 & 70\\

			\hline
			std of $\delta d_{ij}$ (nm)& 6.0 & 11.9 & 17.9 & 23.9 & 29.8 & 35.8 & 41.8 & 47.7 & 59.7 & 71.6 & 83.5\\
			\hline
			Failure rate (\%) & $2.4\ 10^{-4}$ & 0.17 & 1.6 & 4.7 & 9.1 & 14 & 19 & 24 & 33 & 41 & 47\\
			\hline
			Per camera (rad RMS) & $3.6\ 10^{-2}$ & $7.3\ 10^{-2}$ & 0.11 & 0.15 & 0.18 & 0.22 & 0.26 & 0.29 & 0.36 & 0.44 & 0.51\\
			\hline
		\end{tabular}
	}
\end{table}

Now, as an exercise, we assume an identical photon flux on both cameras, and thus an identical readout/photon noise variance in radians on each camera, and that the histogram spreads observed on figure~\ref{fig:onsky_apost_histograms} are the direct product of only measurement noise phenomena such as discussed in section~\ref{sec:noise}.
For the experimental data, we note that 7~nm HWHM then maps to 0.051~rad RMS per camera, and 35~nm HWHM to 0.255~rad RMS.
Mapping these values back to the experimental results shown on figure~\ref{fig:noise_propagation_chart}, we notice that (1) the spread between the least- and most-noisy baselines is slightly above the experimental half-decade; and that (2) such values would place this experiment in the $10^4$-$2\ 10^4$ photons/frame range.
Zero-point calibrations for VAMPIRES place this dataset at $6\ 10^5$ ph/frame using R=+1.86 for Delta Vir.
Placed within figure~\ref{fig:noise_propagation_chart}, this dataset sit further to the right of the calibration source measurement point, atop a noise floor.
The latter could be caused by any combination of seeing, temporally varying AO residuals, or speckle noise, but in all cases, resulting in an RMSE way above the photon noise floor for such illumination.

				\subsection{Temporal analysis}
				\label{sec:sky_ol:results_temporal}

\begin{figure}[ht]
	\centering
	\includegraphics[width=.99\textwidth]{5_sky_timeseries.pdf}
	\caption{%
		Temporal series of the relative H-band Strehl ratio against the modal values of the 3 petal piston modes.
		Top: values of the 3 petal modes and the total peak-to-valley petaling amplitude reconstructed from the SAWFS measurements.
		Bottom: In red, Strehl ratio of the H-band PSF, relative to the maximum in this set. In black: the number of PSF detector pixels exceeding the value of 3000 ADU.
	}
	\label{fig:onsky_timeseries}
\end{figure}

In order to assess whether the open-loop measurement performed with the 2 band SAWFS on sky were successful, we analyze the reconstruction of the 3 petal modes from both cameras after differential dewrapping, and compare this value to the infrared PSF, used as an objective measure of wavefront quality.
In terms of peak-to-valley amplitude, the reconstructed petal wavefront exceeds $\lambda^0 / 2$ for 51\% of the samples. The dewrapper reconstructed baseline values in excess of $\lambda^0 / 2$ for 21\% of baseline measurements.

On figure~\ref{fig:onsky_timeseries}, we show on a time-base synchronized with the SAWFS an empirical Strehl and a surface-spread measurement, both from an H-band PSF.
The empirical Strehl is measured as the ratio between the PSF maximum to the maximum of the entire dataset.
It should be noted that this measure stays for extended periods in the 95-100\% range with very little fluctuations.
This is due to detector saturation during this sequence and therefore a loss of information on the true PSF maximum, rather than actual PSF stability.
The PSF spread is measured as the number of detector pixels that exceed a given illumination threshold, and varies between 32 and 71 pixels.
This spread metric is less sensitive to detector saturation and we observe even better correlation with the peak-to-valley amplitude of the petaling modes: we find a correlation coefficient of 0.74 between the petal peak-to-valley and the PSF spread, which tends to indicate meaningful measurements from the SAWFS.

				\subsection{PSF reconstruction}
				\label{sec:sky_ol:results_psf}

The correlation observed in section~\ref{sec:sky_ol:results_temporal} is however not proof that the SAWFS is performing a proper measurement of the petal modes in the wavefront - merely that it measures something that is correlated with PSF quality.

As to confirm that the SAWFS is performing proper measurements, we performed a direct reconstruction of the H-band PSF from the values measured by the SAWFS, using a direct approach: only far field propagation is simulated, through the Subaru pupil mask, aberrated with only the 3 free petal modes.
We show on figure~\ref{fig:onsky_chuck_recon} some sample results of this reconstruction.

We observe that the main distortion of the PSF core and the area of the first Airy ring are broadly reproduced by the reconstruction, showing that the process is somewhat consistent, and that we successfully reconstruct to better than the 1 wavelength ambiguity pitfall.
Some PSFs, e.g. at 5.70~s, could be excellent matches pending we would additionally simulate the effect of the partially corrected seeing in this $\approx$20-40\% Strehl ratio regime.

Obviously, the seeing conditions during this engineering run would not permit any sort of high-quality matching between the reconstructed PSF and the actual recorded PSF. Also, with only 3 petal degrees of freedom, the simulated PSF is restricted to a limited number of features.
The reconstruction could be improved already by adding global or petal tip-tilt into the reconstruction, which could be partially doable with the 7 hole NRM we are using.
}

\begin{figure}[ht]
	\centering
	\includegraphics[width=.99\textwidth]{5_sky_psf_mosaic.pdf}
	\caption{%
		Samples of H-band PSF reconstruction from SAWFS 3-mode petal data.
		For each insert, the left half shows the on-sky 1\,630~nm PSF, and the right half shows the petal mode reconstruction thereof.
	}
	\label{fig:onsky_chuck_recon}
\end{figure}

			\section{CONCLUSION AND PERSPECTIVES}
			\label{sec:conclusion}

The impact of petaling on 8~m-class telescopes, and its projected aggravation on upcoming Extremely Large Telescopes, is likely to make the design and use of auxiliary WFSs a cornerstone of AO-assisted imaging, in particular for high contrast techniques, so as to circumvent the limitations of the PyWFS with the sensing of discontinuous aberrations at the spider arms.

We have shown that the use of non-redundant masking can enable proper petaling reconstruction, and provide an effective side channel to maintain the PyWFS of SCExAO within its unambiguous capture range in regard to petaling aberrations.
Once an adequate fusion control scheme between the main XAO loop and the SAWFS are implemented, we should be able to consistently improve scientific throughput during nights of prevalent low-wind effect.

We have shown that the use of two parallel spectral channels on synchronized detectors permits the recovery of discontinuous aberrations up to several wavelengths of dynamic range. This enables us to use a dual-channel SAWFS in visible light, a design compatible with scientific observations in the near-infrared -- which account for most of the high-contrast scientific observations performed on Subaru/SCExAO.

It has arisen during this work that unwrapping the phase beyond the half-wavelength capture range is actually a highly noise sensitive process with only two wavelengths.
Work is in progress to improve the unwrapping algorithm for two wavelengths. And in parallel, a redesign of VAMPIRES is currenty being studied that would include successive dichroics of neighboring cutoffs. This would allow multispectral imaging with four or more channels imaged on the same detector, and using NRMs would permit multi-band wavefront sensing, either in parallel with near-infrared science or simultaneously with visible light interferometry using that same NRM.
With more spectral channels, we would be able to implement more robust group delay retrieval techniques that are already well established in interferometry.

On-sky engineering has shown that we obtain a basic yet consistent reconstruction of the LWE-distorted PSF. We hope to be able to confirm these results in better seeing and during a night where there is no physical LWE, so as to obtain precise quantitative results over petaling aberrations introduced artificially.
}%

			\acknowledgments
			\label{sec:acknowledgements}

This work is based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan.
The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Hawaiian community.
We are most fortunate to have the opportunity to conduct observations from this mountain.
The authors also wish to acknowledge the critical importance of the current and recent Subaru Observatory daycrew, technicians, telescope operators, computer support, and office staff employees.
Their expertise, ingenuity, and dedication is indispensable to the continued successful operation of these observatories.
The development of SCExAO was supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Research \#23340051, \#26220704, \#23103002, \#19H00703 \& \#19H00695), the Astrobiology Center of the National Institutes of Natural Sciences, Japan, the Mt Cuba Foundation and the director's contingency fund at Subaru Telescope. VD and NS acknowledge support from NASA (Grant \#80NSSC19K0336); KA acknowledges support from the Heising-Simons foundation.
}%

\bibliographystyle{spiebib}

redpajama_set_name: RedPajamaArXiv


Featuring Molly G's signature buttery leather and a long, slender delicate strap, Fay's our super feminine crossbody/shoulder bag, now with vintage indigo mud cloth. Organized, but playful. Gotta love that fun tassel! Definitely the ideal everyday handbag for your essentials.


Six student groups participated in the "Build and Bust" on Wednesday, April 26, 2017, sponsored by the Interior Design program in the Department of Human Development, Fashion, and Interior Design. In conjunction with Earth Week 2017, each group had to create a shelter out of recycled and reused products.
Groups had to pay an entry fee to have their structure judged. Those wishing to cast a vote paid $1 per vote. All proceeds went to Habitat for Humanity and Austin's Playroom, along with the winning charities of choice from each group.
The grand prize of $100 went to Team Daaja, which it donated to ICCAP.
Team Perez won "Most Structurally Sound," with a $50 reward that was donated to American Heart Association.
Team PHLSV won "Most Creative," with a $50 reward that was donated to Big Hearts, Little Hands of the Indiana County YMCA.
Photo information: Winners of "Most Creative," Team PHLSV, pose in front of their structure.


text:
AL East Round-up: Intriguing 2014 MLB Draft Picks Edition
By Kyle Franzoni
Jun 2, 2014; Miami, FL, USA; Tampa Bay Rays pitching coach
Jim Hickey
(48) talks to starting pitcher
(left) on the pitching mound during the sixth inning against the Miami Marlins at Marlins Ballpark. Mandatory Credit: Steve Mitchell-USA TODAY Sports
No team in the American League East has taken better advantage of the draft than the Tampa Bay Rays, and they've done a great job of shifting from picking from a top 10 spot to the latter half of the draft. Because of this, the Rays have been able to provide a solid stream of talent to their Major League club without having to worry about splurging on free agents. That's been due to having one of the smartest front offices in the game, with a keen eye for talent. That occurred again in this draft when they went out an drafted one of the most polished power-hitting prospects on the board in first baseman Casey Gillaspie, a talent that MLB.com is comparing to
Lance Berkman
. Those are pretty solid comparisons to draw and if the Rays get either out of Gillaspie, who should move quickly, they'll have a winner.
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redpajama_set_name: RedPajamaCommonCrawl


When my editor asked me to write a book of fun children devotionals for girls ages 6-9, I saw a perfect opportunity to help young ladies understand that God is their friend.
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Well, that's awesome. What an encouragement!
See more about God & Me! 3 (Ages 6-9).


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text:
Q: $f:\mathbb{R}^n\to\mathbb{R}^n,f(x)=x\|x\|^2$ Then $f:\mathbb{R}^n\to\mathbb{R}^n,f(x)=x\|x\|^2$ Then
$1.$ $(Df)(0)=0$
$2.$ $(Df)(x)=0\forall x$
$3.$ $f$ is one one
$4$. $f$ has an inverse.
let, $x=(x_1,x_2,x_3,\dots,x_n)$, $\|x\|^2=(x_1^2+\dots,+x_n^2)$
,Then $Df=3\|x\|^2$ am I right?  Then $1$ is true, $2,3,4$ are false.

A: Your $f$ maps $(x_1,\dots,x_n)$ to $$((x\cdot x)x_1,\dots,(x\cdot x)x_n)$$
Let $f_k(x)=(x\cdot x)x_k$. Then $$\nabla f_k(x)=\nabla (x\cdot x)x_k+(x\cdot x)\nabla (x_k)$$
$$\nabla f_k(x)=2x_k x+(x\cdot x)e_{k}$$
Thus $$M_{(Df)(x)}=2 \begin{pmatrix} x_1x_1&x_1x_2&\cdots&x_1x_n\\x_2x_1&x_2x_2&\cdots&x_2x_n\\ \vdots &\vdots&\ddots&\vdots\\x_nx_1&x_nx_2&\cdots&x_nx_n\end{pmatrix}+\Vert x\Vert^2{\bf Id}$$
Note that your functions is of the form $f(x)=\lambda(x)\operatorname{id}(x)$ with $\lambda:\Bbb R^n\to \Bbb R$. We know that $\lambda(x)$ is not injective, but we know that $\operatorname{id}(x)$ is. Note $f$ is injective on every $\{\Vert x\Vert =r\}$, so we must look at $x,y$ with $\Vert x\Vert \neq \Vert y \Vert$, assume $\Vert x\Vert \geq \Vert y \Vert$. Since the norm is always non-negative, $f$ may only fail to be injective when each coordinate of $x$ has the same sign as the corresponding coordinate of $y$. Could you look at what happens in said case? Aim to show $x\neq y\implies f(x)\neq f(y)$.

A: No, if you are looking at the derivative of a map between two vector spaces, it has to be a linear map. In this context, the derivative of $f$ at $x$ is an endomorphism $Df(x):\mathbb R^n\rightarrow \mathbb R^n$.
So when you give $Df=3\|x\|^2$, it can't be a good answer for $n\geq 2$. However if $n=1$, I agree.
To answer question 1) and 2), you can easily compute $Df(x)$ for any $x\in \mathbb R^n$ : since $f(x)=x\|x\|^2=\langle x,x\rangle x$, $$f(x+h)-f(x)=\langle x+h,x+h\rangle (x+h)-\langle x,x\rangle x= \cdots$$
For question 3), assume that $f(x)=f(y)$ and try to prove that $x=y$ i.e. $f$ is injective.
Then by question 3), if $f$ is injective, what else does $f$ need to be invertible ?

redpajama_set_name: RedPajamaStackExchange


Hey, look - it's a bunch of Lego mini-figs. I decided to feature them this day since I had spent much of Christmas and Boxing Day playing with helping my kids build their new Lego sets. And because they are just so cool.
Ah, the sweet torture of those last moments before you can go downstairs on Christmas morning to see what the big man has brought for you. My poor children get these last moments prolonged so that I can capture the anticipation, as well as the growing annoyance.
Whoever it was that decided it would be a good thing to leave Ol' Santa some cookies and milk on Christmas Eve deserves a medal. I'm quite sure that at some point after I took this pictures, this delicious snack was consumed and enjoyed very much, thank you.
Ten years ago, the Mrs. and I took all the change we had collected a large Snapple bottle, and converted it into cash money via Coinstar. We decided that this qualified as "found" money, and thus decided to spend it frivolously. I used my half to purchase this Hallmark Keepsake ornament of the Starship Enterprise 1701-E.
The Mrs. mocked my choice, and said that this was even a waste of found money. She must not have realized at the time how this ornament would continue to bring pleasure year after year. I'd say this was money well spent.
So what did she wisely spend her half of the money on? Neither of us even remembers.
The days until Christmas were counted down this year with the help of a Lego City advent calendar. This day's prize was a mountain climber equipped with an ice axe. Since Mother Nature was kind enough to freeze the lily pond, the subject for this day's photo seemed obvious.
Just like I did on the first days of Spring, Summer, and Fall, once again here is a shot of the oblate spheroid lawn decoration in the back yard. I was hoping for a very snowy, wintry looking picutre, but at least I got some ice.
In Fred City there is a British grocery store, and in yet another unexplained mystery, outside this store sits an Indian. Maybe they sell British cigars there? I don't know. I do know that they sell some tasty British beers there however, and on this day I stopped by to pick my old friend Sam Smith.
I'm not sure when exactly it happened, but I am now certainly a born again Apple guy. I have nothing against PC's or Windows, and by no means think that Microsoft is in any way evil. That being said, here in my laboratory (where things are not as they seem), I have 2 PC's and 2 Macs. One PC is rarely even powered on, and the other I only use when I must for work.
With that admission out of the way, I was feeling a bit jilted that the nearest Apple store was an hour away. That was until I discovered that the great city of Frederick, MD does actually have its own apple store. There were no iPods, Macs, or iPhones for sale that I saw, but they did have quite a selection of apple butter.
Does it make me a bad dad that I often mistake my son for one of several other Tiger Cubs many times at each Cub Scout meeting? I blame it on the hats, which combined with their relative shortness makes them all look overly similar to someone with my vantage point. I'm pretty sure, however, that this one is mine.
My daughter sure has learned how to mug for the camera this year. We attended the Christmas program at her pre-school (in which she was an angel, a reindeer, and just a kid), and every time she saw me hold up the camera, she would turn her head just-so and give me a very cute little fake smile.
To me, the best ornament to top a Christmas is the star. I know there are many Angel supporters out there, but it takes a star to lead the way. I've heard tell that some people top their trees with Santa's, and that makes no sense at all.
Technically speaking, I did leave the house to get this picture. I had to, to capture this my favorite view of our Christmas tree, a view I usually don't get to see. Hopefully the neighbors enjoy it though.
Hey look - no Christmas decorations today. Instead I was able to capture this moment where my daughter was watching my wife play piano. I say "watching" because she seemed much more interested in the motions and the mechanics of the piano then in the actual music being produced. This moment was brief and fleeting as my son soon approached and created a scrum for the prime viewing spot.
The kids were looking for toys to give away, which of course means that a number of toys which had have set neglected have suddenly become the new favorites that we just can't give away because they love them and can we keep them please, because they will play with them everyday. So these Weebles, which were all set to find a new home will be staying here until next year or until we can sneak them away.
Ah, Toys (backwards) R Us. Is there any destination that is more alluring to children and so much not so to adults? Yes there is - Chuck E Cheese. But TRU is definitely in a close 2nd, and even closer still at this time of year. Even worse this year is that there are reports that at our local branch, a strange man has been spotted walking around taking pictures of the toys. These might be just rumors though, because I was there and did not see him.
If not for a house full of Christmas decorations, I really have no idea what I would be taking pictures of at this point in the odyssey. This Kris Kringle is a new addition to the menagerie this year, and hangs on the secondary coat hooks, in the foyer under one of our many "chin mirrors". If you could see the rest of him, you'd see that he bids welcome, but by blocking the coat hooks, he also says "Don't stay too long."
Just like I don't understand the connection between Santa and firefighting, I also fail to grasp exactly what M&M's and Star Wars have to do with Christmas. Even so, this Peanut M&M C-3PO Christmas ornament proves there must be something. There is also a R2D2 M&M ornament that I've not photographed (yet).
What I like about this ornament is that it changes colors depending on which lights it is near. It is not unlike a chameleon in that way. What is even more amazing given that it is made of glass, is that the kids hung this on the tree unsupervised, and still managed not to break it.
First of all, I never really understood why they called it "Peanuts". What does it have to do with everyone's favorite legume anyway? Second, why was Charlie Brown bald. Actually, wasn't Linus displaying some MPB too? That takes us to Schroeder, everyone's favorite classical toy pianist, and the subject of today's photo-of-the-day. "You played it for her, you can play it for me! "
It seems like a very long time ago since I set out on this odyssey to take a good picture everyday. Though some were better than others, I managed to not miss a day. Until now. I did take some pictures this day, but they were all pretty much rubbish, and there was nothing that I felt was good enough to make the cut. So no keeper today.
But now you can imagine that I was wise to name this project Roth365, even though this is a leap year. That gives me a one time, built in "no-day", which turned out to be this day.
Don't worry though, the odyssey continues, and though the calendar is thin, there are still enough days remaining in 2008 for me to take 365 keepers before they we sing Auld Lang Syne.
It was a crisp Saturday afternoon and the snow was just starting to fall when we arrived at the nearby Mayne's Tree Farm for our annual Christmas Tree selection and subsequent chopping down. Usually we need to check out many, many different trees to be sure we get the one that is just right. When I said "we" in the last sentence, what I meant was "Shelley". This year, we found our tree almost right away. Probably not a Christmas miracle, but still very nice.
Why is it that decorating the table somehow makes the meal you eat there better? At this dinner party, not only were the tables fancied up, but so were the guests, myself included.. Luckily I did not need to break my 1+ year streak of not wearing a tie.
These lights adorn a Douglas Fir that we planted in the back yard a few years ago. String increasing numbers of C9's around this tree has become an annual tradition. This will be the last year that I will be able to do this job without the use of a step ladder. A few years from now, we'll probably be just like the Griswalds.
Thank goodness for Christmas decorations. They are just what an inspiration-starved photo-a-day'er needs to help make it through to the end. These are not the first hall-deckers you have seen here, and I assure you they will not be the last.
My son was really into Underdog for about 3 seconds last year. It happens that those 3 seconds occurered at the time when he made his list for Santa, so Christmas morning found this bobble-head waiting for him under the tree. Since then, he has been shaking his noggin on a shelf right next to a bobble-head Darth Vader that for some reason used to be my daughter's.
This Japanese Maple tree from the front yard is back here at Roth365, this time bereft of leafs, ducks, and manti. It just watches as a December begins with rain, and collects some water drops as decorations.
"OK, here is the situation. The giant snow monster is holding your parents and your would-be girlfriend hostage in his cave, and is likely to eat them any time now. You go into the cave, and lure the monster out. We'll drop this giant boulder on its head, then we'll remove all its teeth."
Yeah, that is a Christmas story for the whole family.
Some of my earliest Christmas memories involve attending the Goodwill Fire Company Christmas party back in Pottstown, PA. I'm still not sure how firefighting fits into the Santa mythos, beyond perhaps something involving the chimney, but they are still connected nonetheless. That is why Santa travels the streets of Adamstown, MD each December on his fire truck, soliciting gift requests from children and distributing plastic fireman hats. All this for just the price of whatever you care to drop into the fireman's boot.
Long before apples, oranges, or mangos were doing it, the trend setting banana was wearing stickers. Now, the stickers have gone beyond just the brand mark to become something much more appealing. This particular sticker is quite appropriate since this acronym could go to no other fruit but the banana. If they were to give out titles, the banana would be declared "The Funny Fruit" (not to be confused with beans, which win a different title). How many great laughs has the slipping on a banana peel brought us? The number can't be counted.
Ah, that moment when you are about to sit down for a tasty and delicious Thanksgiving feast. I was thankful for everyone who contributed to this, especially since the only things I brought were my camera and my appetite. Special thanks to Kim and Dave for hosting again, and for setting such a picturesque table.
So they say the day before Thanksgiving is supposed to be some really busy travel day. I took the NYC subway to New York Penn Station, then Amtrak to Union Station in DC, then DC Metro to Shady Grove, and it really was not that bad. In fact, I had enough energy left at the end to take a few pictures, including this one. I also wanted another try at this photo of tables in Union Station which I felt was very close to being a great shot. Unfortunately, I couldn't do any better.
A day later, and I was still in New York and it was still raining. Luckily, my $3 umbrella that I had acquired from a street vendor was doing a surprisingly good job of keeping me dry. This lion, part of pair that were guarding a bank, was not so lucky.
New York rained on me during my walk back to the hotel. I did not mind because I am water-resistant, and I knew it was give me the opportunity to get some reflection shots.
I've always said it would be a cold day in November before I walk across the Brooklyn Bridge. OK, maybe I've never said that before, but now I wish I had, because it was. Boy, what a bridge. For Shelley's last day in town we decided to walk from Chinatown, to Soho, to Greenwich Village, then down to and across this famous bridge. The bridge, and the many other sights we saw along the way, made it a walk well worthwhile.


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San Francisco Ballet makes the beloved Nutcracker its own, resetting it during the 1915 Panama Pacific International Exhibition and introducing Dance in America viewers to the dazzling Maria Kochetkova and Davit Karapetyan. Recorded in December 2007 by KQED Public Television to help commemorate the company's 75th anniversary, the work is choreographed by Artistic Director Helgi Tomasson and features sets and costumes by, respectively, Michael Yeargan and Martin Pakledinaz, both repeat Tony Award-winning designers. "Striking, elegant and beautiful," assessed The New York Times.
Introduced by Olympic champion figure skater Kristi Yamaguchi, a native of the Bay Area and winner of 2008's Dancing with the Stars, the production encores in high definition and 5.1 surround sound Sunday, December 12 at 9pm EST (check local listings) on THIRTEEN's Great Performances on PBS. San Francisco Ballet Music Director and Principal Conductor Martin West conducts Tchaikovsky's sprightly score.
Tchaikovsky's beguiling score is one of the most popular pieces of music ever written. Think "Dance of the Sugar Plum Fairy" and "Waltz of the Snowflakes." Inspired by E.T.A. Hoffman's 1816 story, The Nutcracker and The Mouse King, it was first proposed to Tchaikovsky by legendary choreographer Marius Petipa as a follow-up to Tchaikovsky's other successful ballets at Russia's famed Mariinsky Theatre: Swan Lake (1877) and The Sleeping Beauty (1890). The composer began work on it in 1891.
San Francisco Ballet's Nutcracker was recorded on stage in performance at the War Memorial Opera House December 19 and 21, 2007. It is a co-production of San Francisco Ballet and KQED Public Television San Francisco, in association with Thirteen for WNET.ORG. Matthew Diamond (Dance in America's Emmy Award-winning Swan Lake with American Ballet Theatre; Great Performances' Crazy for You) directs; Judy Flannery (Great Performances' A Streetcar Named Desire From the San Francisco Opera) produced. Michael Isip is Executive Producer for KQED.
An expanded version of San Francisco Ballet's Nutcracker, featuring additional behind-the-scenes interviews with the production's creators and a background piece on the 1915 World's Fair, is available on DVD from Opus Arte/Naxos of America.
Great Performances is funded by the Irene Diamond Fund, the National Endowment for the Arts, Vivian Milstein, the LuEsther T. Mertz Charitable Trust, the Corporation for Public Broadcasting, public television viewers and PBS. Major corporate funding for this telecast was provided by First Republic Bank, a division of Merrill Lynch Bank & Trust, Co., FSB. Special funding for the telecast was provided by Jim and Cecilia Herbert & Family. Additional support was provided by The Flora Family Foundation and members of the San Francisco Ballet's 75th Anniversary Sponsors Council: major sponsors include the Richard and Rhoda Goldman Fund, The Hellman Family and Yurie and Carl Pascarella; with additional sponsors including Stuart Francis and Diana Stark; Stephen and Margaret Gill Family Foundation; Cecilia and Jim Herbert; George Frederick Jewett Foundation, Lucille Jewett, Trustee; Barbara Ravizza and John Osterweis; Kathleen Scutchfield; The Smelick Family; The Swanson Foundation; Ms. Susan A. Van Wagner; E.L. Wiegand Foundation; Diane B. Wilsey; and Akiko Yamazaki and Jerry Yang.
© 2018 WNET. All rights reserved.
PBS is a 501(c)(3) not-for-profit organization.


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Impact & Case Studies
Help Arrives for Student Loan Borrowers
by SpringFour | Apr, 24, 2013 | Default | 0 comments
We've been inspired recently by former British prime minister Tony Blair, who when he first took office described his priorities as "Education, education, education." He made good on his promise, raising per pupil funding 48%, adding 35,000 teachers, and raising teaching pay 18%.
In this country, we find that education is not always lifting its students higher, but rather saddling them with tremendous debt that siphons off much of the money they make during their early earning years. Some are forecasting a student loan crisis that may rival the recent housing crisis in this country.
This is why we at MK are enthusiastic about StudentLoanHelp.org, a new initiative sponsored by the Student Loan Alliance.
The site brings together student loan counselors (many of whom are MK counseling clients) to support those whose education left them struggling financially. It offers online loan advice and assistance, and gives practical, actionable options for those in need.
So a tip of the MK hat to this new initiative, which proves that education should lift us up–not drive us down.
Here are the LendIt Fintech 2021 Industry Awards finalists
Mariner Finance Personal Loans Review: Best for Fair Credit Borrowers
Best in Class: 2021 User Survey Shows SpringFour's Far-Reaching Impacts
Copyright 2018 MortgageKeeper Referral Services Inc., dba Spring Four | All Rights Reserved
Maggie Kaiser
Client Success Manager
Maggie Kaiser joins the SpringFour team as a Client Success Manager. Maggie brings 7 years of experience of working in Corporate Social Responsibility and managing leaders in supply chain management. She has worked with several of the top Fortune 500 companies developing and executing their internal Code of Conduct. Maggie will be taking part in strategic efforts to boost client engagement and support SpringFour's client deployment efforts. Maggie is bilingual in Spanish and has lived in several countries, including Chile, where she worked in international trade and focused on earthquake relief organizations.
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Dr. J. Michael Collins, Ph.D.
Dr. Collins is a nationally recognized expert in the loss mitigation/foreclosure industry and professor of Consumer Finance at the University of Wisconsin-Madison. His studies on consumer behavior insights focus on the role of information in consumer decision-making, especially for low-income households. Michael has studied consumers in the financial marketplace for more than a decade and has published many articles on consumer responses to foreclosure, the role of default counseling, and the effects of consumer protection policies.
Michael's LinkedIn


I know this video is a little off topic, well okay, it's A LOT off topic, but I thought you could use a little laugh. Not all of you may be cat lovers, but even if you know just a little about cats, or the expressions they give off from time to time, you will get this and hopefully laugh.
Sometimes with this illness, I tend to get too serious for my own good. In a sense, I ketch myself. My OCD used to be about cleaning, but now I find that I will obsess about eating perfect, thinking perfect, or exercising perfect so I feel okay. And honestly, that's not how I should be. That kind of thinking will eventually get me into the same trouble I had BD (Before Diagnosis).
So please, have a laugh, remember what it's like to just feel. We OCD people forget to do that because we are ALWAYS, ALWAYS, ALWAYS trying to strive for perfection.
Oh, and dog lovers, I haven't forgotten about you. How can I? Sport is just as much a part of my life as Onyx! I'll post a "Sad Dog Diary" soon!


Robert "Bob" Dreyfuss is an American investigative journalist and contributing editor for The Nation magazine. His work has appeared in Rolling Stone, The Diplomat, Mother Jones, The American Prospect, TomPaine.com, and other progressive publications. In his book "Devil's Game: How the United States Helped Unleash Fundamentalist Islam (American Empire Project)" published in 2006, Dreyfuss blamed rise of Islamism on the U.S.
Robert Dreyfuss is completely wrong. Islamic fundamentalism does not need help to rise, it nurtures on its Islamic ideology, the doctrine of war, hate, revenge and lack of human evolution. And it was Russia, which long before the U.S. funded Islamists everywhere in the Middle East. Abu Ammar was not a Communist, Hezbollah was not Communist. Even the PKK was not Communist, it took Ocalan decades to create a secular movement, and at the end the Syria war made out of the PKK a communal socialist movement a la American Murray Bookchin. And this only occurred because Russia dropped its support to the PKK in favor of Assad and this gave the U.S. the possibility to fill the gap and enter the Syrian arena from the Kurdish door. In return the Kurds switched their doctrine to become compatible with the U.S. support, the same U.S. they hated and fought for decades when they were supported by Russia. This is a sample of how a doctrine changes with change of alliances or better said when proxies fill a new role.
What strikes me is Iran, the only proxy which never changed its doctrine. The Islamic doctrine of Iran will not change despite its alliance or being used by Russia. Islam is deeply rooted in Iran and will remain as long as Bab Al-Ijtihad remains open and allows it to update Islam a bit.
Back to Dreyfuss, Russia was in Afghanistan and the Mujahideen existed before the U.S. intervention. Already, before Russia and the U.S. thought of supporting and funding Mujahideen, I must clarify that this is the only option most Muslim offer. It is not the case that Muslim want secular democracies and the U.S. and Russia are forcing them to be Mujahideen. Thus, before condemning foreign powers which are exploiting the status quo, you must realize that the status quo is already a disaster: The Islamic doctrine. This is what Muslim offer, and nothing else. Whether in Afghanistan or in Zimbabwe, this is what Muslim want and this is what Muslim offer.
Already in the 20s, Muslim had only Jihad and Mujahideen to offer when the Ottoman Caliphate fell and the last Jihad was called. Hassan Al-Banna founded the Muslim Brotherhood in about 1926-27 to relaunch the Islamic Caliphate against the foreign forces: The United Kingdom and France. Certainly, it was neither a Zionist, nor Soros, nor Clinton or CIA plot. Also Hizb Al-Tahrir which is ISIS, was created in 1953, to establish an Islamic Caliphate. Hezbollah was created in 1982, Iran itself established the Islamic Caliphate in 1979. None of aforementioned was funded or armed by the CIA, Hillary or the Jews. At the opposite, long before the CIA, it was Russia, which funded and armed the Palestinian Fedayeen and Abu Ammar. In Afghanistan, this is what the Afghan offered: Islam fundamentalism. This is how Muslim "struggle" (Youjahidoun – launch Jihad) against foreign forces. This was and still is their choice. Yesterday, Hassan Nasrallah, head of Hezbollah called for Jihad against Trump's decision, and it was not a Zionist or Soros or CIA plot. Also the Sunni who called for Jihad against Trump's decision were not paid by US and Israeli intelligence.
I will republish here my tweets in which I corrected Robert Dreyfuss. Unfortunately, my twitter accounts get permanently suspended because I am being reported by the RIAH network which is trying to protect Sarah Abdallah @sahouraxo from being discarded as a Hezbollah PsyOp.
14/ Why I mentioned #Israel? Long before war in #Afghanistan, #Russia supported Communists & #Islamists to thwart U.S. influence from M.E.
16/ #Russian armed factions in M.E. already in 40s to fight Israel = U.S. & Europe. It armed Communists: Syria, Iraq, Iran, Lebanon, Turkey.
Note: Islamic Fundamentalism does not need your help. It is there and will prevail till Islam is reformed or abolished.


I'd also like to become familiar with reading tab as well. I know a little about tab but would like to know more.
Well, there's not much to explain. It's a pretty clear set of principles, but there's a need to practice at it to become more fluent. Very few banjo players become fluent enough to sight-read tab, the way a lot of piano or violin players can. A certain amount of fluency helps, though, to make sense of Scruggs style, which is not a linear melody, and needs a bit of speed to sound coherent. At camp I can review the principles of tab-reading if enough people need it, but I think of that topic as something that can be learned mostly from a book (Most books have a "how to read tab" section.) I do have some helpful hints, mainly that you get hold of a recording of the tabbed piece, and listen closely. You're looking for more than reproducing a sequence of notes. Tone and feel are a big part of the musicianship. We work on that quite a bit at the camp.


Missed it on E4? Well, there's not getting away from it; here it is from the beginning courtesy of RTE. Former juvenile detention inmate Emily Thorne has become a wealthy young woman and returns to her child-hood home in the Hamptons, a glamorous coastal resort where some of America's richest and most powerful people reside. However, she has no intention of relaxing, but is instead seeking revenge on Victoria and Conrad Grayson, a high-profile couple who framed her father for their crimes - destroying his life in the process. Uber glossy drama, starring Emily VanCamp, Madeleine Stowe, and a load of well dodgy hair pieces.


Concatenating 100 single letter strings.
The results are mixed, as you can clearly see on the graph below.
As expected concatenating a few strings doesn't make a big difference. Doing the same for a lot more does show a big hit for both the StringStream and the sprintf methods. But when combining strings and integers the native addition struggles. The same is true for doubles, but for some reason the StringStream can handle integers efficiently, but not doubles.
Sprintf handles integers and double very well with only a small difference in performance to the scenario with only strings. The StringStream chokes on the doubles even though it handled the integers very nicely. Note that the format in which the StringStream prints the doubles differ from the test, as it cuts off based on precision where the others have a fixed amount of digits that are being printed.
There are a couple of side remarks to be made involving usability. The sprintf method works with c style char arrays, and thus forces you to convert an actual string to and from the c style format. The native + operators only work on strings, and thus you have to do the conversion from numbers yourself. This might be a reason why they perform badly with integers and doubles, but this is something I will investigate in a next blog post. Stringstream does not have any of these downsides and is in my opinion the nicest one to use.


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Mortal Kombat Trailer Promises a Bloody, Action Movie True to the Games
April 16 — get over here!
By Akhil Arora | Updated: 19 February 2021 11:53 IST
Photo Credit: Warner Bros.
Ludi Lin as Liu Kang, Max Huang as Kung Lao in Mortal Kombat movie
First trailer introduces Mortal Kombat movie characters
Mortal Kombat (2021 movie) release date is April 16
Available on HBO Max in the US, in cinemas worldwide
Mortal Kombat trailer is out now — get over here! Warner Bros. Pictures has unveiled a two-and-a-half-minute first trailer for its R-rated (certified "A" in India) adaptation of the Mortal Kombat video game series, which features an action-packed and bloody look at the fantasy movie. In today's age, Mortal Kombat essentially falls into the superhero genre, given the variety of powers at hand here: fire, ice, lightning, dual pair of hands, and more. Aquaman director James Wan is a producer on Mortal Kombat, with Simon McQuoid making his feature directorial debut.
Sonya Blade (Jessica McNamee) reveals at the start of the Mortal Kombat trailer that she first encountered a superhuman on a Brazil mission seven years ago. More importantly, the said superhuman had the same dragon marking as our protagonist, Cole Young (Lewis Tan). Cole believes it's a birthmark, but Jax (Mehcad Brooks) tells him he's been "chosen". Blade adds: "Throughout history, different cultures all over the world reference a great tournament of champions".
The Mortal Kombat trailer below is age-restricted (as Mortal Kombat is R-rated) and will only play if you're signed into YouTube.
As you've no doubt already guessed, this tournament is known as "Mortal Kombat". Enter the fellowship of champions: Sonya (McNamee), Kano (Josh Lawson) who has a laser in one of his eyes, Liu Kang (Ludi Lin) who can control fire like he's been transported from Avatar: The Last Airbender, and Jax (Brooks) who has a pair of cybernetic arms, Kung Lao (Max Huang), and a Lord Raiden (Tadanobu Asano) who can manipulate lightning. This group is tasked with saving Earth, obviously.
The villain introduces himself deep into the Mortal Kombat trailer, and it's obviously the superhuman we're shown at the beginning: Sub-Zero (Joe Taslim). He can do wondrous things with ice, be it creating a sword made of ice or a wall that he then smashes enemies into. In response, his opponent launches a grappling hook and shouts his famous line: "Get over here".
In addition to McNamee, Tan, Brooks, Lawson, Lin, Huang, and Asano, Mortal Kombat also stars Chin Han as Shang Tsung, Hiroyuki Sanada as Scorpion, Sisi Stringer as Mileena, Daniel Nelson as Kabal, Elissa Cadwell as Nitara, Matilda Kimber as Emily Young, and Laura Brent as Alison Young. McQuoid directs off a script by Greg Russo and Dave Callaham. Mortal Kombat is a production of New Line Cinema, Atomic Monster Productions, and Broken Road Productions for Warner Bros.
Mortal Kombat is out April 16 on HBO Max in the US and in cinemas worldwide, including India.
Further reading: Mortal Kombat, Warner Bros, HBO Max, WarnerMedia, New Line Cinema
Akhil Arora Email Akhil
Akhil Arora covers entertainment for Gadgets 360, interviewing stars such as Christian Bale and Anurag Kashyap, covering series premieres, product and service launches across the globe, and looking at American blockbusters and Indian dramas from a global socio-political and feminist perspective. As a Rotten Tomatoes-certified film critic, Akhil has reviewed over 150 movies and TV shows in over half a decade at Gadgets 360. When he is not completely caught up with new film and TV releases, Akhil ...More
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MESSAGE Akhil Arora


In partnership with iHeartRadio, the CT Lottery announced its 5th Annual "Give a Child a Toy, Not a Ticket" Holiday Toy Drive starting November 9th through December 21st. The toy drive helps the CT Lottery spread the Responsible Gambling message that lottery tickets are not suitable gifts for children, while also encouraging toy donations for Connecticut Children's Medical Center.
Since 2008, the CT Lottery has partnered with the International Centre for Youth Gambling Problems and High‐Risk Behaviors at McGill University and the National Council on Problem Gambling (NCPG) during the holidays to promote responsible gifting as part of CT Lottery's commitment to responsible gambling.
"Research has shown that young people report their first gambling experience, on average, around 9-11 years of age, and approximately 80% of high-school aged adolescents report having gambled for money during the past year. Without a doubt, early gambling experiences are a risk factor for later problem gambling," said CT Lottery's Interim Vice President, Chelsea Turner.
Connecticut Children's Medical Center is always in need of toys to help provide comfort and healing to kids who are in the hospital during the holidays, and other times throughout the year. On average, 150 children are treated daily in the hospital's emergency department alone, and each child receives a toy.
Toys are also given to every child who has a procedure, celebrates a birthday or special event; they are used in multiple playrooms throughout the hospital, and utilized as a distraction from pain before shots, tests and surgeries. In total, the yearly need for donated toys is great — 73,000 — ranging from a simple deck of cards or silly bands, to the more substantial, board games and video games.
The CT Lottery reminds the public that purchasers must be 18 or older. If you gamble, use your GameSense. If you or someone you know is affected by a gambling problem, please call the CT Council on Problem Gambling's Helpline at 1-888-789-7777 or visit ccpg.org for more information.
Connecticut Children's Medical Center is a nationally recognized, 187-bed not-for-profit children's hospital serving as the primary teaching hospital for the Department of Pediatrics at the University of Connecticut School of Medicine.
With a medical staff of nearly 1,100, practicing in more than 30 specialties, Connecticut Children's is the only free-standing children's hospital in Connecticut that offers comprehensive, world-class health care to children.
For information about Connecticut Children's, visit connecticutchildrens.org or on Facebook (facebook.com/connecticutchildrens) and Twitter (twitter.com/ctchildrens).