#  XMM-Newton and NuSTAR Observations of an Optically Quiescent Quasar

Claire Greenwell School of Physics & Astronomy, University of Southampton,
Highfield, Southampton SO17 1BJ, UK  European Southern Observatory, Karl-
Schwarzschild-Strasse 2, D-85748, Germany  Poshak Gandhi  School of Physics &
Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK
George Lansbury  European Southern Observatory, Karl-Schwarzschild-Strasse 2,
D-85748, Germany  Peter Boorman  Astronomical Institute, Academy of Sciences,
Boční II 1401, CZ-14131 Prague, Czechia  School of Physics & Astronomy,
University of Southampton, Highfield, Southampton SO17 1BJ, UK  Vincenzo
Mainieri  European Southern Observatory, Karl-Schwarzschild-Strasse 2,
D-85748, Germany  Daniel Stern Jet Propulsion Laboratory, California Institute
of Technology, 4800 Oak Grove Drive, Mail Stop 169-221, Pasadena, CA 91109,
USA

###### Abstract

Optically quiescent quasars (OQQs) represent a recently systematised class of
infrared-luminous active galactic nuclei (AGN) which have galaxy-like optical
continua. They may represent an interesting, brief phase in the AGN life
cycle, e.g. either cocooned within high-covering-factor media or indicative of
recent triggering, though their nature remains unclear. Here, we present the
first targeted simultaneous X-ray observations of an OQQ, our previously
identified prototype, SDSS J075139.06+402811.2 at $z$=0.587. The source is
significantly detected over 0.5–16 keV with XMM-Newton and NuSTAR,
unambiguously confirming the presence of current accretion activity. Spectral
modelling yields an intrinsic luminosity $L_{\rm 2-10\,keV}$ $\approx$
4.4$\times$1043 erg s-1, well within the AGN regime, but underluminous
relative to its infrared power. It is lightly obscured, with log $N_{\rm H}$
[cm-2] $\approx$ 22.

Active galactic nuclei (16), X-ray active galactic nuclei (2035), X-ray
astronomy (1810), Surveys (1671), Infrared galaxies (790)

††facilities: XMM-Newton, NuSTAR, SDSS, WISE††software: astropy (Astropy
Collaboration et al., 2013, 2018), xspec (Arnaud, 1996), corner (Foreman-
Mackey, 2016), BXA (Buchner et al., 2014), UltraNest (Buchner, 2021)

##  1 Introduction

Knowledge of the demographics of the AGN population is essential to our
understanding of how they evolve and influence their host galaxies. The
majority of AGN are affected by obscuration, which hides central AGN
signatures (e.g., Ananna et al., 2020). This obscuration can take many forms,
both stable (resulting in diverse AGN classes, e.g. Seyfert 1, Seyfert 2;
Padovani et al., 2017), and transient (some ‘changing’ look AGN (CLAGN), e.g.
Risaliti et al., 2005; Ricci et al., 2016). CLAGN can also present with a
change in intrinsic flux, likely due to change in accretion state (e.g., Stern
et al., 2018). Selecting an unbiased sample of AGN across these properties is
challenging (e.g., Hickox & Alexander, 2018; Asmus et al., 2020), and in this
work we address a gap in current samples which could represent an interesting
and unusual phase of obscuration.

AGN selection in each portion of the electromagnetic spectrum has both
advantages and drawbacks (Brandt & Alexander, 2015; Padovani et al., 2017).
Optical selection, using typical AGN emission lines, can miss heavily obscured
or intrinsically faint objects (Hickox & Alexander, 2018). Infrared (IR)
selection offers the chance to investigate AGN without optical signatures –
the majority of IR emission from AGN is reprocessed in the dusty regions, and
therefore relatively unbiased (Gandhi et al., 2009; Asmus et al., 2015).
Multi-wavelength studies using combinations of large surveys can be used to
select AGN with interesting properties; furthermore extreme, unusual objects
can be found in these vast datasets.

To systematically search for AGN with rare properties, we began an
investigation based on bright, AGN-coloured IR sources from WISE (Wright et
al., 2010) with no clear optical signatures of AGN presence – specifically the
[O iii] $\lambda$5007 Å forbidden line, amongst the strongest lines found in
the narrow-line regions of AGN. This optical–IR disparity would set any such
AGN apart from standard selection techniques. We designate such sources as
‘Optically Quiescent Quasars (OQQs)’. Source powers were chosen to lie in the
quasar regime in order to mitigate host galaxy dilution (Moran et al., 2002)
as a possible cause of the lack of optical emission lines. An in-depth study
of a single, prototypical OQQ was presented in Greenwell et al. (2021), and
this paper demonstrates how X-ray observations provide an important tool for
analysing the intrinsic emission of AGN – particularly in the case of AGN with
atypical properties. The results from our full survey will be discussed in
detail in Greenwell et al. (in prep.).

Two likely physical scenarios that may explain the observed properties of OQQs
are:

  * •

‘Cocooned’ AGN – the optical emission lines are not seen because the AGN is
completely enshrouded in a (presumably transient) ‘cocoon’ of gas and dust.

  * •

‘Young’ AGN – the AGN has recently switched on, and has not yet ionised the
narrow line region (NLR): no [O iii] line has yet been excited.

Both scenarios are interesting from an evolutionary perspective. AGN growth
within fully enshrouding cocoons is suggested by some models (Fabian, 1999),
and OQQs would represent a systematic search for this class of source, though
such candidates appear in various prior sub-samples (e.g., Gandhi et al.,
2002; Hviding et al., 2018). Similarly, in the young AGN scenario, it may be
possible to constrain the duty cycle of NLR excitation (Schawinski et al.,
2015; Gezari et al., 2017). However, the foremost requirement is an
independent confirmation of the AGN nature of OQQs. This is especially
important in the absence of optical AGN spectral signatures, and this is what
we present herein.

##  2 Data

In order to (a) confirm the presence of an AGN, and (b) constrain its spectral
properties, the optimal tracer is X-ray emission. Luminous, nuclear X-ray
radiation is unlikely to originate from any source other than an AGN – intense
star formation may produce (weaker) X-rays, but given the optically quiescent
nature of OQQs ($<$0.4 $M_{\odot}$ per year, stellar mass $\sim$
10${}^{11}M_{\odot}$; Greenwell et al., 2021), sufficient star formation
processes are not likely. XMM-Newton provides good angular resolution and
sensitivity, ideal to examine the soft X-rays. NuSTAR (Harrison et al., 2013)
looks at the harder X-rays, allowing us to measure the intrinsic X-ray
luminosity if SDSS J075139.06+402811.2 (hereafter OQQ J0751+4028) proves to be
heavily obscured. Based on the IR–X-ray relationship (Asmus et al., 2015;
Stern, 2015) we predict that OQQ J0751+4028 should be easily detected (under
the assumption that it is indeed an AGN, and not heavily Compton-thick, at
$z$=0.587, L${}_{2-10\textrm{ keV}}^{\rm predicted}\sim$2.6 $\times$ 1044 erg
s-1), and analysis of its properties should be possible.

This analysis uses the following coordinated observations:

  * •

NuSTAR OBSID 60701009002: 50.6 ks, 2021 September 25 (start time: 12:06:09)

  * •

XMM-Newton OBSID 0884080101: 36.9 ks111After cleaning 16.4/28.3/29.3 ks on
pn/MOS1/MOS2. of exposure, 2021 September 25 (start time: 13:28:37)

The data were reduced using standard recommended selection criteria, including
removal of appropriate background, using the XMM-Newton Science Analysis
Software222http://xmm.esa.int/sas/ and
HEASoft333https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/. The target was
detected significantly with XMM-Newton pn, MOS1 and MOS24440.5-10 keV; net
counts 87/36/65, and with NuSTAR FPMA5553-16 keV; net counts 55. Not detected
in FPMB alone, due to higher background flux.. Source extraction regions were
circles with radii 45 and 20 arcsec for NuSTAR and XMM-Newton respectively.
Background regions were annuli with inner radius 100 arcsec, outer radius 180
arcsec (partially cutout to avoid a chip edge) and circles of radius 90 arcsec
for NuSTAR and XMM-Newton respectively. In optical data (PanSTARRS) it appears
small and red, with no visible morphological disturbances (see Figure 1).

Figure 1: (left) XMM-Newton pn image; (right) PanSTARRS irg bands converted to
RGB image. Green circles have 20 arcsec radius, cyan circle has 6 arcsec
radius; all are centred on the optical source coordinates.

##  3 Methods

The data were fit within xspec (Arnaud, 1996), v.12.12.0 with several models
covering various types and structures of obscuration, with different levels of
complexity. Relevant parameters were allowed to vary freely (although tied
between datasets): normalisation, $\Gamma$ and $N_{\rm H}$.

Under the assumption that OQQ J0751+4028 is an obscured AGN, the most basic
combination of models we might expect to make a reasonable fit to the data is
an absorbed powerlaw (photoelectric absorption at the source redshift and
Compton scattering attenuating an intrinsic powerlaw; see top left panel in
Figure 2). This model can produce an acceptable fit to the data, with light
absorption (see Table 1). However, the best fit $\Gamma$=1.08$\pm$0.16 is
unusually hard for an AGN compared to typical intrinsic spectral indices of
$\Gamma\sim$1.9 (Ricci et al., 2017a). There is some degeneracy between
$N_{\rm H}$ and $\Gamma$ values, so in order to investigate the likelihood of
a more typical intrinsic AGN power law, we fit the same model, but with a
fixed $\Gamma$=1.9. This also produces an acceptable fit, with a slight
increase in log($N_{\rm H}$; cm-2)=21.56 to 22.30 (see Table 1).

Given the consistently hard $\Gamma$ seen in the absorbed powerlaw model we
next investigate two more physically realistic models, still relatively
simple: torus reprocessing (mytorus in coupled mode with covering factor fixed
at 0.5; Murphy & Yaqoob, 2009); and the spherical obscuration (trans model
from BNtorus; Brightman & Nandra, 2011, hereafter BNsphere).

BNsphere represents the physically expected obscuring structure around a
‘Cocooned’ AGN. mytorus does not specifically allow full covering, and is
restricted to $\Gamma\geq$1.4, higher than previously found $\Gamma$ values.
BNsphere is also limited, but to $\Gamma\geq$ 1.0.

Other parameters are fixed to simplify the modelling. mytorus inclination was
set to 90 $\deg$ (i.e., through the torus, to fit with our assumption of an
obscured AGN). BNsphere iron and total elemental abundances were set to solar
values.

The results for the models thus far consistently produce a hard $\Gamma$
($\leq$ 1.5). This would be an unusual intrinsic value for an AGN, and could
indicate that we are underestimating the optical depth of obscuration present
in the system, a possibility also hinted at by the lower than expected
luminosity. None of the models above can produce a log($N_{\rm H}$) greater
than $\sim$22.3, thus we propose an alternative: a thick spherical obscurer
(represented in xspec with BNsphere) in tandem with a scattered fraction
(constant) of the intrinsic powerlaw (zcutoffpl). The scattered fraction
represents a ‘leak’ through Compton thin obscuration from an otherwise Compton
thick sphere. With this we can investigate higher $N_{\rm H}$ values while
still providing a satisfactory fit to the softer X-rays, i.e. dominated by the
scattered powerlaw rather than a Compton hump. Here we show the results with
scattering fraction fixed at 12%, which produces an intrinsic X-ray luminosity
close to that predicted from the 12 µm luminosity.

Fixing the value of $\Gamma$ makes a firm assumption about the nature of the
intrinsic AGN emission, which we can make less stringent with Bayesian X-ray
Analysis (BXA) (Buchner et al., 2014). We can include knowledge about the
likely physical characteristics by selecting an appropriate prior: a Gaussian
prior for $\Gamma$666$N_{\rm H}$ and normalisation have log uniform priors. is
appropriate as it allows a physically motivated preference towards likely
values, and excludes unphysical values. We try (a) a loose Gaussian prior:
$\Gamma$=2.0$\pm$0.3; and (b) a stricter Gaussian prior $\Gamma$=1.9$\pm$0.1.
As shown in Table 1, these both produce an acceptable fit to the data but
struggle to produce a $\Gamma$ value not unusually hard for an AGN. We can use
the Bayesian evidence to compare the models, and therefore determine which is
most likely to have produced the observed data.

The final set of models we compare is: (a) cabs*zwabs*pow: with uniform,
single value and Gaussian priors on $\Gamma$; (b) mytorus; (c)
BNsphere777BNtorus is known to have inaccuracies in the reflected component
(e.g. Baloković et al., 2018); here we only consider the spherical component
with no opening angle which should not be affected.; and (d) ‘leaky sphere’.

Table 1: Spectral modelling results. Column details: (1) xspec model; (2) $\Gamma$ prior; (3) $\Gamma$; (4) $N_{\rm H}$; (5) ‘sphere’ $N_{\rm H}$; (6) unabsorbed 2-10 keV luminosity; (7) fit statistic; (8) Bayes factor compared to BNsphere. Model |  $\Gamma$ prior | $\Gamma$ | $\log N_{\rm H}$ | $\log N_{\rm H,sphere}$ | $\log L_{2-10\textrm{ keV}}$ | cstat/d.o.f. | Bayes factor
---|---|---|---|---|---|---|---
|  |  | (cm-2) | (cm-2) | (erg s-1) |  | (normalised)
cabs*zwabs*pow | Uniform | 0.98${}_{-0.09}^{+0.18}$ | 21.62${}_{-0.44}^{+0.27}$ |  | 43.64$\pm$0.04 | 334.1/377 | –
cabs*zwabs*pow | Fixed 1.9 | 1.90 | 22.30${}_{-0.11}^{+0.08}$ |  | 43.68$\pm$0.05 | 346.2/378 | 31.6
cabs*zwabs*pow | 1.9$\pm$0.1 | 1.79${}_{-0.10}^{+0.09}$ | 22.26${}_{-0.13}^{+0.08}$ |  | 43.67$\pm$0.05 | 337.7/377 | 12.6
cabs*zwabs*pow | 2.0$\pm$0.3 | 1.26${}_{-0.16}^{+0.25}$ | 22.03${}_{-0.41}^{+0.15}$ |  | 43.64$\pm$0.05 | 334.1/377 | 1.6
mytorus | 2.0$\pm$0.3 | 1.47${}_{-0.08}^{+0.17}$ | 22.05${}_{-0.00}^{+0.12}$ |  | 43.65$\pm$0.04 | 336.6/377 | 2.0
BNsphere | 2.0$\pm$0.3 | 1.32${}_{-0.19}^{+0.21}$ | 21.95${}_{-0.36}^{+0.15}$ |  | 43.64$\pm$0.05 | 334.1/377 | best ($\equiv$1.0)
‘leaky sphere’, 12% | 2.0$\pm$0.3 | 2.19${}_{-0.22}^{-0.18}$ | 22.26${}_{-0.17}^{-0.10}$ | 24.08${}_{-0.14}^{-0.14}$ | 44.45$\pm$0.09 | 341.9/376 | 6.3

##  4 Results

Across all models, the results show that the data can be explained by an
obscured AGN. The parameters vary, and in some cases may indicate unusual
values, but all are consistent with the presence of an AGN. Full results for
all models are shown in Table 1. None of the first six models show significant
residuals, except possibly towards the hard end, and all are reasonable fits
to the data (see Figure 2).

The preferred solution according to the Bayes factors is BNsphere (Table
1)888cabs*zwabs*pow with uniform prior fit is discarded from this point; the
lack of constraint allows values of $\Gamma$ that are not physically likely..
Comparison of (a) BNsphere and (b) ‘leaky sphere’ (scattering fraction 12%)
shows that LS is not favoured. However, it is also not strongly counter-
indicated (i.e. the relative Bayes factor is low999A value of 6.3 is
‘substantial evidence’ in favour of BNsphere, but not decisive, according to
the Jeffreys scale (Buchner et al., 2014).).

BNsphere returns a preferred $\Gamma$=1.32${}^{+0.21}_{-0.19}$ — unusually
hard but not impossible for an AGN (e.g.; Ricci et al., 2017a) — and log
($N_{\rm H}$ / cm-2) = 21.95 (see Figure 3). Forcing $\Gamma$ to a more
typical AGN value of 1.9 increases the log($N_{\rm H}$ / cm-2) slightly to
22.3, but does not significantly affect the intrinsic luminosity (see Figure
3). The 12% ‘leaky sphere’ model produces a softer $\Gamma$ and, if closer to
the truth, may imply a luminosity much closer to expected.

Figure 2: Spectra and ratio between data and model for (top) cabs*zwabs*pow,
$\Gamma$=1.79; (middle) BNsphere, $\Gamma$=1.35; (bottom) ‘leaky sphere’,
$\Gamma$=2.19. Data sShown is XMM-Newton-pn (black), XMM-Newton-MOS (red) and
NuSTAR FPMA (blue), binned to a minimum of 2 counts per bin.

That BNsphere is a reasonable fit to the data implies that the ‘cocooned AGN’
scenario may be a feasible explanation for the observed properties. Obscuring
material relatively close to the AGN may prevent ionizing radiation from
within reaching farther out, and thus no narrow [O iii] emission. We can also
consider a situation where the NLR exists within a cocoon on intermediate
scales between the torus and the inner galaxy (perhaps $\sim$ tens of pc),
just large enough to cocoon the inner NLRDepending on the gas–to–dust ratio in
the obscuring material, relatively thin columns may be sufficient to extinct
any [O iii]. Based on the [O iii] deficit between the general OQQ population
and QSO2s (Greenwell et al., in prep.), a median $A_{\rm V}$ = 4.7 mag is
sufficient to extinct the theoretical [O iii] line. This is equivalent to an
NLR obscuring neutral gas column density of log($N_{\rm H}$/cm-2)$\sim$ 22.8
(assuming gas–to–dust ratios in AGN environments from Maiolino et al., 2001).
This is higher than found in this analysis; however, the NLR–obscuring column
is distinct from the line of sight X-ray–obscuring column, which may explain
this difference.

The Fe K$\alpha$ line (rest energy 6.4 keV) observed in many AGN spectra (e.g.
Nandra, 2006) originates from reprocessing of AGN emission in optically thick
obscuring matter. For lightly obscured AGN, Shu et al. (2010) find a
relationship between detected narrow Fe K$\alpha$ EW and unabsorbed 2-10 keV
luminosity101010With large scatter, and from higher resolution Chandra data.,
which we can use to roughly estimate an expected Fe K$\alpha$ EW of 45 eV. We
place an upper limit on the equivalent width (EW) of a putative narrow line by
adding an unresolved Gaussian component to our transmission spectrum, with a
width of 0.1 keV, finding an EW$\lesssim$26 eV – a low value that implies no
line is likely to be present, further reinforcing the conclusion that OQQ
J0751+4028 is only lightly obscured.

The intrinsic rest frame 2-10 keV luminosity (according to BNsphere) is 4.39
$\times$ 1043 erg s-1. The IR luminosity (1.30 $\times$ 1045 erg s-1 at 12 µm)
of OQQ J0751+4028 implies a 2-10 keV luminosity of 2.61 $\times$ 1044 erg s-1
(from the 6 µm/2-10 keV relation; Stern, 2015). Comparing these values, we
find that the unabsorbed luminosity is $\sim$6 times lower than expected, but
still easily above the threshold of 1042-43 erg s-1 generally accepted for an
AGN. In Figure 4 we compare the properties of OQQ J0751+4028 against a sample
of Type 2 QSOs selected from SDSS with significant [O iii] emission (QSO2s;
Reyes et al., 2008; Yuan et al., 2016). Figure 4 shows that OQQ J0751+4028
lies below the IR-predicted values from Asmus et al. (2015) or Stern (2015),
and also below the majority of QSO2s, which tend to fall closer to their
predicted values. Figure 4 (right hand panel) shows the measured X-ray
luminosities of the QSO2s, along with the reported [O iii]/X-ray relationship
from Lamastra et al. (2009) – the majority of QSO2s lie close to the empirical
prediction, but OQQ J0751+4028 is far from typical. Conversely, if we consider
the ‘leaky sphere’ model, the intrinsic X-ray luminosity may be closer to IR-
predicted expectations (see Table 1); however, it would be further offset from
the [O iii]/X-ray relationship.

Figure 3: Corner plot of results with: (a) cabs*zwabs*pow, restrictive prior
on $\Gamma$ (blue); (b) BNsphere, physically representative prior on $\Gamma$
(orange), (c) cabs*zwabs*pow, fixed $\Gamma$=1.9 (green). Best fit values for
each parameter are shown with a solid line. (top right) $L_{2-10}$ vs.
$\Gamma$ contour with the IR-predicted luminosity shown (Stern, 2015, dashed
line) – the luminosity contours for the lightly obscured models are decisively
below this level. Also shown are the results for the 12% scattered ‘leaky
sphere’, which is closer to predicted (pink). Figure 4: A comparison between
OQQ J0751+4028 and QSO2s: (left) unabsorbed 2-10 keV luminosity against 12 µm
luminosity. X-ray luminosities for QSO2s are from Vignali et al. (2006) (V06;
green diamonds), Vignali et al. (2010) (V10; orange diamonds), and Lamastra et
al. (2009) (L09; pink diamonds). Relationships from Asmus et al. (2015, A15),
and Stern (2015, S15; 12 µm luminosities were converted to 6µm luminosities
using a relationship derived from the QSO template of ()), are shown as grey
lines. (right) unabsorbed 2-10 keV luminosity against [O iii] luminosity, with
the relationship from Lamastra et al. (2009, L09).

##  5 Discussion

One important aim of this work is to place OQQ J0751+4028 (and in the future,
its fellow OQQs) into context with the wider ranks of AGN. We begin by
considering what the results from this X-ray study allow us to infer about the
intrinsic nature of this object. Crucially, the absorption-corrected
luminosity shows that OQQ J0751+4028 is an AGN, regardless of the specific
best-fit model that we adopt. This confirms the presence of ongoing accretion
activity, and gives credence to our IR selection, despite the apparent optical
quiescence.

OQQ J0751+4028 must be obscured in X-rays, but is less likely to be Compton
thick than thin. The Bayes factor for the highly obscured ‘leaky sphere’
compared to the lightly obscured BNsphere is $\sim$6: a less likely fit but
not decisively so. Recalling from the introduction our suggested scenarios
regarding the nature of an optically quiescent AGN (‘cocooned’ and ‘young’
AGN), we can only conclude at this stage that both remain possible. Nuclear
optical extinction is also required in both scenarios in order to hide the
broad line region, which we do not see.

The light obscuration we observe could be a more physically likely possibility
for enshrouding material than optically thick material, supporting the idea of
a ‘cocooned’ AGN, or similar to larger-scale host obscuration (e.g., Buchner &
Bauer, 2017). This interpretation could be consistent with a low intrinsic
X-ray luminosity AGN if the Eddington ratio is low, as higher intensity AGN
are associated with lower covering factors (e.g., Ricci et al., 2017b).

An AGN in the process of switching on (a ‘young’ AGN) might also show weak
X-ray emission as it transitions to full accretion power. Kollatschny et al.
(2020) present the opposite case – a switching off AGN – in which they see a
dramatic decrease in observed X-ray luminosity concurrent with a change in
type from Seyfert 1 to 1.9 (i.e. a reduction in the broad emission lines, but
still with clear narrow lines). They find no evidence that this change is
caused by absorption, indicating that it is an intrinsic luminosity change.
Reversing this, we might expect to see the X-ray increase before the
appearance of narrow lines.

Finally, we must consider the possibility that OQQ J0751+4028 is a fully
‘mature’ AGN intrinsically lacking [O iii]. Analysis of relationships between
various emission-line properties of AGN has shown that many of these
properties correlate (Eigenvector 1; Boroson & Green, 1992). Shen & Ho (2014)
show that the observed anti-correlation between [O iii] and the relative
strength of Fe II emission can be explained by changes in Eddington ratio; an
AGN seen to lack [O iii] could then be explained by a very high accretion
rate. The higher $\Gamma$ and intrinsic luminosities of the ‘Leaky Sphere’
model may suggest this to be the case, however a low ‘leak fraction’ would be
required and the fit statistics indicate this is unlikely. The stellar mass of
OQQ J0751+4028, while uncertain, implies a high BH mass ($\sim 5\times
10^{8}M_{\odot}$; Kormendy & Ho, 2013), and consequently a very high
luminosity to reach Eddington accretion levels – higher than seen in the WISE
measurements.

OQQ-like objects are not new. For example, other groups of AGN that have
notable similarities to OQQs include weak line quasars (WLQs) with weak X-ray
emission and weak or absent emission lines (e.g., Wu et al., 2012), and X-ray
bright, optically normal galaxies (XBONGs) selected as AGN in X-rays, but
showing no optical AGN signatures. In some cases, this is due to dilution by
bright host galaxies of lower luminosity AGN (Moran et al., 2002) – in
contrast to the OQQs, where AGN emission in the IR is bright, and dominates
over their hosts.

Our OQQ selection is a first attempt to systematically search for this class
of optically quiescent AGN and our work unambiguously establishes that some
AGN can present bright ongoing nuclear accretion activity in X-rays, yet show
no signs of this in the optical. Details of our full sample will be presented
in Greenwell et al. (in prep.).

##  6 Summary

We present the first targeted, simultaneous, hard and soft X-ray observations
of an optically quiescent quasar, demonstrating unequivocally that OQQ
J0751+4028 is an AGN. It is lightly obscured ($N_{\rm H}$ $\approx$ 1022 cm-2)
and, while bright enough to confirm the presence of an AGN (L${}_{2-10\textrm{
keV}}$=4.37 $\times$ 1043 erg s-1), our most likely model suggests it is less
X-ray luminous than would be expected given its IR properties, and in
comparison to an [O iii]-bright population. This result shows conclusively
that the OQQ selection technique introduced in Greenwell et al. (2021), and
discussed in depth in Greenwell et al. (in prep.), can uncover previously
unknown AGN.

We thank the referee for their helpful comments and suggestions. This research
is funded by UKRI. CG is supported by a University of Southampton Mayflower
studentship. PG acknowledges support from STFC and a UGC-UKIERI Thematic
partnership (STFC grant number ST/V001000/1). PGB acknowledges financial
support from the Czech Science Foundation project No. 22-22643S. This
publication makes use of data products from WISE which is a project of
University of California, Los Angeles, and the Jet Propulsion Laboratory
(JPL)/California Institute of Technology (Caltech), funded by the National
Aeronautics and Space Administration (NASA). Funding for SDSS-III has been
provided by the Alfred P. Sloan Foundation, the Participating Institutions,
the National Science Foundation, and the U.S. Department of Energy Office of
Science. The SDSS-III web site is http://www.sdss3.org/. This work made use of
observations obtained with XMM-Newton, an ESA science mission with instruments
and contributions directly funded by ESA Member States and NASA. This research
made use of data from the NuSTAR mission, a project led by Caltech, managed by
JPL, and funded by NASA. This research has made use of the NuSTAR Data
Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center
(ASDC, Italy) and the Caltech (USA). The NASA/IPAC Infrared Science Archive
(IRSA) operated by JPL under contract with NASA was used. This research has
made use of data obtained through the High Energy Astrophysics Science Archive
Research Center Online Service, provided by the NASA/Goddard Space Flight
Center.

##  Appendix A xspec Models

The models used in xspec are as follows:

  * •

Absorbed powerlaw: constant*phabs*cabs*zwabs*pow

  * •

mytorus: constant*phabs(zpowerlw*etable{mytorus_Ezero_v00.fits} \+
constant*atable{mytorus_scatteredH500_v00.fits})

  * •

BNsphere: constant*phabs*atable{sphere0708.fits}

  * •

‘leaky sphere’:
constant*phabs*(atable{sphere0708.fits}+constant*zwabs*zcutoffpl)

  * •

Absorbed powerlaw with neutral iron line:
constant*phabs(cabs*zwabs*powerlaw+zgauss)

All models include Galactic absorption (phabs) of $N_{\rm H}$=5.6 $\times$
1020 cm-2 (HI4PI Collaboration et al., 2016). A cross calibration constant of
0.93:1.02:0.98:1.00 (e.g. Madsen et al., 2015) was used for XMM-
Newton(pn):XMM-Newton(MOS1):XMM-Newton(MOS2):NuSTAR; this was fixed because
the observations were simultaneous. Spectra were binned to 3/1 counts per bin
for NuSTAR/XMM-Newton, and fit with wstat (Wachter et al., 1979) – the version
of cstat (Cash, 1979) used by xspec when a background is included:
https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node318.html#AppendixStatistics..

##  Appendix B Data Availability

The optical and IR data underlying this article are publicly available from
the WISE All-Sky Survey (DOI 10.26131/IRSA1) and SDSS DR15. X-ray data are
currently in the proprietary period, but will become publically available with
the Observation IDs listed above.

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algorithm[ALG.]

††thanks: Correspondence should be addressed to
<EMAIL_ADDRESS>
# Optofluidic adaptive optics in multi-photon microscopy

Maximilian Sohmen *  — Institute for Biomedical Physics, Medical University of
Innsbruck, 6020 Innsbruck, Austria  Juan D. Muñoz-Bolaños *  — Institute for
Biomedical Physics, Medical University of Innsbruck, 6020 Innsbruck, Austria
Pouya Rajaeipour *  — Phaseform GmbH, 79110 Freiburg, Germany  Monika Ritsch-
Marte *  — Institute for Biomedical Physics, Medical University of Innsbruck,
6020 Innsbruck, Austria  Çağlar Ataman *  — Phaseform GmbH, 79110 Freiburg,
Germany  Microsystems for Biomedical Imaging Laboratory, Department of
Microsystems Engineering, University of Freiburg, 79110 Freiburg, Germany
Alexander Jesacher *  — Institute for Biomedical Physics, Medical University
of Innsbruck, 6020 Innsbruck, Austria

###### Abstract

Adaptive optics in combination with multi-photon techniques is a powerful
approach to image deep into a specimen. Remarkably, virtually all adaptive
optics schemes today rely on wavefront modulators which are reflective,
diffractive, or both. This, however, can pose a severe limitation for
applications. Here, we present a fast and robust sensorless adaptive optics
scheme adapted for transmissive wavefront modulators. We study our scheme in
numerical simulations and in experiments with a novel, optofluidic wavefront
shaping device which is transmissive, refractive, polarisation-independent and
broadband. We demonstrate scatter correction of two”=photon”=excited
fluorescence images of microbeads as well as brain cells and benchmark our
device against a liquid-crystal spatial light modulator. Our method and
technology could open new routes for adaptive optics in scenarios where
previously the restriction to reflective and diffractive devices may have
staggered innovation and progress.

##  I Introduction

Optical microscopy is a potent and indispensable tool in many branches of
science, in particular for biomedical research. However, due to light
scattering inside the sample, conventional light microscopy is typically
limited to the sample’s most superficial tens of micrometres. Prominent
approaches to lift this limitation and increase the imaging depth include
multi-photon techniques [1] and adaptive optics (AO) [2, 3]. For the present
work, we rely on a combination of both, two-photon excited fluorescence (TPEF)
microscopy as well as sensorless AO – an approach that has been followed
successfully in a variety of different ways in the recent past, by many groups
worldwide [4, 5, 6, 7, 8, 9, 10, 11], including ours [12, 13, 14].

AO relies on active shaping of a light field’s wavefront to improve image
quality. The overwhelming majority of wavefront shaping devices on the market
today – such as deformable mirrors, liquid”=crystal”=on”=silicon spatial light
modulators (LCoS-SLMs), or microoptoelectromechanical systems (MOEMS) [15, 16]
– operates in reflection rather than transmission of a light field. In
addition, many of these devices (of the above, e.g., LCoS-SLMs and MOEMS) are
diffractive rather than reflective optical elements. While being reflective or
diffractive is no fundamental problem in numerous cases, in others – some of
them very relevant for applications – it can present a serious challenge.

A novel kind of transmissive, refractive wavefront modulator that may present
a well-suited alternative for such scenarios is the deformable phase plate
(DPP), a transparent multi-electrode optofluidic device recently developed by
some of us [17, 18, 19, 20, 21]. The following three aspects may help to
illustrate where the DPP can offer advantages compared to established
wavefront modulators.

First, device integration: compared to a reflective device, integrating the
DPP into a pre-existing (e.g., commercial) imaging system is much easier and
does not require additional beam folding optics. Similarly, stacking several
wavefront modulators in series (as, e.g., in woofer-tweeter arrangements [20]
or for multi-conjugate AO) is far more straightforward using transmissive
elements. Second, polarisation independence: whereas, e.g., liquid-crystal
SLMs can only shape light that is linearly polarised along a specific
direction, the DPP can shape light of arbitrary polarisation. This allows, on
the one hand, to freely combine the DPP with polarisation-optical elements or,
on the other hand, to shape unpolarised light such as the fluorescence from a
microscopy sample. Third, low chromatic dispersion: whereas, by principle,
pixelated holograms – displayed, e.g., on a liquid-crystal SLM or a MOEMS –
are highly dispersive and typically only allow to shape wavelengths up to some
tens of nanometres around a chosen design value, the DPP – with a dispersion
as low as less than 1 mm of fused silica [21] – enables broadband operation.
Two immediate benefits are evident: on the one hand, in applications involving
short laser pulses, a drastic reduction of optical peak intensity due to pulse
dispersion can be avoided. On the other hand, in the imaging context,
broadband operation offers, e.g., to address different fluorophore classes in
parallel using several excitation wavelengths, or to route both excitation
light and returning (even multi-photon-excited) fluorescence signal through
the device on a shared path (e.g., when imaging back onto a pinhole as in
confocal microscopy).

In our opinion, a practical AO approach that seeks to fully exploit the
benefits of the DPP should therefore be guided by the following key criteria:
(i) simple integration – maintaining the possibility to easily insert the DPP
into the optical path of a microscope; (ii) high speed – carrying out a
complete AO correction run should be fast (timescale seconds or less); (iii)
accuracy – measuring and compensating aberrations as accurately as possible;
(iv) robustness and user-friendliness – the corrections should converge
reliably without requiring parameter tweaking by the user, ideally over a wide
range of aberration severity [14].

This work is structured as follows. In Section II, we present our approach to
meet the above criteria (i)–(iv), including a brief description of the DPP
device, our wavefront sensing strategy, and sketches of the optical layout as
well as our AO algorithm. In Section III.1, we compare different algorithm
variants in numerical simulations. In Section III.2, we experimentally
demonstrate correction of strong aberrations through combination of our
sensorless AO algorithm with DPP wavefront shaping. To this end, we present
TPEF microscope images of two kinds of samples, standardised fluorescent beads
as well as fluorescence-labelled brain cells. Finally, we discuss our main
findings (Section IV), give a brief Summary and Outlook (Section V), and
provide information on our Materials and Methods (Section VI).

##  II General approach

Before we proceed to our numerical simulations and experimental results, we
will sketch our general approach and the design considerations that have
guided us in our development process.

###  II.1 The deformable phase plate (DPP)

The DPP is a transparent optofluidic device designed for wavefront modulation
of a light field in transmission [17, 18, 19, 20, 21]. The DPP’s fluid chamber
is formed by a micro-machined ring spacer, placed on a glass substrate and
spanned by a deformable polymeric membrane (see Fig. 1). Channels in the glass
substrate through which the chamber is filled with liquid are sealed after
manufacture. On the glass substrate, contact pads in the periphery
individually connect to 63 transparent electrodes in and around the central
aperture. Application of a voltage between any of these electrodes and the
grounded, conductive membrane gives rise to an electrostatic force which
deforms the membrane. If, consequently, the fluid chamber’s local thickness
changes from $\ell$ to $\ell^{\prime}=\ell+\Delta\ell$, the corresponding
phase shift for a transmitted light field of wavelength $\lambda$ is
$\Delta\varphi=2\pi(\Delta\ell/\lambda)\Delta n$, where $\Delta n$ is the
according difference in refractive index between the fluid and air. While
electrostatic actuation alone would only enable a unidirectional pulling of
the membrane, hydro-mechanical coupling by the liquid inside the sealed
chamber establishes a bidirectional push-pull mechanism, where a positive
displacement in one membrane portion leads to a negative displacement in the
other portions, and vice versa.

Figure 1: The deformable phase plate (DPP). (a) Top-view drawing. Each of the
transparent electrodes in the centre region can be set to an individual
electric potential through connected contact pads. (b) Cross-sectional drawing
and principle of operation. A voltage between an array electrode and the
grounded membrane results in a membrane deformation. The locally varying
optical path length leads to a wavefront modulation of an oncoming light
field. (c) Photograph of the DPP naked and (d) readily assembled in its 30-mm
cage-compatible housing.

The DPP action is independent of polarisation, free from diffractive losses,
nearly non-dispersive, gravity-neutral (see Methods), and shows no observable
hysteresis, allowing for operation with open-loop control. For wavelengths
between 400 and 2200 nm, the present DDP (Delta 7, Phaseform GmbH, Freiburg i.
Br., Germany) shows $>85\,\%$ transmission of power, limited primarily by
Fresnel reflection at uncoated surfaces; only below 400 nm absorption by the
polymeric membrane becomes appreciable. The maximum stroke of the DPP is
highest for low-order Zernike modes, e.g., about $\pm 4$ µm (peak-valley)
optical path difference for a defocus aberration at 632 nm wavelength. The
rise time (10 % to 90 % of set value) of the DPP is about 50 ms, limited by
fluid flow.

###  II.2 Wavefront sensing strategy

The idea of sensorless AO is to conduct many cycles of applying test modes to
the wavefront modulator while measuring their effect on the target signal
(e.g., fluorescence intensity) and to construct a wavefront correction pattern
from this information [2, 3]. In our case, however, faced with the
comparatively long switching time of the DPP, it is desirable to follow a
wavefront sensing strategy where taking fast measurements of individual modes
is decoupled from the limited wavefront modulator speed.

Focus Scanning Holographic Aberration Probing (F” SHARP), as introduced by
Papadopoulos et al. [10], was one of the first methods to employ such a
decoupling. The basic principle of F” SHARP is to split the laser beam for
fluorescence excitation in an interferometer and to vary the angle between the
two interferometer arms – a stronger, static reference beam and a weaker,
scanned probe beam – using a fast piezo mirror. The recorded interferogram
then directly reveals the aberrations accumulated along the optical path to
the sample plane, which can in turn be compensated by a wavefront modulator.
The wavefront modulator itself is kept constant during the (fast) piezo
scanning operation and only has to be switched once per algorithm iteration
(after the aberration field has been determined), wherefore the wavefront
modulator switching time is in general not too limiting for the total
algorithm speed. Besides this speed advantage, F” SHARP exhibits a very robust
operation: in contrast, e.g., to modal wavefront sensing techniques [4, 5],
the F”=SHARP algorithm converges reliably even if the aberrations are
comparatively strong [10].

To-date, F” SHARP-type methods have been used exclusively in combination with
LCoS-SLMs [10, 22, 23, 24], i.e., wavefront modulators that are reflective and
diffractive. Here, we present and test a novel variant fit for use in
combination with transmissive (and, as in case of the DPP, refractive)
wavefront modulators.

###  II.3 Optical layout

A schematic of our optical setup is presented in Fig. 2. This setup is based
on the original F” SHARP implementation [10], yet with two crucial
modifications. First, instead of a Mach-Zehnder, our setup features a
Michelson interferometer, bearing the advantage that distances which are not
common path between the two arms can be kept as short as possible, helping to
minimise relative vibrations, drifts, and alignment maintenance. Second,
instead of shaping only the static reference beam, in our DPP version both,
static reference and scanned probe beam are wavefront-shaped.

Figure 2: Sketch of the optical layout. BSC = (non-polarising) beam splitter
cube, DPP = deformable phase plate, PMT = photomultiplier tube, SLM = spatial
light modulator.

These two modifications greatly simplify integrating F” SHARP into pre-
existing optical setups: the Michelson interferometer, on the one hand, can be
designed as a highly stable and compact add-on module in the early excitation
path; the DPP, on the other hand, being transmissive, can be inserted almost
everywhere along the downstream optical path. In our case, the DPP is located
close to a pupil-conjugate plane (within some millimetres accuracy).

###  II.4 Algorithm outline

Figure 3: Diagrammatic algorithm outline. Overview of critical steps shared
and differing between the original and our F” SHARP variant. Functions with
names ending with an exclamation mark modify their argument. FT!($\ldots$):
Fourier transform; optimise($\ldots$): find the voltages that optimally
reproduce a target phase mask (e.g., in Zernike basis) at given constraints
[17]. IM denotes the influence matrix, u_lim the voltage limit of the DPP
electrodes (see main text).

Figure 3 provides a diagrammatic overview over important algorithm steps
shared and differing between the original and our variant of F” SHARP.

In Step 1, the phase correction mask is initialised flat. In Step 2, by phase-
stepping the piezo in the probe arm at a range of different tip/tilt angles
and measuring the TPEF intensity generated in the object plane, we
interferometrically obtain an estimate of the aberrations in the excitation
path. In Step 3, the field obtained through interferometry is propagated
numerically to the wavefront modulator location (in our case, where the DPP is
pupil-conjugate, this corresponds to a Fourier transform). In Step 4, the old
phase mask (from a previous iteration) is either replaced by the negative new
mask in case only the static beam is shaped (as for F” SHARP with SLM;
abbreviated 1-B), or the new mask is subtracted from the old mask in case both
beams are shaped (as with DPP; abbreviated 2-B). In Step 5, the target phase
mask is prepared for display. This includes minor numerical adjustments such
as, e.g., rotations and flips to account for the relative orientation between
optical elements (e.g., the wavefront modulator and the piezo scan axes). For
diffractive wavefront modulators such as an SLM, the target phase mask needs
to be resized from the number of measured (piezo scan) pixels to the number of
displayed (SLM) pixels. For refractive wavefront modulators such as the DPP,
the target phase mask needs to be phase unwrapped. Subsequently, we decompose
the target phase mask into Zernike modes and determine the DPP electrode
voltages which lead to the closest possible reproduction of this mode
combination, following the optimisation procedure of Ref. [17]. After sending
the update command to the wavefront modulator, we pause in Step 6 until the
device has switched. Afterwards, the algorithm either ends or jumps back to
Step 2 for another iteration.

##  III Results

###  III.1 Numerical simulations

Table 1: F” SHARP variants covered in this work. Variant |  1-B |  2-B |  2-BI
---|---|---|---
number of shaped beams |  1 |  2 |  2
phase unwrapping |  $\times$ |  $\times$ |  ✓
influence matrix |  $\times$ |  $\times$ |  ✓
Zernike decomposition |  $\times$ |  $\times$ |  ✓
Figure 4: Simulated algorithm progress. Comparison of simulation results for
moderate ($L/l_{s}=1,\sigma/d_{0}=1$; left) and high turbidity
($L/l_{s}=3,\sigma/d_{0}=3$; right). (a, b) Examples of the focal-plane
intensity distributions before AO correction, for scatter masks at the
respective turbidity levels. The colour scale represents normalised intensity,
such that the respective maximum value equals the Strehl ratio. For
comparison, the grey dashed circles give the Airy disk diameter
(Ø$/2{}=1.22\,d_{0}$) of a perfect focus. (c, d) Improvement of Strehl ratio
with algorithm iterations for a 2D fluorescent layer sample. The different
methods plotted are F” SHARP correcting one (1-B) or two beams, with (2-BI)
and without (2-B) considering the influence matrix and voltage limits of the
DPP. Iteration 0 corresponds to the value before correction. Markers give the
mean, colour-shaded areas the standard deviation over 100 simulation runs with
different random scatter masks at the respective level of turbidity. (e, f)
Corresponding Strehl ratio improvements assuming a point-like fluorescent
sample.

We have performed numerical simulations of our AO variants to accompany the
experiments presented in the following Section III.2. Our numerical model,
whose general outline is sketched in Fig. 3, is based on the code provided
with Ref. [12]. In brief, we consider an excitation light field – disturbed by
a phase-only scatter mask – which illuminates a fluorescent sample in the
focal plane. Our random scatter masks are located in the pupil, obtained
following the recipe described in Ref. [14], and characterised by two
parameters, a ‘thickness’, $L$, and the width of their spatial-frequency
content, $\sigma$. We state $L$ in units of the photon scattering mean free
path, $l_{s}$; note that in many animal or human tissues photons are scattered
predominantly into the forward direction, such that it typically takes around
ten consecutive scattering events until a photon’s travelling direction
becomes fully randomised (i.e., to enter the diffusive radiation transport
regime) [25, 26]. The spatial frequency distribution of the scatterer is
assumed Gaussian, centred about zero, and its standard deviation, $\sigma$, is
expressed in units of the spatial resolution, $d_{0}=\lambda/(2\,\text{NA})$,
where NA denotes the numerical aperture.

Our simulations follow the algorithmic procedure presented in Section II.4.
For each iteration, we consider $N_{\text{S}}=60$ different piezo mirror
tip/tilt angles (in $k$-space, these can be imagined as the elements within
the incircle of a $10{\times}10$ square grid), which is close to the number of
degrees of freedom of the DPP, 63. We mainly present simulation results for a
maximally unstructured sample – a homogeneous 2D fluorescent layer –, but
complement this with examples for a maximally structured, point-like
fluorescent sample. Note that, generally, the layer sample is ‘tougher’ for
indirect wavefront sensing than the point-like sample. Furthermore, in this
work we aim primarily at high”=signal”=level scenarios, where we can safely
neglect the effect of photon shot noise in our simulations. We numerically
compare three different algorithm variants: F” SHARP correcting one (1-B) or
two beams, with (2-BI) and without (2-B) considering the influence matrix of
the DPP. This influence matrix relates a target phase pattern to the voltages
that need to be applied to the 63 electrodes, thus incorporating the DPP’s
limited voltage (i.e., stroke) and spatial modulation frequency [17]. For the
current DPP driver software, the required format of the target phase pattern
was a vector of Zernike mode amplitudes of length 91 (i.e., up to 11th radial
order). The defining features of all variants are summarised in Table 1.

Figures 4 (a) and (b) illustrate the effect of scatter masks at moderate
($L/l_{s}=1,\sigma/d_{0}=1$) and high turbidity ($L/l_{s}=3,\sigma/d_{0}=3$),
respectively. Compared to a perfect, Airy-shaped focal spot (grey dashed
circle), optical power is spread out over the focal plane. It is intuitively
clear that scanning such a distorted ‘focus’ over a sample will produce a
worse image than a perfect focus. Quantitatively, the deviation from a perfect
focus is captured by a reduced Strehl ratio. Starting from distorted ‘foci’
like in Figs 4 (a, b), successive iterations of our correction algorithm
variants can bring the Strehl ratio back close to unity, restoring an almost
perfect focus. This is plotted in Figs 4 (c, d) for the layer sample. Whereas
at moderate turbidity [Fig. 4 (c)] all three variants exhibit a very similar
performance, reaching a final Strehl ratio of about 0.95, at high turbidity
[Fig. 4 (d)] variants 2-B and 1-B [both 0.8(2)] perform slightly better than
variant 2-BI [0.6(2)]. Here and throughout this work, a character in
parentheses (if present) gives the one-$\sigma$ standard deviation of the last
digit. Figures 4 (e, f) show the corresponding performances for the point-like
sample, where we observe that the algorithms reach their final value much
quicker (not later than after the second iteration). Again, at moderate
turbidity, all methods perform similarly, reaching a final Strehl ratio of
about 0.95, whereas at high turbidity variants 2-B [0.947(2)] and 1-B
[0.87(3)] perform better than variant 2-BI [0.7(1)].

To illustrate how the algorithm performance depends on the scatterer
characteristics (thickness $L$ and spectral width $\sigma$), we present
respective overview simulations for a layer sample in Fig. 5. We compare the
Strehl ratios before AO (a), reached after the 3rd (b, d, f) and after the
10th (c, e, g) algorithm iteration by variants 1-B, 2-B, and 2-BI,
respectively. As marked by the black dotted line in Fig. 5 (a), the turbidity
range covered by our analysis extends substantially beyond the ballistic
($L<l_{s}$) and into the multiple-scattering ($L>l_{s}$) photon travel regime
[26], where ‘traditional’ sensorless AO methods (such as, e.g., the
$3N$-algorithm [27]) typically fail. Figures 5 (b, c) and (d, e) in general
look quite similar and do not hint at stark systematic differences between the
1-B and the 2-B method with respect to the scatterer characteristics.
Comparing them to the 2-BI method [Figs 5 (f, g)], we see that taking the DPP
influence matrix into account leads to a slightly lower performance,
especially at high $L$ and/or $\sigma$. This is plausible, since in general,
the higher $L$ and $\sigma$, the higher will be the stroke (hence, voltage) of
DPP electrodes required to display the unwrapped correction phase mask. The
more of the 63 DPP electrodes clip at the internal voltage limit of 400 V, the
less accurate becomes the compensation pattern, staggering the DPP correction
performance at high turbidity. The percentage of electrodes clipping at their
voltage limit is shown in Figs 5 (h, i).

Figure 5: Survey of simulated algorithm performance with respect to scatterer
characteristics. Strehl ratios (blue colour scale) before correction (left
column), after the 3rd (centre column) and after the 10th (right column)
algorithm iteration for a layer sample, as a function of scatterer thickness,
$L/l_{s}$, and spectral width, $\sigma/d_{0}$. Rows 1–3 correspond to the F”
SHARP variants 1-B, 2-B, and 2-BI, respectively (see main text). In subfigure
(a), the black dotted line marks the crossover from the ballistic to the
multiple-scattering photon travel regime [26], and the white and black cross
correspond to the turbidity levels of the left and right grey box in Fig. 4 4,
respectively. (h, i) Row 4 (red colour scale) shows how many of the DPP
electrodes have reached their voltage limit (‘clip’), in relation to the total
number of 63 electrodes. All data shown are the mean over 15 simulation runs
with different random scatter masks.

###  III.2 Experiments

We analysed the performance of our new AO scatter correction approaches by
experimental fluorescence imaging using a home-built two-photon microscope and
the AO module outlined in Section II.3. We compared the performance of the DPP
and its adapted F” SHARP variant (2-BI) to an LCoS-SLM (HSP1920-500-1200-HSP8,
1920$\times$1152 pixels, pixel size 9.2 µm, Meadowlark Optics, Inc.,
Frederick, CO, USA) with original F” SHARP (1-B), cf. Fig. 2. We investigated
the performance of the AO schemes using two different kinds of samples,
fluorescent beads (Section III.2.1) and brain cells labelled by green
fluorescent protein (GFP, Section III.2.2).

We are aware that due to the big difference in the number of degrees of
freedom between the DPP and the SLM a direct comparison is not strictly
‘fair’; our results should therefore be considered as benchmark tests of a new
technology (which will be further developed in the future) against an
established gold standard.

####  III.2.1 Fluorescent beads

Figure 6: Imaging fluorescent beads. Two-photon images of a sample of
fluorescent beads (Ø 0.5 µm), aberrated by a nail-polish slide (cf. Fig. 2).
The colour scales are common for all subfigures (a–c) and two-photon excited
fluorescence (TPEF) intensities are normalised to the highest occurring value
[here: in (c)]. (a) The beads without AO. The main panel gives the recorded
TPEF intensity in linear (blue) colour scale. The upper right inset is the
same image in logarithmic (red) colour scale, the line plot shows an intensity
cut along the dotted line in linear scale, and the top-left black scale bar
corresponds to 1 µm. The black cross ($\times$) marks the pixel selected for
signal collection in subsequent AO trials. (b–c) The same image window after
application of our AO schemes. (b) F” SHARP using the DPP (blank SLM, 2-BI);
the upper left inset shows the correction phase mask. (c) F” SHARP using the
SLM (blank DPP, 1-B). (d) The amplitudes of fitted Zernike modes (excluding
piston, tip, tilt; in OSA single-indexing scheme [28]) corresponding to the
correction of subfigure (b); see main text.

In a first series of measurements, we tested our methods by imaging of 0.5-µm
diameter fluorescent beads (TetraSpeck T$7284$, Thermo Fisher Scientific,
Inc., Waltham, MA, USA) dryed onto a glass slide, embedded in mounting medium
and covered by a glass slip. To introduce moderate aberrations, we placed a
(nail-polish) scatterer slide in the light path (see Fig. 2 and Methods). To
disentangle different effects, we recorded sets of three different consecutive
measurements. Figure 6 shows a representative example of such a measurement
set, with all subfigures (a–c) sharing the same colour scales and TPEF
intensities normalised to the highest value occurring in the set.

Figure 6 (a) shows a TPEF image of the beads (aberrated by effect of the
scatterer slide) before application of corrective AO, the length of the scale
bar corresponding to 1 µm in the object plane. The main panel shows the
recorded normalised TPEF signal in linear (blue) colour scale, where barely
any structure is visible. Also the intensity cut along the dotted line,
plotted in the lower left inset in linear scale, appears essentially flat.
Only in logarithmic colour scale (upper right inset; red colour scale), some
diffuse patches are discernible and hint at an underlying structure.

In contrast, Figs 6 (b, c) present the identical image window after applying
the DPP and the SLM AO scheme, respectively, each running for 3 iterations and
scanning over $N_{\text{S}}=20{\times}20$ focal points using the piezo mirror.
The exact choice of $N_{\text{S}}$ is largely arbitrary and uncritical for our
conclusions. Note, however, that while in our simulations (where
$N_{\text{S}}<91$) the required switch from a (square) pixel-by-pixel to a
Zernike basis is without consequences, in the experiments (where
$N_{\text{S}}>91$) both the Zernike decomposition of the target phase pattern
as well as the restriction to 63 electrodes have a low-pass filtering effect
and lead to an expected, systematic disadvantage of the DPP compared to the
SLM correction performance.

Figure 6 (b) was recorded after running F” SHARP (variant 2-BI), using solely
the DPP for phase shaping (i.e., leaving the SLM constantly blank). As
described above, the procedure in every algorithm iteration involved
interferometrical retrieval of a corrective phase mask (greyscale inset),
unwrapping, decomposition into Zernike modes, determination of the optimum
electrode voltages using the DPP influence matrix, and feeding the 63 control
voltage values to the DPP. Compared to Fig. 6 (a), a striking improvement in
terms of both signal level as well as structure clarity is observable in Fig.
6 (b). In the main panel as well as in the log-scale inset several distinct
beads are clearly visible. The total signal enhancement, by a factor of
$\eta\sim 9$ (see Methods), is particularly evident in the intensity cut. The
retrieved phase mask leading to this improvement is shown in the upper left
inset of Fig. 6 (b); the magnitudes of fitted Zernike modes (normalised
according to Ref. [28]) passed on for voltage optimisation are shown in the
bar chart, Fig. 6 (d).

In Fig. 6 (c), we show the bead image after our benchmark AO scheme, i.e.,
running F” SHARP using solely the SLM (constant, flat DPP; variant 1-B) and
displaying a correction mask at the native SLM resolution (in the current
case, using a display patch of 950${\times}$950 pixels). Compared to Fig. 6
(a), the signal enhancement in Fig. 6 (c) is by a factor of $\eta\sim 14$.

On the one hand, it seems plausible that the lower signal enhancement observed
for the DPP compared to the SLM is, at least in part, caused by its lower
number of degrees of freedom. On the other hand, contrasting Figs 6 (b) and
(c), it appears that the DPP correction is more ‘homogeneous’ over the field
of view. This is probably the downside of the SLM’s higher number of degrees
of freedom: higher spatial frequency components will enhance the signal inside
the isoplanatic patch, but at the same time reduce the size of the isoplanatic
patch and – since the scatterer is not located in the pupil plane – decrease
the signal outside the isoplanatic patch. Therefore, if for an imaging
application the size of the isoplanatic patch is of high importance, it can be
advantageous to perform AO restricted to low spatial frequencies.

When starting from an aberrated (uncorrected) initial image, it is typically
not clear to the user a priori which pixel should be picked for signal
optimisation [see, e.g., the cross in Fig. 6 (a)]. For typical samples (such
as the beads or brain tissue studied in this work), however, the performance
of an AO algorithm will depend on this choice, since in general between
different pixels determining factors like aberrations or signal-to-noise ratio
are not identical. A practical measure of how much the performance of our
algorithms depends on the particular choice of the target pixel is the
relative spread of enhancement, $\langle\sigma_{\eta}/\eta\rangle$ (see
Methods for definition). We find $\langle\sigma_{\eta}/\eta\rangle\sim 50\,\%$
using the DPP and $\langle\sigma_{\eta}/\eta\rangle\sim 40\,\%$ using the SLM.

####  III.2.2 Brain cells

In a second series of measurements, we have tested our variants by imaging of
microglia in coronal slices of fixed mouse brain (see Methods). We imaged
cells expressing GFP at a depth of about 0.2 mm, such that the light on the
way in and out was aberrated by propagation through brain tissue (without
scatterer slide). For ease of comparison, the brain image data (Fig. 7) were
taken in an identical procedure and are presented in analogous form to the
bead data (Fig. 6) of the previous Section III.2.1.

Figure 7 (a) shows a fluorescence image of the glia cell aberrated by light
scattering in its surrounding tissue, before application of AO. Whereas,
again, neither in the linear scale of normalised TPEF intensity (main panel,
blue) nor in the intensity cut clear structure is visible, the log-scale (red)
inset reveals faint hints of the presence of a cell body. Figures 7 (b, c)
show the same cell after 3 iterations of our respective AO correction methods,
again sampling 20${\times}$20 points around the focus of the strong beam using
the piezo scanner.

Figure 7 (b) shows an image after running F” SHARP (variant 2-BI) using solely
the DPP. A clear improvement in signal level as well as in structure clarity
is found: in the linear-scale main panel as well as in the intensity cut we
observe an enhancement of total signal by a factor of $\eta\sim 5$; especially
in the log-scale inset, besides the pronounced cell soma, fine cellular
processes start to become visible.

Figure 7 (c) shows the image corrected using our SLM benchmark scheme (F”
SHARP variant 1-B). As for the beads, with this method we obtain the visually
clearest image with the highest signal enhancement of $\eta\sim 8$.

Figure 7: Imaging into brain tissue. Two-photon fluorescence images of a
microglia cell expressing GFP, located 0.2 mm deep inside fixed mouse brain
tissue (no scatterer slide). Correction procedures and presentation of data
are analogous to Fig. 6; the scale bar corresponds to 1 µm. (a) The cell
aberrated by light scattering in the surrounding tissue, before correction.
(b) F” SHARP (2-BI) using the DPP. (c) F” SHARP (1-B) using the SLM. (d)
fitted Zernike mode amplitudes for the correction of subfigure (b).

For convenience of comparison, important parameters and results of the
measurement sets presented in Figs 6, 7 are summarised in Table 2.

Table 2: Key characteristics of the experimental data presented in Figs 6, 7. Correction |  none |  DPP |  SLM
---|---|---|---
subfigure |  (a) |  (b) |  (c)
display segments |  |  63 |  $950^{2}$
F” SHARP variant |  |  2-BI |  1-B
$\eta$, beads |  1 |  9 |  14
$\langle\sigma_{\eta}/\eta\rangle$, beads |  |  $\pm 50\,\%$ |  $\pm 40\,\%$
$\eta$, brain cells |  1 |  5 |  8

##  IV Discussion

Let us now assess the correction performance of our F” SHARP variants with
respect to several decisive properties, such as optical stability, dependence
on sample characteristics, correction speed, and others.

Optical stability. Generally, the performance of an F” SHARP”=type technique
drops quickly and substantially if the relative alignment between static
reference and scanned probe beam is suboptimal. Our Michelson layout keeps the
distances which are not common-path between the two beams to a minimum (in our
case, about 4 cm round-trip) and is hence far stabler than a (typically much
larger) Mach-Zehnder interferometer. In our experiments, F” SHARP performance
was observed to be stable over a couple of weeks (possibly longer) without
requiring realignment.

DPP vs LCoS-SLM. Generally, we find that the SLM yields a higher AO correction
performance than the DPP, as expected for several reasons. First, the (around
$7{\times}10^{5}$) SLM pixels imaged into our objective pupil provide far more
than sufficient degrees of freedom for displaying a correction pattern
constructed from 20$\times$20 measured modes, whereas the restriction to 63
DPP electrodes necessarily constitutes a loss of accuracy. Second, in contrast
to the SLM where arbitrary phase shifts can be assigned to each pixel with
high precision, the DPP faces mechanical limitations posed by its elastic
membrane. Third, as discussed later, the steps of phase unwrapping and Zernike
decomposition (currently) needed for DPP F” SHARP can decrease the AO
performance. Nevertheless, as we have seen, in the regimes of turbidity
studied in this work the DPP can deliver an AO performance of similar quality
as the SLM.

Enhancement spread. The relative signal enhancement was found experimentally
to vary by about $40\,\%$ (SLM) to $50\,\%$ (DPP), depending on the exact
choice of target pixel around a fluorescent bead. Thus, if a correction run
does not immediately yield a satisfactory result, it can be worthwhile to try
again with a nearby target pixel.

Role of turbidity. In regimes of moderate turbidity, as introduced by the
scatterer slide (Fig. 6) or about two hundred microns of brain tissue (Fig.
7), our experiments showed an aberration correction performance of the DPP
slightly lower, but on the same order of magnitude as when using the SLM. In
regimes of very high turbidity, beyond the display capabilities of the DPP,
its AO performance drops compared to the SLM.

Role of the sample structure. Our simulations and experience from experiments
confirm that generally, F” SHARP convergence is faster and correction
performance is better for sparse, structured (e.g., beads) than for
unstructured (e.g., layer) samples. This behaviour does not come unexpectedly:
in contrast to a point sample, for a homogeneous layer sample initially the
sum of signal contributions from many speckles in the focal plane is recorded,
each with its individual response to the applied test modes. It thus takes
some iterations until the algorithm ultimately converges onto the strongest
speckle.

Correction speed. In our experiment – currently not highly optimised for speed
(data handling, computations, mirror flyback, etc.) – performing a full F”
SHARP correction typically takes some seconds. Let us estimate the potential
speed after some experimental refinement. For correct actuation of the
$N_{\text{S}}=63$ segments of the DPP, we need to sample (at least)
$N_{\text{S}}$ measurement points in the objective pupil using the piezo
mirror. Let us conservatively assume a signal dwell time of $t_{\text{d}}=0.5$
ms per piezo step and $N_{\text{P}}=3$ phase steps per iteration. Considering
$N_{\text{I}}=3$ iterations and a switching time (including safety margin) of
$t_{\text{s}}=100$ ms for the DPP, we arrive at a minimum total correction
time
$t_{\text{c}}=N_{\text{I}}\,(N_{\text{P}}\,N_{\text{S}}\,t_{\text{d}}+t_{\text{s}})\sim
500$ ms. Hence, achieving F-SHARP AO corrections with the DPP in under a
second seems well within reach. This can be contrasted to the time needed for
obtaining a DPP correction using a ‘traditional’ sensorless AO method such as
the $3N$-algorithm [27]. Assuming a case where this algorithm converges, we
get
$t_{\text{c}}=3\,N_{\text{I}}\,N_{\text{S}}\,(t_{\text{d}}+t_{\text{s}})\sim
57$ s, clearly highlighting the advantage of the F-SHARP procedure.

### Identified challenges

Phase unwrapping. We have found in our experiments and simulations that phase
unwrapping (as necessary when working with a refractive wavefront modulator
such as the DPP) is a critical step which can, if accuracy is insufficient,
seriously disturb the AO performance. Especially when noise is present,
standard unwrapping routines often fail to deliver satisfactory results.
However, we have made good experience using more advanced unwrapping methods
based on network programming [29] or on the transport of intensity equation
[30].

Zernike decomposition. We know from numerical simulations that an intermediate
change from pixel”=by”=pixel to Zernike basis (variant 2-BI), as currently
required in our experiments [Figs 6 (b), 7 (b)] for technical reasons, is in
general detrimental for the F” SHARP performance. The reason is that the
Zernike fitting step (especially in combination with imperfect phase
unwrapping) leads to a higher percentage of DPP electrodes clipping at the
voltage limit, and hence a higher discrepancy between target and displayed
phase mask. We therefore expect that our experimental results could be
improved even further by implementing a DPP driver that does not require
intermediate Zernike fitting.

Device limitations. The present DPP model features 63 electrodes, which allow
for a reasonable F” SHARP correction performance in moderately turbid regimes.
To correct for scatterers of a greater thickness, $L$, the DPP would require
larger stroke. To correct for higher spatial frequencies (e.g., larger
$\sigma$), the DPP would additionally require a finer resolution, i.e., a
larger number of actuator electrodes.

##  V Summary & Outlook

To conclude, we have demonstrated scatter correction for multi-photon
microscopy using a transmissive, refractive wavefront modulator, the
optofluidic deformable phase plate (DPP). We have developed a sensorless
adaptive optics approach based on a compact and stable Michelson
interferometer in combination with a robust, modified F”=SHARP”=type
algorithm, which enables fast correction even when using speed-limited
wavefront modulators such as the DPP. In numerical simulations and experiments
we have investigated the AO performance with respect to important experimental
parameters such as the number of algorithm iterations, sample type, and
turbidity regime, and have benchmarked the DPP against an LCoS-SLM. We have
shown that our DPP AO scheme yields significant image improvements for two
common microscopy samples suffering from light scattering, fluorescent beads
and GFP-labelled brain cells, and have observed a correction performance which
is lower, but altogether comparable to an LCoS-SLM.

At this point, let us emphasise again that the DPP itself is still a young
development which will surely see further technological improvements in the
near future, but also recall the primary aim of this work: not to prove
superiority of the DPP over an LCoS-SLM, but to demonstrate that F” SHARP
adaptive optics using a DPP is feasible, and hence can present an alternative
for applications where employing a reflective/””diffractive wavefront
modulator is inconvenient or even impossible.

We see great potential for the DPP in combination with our F” SHARP variant as
an add-on AO system which can easily be fitted into pre-existing (e.g.,
commercial) imaging systems, where a reflective device typically can be
accommodated only with severe difficulty. Near-term directions for future
research include implementing a DPP driver which does not require a basis
change of the target phase mask into Zernike modes. Ideally, the DPP influence
matrix (which relates the target phase mask to the optimal individual
electrode voltages) should be constructed directly in the basis of mechanical
eigenmodes of the DPP polymeric membrane. This is expected to lead to a lower
percentage of electrodes clipping at the voltage limit and hence to better –
and possibly faster converging – AO corrections. Longer-term research goals
include the development of next-generation DPP devices featuring a higher
number of electrodes (i.e., shapeable modes) and/or larger stroke, which would
allow to address AO regimes of even higher turbidity, or devices with faster
settling times.

##  VI Materials & Methods

Laser source. For our experiments, we used a mode-locked Ti:sapphire laser
(MaiTai DeepSee, MKS Spectra-Physics, Andover, MA, USA) with about 100 fs
pulse duration, a centre wavelength $\lambda_{l}$ tunable from 700 to 1100 nm,
and a maximum time-averaged power of about 200 mW in the sample plane. In the
experiments presented in this work, we set our laser centre wavelength to
$\lambda_{l}=800$ nm for the bead images and to $\lambda_{l}=900$ nm for the
glia cell images.

Imaging system. For general aspects of our TPEF microscopy setup, see Refs
[12, 13]. In brief, our laser beam is adjusted in intensity and diameter,
passed through the optical setup sketched in Fig. 2, through a dichroic
mirror, and focused by the objective lens (XLUMPLFLN20XW, $\text{NA}=1$, water
immersion, Olympus Corp., Tokyo, Japan) into the sample plane. The epi-TPEF
signal is collected by the objective, reflected by the dichroic mirror and
focused onto a photomultiplier tube (H10769A-40, Hamamatsu Photonics K.K.,
Hamamatsu, Japan) operated in photon counting mode.

DPP mounting. The electromechanical structure of the current DPP is designed
such that it performs virtually identically in vertical and horizontal
orientation, i.e., gravitational sag is uncritical [21]. Nevertheless, for our
measurements the DPP was mounted in vertical orientation inside a 30-mm cage
system, so any potentially detrimental gravity effects would have been
maximal.

Vibration management. Our experiment is set up on a standard optical table
with pneumatic vibration isolation. We used standard optomechanics and did not
take higher vibration prevention efforts than usual for optics experiments.

Mouse brain samples. The brain cells shown in this work were resting
CX3Cr-1GFP microglia in coronal slices of mouse brain fixed by perfusion (cf.
Refs [12, 14] for details), placed on a microscopy slide, embedded in mounting
medium, and covered by a glass slip. While the fresh brain slices were
initially cut to a thickness of around 0.6 mm, until the time of recording the
images shown in Fig. 7 (some weeks later) the slices were – presumably by
shrinkage due to evaporation of water – reduced to a maximum thickness of
around 0.2 mm, which is the depth we state in the main text. However, this
reduction of thickness by a factor of around three might explain why the
scattering seems severe for a depth of ‘only’ 0.2 mm.

Optional scatterer slide. The scatterer slide was prepared through rough
manual application of transparent nail polish to a glass slide and letting
dry. It was subsequently placed in the excitation path in conjugate position
to a plane in the focusing cone of the objective lens (cf. Fig. 2). Being
located before the dichroic mirror, the aberrations by the nail polish slide
affect only the excitation light, not the emitted fluorescence light. However,
since for signal recording we collect all photons emitted into our objective’s
numerical aperture (without, e.g., re-imaging onto a pinhole as in confocal
microscopy), this already captures the critical difficulty for typical multi-
photon imaging applications.

Signal enhancement. We calculate the enhancement factor for subfigure (x)
relative to subfigure (a) in the image set as
$\eta_{x}=\max_{m}{(I_{x})}/\max_{m}{(I_{a})}$, where $\max_{m}{(\ldots)}$ is
the mean over the respective brightest $m=9$ pixels of the image.

Relative spread of enhancement. To assess the variation of the AO algorithm
performance with the choice of target pixel, we investigated 5 different beads
of the same kind as shown in Fig. 6. For each bead, 3 pairs of measurements
were taken. Each pair of measurements consisted of (i) picking a new target
pixel in the region where the bead is suspected, (ii) running F” SHARP with
the SLM (variant 1-B), and then (iii) anew with the DPP (variant 2-BI). Note
that by interleaving measurements with SLM and DPP we have aimed to mitigate
systematic errors due to, e.g., fluorophore bleaching. From the respective 3
runs per bead we calculate the relative standard deviation of enhancement,
$\sigma_{\eta}/\eta$, for both variants. Finally, we compute the corresponding
mean values over the five beads, $\langle\sigma_{\eta}/\eta\rangle$.

## Conflict of Interest Statement

The Innsbruck team declares that its research was conducted in the absence of
any commercial or financial relationships that could be construed as a
potential conflict of interest. Members of the Freiburg team are with the
commercial company Phaseform GmbH.

## Author Contributions

The Innsbruck team conceived, assembled, and conducted the experiments. M.S.
and J.D.M.B. took the experimental data. M.S. and A.J. performed the numerical
simulations. M.S. wrote the manuscript with input from all other authors. The
Freiburg team provided the DPP device, practical advice on how to operate it,
the DPP driver software, and valuable input for Section II.1.

## Funding

The Innsbruck team acknowledges funding from the Austrian Science Fund (FWF)
under the grant numbers P32146-N36, M 3060-NBL, and I3984.

## Acknowledgements

We would like to thank Kai K. Kummer and Jeiny Luna Choconta, Institute for
Physiology, Medical University of Innsbruck, for preparing the brain sample.

## Data Availability Statement

The data sets presented in this work are willingly available upon reasonable
request.

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