1 Max Planck Institute for Gravitational Physics (Albert Einstein Institute),
Callinstraße 38, 30167 Hannover, Germany
2 Institut für Gravitationsphysik der Leibniz Universität Hannover,
Callinstraße 38, 30167 Hannover, Germany
3 Fraunhofer Institute for Applied Optics and Precision Engineering,
Albert-Einstein-Str. 7, 07745 Jena, Germany
4 Institute of Applied Physics, Abbe Center of Photonics,
Friedrich-Schiller-Universität Jena, Albert-Einstein-Str. 15, 07745 Jena,
Germany
5 Institut für Experimentalphysik,
Luruper Chaussee 149, 22761 Hamburg, Germany

# An Experiment to Test the Mechanical Losses of Different Bonding Techniques
in Fused Silica

Jonathan J. Carter1,2 Pascal Birckigt3,4 Oliver Gerberding5 Qingfeng Li4
Rick Strüning2 Tobias Ullsperger4 and Sina M. Koehlenbeck1,2

## Abstract

High-purity glasses are used for their low optical and mechanical loss, which
makes them an excellent material for oscillators in optical systems, such as
inertial sensors. Complex geometries often require the assembly of multiple
pieces of glass and their permanent bonding. One common method is hydroxide
catalysis bonding, which leaves an enclosed medium layer. This layer has
different mechanical properties to the bulk glass around it. The higher
mechanical loss of this layer makes it more susceptible to displacement noise
originating from the conversion of energy from oscillation to heat and vice
versa. Therefore, other methods are needed to bond together glass assemblies.
To investigate this, we have set up an experiment to measure the mechanical
losses of several different types of bond commonly used in fused silica
manufacturing, namely; plasma activated direct bonding, hydroxide catalysis
bonding, laser welding, and adhesive bonding. In this paper we present the
experimental design and show initial results of the first test sample.

##  1 Introduction

Intrinsic thermal noise is a limit to the performance of many high precision
optomechanical devices [1]. Via the fluctuation dissipation theorem, the
thermal noise is directly linked to the mechanical dissipation of the device.
To prevent additional loss channels, many optomechanical measurement devices
are constructed monolithically [2, 3]. One-piece constructions can be
impractical, and complex components must then be assembled from multiple parts
due to their geometry and size [4]. There are now a wide variety of glass
bonding techniques available to construct quasi-monolithic assemblies, such as
optical contacting and hydroxide catalysis bonding. The associated losses, in
particular of hydroxide catalysis bonding [5, 6], have been studied in the
course of the construction of the advanced Laser Interferometer Gravitational-
Wave Observatories (aLIGO). Others, such as plasma activated direct bonding
[7], have no measurements of their intrinsic losses in the literature to the
authors’ knowledge.

This paper details work ongoing to measure the mechanical losses of several
fused silica bonding techniques. The production process, manufacturing of the
test samples, and the experiment to measure he mechanical Quality factor, $Q$,
are detailed, as well as results from the first tested sample.

##  2 Micro-Oscillator Design

Figure 1: The test sample design. There are three separate glass parts
depicted in green, blue and violet. The large round base, in green, is
attached to the flexure piece, in blue, via silicate bonding. This bonding
interface is necessary, but not under investigation, as it is far from any
oscillating parts. The flexure piece is attached to the test mass, in violet,
at a distance of $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the
flexures. This connection is created with the bonding technique under
investigation. In the case of monolithic control samples, there is no bonding
interface here, but bulk glass. The flexure piece uses a parallelogram
geometry to oscillate in plane.

A micro-oscillator with bonding interfaces in key locations was designed for
this experiment. The $Q$ factor is related to the mechanical loss angle,
$\phi$ by

$Q=\frac{1}{\phi}.$ (1)

By measuring the $Q$ factor, and understanding all loss terms, it is possible
to infer what contribution is due to the bonding interface itself.

Our device design is shown in FIGURE 1. It takes inspiration from work by
Guzmán et al. [8], who showed that a device using parallelogram flexure
structures can make for a high $Q$ factor oscillation along one spatial
direction. The bonding interface between two fused silica parts are varied
between the bonding techniques listed in a separate section below.

The bonding surfaces is located in the top part of the assembly, between the
test mass and the flexure piece. As this part is only held up by glass
flexures of $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thickness, it is able
to move with respect to the base. The flexures are bent by the oscillation
which induce stress along their length and in the corners of the base and test
mass. The bonding surface is as close as possible to this deformation induced
stress, thus contributing a loss channel and lowering the $Q$ factor of the
oscillation.

Finite Element Analysis (FEA) with COMSOL Multiphysics was used to analyse the
oscillations as well as the induced stress in the design. It was found that
the first eigen mode was a horizontal motion at approximately
$2.1\text{\,}\mathrm{kHz}$. This is the mode desired and excited during
measurements of the $Q$ factor. A second, vertical mode occurs at
$5.1\text{\,}\mathrm{kHz}$. This is undesired, but as it is more than a factor
of two above in frequency and orthogonal, cross contamination is expected to
be low. The next modes occur in the tens of $\mathrm{kHz}$ and are all
rotational. These are assumed to be too high in frequency to interfere with
the measurement.

FEA is also used to measure the strain energy distribution across the flexure
elements. This is necessary for two aspects, the first is estimating the
contribution of the material effect to the $Q$ factor of the oscillator, the
second is for calculating the energy in the bonding interface and so derive
its actual loss coefficient. The distribution of strain energy was simulated
by applying a fixed extension on the test mass and simulating how the strain
energy distribution changed in segments along the length of the flexures. This
was then normalised with the total strain energy in the system to produce
FIGURE 2.

Figure 2:  Normalised ratio of strain energy distribution across the geometry
estimated by FEA. The strain distribution peaks in the corners of the
oscillating part and decaying rapidly as it disperses into the bulk. The
location of the bonding surface is shown with the dashed line and is as close
as possible to the flexures to maximise strain across the bonding interface.

The leading limiting source of loss in the design is from the material itself
which we will describe with its respective $Q$ factor $Q_{\mathrm{{Mat}}}$.
This term can be subdivided further into bulk and surface loss. Bulk loss is
the loss in the volume of the oscillator intrinsic to the material it is made
from. As such, the experiment uses a low loss Corning 7980-0F fused Silica
with an intrinsic $Q$ factor of $1.1\times 10^{7}$ as measured by [16].

Surface loss can be understood in a similar manner to bulk loss. At the
surface of the oscillator damage occurs that breaks the regular structure and
allows contaminates to penetrate in the material acting as an additional loss
source. This leads to an understanding of a low loss bulk with a surface layer
of depth, $d_{\rm{s}}$, with a higher loss. The associate $Q$ factor can be
described mathematically as

$\frac{1}{Q_{\mathrm{{Mat}}}}=\phi_{\text{Bulk }}+\phi_{\text{Surf
}}d_{\rm{s}}\frac{\int_{S}\epsilon^{2}(\vec{r})\mathrm{d}S}{\int_{V}\epsilon^{2}(\vec{r})\mathrm{d}V},$
(2)

where $\phi$ is the loss angle in the bulk and surface layer respectively, and
$\epsilon$ is the strain energy density. Gretarsson et al. [17] made
measurements of some of these factors in the late 90s. This estimated the
approximate contribution $\phi_{\rm{Surf}}$ as $10^{-5}$ and a $d_{\rm{s}}$ of
$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Although these values depend
heavily on the treatment of samples, we assume it to be comparable.
Substituting in values from FIGURE 2 gives a $Q_{\rm{Mat}}$ of
$9\text{\times}{10}^{6}\text{\,}$.

Contributions to the $Q$ factor from thermoelastic damping, $Q_{\rm{TED}}$,
can be estimated using the Zener approximation. By following the method of
Lifshitz [18], an estimated contribution of $Q_{\rm{TED}}$ as
$2\text{\times}{10}^{7}\text{\,}$ is reached for this design. The contribution
of Akheizer loss, see [19] for details, is also very similar with $Q_{\rm{ph-
ph}}$ of $2\text{\times}{10}^{7}\text{\,}$. Air pressure damping is minimised
by performing the tests under vacuum, leaving only frictional losses as the
unknown loss term. As this does not belong to the sample itself, we can
estimate the theoretical limit of the $Q$ factor of this oscillator design as
$4.5\text{\times}{10}^{6}\text{\,}$.

Several samples of each bonding technique have now been produced and are ready
for testing. An exemplary sample is shown in FIGURE 3. In addition, several
devices with no bonding interface, i. e., monolithically, were produced, which
act as a reference for the bonded samples.

Figure 3: Photo of an exemplary test sample.

All samples were produced from double-side polished cylindrical pieces of
Corning 7980-0F fused silica $1\text{\,}$” in diameter round plates. The
sample manufacturing steps are shown in FIGURE 4. As a final manufacturing
step, the thin flexures were exposed by precise micro-machining using an
ultrashort pulsed laser system, TruMicro5070. Starting from the backside of
the cuboid, the focused laser pulses were scanned across the whole rectangular
area except of the thin flexures at the edges. During the layer-wise ablation
process the focal position was continuously moved up to realise taper-free
cuts, leaving flexible elements of only
$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ width.

Figure 4: Schematic manufacturing steps for producing the test samples.
Firstly, two round plates are joined using a certain bonding technique. Then,
it is cut into cuboids via diamond sawing, which are then carefully polished
from all sides. Meanwhile, a segment of another round plate is cut off to form
the base. The cuboid is joined with the base. Finally, laser ablation is
applied using an ultrashort pulsed laser.

##  3 Bonding Techniques

This section describes the various joining techniques for fused silica pieces
under investigation ranging from simple gluing to glass welding.

###  3.0.1 Hydroxide Catalysis Bonding

Hydroxide-catalysis bonding, also called silicate bonding, is a form of
bonding between glass surfaces invented by Gwo et al. at Stanford [11]. It has
been used extensively in the gravitational wave community because of its low
mechanical loss and high strength and so is well studied [5, 6, 12]. The
bonding process uses two polished, flat surfaces of silica based glass. One
surface is treated with a hydrous solution, here a sodium silicate solution,
then, the other surface is put into contact. During curing, the solution forms
long siloxane chains. After the water has evaporated, these interact and
tangle together forming a strong, highly stiff interlayer [13].

###  3.0.2 Adhesive Bonding

Adhesive bonding is a broad term used to describe any bonding method with an
organic glue as medium between the two surfaces. In this specific case, Epotec
301-2 was used. While this is the least promising bonding technique in terms
of thermal noise performance, it is the simplest bonding technique. Knowing
what level of thermal noise this bonding can achieve is therefore of broad
interest to the community.

###  3.0.3 Plasma Activated Bonding

Plasma activated bonding, which is a low-temperature direct process, is
performed by optically contacting two clean, highly polished, highly flat
surfaces. Surfaces are prepared via chemical cleaning and a plasma-activation
step. After contacting, a force of several $\mathrm{kPa}$ is applied. Then, a
process of thermal annealing converts the resulting hydrogen bonds into strong
covalent bonds, making a stable interface [9, 10]. As direct bonding yields a
high-strength, interlayer-free interface, it is perhaps the most promising
bonding technique in terms of thermal noise performance.

###  3.0.4 Ultrashort Pulse Laser (USP) Glass Welding

In USP glass welding, the lasers have a wavelength to which the glass is
transparent. Significant energy input can only be established via nonlinear
absorption, e.g. multiphoton ionisation, when high intensity, of order
hundreds of $\mathrm{TW}\text{\,}{\mathrm{cm}}^{-2}$, is reached by tight
focusing. When two glass surfaces are brought together and the laser beam is
focused at the interface, the glass near the focal volume is melted across the
interface so that a new joint is formed. Here, the melting points are placed
on a grid with a distance of $50\text{\,}\mathrm{\SIUnitSymbolMicro m}$. More
details are given in [14]. Previous studies have investigated the mechanical
loss of this bonding technique and found it to be less than the surface loss
of their tested samples and thus was not detectable [15].

##  4 Experiment

In order to measure the $Q$ factor of the samples, two things are needed, a
way to excite motion and a way to measure the samples response. A piezo
element attached to the mount of the oscillator can do the former. As the
device is made of optical grade fused silica, an interferometer can do the
later.

The interferometer is a homodyne interferometer in a Mach Zehnder
configuration, as shown in FIGURE 5. A piezo driven mirror in one arm keeps
the interferometer on the mid fringe operating point, ensuring a linear
response of the interferometer readout. A shear-piezo mounted under the sample
causes excitation for measurement of the mechanical response of the
oscillator.

Figure 5: Left: The experimental schematics of the interferometer used to test
the samples. The experiment uses laser light from at
$1064\text{\,}\mathrm{nm}$ laser. This is sent onto a breadboard in vacuum via
optical fibre feedthroughs. It is coupled out and send into Mach Zehnder
interferometer. The power is not distributed evenly, but rather via a
$1.5\text{/}98.5\text{\,}$ beamsplitter to compensate for the low reflectivity
of fused silica. M1 is driven by a controller to keep the interferometer at
the operating point, which is the mid-fringe. The sample is in a custom mount
attached to a shear-piezo which is driven allowing for a measure of its
transfer function.

After setting up the experiment in a vacuum environment, the first step was to
measure the background noise of the interferometric readout. For this purpose,
we used a device that was shaped like the test pieces but had no bending
geometry, allowing it to remain a rigid piece. It was found that there were no
significant resonance peaks in the region of interest, and a noise floor of
$1\text{\times}{10}^{-11}\text{\,}\mathrm{m}\mathrm{Hz}\textsuperscript{-1/2}$
was achieved.

##  5 Results & Discussion

The first sample under test was one of the monolithic reference samples with
bending flexures. Since no loss channel from a bond is present this will give
the intrinsic loss of the sample material and geometry and the experimental
set-up.

An excitation signal was applied to the shear-piezo, driving the sample across
Fourier frequencies from $2\text{\,}\mathrm{kHz}4\text{\,}\mathrm{kHz}$. The
displacement of the test mass was recorded with the interferometer and the
transfer function from the driving displacement to the test mass displacement
was calculated. The amplitude of the transfer function was then fit with the
model of a simple damped harmonic oscillator, given by

$\tilde{X}=\left|\frac{\omega_{\rm{0}}^{2}}{\left(-\omega^{2}+{\omega_{0}}^{2}+\frac{i\omega_{0}\omega}{Q}\right)}\right|,$
(3)

where $\omega_{\rm{0}}$ is the natural angular frequency, and $\tilde{X}$ is
the magnitude of the frequency response to stimulation. The fit was done using
MATLABs Nlinfit function. The result of this fit is shown in FIGURE 6.

The $Q$ factor is $257.7\text{\,}$, three orders of magnitude below where it
is expected to be. The cause of the discrepancy is unknown, though there are
two ideas that are being investigated. The first is that contaminants had
entered the flexures. There is also some concerns that the largely unknown
term of frictional loss are limiting the measurements. Alternatives to the
currently used clamp are being investigated. It is hoped that improving the
rigidity of the clamp will lead to less differential motion and so less
friction.

Figure 6: The fit and measured absolute transfer function of monolithic sample
13. The peak location has a deviation of 30$\%$ from the value predicted by
FEA simulation. As the resonance frequency is strongly dependent on flexure
thickness the difference is mainly attributed to the small variations in
thickness seen along the flexures.

##  6 Conclusions

This paper reports ongoing efforts to measure the mechanical loss intrinsic to
several bonding techniques commonly used in fused silica manufacturing.

A mechanical oscillator geometry has been designed for the purpose of
measuring the loss in bonding interfaces. The oscillator design has a
promising theoretical $Q$ factor and artificially induced loss channel to
measure the bonding interfaces. Several test pieces have been produced. By
using interferometry, a means of measuring the $Q$ factor of the sample has
been achieved. This will in turn allow for an estimation of the mechanical
loss due to the bond. However, the $Q$ factor of the substrate is not what it
is expected to be. There are several reasons this could be the case and
ongoing investigations seek to answer why.

Overall the experiment still has promise to produce measurements of the
mechanical loss of several in glass bonding techniques. By knowing this,
larger fused silica glass assemblies can be made, without being limited by
thermal noise. It is hoped that this will prove valuable information both to
the specific field of gravitational wave astronomy and the broader glass
optomechanical sensor design field as a whole.

##  7 Acknowledgements

We would like to thank Prof. Dr. Gerhard Heinzel, Prof. Dr. Benno Willke,
Prof. Dr. Uwe Zeitner, Dr.-Ing. Stefan Risse, and Dr. Harald Lück for their
continuing support of the project and are gratefully for their advice and
ideas.

This project was supported by the Max Planck and Fraunhofer Institute
Cooperation ”High-QG”.

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Zanmar Sanchez  INAF - Osservatorio Astronomico di Capodimonte, Sal.
Moiariello 16, I-80131, Naples, Italy  M. Stritzinger  Aarhus University, Ny
Munkegade 120, D-8000 Aarhus, Denmark  A. Sulich  INAF - Osservatorio
Astronomico di Trieste, Via G.B. Tiepolo 11, I-34143 Trieste, Italy  H.
Ventura  FGG-INAF, TNG, Rambla J.A. Fernández Pérez 7, E-38712 Breña Baja
(TF), Spain

###### Abstract

SOXS (Son Of X-Shooter) is the new ESO instrument that is going to be
installed on the 3.58-m New Technology Telescope at the La Silla Observatory.
SOXS is a single object spectrograph offering a wide simultaneous spectral
coverage from U- to H-band. Although such an instrument may have potentially a
large variety of applications, the consortium designed it with a clear science
case: it is going to provide the spectroscopic counterparts to the ongoing and
upcoming imaging surveys, becoming one of the main follow-up instruments in
the Southern hemisphere for the classification and characterization of
transients. The NTT+SOXS system is specialized to observe all transients and
variable sources discovered by imaging surveys with a flexible schedule
maintained by the consortium, based on a remote scheduler which will interface
with the observatory software infrastructure. SOXS is realized timely to be
highly synergic with transients discovery machines like the Vera C. Rubin
Observatory. The instrument has been integrated and tested in Italy,
collecting and assembling subsystems coming from all partners spread over six
countries in three continents. The first preparatory activities in Chile have
been completed at the telescope. This article gives an updated status of the
project before the shipping of the instrument to Chile.

###### keywords:

Spectrograph, Instrumentation, Transients

---
Figure 1:  The SOXS instrument fully assembled in the integration hall of the
Padova Astronomical Observatory. It is mounted on the NTT simulator flange,
providing the same interfaces of the real telescope at the Nasmyth focus. The
instrument can be rotated and tested in all gravity conditions. The co-rotator
structure is visible in the center with two lateral cable-wraps which safely
support the cables during the rotation. The two black cabinets on the left and
right host most of the control electronics. The only missing part in this
picture is the Nasmyth platform, which has already been shipped and installed
in Chile.
---
Figure 2:  The five main subsystems of SOXS. The Common Path, the heart of the
system, is surrounded by the other four: the two spectrographs working
simultaneously on the left (UV-VIS) and right (NIR), the Acquisition and
Guiding Camera on the top, the Calibration Unit on the bottom.
---
Figure 3:  The UV-VIS spectrograph of SOXS. The detector is cooled through a
Continuous Flow Cryostat with liquid nitrogen.
---
Figure 4:  Left: UVVIS four traces when fed through the CP using SoXS CBX
arclamps. Right: Measured spectral resolution, shown average resolution of
R$\sim$4500, meeting all system requirements, and achieving goals in most
cased – see text for further details.
---
Figure 5:  The NIR spectrograph of SOXS. The cryostat is cooled with a
CryoCooler.
---
Figure 6:  Inner view of the NIR spectrograph.
---
Figure 7:  Echelle cross-dispersed spectral format of the NIR spectrograph.
Left: using continuum (QTH) lamp. Right: using arc lamps with 0.5 arcsec slit.
---
Figure 8:  Measurements of the NIR spectrograph resolution.
---
Figure 9:  The SOXS platform fully assembled and installed at the NTT in the
La Silla Observatory. It will support the co-rotator structure as well as the
two electronic cabinets.

##  1 INTRODUCTION

The SOXS instrument has been introduced in previous contributions, reporting
on the status of the project at regular intervals[1, 2, 3, 4]. The project
originated with an ESO call for new scientific ideas at the NTT telescope. The
SOXS consortium participated with a proposal for a new instrument fully
dedicated to the spectroscopic follow-up of transient sources, which was
selected. The SOXS concept fits with the strategy of dedication of medium
class telescopes to specific science cases. In fact, having lot of observing
time is a winning factor in many cases, and this is where nowadays the 4-m
class telescope can be strategic. The project was officially adopted and
kicked-off in 2016, receiving financial support from the partners. Afterwards,
it has went through all the regular steps of ESO projects, having preliminar
and final design phases and reviews. The procurement and then the assembly and
integration phases started later on, and after several years they are now
concluded. This paper is about the progress of the project towards the first
light of the instrument, that will be in 2025. More details on each subsystem
can be found in a set of related articles[5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35].

##  2 Scientific case

There is a wide expectation for the upcoming golden era in the study of
astrophysical transients. In fact, many new facilities are coming out from
ground and space at all wavelenghts with unprecedented capabilities, greatly
boosting this kind of science.

A big step forward will come e.g. from the imaging all-sky surveys. In that
domain the Vera C. Rubin Observatory is going to be a game-changer, as it will
discover a large amount of new sources every day at an unprecedently high
rate. But all these sources would need a spectroscopic follow up to understand
what they are, and there are currently no facilities with the capability of
providing spectroscopy for the number of new sources that will continuously
come out. This is where SOXS wants to play a role: being dedicated to the
study of transients, it will be available every night for the classification
and characterization of the most interesting targets selected by the
consortium. Members of the collaboration will work every day to the selection
of the most appropriate sources for the next night, with a highly dynamic
scheduling imposed by the full dedication to the time-domain and multi-
messenger astronomy.

The consortium is organized to deal with all kind of astrophysical transients.
A non-exhaustive list of the scientific cases is:

  * •

Supernovae

  * •

Multimessenger event counterparts (Gravitational Waves, neutrino)

  * •

Gamma-Ray Bursts

  * •

Fast Radio Bursts

  * •

Tidal disruption events

  * •

X-ray binaries

  * •

Magnetars

  * •

AGN, Blazars

  * •

Young Stellar Objects, Stellar Variability, Exoplanets

  * •

Asteroids and Comets

##  3 Instrument Description

Fig. 1 shows SOXS fully assembled at the Astronomical Observatory of Padova,
where the assembly, integration and test of the system have been performed. It
is mounted on the NTT Simulator provided by ESO, which reproduces exactly the
real interfaces of the telescope. The instrument is composed of two
spectroscopic channels, working simultaneously in the UV-VIS (350-850 nm) and
NIR (800-2000 nm) bands. It is also equipped with an Acquisition and Guiding
Camera, that is usable also as an imaging channel for photometry, and a
Calibration Unit with lamps for calibration in wavelength and flux. The heart
of the system is the Common Path, which receives a F/11 beam from the
telescope and transmits a F/6.5 beam to the spectrographs through a dicroich
and a set of folding mirrors. The Common Path also hosts most of the
mechanisms, e.g. to select the light coming from the calibration lamps,
deviate the light to the imaging camera, counter-rotate the atmospheric
dispersion corrector prisms, only for visible wavelengths, compensate the
flexures with tip-tilt mirrors and so on. Fig. 2 highlights the instrument
subsystems and their relative positions.

##  4 Status

This section summarizes the latest results on the three scientific channels,
that are the two spectrographs working simulataneously and the imaging camera.

###  4.1 UV-VIS Spectrograph

The UV-VIS spectrograph (Fig.3) has gone through extensive assembly,
integration and test period during 2023-24. Following assembly of the various
optical components, the science detector has been installed and the camera has
been aligned to balance image quality and resolution between the four traces.
Initial alignment was performed using a stand-alone F/6.5 relay with a
50$\mu$m multimode fiber as a source. Slit alignment was completed using a 3mm
liquid fiber and the F/6.5 relay. Alignment of the spectrograph to the Common
Path is mitigated, as the telescope focus will be adjusted on sky based on the
Common Path image plane being coincident with the spectrograph object plane.

Using Hg and Kr arclamps, the image quality and spectral resolution has been
inspected in a standalone mode, as well as through the spectrograph Common
Path using the Calibration Unit arc lamps, see Fig. 4 left panel. We derive
consistent results between the two modes, with average resolution of
R=[4830,4560,4480,4350] for 1 arcsec slit width in the four traces of the
spectrograph (u, g ,r ,I respectively), significantly higher than the system
requirements (R=3500), and either achieving or close to the system goal
resolution of R=4500, see Fig. 4 right panel. The derived resolution are
likely lower limits, as the line width of some of the lines showed below are
limiting the spectral resolution, and not the system response. Currently, the
UV-VIS spectrograph is going through flexure tests, in which we discovered a
flexure in the spatial direction when completing a rotation on the Nasmyth
flange. This residual problem is going to be mitigated by introducing
additional supports to the component, which is expected to fix the issue.

###  4.2 NIR Spectrograph

In the last two years the NIR spectrograph (Fig. 5) has been fully integrated,
aligned and tested. All sub-benches were carefully installed and aligned into
the optical bench, inside the D-shape vacuum vessel (Fig.6), undergoing
mechanical measurements performed with an articulated arm and then optical
tests. The functional and performance verification tests show that the
spectral format, image quality and resolving power, as well as thermal+dark
current noise level are all in agreement with design and compliant with
requirements.

Real data in terms of spectral format (Fig.7 shows the echelle cross-dispersed
spectra for continuum and arc lamp sources) and image quality have been
compared with simulated frames, generated through the SOXS End-to-End
simulator. This approach allowed to confirm the performance were satisfactory.
Flexure and spectral stability tests were executed, coming to the conclusion
they are relatively small and repeatable, The compensation of the flexures is
expected to be implemented through a look-up-table mapping the position of the
tip-tilt mirror included in the Common Path as a function of the rotator
angle.

The Resolving Power estimations were derived from the FWHM values computed for
a set of 25 wavelengths, taking into account their linear dispersion. The
outcome of the current analysis is that the resolution for 1 arcsec slit is in
agreement with theoretical design values, as shown in Fig.8.

###  4.3 AGC Camera

The Acquisition and Guiding Camera is also considered an additional scientific
channel. Thus, its performance have been carefully checked and characterized.
The unit acts as a focal reducer, reducing the incoming F/11 beam to a F/3.6.
Each pixel of the CCD corresponds to approximately 0.2 arcsec, resulting in a
3.5 arcmin unvignetted field of view. The image quality specifications is such
that over 80$\%$ of the geometrically encircled energy is contained in two
pixels in a Field of View with a radius of 3.5 arcmin.

Tests with all filters show the FWHM is in fact contained within a radius of 2
pixels, indicating satisfactory performance. The results suggest that the
system always keeps a high level of precision and focus. Additionally, the
flexure testa revealed that the PSF center of mass shifted by just 1 pixel, on
average, during a full rotation of the flange. This limited displacement
proves a good stability and robustness of the system’s alignment under all
gravity conditions.

##  5 Preliminary activities at the observatory

SOXS is designed to replace the SOFI instrument at one of the Nasmyth foci of
the NTT. Thus, in late 2023 ESO decomissioned and removed SOFI, leaving room
for the new instrument. The old Nasmyth platform was removed as well, because
the SOXS team designed a new lighter platform tailored to the real needs of
the new project. This new platform was manufactured in Italy and shipped to
Chile in 2023. In November 2023 the SOXS team worked in Chile for the
installation of the new platform on the telescope. Fig. 9 shows the current
status in the NTT Nasmyth room, with the new platform waiting for the arrival
of the instrument (Fig. 1). Of course the visit of the consortium onsite has
been extremely useful also to prepare the arrival of the instrument itself,
allowing a cross-check of the interfaces at the telescope between the NTT and
SOXS.

##  6 Conclusions

SOXS has been fully assembled in Italy in all its components, merging
subsystems provided by different partners of the consortium. All subsystems
have been individually tested at the integration site and, when necessary,
improved. The interfaces have been checked and the control system has been
tuned in parallel. The preliminary integration in Italy is now completed and
the final period of system tuning and tests is ongoing. The activities in
Chile have been started as well, completing the installation of the Nasmyth
platform which will host the instrument in La Silla. The process of the
Preliminary Acceptance in Europe is about to start and the shipment of the
instrument to Chile is planned within end of 2024, with integration and
commissioning in 2025.

## References

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# CMB-GAN: Fast Simulations of Cosmic Microwave background Anisotropy maps
using Deep Learning

Amit Mishra  Pranath Reddy  Rahul Nigam  Birla Institute of Technology &
Science Pilani - Hyderabad Campus, Hyderabad, India

###### Abstract

Cosmic Microwave Background (CMB) has been a cornerstone in many cosmology
experiments and studies since it was discovered back in 1964. Traditional
computational models like CAMB that are used for generating CMB temperature
anisotropy maps are extremely resource intensive and act as a bottleneck in
cosmology experiments that require a large amount of CMB data for analysis. In
this paper, we present a new approach to the generation of CMB temperature
maps using a specific class of neural networks called Generative Adversarial
Network (GAN). We train our deep generative model to learn the complex
distribution of CMB maps and efficiently generate new sets of CMB data in the
form of 2D patches of anisotropy maps without losing much accuracy. We limit
our experiment to the generation of 56∘ and 112∘ square patches of CMB maps.
We have also trained a Multilayer perceptron model for estimation of baryon
density from a CMB map, we will be using this model for the performance
evaluation of our generative model using diagnostic measures like Histogram of
pixel intensities, the standard deviation of pixel intensity distribution,
Power Spectrum, Cross power spectrum, Correlation matrix of the power spectrum
and Peak count. We show that the GAN model is able to efficiently generate CMB
samples of multiple sizes and is sensitive to the cosmological parameters
corresponding to the underlying distribution of the data. The primiary
advantage of this method is the exponential reduction in the computational
time needed to generate the CMB data, the GAN model is able to generate the
samples within seconds as opposed to hours required by the CAMB package with
an acceptable value to error and loss of information. We hope that future
iterations of this methodology will replace traditional statistical methods of
CMB data generation and help in large scale cosmological experiments.

###### keywords:

cosmic microwave background radiation , deep learning , generative adversarial
networks

##  1 Introduction

The variations in temperature of the Cosmic Microwave Background (CMB) are
similar to the ripples on the cosmic pond and enclose a lot of information
about the universe. To collect this information we look at the scales at which
these temperature fluctuations occur. The amount of temperature fluctuations
(in micro Kelvin) is plotted against the multipole moment (l). This is the
angular power spectrum graph of a CMB temperature map. Such graphs contain
several peaks which provide a lot of information and we exploit this for our
use.

The first peak is an indication of the geometry of the universe, whether it is
flat or curved (Hu, Wayne, et al., 2004).. CMB radiation is distorted by the
curvature of the universe since the radiation comes from all directions of the
visible universe. The fluctuations will appear undistorted if the universe is
flat. The fluctuations would appear magnified if the universe is positively
curved and de-magnified if it is negatively curved. The second peak reveals
information about the number of baryons present in the universe. Due to the
initial fluctuations in the universe, all matter would tend to gravitationally
group towards the higher density fluctuations. However, baryon matter which is
interactive with light would heat up as it clumps up, and the resultant
pressure would try to push against the grouped matter. This implies that the
second peak will be more damped if there is more matter. Thus, the ratio of
the first and second peak gives us the baryon density(Bucher, M., 2015).

The anisotropy of the cosmic microwave background (CMB) consists of the small
temperature fluctuations in the blackbody radiation left over from the Big
Bang. The CMB temperature maps are an incredible source of information for
cosmological analysis and the advent of big data methods (Alex Krizhevsky,
Geoffrey E Hinton, 2012) have opened a new avenue for the analysis of CMB.
Modern data analysis methods such as machine learning and deep learning
require a large amount of data and traditional methods such as CAMB and healpy
(Gorski, K. M., Hivon, E., Banday, A. J., et al. 2005) are computationally
expensive and inefficient for generating a large number of CMB maps. Here we
demonstrate the use of deep generative models to generate synthetic samples of
CMB all-sky maps which can be used for cosmological analysis. Deep generative
models are capable of learning complex distributions from a given dataset and
then generate new, statistically consistent data samples (I. J. Goodfellow,
2014). We generate the dataset for the training of our generative model by
snipping 128x128 and 256x256 resolution patches from the CMB maps which
effectively gave us 56∘ and 112∘ patches respectively. We also train a
multilayer perceptron network (MLP) to predict the baryon density of a given
CMB map, this helps us in comparing the samples generated by the generative
model with the samples of our dataset by correlating the baryon density
predictions given by the MLP model. We use various diagnostic metrics like the
histogram of pixel intensities, the standard deviation of pixel intensity
distribution, Power Spectrum, Cross power spectrum, Correlation matrix of the
power spectrum and Peak count to evaluate the performance of our generative
model. The practical advantage of this method is that once the model has been
trained, the generation process is extremely fast, thus giving us the ability
to generate a large number of samples that can be used for scientific study.

##  2 Methodology

###  2.1 CAMB and Data Generation

We use standard cosmological software CAMB to generate CMB temperature maps
for training. CAMB is used to compute CMB, CMB lensing and other related
cosmological functions. CAMB takes several parameters as input to generate a
file containing the initial angular power spectrum data of the universe. The
Curved correlation function is used as the lensing method and we include
reionization. Other physical parameters which are input to CAMB include Hubble
constant, the temperature of CMB, baryon density, cold dark matter density,
the effective mass density of dark energy, maximum multipoles data, redshift
and helium fraction. This power spectrum file is in turn used by healpy to
generate random gaussian CMB temperature maps which are used for training the
neural network.

Anisotropy from dipole effect due to the movement of the earth relative to the
CMB rest frame and galactic contaminants along the equator corresponding to
the galactic plane is removed while generating the temperature maps. The
generated full-sky maps have the galactic center at the center of the
mollweide projection.

Figure 1: A random full sky CMB temperature map generated using healpy and
CAMB Figure 2: Sample patches cropped along the equator of the full sky CMB
temperature map

###  2.2 Implementation and Training

The method proposed in this paper comprises two steps, Baryon density
estimation and CMB data generation using a traditional Artificial Neural
Network and a Deep generative model. We use a Generative Adversarial Network
trained on CMB patches obtained using CAMB for the generation of new CMB data
and a Multilayer perceptron network trained on labeled CMB data for baryon
density estimation which will be used for diagnosis and performance evaluation
of our Generative network. We first train an image classifier using a
multilayer perceptron network with the baryon density obtained from the power
spectrum of CMB as the classes/labels of our data. Here we use a dataset with
a large number of classes to approximate our classifier as a regression model,
this helps us in predicting the baryon density of the input test images with a
higher degree of precision. Convolutional neural networks (CNN) are one of the
most famous set of neural network architectures used for classifying images,
CNN takes advantage of local spatial coherence of the input (Rippel, Snoek,
Adams, 2015) because we assume that the spatially close images used for
training are correlated, but in the case of the CMB dataset , the pixels in
the images are random noise following a gaussian distribution, the CNN network
will not be able to find any common features in the inputs and thus the
training accuracy and test error will be less than favorable. We have tested
Resnet-101 and Inception v2 CNN architectures. The training accuracy of resnet
network was very low whereas the inception network was suffering from high
variance problem (Liu, Wei, Zhang, Yang, 2017). For this reason, we will be
using a Multi-Layer perceptron network. A multilayer perceptron is one of the
most commonly used architectures of feedforward artificial neural networks, it
consists of three classes of layers and nodes, the input layer, hidden layers,
and an output layer. Each node in a layer is connected to the nodes of the
next layer via a non-linear activation function. Multilayer perceptron makes
use of one of the most famous techniques of supervised learning called
backpropagation (Goodfellow, Bengio, Courville, 2018) for training the
network. A multilayer perceptron can be distinguished from a linear perceptron
from its characteristic use of fully connected multilayers. This makes
multilayer perceptrons suitable for working with non-linearly separable data
(Bullinaria, 2015) and can be perceived as a logistic regression classifier.
The weights of the fully connected layers are updated once a batch of data has
been passed through the network by measuring the error of the output with the
expected result (predetermined labels), this is the essence of learning in
neural networks and is carried out with the help of an iterative algorithm
called backpropagation. This is an example of supervised learning.
Backpropagation uses an iterative optimization algorithm called gradient
descent (Goodfellow, Bengio, Courville, 2018) to update the weights of the
network. We continue to train the network until the training accuracy and the
testing cost gets saturated. We have used a softmax cross-entropy function as
our loss function. consider a mapping of input x to category y, we have

Objective:

$min[-E_{x,y~{}p(data)}log(P(Y|X)]$

where, E is the expectation function
P(data) is the true data distribution
P(y|x) is the distribution of our parametric model.

We now train our generative model to generate the CMB data. The primary
difference between a discriminative algorithm and a generative algorithm is
that a discriminative algorithms map features to labels whereas a generative
algorithm tries to predict the features given a certain label. Discriminative
models learn the boundary between classes and Generative models model the
distribution of individual classes. In this experiment, we use a Deep
Convolutional Generative Adversarial Network which has the ability to mimic
complex distributions of data. The primary goal of the Generative Adversarial
Network is to generate new samples from the same distribution as that of the
training data. The most notable feature of GAN is that it consists of a pair
of networks: a generative network (G) and a discriminative network (D). The
two networks are in a two-player game setting where the Generator network
tries to fool the discriminator by generating images that match very closely
to the training data and the Discriminator network tries to differentiate
between real and generated images thus training jointly in a minimax game. The
Discriminator tries to classify a sample x and outputs the likelihood in (0,1)
of the real image, whereas the Generator uses a random variable z drawn from a
given prior distribution.

Objective :

$min_{G}max_{D}[E_{x\sim p(x)}\\{log(D(x)\\}+E_{z\sim
p(z)}\\{log(1-D(G(z))\\}]$

where,
E is the expectation function
P(x) is the true data distribution
P(z) is the prior distribution ( usually a Gaussian )

The Discriminator D tries to maximize the objective such that D(x) is close to
1 (real) and D(G(z)) is close to 0 (fake) and the Generator G tries to
minimize the objective such that D(G(z)) is close to 1 (discriminator is
fooled into thinking generated G(z) is real). This training process is
essentially trying to reduce the Jensen-Shannon divergence between P(x) and
P(z). We have used the Tensorflow library to implement the MLP model and the
GAN model. We have used Adam optimization (Kingma, Ba, 2017) algorithm instead
of the traditional stochastic gradient descent for updating the weights of the
network (Michelucci, Umberto, 2018) and used L2 regularization, also known as
ridge regularization to prevent our model from overfitting. In L2
regularization, we add a squared error term as a penalty to the loss function
(Goodfellow, Bengio, Courville, 2018). The training of the network is done in
the Google Cloud platform using a Tesla K80 GPU.

###  2.3 Network Configuration

####  2.3.1 MLP Network:

Table 1: Network Configuration No of hidden layers |  No of Nodes in each hidden layer |  Learning Rate
---|---|---
5 |  3223 |  0.001
Batch size |  No of epochs |  Regularization parameter
---|---|---
512 |  50000 |  0.01

The learning rate determines how fast the weights or the coefficients of the
network are updated. An epoch can be defined as the number of times the
algorithm perceives the entire data-set. Hence, an epoch is completed when all
the samples of the data have been perused. An iteration can be defined as the
number of times a “batch of data” has been passed through the algorithm. In
the case of a multilayer perceptron, that means the forward pass and backward
pass. Hence, an iteration is completed once a batch of data has passed through
the network. The batch size is the number of training examples passed through
the network at once (Shen, 2017 & Svozil, Kvasnicka, Pospichal, 1997).

####  2.3.2 GAN Network:

We use a modified version (Alec Radford, 2015) of the standard GAN
architecture incorporating convolution layer with a kernel Size of 5x5.

Table 2: Discriminator Network Configuration No of hidden layers |  Operations |  Outputs |  Batch Size
---|---|---|---
5 (for 56∘ patches) 6 (for 112∘ patches) |  Conv/ linear |  Leaky-Relu-BatchNorm/ sigmoid |  50
No of epochs |  Learning Rate |  Regularization parameter
---|---|---
2000 |  0.000001 |  0.01

Dimension of the gaussian prior distribution ( linear input of generator) =
200

Table 3: Generator Network Configuration No of hidden layers |  Operations |  Outputs |  Batch Size
---|---|---|---
5 (for 56∘ patches) 6 (for 112∘ patches) |  linear/DeConv |  Relu-BatchNorm/ tanh |  50
No of epochs |  Learning Rate |  Regularization parameter
---|---|---
2000 |  0.000001 |  0.01

##  3 Results

Here we present the results obtained after training the Multilayer Perceptron
and the Generative adversarial network. We have focused our study on two
classes of CMB simulations, 56∘ patches and 112∘ patches. We have generated
100 random samples using the trained GAN model and then passed them as the
input to the trained MLP model to predict the corresponding baryon densities.
We have then extracted the patches from CAMB training dataset whose baryon
densities matches the predictions obtained from the MLP model and used them
for comparison and evaluation in various metrics. The similarities in the
power spectrum and other metrics have shown that out GAN model is capable of
reconstructing the complex distribution underlying the CMB and the subtle but
consistent discrepancies in the results ensure the model isn’t just memorizing
the input data but rather recreating the distribution from the ground up.

###  3.1 56∘ patches

Figure 3: Sample patches (56∘s) from the maps generated using CAMB Figure 4:
Sample patches (56∘s) generated by trained GAN model

---
(a)

---
(b)

Figure 5: Distribution of pixel intensities of (a) a random sample patch from
a map generated using CAMB and (b) a random sample patch generated using
trained GAN model.

Figures 5-11 represent the diagnostic results obtained from the 56∘ patches
generated by the GAN model.
We have generated 100 random samples using the trained GAN model and then
passed them as the input to the trained MLP model to predict the corresponding
baryon densities. We have then extracted the patches from CAMB training
dataset whose baryon densities matches the predictions obtained from the MLP
model and used them for comparison and evaluation in various metrics. The
similarities in the power spectrum and other metrics have shown that out GAN
model is capable of reconstructing the complex distribution underlying the CMB
and the subtle but consistent discrepancies in the results ensure the model
isn’t just memorizing the input data but rather recreating the distribution
from the ground up.

Figure 6: The plot of the standard deviation of the pixel intensity
distribution of patches generated using GAN and the corresponding matched CAMB
patches  Figure 7: The power spectrum of the 2D image of a random sample patch
from a map generated by CAMB and of a patch generated by trained GAN model.
Figure 8: Cross Power Spectrum obtained using pairs of CAMB patches, pairs of
GAN patches and between a CAMB and a GAN patch. Figure 9: Correlation Matrix
of the power spectrum of 100 GAN samples (right) and the corresponding matched
CAMB samples (left).

Figure 10: Peak Count of patches generated using GAN and the corresponding
matched CAMB patches. Figure 11: Total peak count of patches generated using
GAN and the corresponding matched CAMB patches.

###  3.2 112∘ patches

Figure 12: Sample patches (112∘s) from the maps generated using CAMB. Figure
13: Sample patches (112∘s) generated by trained GAN model. Figure 14: The
power spectrum of the 2D image of a random sample patch from a map generated
by CAMB and of a patch generated by trained GAN model. Figure 15: Cross Power
Spectrum obtained using pairs of CAMB patches, pairs of GAN patches and
between a CAMB and a GAN patch. Figure 16: Peak Count of patches generated
using GAN and the corresponding matched CAMB patches. Figure 17: Total peak
count of patches generated using GAN and the corresponding matched CAMB
patches.

The random samples shown in Fig 13 and the subsequent results shown in Fig
14-17 follow a similar trend as we have seen with the results obtained from
the model trained on 56◦ patches. This shows that the model is invariant to
scale and is able to recreate the distribution of larger structures and can
probably be extended to the generation of full-sky CMB maps. The higher
deviation in the diagnostic metrics compared to the results of 56◦ patches can
be attributed to the fact that we have used 2D projections of spherical maps
and we can observe a loss of spatial information when we take larger
projections. This can be solved by training the model with spherical CMB
patches instead of 2D images and replacing the convolutional layers in the
model with spherical convolutional layers.

##  4 Parameter variation

To check the invariance of our model with respect to the change in the
parameters corresponding to the input data that is used for training the
models, we have trained two GAN models on CAMB data with Hubble constants 65
and 75 respectively. We have then used the trained model to generate 100
random samples for comparison. As seen in Fig 18, the standard deviation of
the pixel intensity distributions of the samples with H = 65 are consistently
higher than the ones obtained from the samples with H = 75, the average
standard deviation of ( H = 65 ) samples is 15.6312 whereas that of the ( H =
75 ) samples is 14.2705 giving us a relative difference of 9.16%.

Relative difference :

$\frac{|H_{1}-H_{2}|}{[\frac{(H_{1}+H_{2})}{2}]}\times 100$

We can also observe a noticeable variation in the correlation matrix (Fig 19)
of samples of both the models. This shows that the model is sensitive to the
change in the cosmological parameters that define the underlying distribution.

Figure 18: The plot of the standard deviation of the pixel intensity
distribution of patches generated using GAN model trained on H = 65 data and H
= 75 data. Figure 19: Correlation matrix of power spectrum of GAN samples
obtained from H = 65 model on the left and GAN samples obtained from H = 75
model on the right

We have also trained our model using 6 different values of Hubble’s constant.
Apart from an anomaly of H=73, as seen in Table 4 and Fig 20, the standard
deviation of pixel intensity distribution appears to be decreasing with
increase in Hubble’s constant.

Table 4: Results Hubble Constant |  Average standard Deviation in pixel intensity distribution
---|---
65 |  15.63120985989387
67 |  15.602640108842536
69 |  15.226652267061267
71 |  15.008699629159153
73 |  15.093389253196806
75 |  14.27058023246263
Figure 20: The plot of the average standard deviation of the pixel intensity
distribution of 200 random samples vs the Hubble constant value corresponding
to the training data

As seen in Table 5 and Fig 21, we have also found the values of average
standard deviation in the uncertainty of CMB Temperature using the scaling
factor found from the average value of the mean of pixel intensity
(luminosity) values and the average value of the mean of CMB temperature
uncertainty values obtained from the temperature maps.

Table 5: Results Hubble Constant |  Average standard Deviation in uncertainty of CMB Temperature (mK)
---|---
65 |  0.0544641458533
67 |  0.0543645996824
69 |  0.0530545375159
71 |  0.0522951206591
73 |  0.0525902064571
75 |  0.0497232760713
Figure 21: The plot of the average standard deviation of the uncertainty of
CMB Temperature of 200 random samples vs the Hubble constant value
corresponding to the training data

We see a decreasing trend in standard deviation of uncertainty in CMB
temperature with increasing Hubble’s constant. This is expected since a higher
Hubble’s constant means a younger universe which in turn means the universe
had lesser number of structures formed and result in lesser dispersion of
relativistic particles and hence the lesser standard deviation in uncertainty
in CMB temperature.

##  5 Conclusion and future plans

We have successfully presented the ability of Generative adversarial networks
to learn the complex distribution behind flat CMB anisotropy maps. We have
trained a deep convolutional generative adversarial network on a dataset of
56◦ CMB patches and 112◦ CMB patches obtained using CAMB. The patches
generated by the GAN models are very similar to our training data, that are,
the patches obtained by CAMB and healpy. The power spectrum of the patches
generated by GAN and the patches obtained by CAMB are in very close agreement
and a similar trend can be seen in other diagnostic metrics as well. We have
also seen that our model is invariant to scale, that is, the size of the patch
that has been used for training. The models trained on data with different
values of Hubble constant have generated patches with significantly different
properties, showing that our model is sensitive to change in cosmological
parameters. We have shown that deep learning can be a viable alternative to
traditional methods of CMB data generation and computationally much more
efficient for cosmological experiments that require a large amount of CMB
data, we hope to extend this study to the simulation of full-sky maps using
spherical convolutional layers and generative adversarial networks in the
future. We have trained our deep generative model using patches of CMB instead
of full-sky maps because we were constrained by limited computational power.
We hope to further improve our model and train using full-sky maps to present
a viable method of CMB data generation for cosmological analysis.

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