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# The optical design of the LiteBIRD Middle and High Frequency Telescope

L. Lamagna  Physics Department, Sapienza University of Rome, Italy  INFN
Sezione di Roma1, Italy  J.E. Gudmundsson  The Oskar Klein Centre, Department
of Physics, Stockholm University, Sweden  H. Imada  National Astronomical
Observatory of Japan, Osawa, Mitaka, Japan  P. Hargrave  School of Physics and
Astronomy, Cardiff University, UK  C. Franceschet  Physics Department,
Università degli Studi di Milano Statale, Italy  INFN Sezione di Milano, Italy
M. De Petris  Physics Department, Sapienza University of Rome, Italy  INFN
Sezione di Roma1, Italy  J. Austermann  National Institute of Standards and
Technology, Boulder, Colorado, US  S. Bounissou  Institut d’Astrophysique
Spatiale, Université Paris-Saclay, France  F. Columbro  Physics Department,
Sapienza University of Rome, Italy  INFN Sezione di Roma1, Italy  P. de
Bernardis  Physics Department, Sapienza University of Rome, Italy  INFN
Sezione di Roma1, Italy  S. Henrot-Versillé  Université Paris-Saclay,
CNRS/IN2P3, IJCLab, Orsay, France  J. Hubmayr  National Institute of Standards
and Technology, Boulder, Colorado, US  G. Jaehnig  Center for Astrophysics and
Space Astronomy, University of Colorado Boulder, US  R. Keskitalo
Computational Cosmology Center, Lawrence Berkeley National Lab, US  B. Maffei
Institut d’Astrophysique Spatiale, Université Paris-Saclay, France  S. Masi
Physics Department, Sapienza University of Rome, Italy  INFN Sezione di Roma1,
Italy  T. Matsumura  Kavli Institute for the Physics and Mathematics of the
Universe, Kashiwa, Japan  L. Montier  Institut de Recherche en Astrophysique
et Planétologie, Toulouse, France  B. Mot  Institut de Recherche en
Astrophysique et Planétologie, Toulouse, France  F. Noviello  School of
Physics and Astronomy, Cardiff University, UK  C. O’Sullivan  Department of
Experimental Physics, Maynooth University, Ireland  A. Paiella  Physics
Department, Sapienza University of Rome, Italy  INFN Sezione di Roma1, Italy
G. Pisano  Physics Department, Sapienza University of Rome, Italy  S. Realini
Physics Department, Università degli Studi di Milano Statale, Italy  INFN
Sezione di Milano, Italy  A. Ritacco  Institut d’Astrophysique Spatiale,
Université Paris-Saclay, France  Département de Physique, Ecole Normale
Supérieure, Paris, France  G. Savini  Department of Physics and Astronomy,
University College London, UK  A. Suzuki  Physics Division, Lawrence Berkeley
National Lab, US  N. Trappe  Department of Experimental Physics, Maynooth
University, Ireland  B. Winterp LiteBIRD Joint Study Group Members are listed
at this link for the Litebird Joint Study Group  LiteBIRD Joint Study Group
Members are listed at this link

###### Abstract

LiteBIRD is a JAXA strategic L-class mission devoted to the measurement of
polarization of the Cosmic Microwave Background, searching for the signature
of primordial gravitational waves in the B-modes pattern of the polarization.
The onboard instrumentation includes a Middle and High Frequency Telescope
(MHFT), based on a pair of cryogenically cooled refractive telescopes
covering, respectively, the 89-224 GHz and the 166-448 GHz bands. Given the
high target sensitivity and the careful systematics control needed to achieve
the scientific goals of the mission, optical modeling and characterization are
performed with the aim to capture most of the physical effects potentially
affecting the real performance of the two refractors. We describe the main
features of the MHFT, its design drivers and the major challenges in system
optimization and characterization. We provide the current status of the
development of the optical system and we describe the current plan of
activities related to optical performance simulation and validation.

###### keywords:

LiteBIRD, Cosmic Microwave Background, polarization measurements, millimeter
wavelengths, refractive telescopes, space telescopes, optical modeling

##  1 INTRODUCTION

LiteBIRD is a planned JAXA satellite which will be inserted into a L2
Lissajous orbit by the end of 2020s with a JAXA H3 rocket, for three years of
observations.[1] The main aim of this experiment is to detect or constrain the
amplitude of a hypothesized primordial $B$-mode signal in the Cosmic Microwave
Background (CMB). LiteBIRD comprises two telescopes, the Low Frequency
Telescope (LFT), with a frequency range of 34-$161\text{\,}\mathrm{GHz}$ and
the Middle and High Frequency Telescope (MHFT) operating in the
89-$448\text{\,}\mathrm{GHz}$ range. Together, the two instruments will
observe the sky in 15 spectral bands. This proceeding is dedicated to the
optical design of the MHFT. We will review the baseline design and discuss
initial results of various optical simulations.

##  2 Middle and High Frequency Telescope Design

###  2.1 Choice of refractive over reflective design

Polarization modulation affected the MHFT design from its earliest development
phases. In fact, the MHFT trade-off analysis has been mainly driven by the
constraints due to the Half Wave Plate (HWP) technology. The wide frequency
coverage, from 89 GHz to 448 GHz, associated to the limited mass budget placed
strong constraints on the HWP material. The weight of a multi-layer sapphire
HWP, and the difficulty in applying an anti-reflection coating (ARC) for the
highest frequency channels led to discard this solution in favour of a
metamaterial-based design (mHWP)[2, 3, 4, 5]. In the framework of the ESA CDF
(Concurrent Design Facility) study, the two following designs have been
studied:

  * •

Option A - fully reflective: single reflective optics + reflective mHWP[3]
covering the full frequency range.

  * •

Option B - fully refractive: two telescopes with refractive optics +
transmissive mHWP[2], by splitting the total frequency range into mid-
frequency (MFT) and high-frequency (HFT) ranges.

Following the end of the ESA-CDF study, further work and optimizations have
been done on the design of both option A & B and most of the issues identified
during the CDF have been addressed. Among the possible implementations of mHWP
technology, the safest and less prone to unknown optical systematics was
determined to be a transmissive, mesh-based multilayer design, where the
incoming polarization is rotated while being transmitted through a rotating
flat reactive structure, located along the optical path from the sky to the
telescope. Given the broad spectral coverage, a separation of the MHFT into
two distinct optical assemblies (MFT, 89-$224\text{\,}\mathrm{GHz}$ and HFT,
166-$448\text{\,}\mathrm{GHz}$) has been proposed, each with its own
polarization modulator, in order to mitigate the bandwidth issues of the mHWP
technology. In combination with mass/volume considerations for the telescope
assemblies, and other major system-level tradeoff considerations, this study
brought to the choice of the fully refractive, on-axis dual-lens solution as a
baseline for both the MFT and for the HFT (see Fig. 1).

In this configuration, the continuously rotating polarization modulator is the
first optical element of the chain, and two AR-coated plastic lenses in a
telecentric configuration focus radiation on a flat focal surface where the
Transition Edge Sensor (TES) arrays are accommodated. The aperture stop of the
system is located skywards of the objective lens, and the HWP is placed
skywards of the aperture stop, just as close to it as practically allowed by
mechanical and thermal considerations, in order to optimize the size and mass
of the PMU mechanism. Quasi-optical filters, based on plastic-embedded metal-
mesh technology, are placed along the optical chain to prevent far-infrared
radiation from propagating all the way to the focal plane, controlling the
overall power loading on the detectors. Microwave absorbing layers on the tube
walls and around the aperture stop are implemented to ensure further control
of in-band stray-light. Final frequency selection and band refinement for each
subset of detectors take place on the focal plane assemblies. The whole
telescope unit, including the tube, the PMU, the lenses and the filters, is
cooled down to 4.8 K. A 1.8 K cold baffle surrounds the 100 mK Focal Plane
Unit (FPU), to provide both additional loading control for the environment
surrounding the FPUs and a stage of magnetic shielding for the Transition Edge
detectors. Cold forebaffles at the sky input of the tubes will be designed to
ensure reliable control of beam far sidelobes and prevent radiation pickup
from the emissive payload structure in close proximity to each telescope.

---
Figure 1:  MHFT overview, the various subsystems composing the telescopes are
identified, and held by the mechanical structure. The optical front baffles
still have to be designed.

The major strengths of the fully refractive configuration are:

  1. 1.

In addition to being simple and conventional, the design strongly benefits
from the broad expertise gained on many current and upcoming sub-orbital CMB
experiments, such as BICEP2[6], Keck[7], SPIDER[8], LSPE[9], and Simons
Observatory[10]

  2. 2.

With these very compact on-axis designs, the MFT and HFT telescopes offer the
necessary design flexibility to match the volume and mass constraints, to
mitigate stray-light issues, and to split the entire frequency range in two
bands.

  3. 3.

This choice has also obvious simplifications for the design of the separate
filtering chains.

  4. 4.

Dealing with two smaller compact telescopes will be considerably more
practical for the Assembly Integration and Test (AIT) and the Assembly
Integration Verification (AIV) phases of the project, and for all the ground
calibration activities.

On the other hand, the use of dielectric lenses implies the need for a careful
design and modeling, and a dedicated performance validation effort. This is
needed to address both the issues related to intrinsic frequency, polarization
and temperature-dependent properties of the refracting materials, as well as
to understand the higher order optical coupling effects arising from a broad
set of non-idealities, such as imperfect dielectric-to-vacuum matching at the
optical interfaces (usually compensated through custom, but not ideal, anti-
reflection coatings), imperfectly absorbing tube surfaces and focal planes,
scattering off internal surfaces, and thermal radiation pickup from the
payload environment. Some of these issues are also exacerbated by the
modulation from the transmissive HWP: since scattered radiation is likely to
be polarized with a well defined but not optimized frequency dependence. If
the stray optical paths involve a reflection on the rotating HWP, this will
result in a partial modulation of this stray radiation and therefore in a
spurious contribution in the signal bandpass, should this radiation propagate
back on the detectors.

###  2.2 Baseline optical design parameters

The LiteBIRD MHFT optical designs are based on a simple two-lens refractor
concept. Figure 2 shows a ray trace diagram of the two telescope designs. Both
telescopes employ two polypropylene (PP) or ultra-high molecular weight
polyethylene (UHMW-PE) lenses with an assumed index of refraction
$n_{\mathrm{r}}=1.52$. The final choice of the plastic material will affect
the lens profiles very marginally, even if different high-frequency losses for
the plastics may be relevant for HFT.

The lenses will employ one or multi-layer anti-reflection (AR) coatings to
support the broad frequency range covered by these telescopes[11]. A slight
preference for PP lenses emerges in this context, due to the higher melting
temperature making the ARC application easier and more reliable.

The aperture stop is located skywards of the primary lens such that the two
telescopes both have an effective (working) $f$-number of 2.2 at the center of
the focal plane. The effective $f$-number grows to 2.40-2.45 at the edge of
the focal plane. The Strehl ratios and the f-number of the MFT and HFT are
shown in Figure 3. It is clear that the designs support more than a $None$
diffraction-limited field of view.  The telescope apertures, which are placed
skywards of the primary lens, have diameters of $300\text{\,}\mathrm{mm}$ and
$200\text{\,}\mathrm{mm}$ for the MFT and HFT, respectively. The designs are
fully telecentric with a chief ray angle of incidence not exceeding $None$
across the field of view.

|
---|---
Figure 2: Ray diagrams of MFT (left) and HFT (right). The on-axis and off-axis fields (14 deg) are the blue and red rays, respectively. The telescope aperture is located at $z=0$. |
---|---
Figure 3: Left: Strehl ratio as a function of field angle for the lowest and
highest frequency bands on the MFT and HFT. Right: The effective (working)
$f$-number variation as a function of field angle for the MFT and HFT.

##  3 Preliminary optical modeling results

Numerical studies are required for the design optimization of MHFT, both
because of the complex interplay between different physical aspects of
radiation propagation through the different parts of the telescopes, as well
as for the broad range of frequencies covered by the two telescopes.
Commercially available software tools provide an effective and informative
support in this activity, but they often need to be complemented by custom
post-processing tools developed for specific studies. In addition, dielectrics
with compliant nominal properties are used as lens materials and in the
absorptive coatings. Especially at the highest frequencies, these need to be
carefully treated in order to capture all the relevant processes affecting the
telescope performance, including e.g. dielectric losses and unwanted
polarization-sensitive scattering,

Numerical simulations are being performed:

  * •

At the subsystem level, to refine the design of telescope elements, identify
critical tolerances, optimize surface coatings, investigate the broadband
behavior of surface shapes and inspect the feasibility of competing solutions
for focal plane coupling.

  * •

At the system level, in order to provide a global picture of the receiver
performance, e.g. by delivering performance-relevant quantities like
polarization-sensitive sky beams and realistic sidelobe pickup as a function
of the detector position on the focal plane. These data products are helpful
to inform more accurate TOD-based simulations of the observed microwave sky
and to provide inputs for the design and planning of RF–testing and
calibration procedures.

###  3.1 Preliminary tolerancing results.

Simple geometrical tolerancing has been performed using Zemax. This work
suggests that the MHFT design is relatively robust to error in alignment that
result in translation and rotation errors with respect to specifications. Out
of the tolerancing studies considered so far, the constraints on lens index of
refraction are found to be the most stringent. By using the Strehl ratio as a
simple performance metric, we find that an uncertainty of 0.01 in the plastic
refractive index (assuming a reference value of $n=1.52$), preserves a Strehl
ratio greater than 0.8 across the whole field of view of MFT (see Fig. 4)

Figure 4: MFT Strehl ratio across the field of view, as a function of lens
refractive index.

More advanced tolerancing studies are planned for future design iterations.
These will include surface error analyses on different scales, more realistic
representation of the tube structures and a dedicated focus on the high-
frequency behavior of dielectric materials for the HFT.

| MFT |  | HFT
---|---|---|---
| 100 | 119 | 140 | 166 | 195 |  | 195 | 238 | 280 | 337 | 402
FWHM [arcmin] | 37.8 | 33.4 | 30.4 | 28.3 | 27.2 |  | 28.6 | 24.6 | 22.4 | 20.6 | 17.7
Edge taper [dB] | -9.5 | -13.1 | -17.9 | -24.9 | -34.3 |  | -8.4 | -12.1 | -17.1 | -24.6 | -26.1
Ellipticity | 0.002 | 0.003 | 0.005 | 0.008 | 0.011 |  | 0.003 | 0.005 | 0.008 | 0.010 | 0.0115
Table 1: Mean predicted optical parameters for the each of the five MFT and
HFT frequency bands. The mean is estimated from 12 and 7 simulations for MFT
and HFT, respectively (see dicussion in Section 3.2).

###  3.2 Baseline physical optics simulation results

Simple physical optics simulations are used to predict the far field response
of the proposed optical design. These simulations can be used to study the
expected variation in beam size and beam ellipticity as a function of
frequency and field location. The same framework can be used to estimate
spillover past lenses and the aperture stop (see Section 3.3). For this work,
we make use of a simulation framework first described in Ref. 12. We refer the
reader to this work for a more detailed discussion of the simulation and
analysis methodology. Key optical properties derived from these physical
optics simulations are summarized in Table 1.

The physical optics simulations use Gaussian pixel beams as input. The width
of the Gaussian beams correspond to the assumed pixel apertures, 11.6 and
$6.6\text{\,}\mathrm{mm}$ for the MFT and HFT, respectively. In order to
optimize time usage, the simulations are run for a single frequency within a
given band. Moreover, because of the azimuthal symmetry of the two-lens
refractor design, we only run simulations for a handful of detectors along a
radial line from the center of the focal plane out to its edge, this number of
detectors being 7 and 12 for the MFT and HFT, respectively. These physical
optics simulations involve only the two lenses and the cold aperture stop,
also assuming perfect mechanical alignment and material properties while
ignoring any reflections. Figure 5 shows the predicted beam ellipticity as a
function of field angle for the MFT and HFT frequency bands. We define the
beam ellipticity as

$e=\frac{\sigma_{\mathrm{max}}-\sigma_{\mathrm{min}}}{\sigma_{\mathrm{max}}+\sigma_{\mathrm{min}}},$
(1)

where $\sigma_{\mathrm{max}}$ and $\sigma_{\mathrm{min}}$ correspond to the
widths of the best fit Gaussian envelope to the semi-major and semi-minor axis
of the co-polarized far field beam response.

As expected, the beam ellipticity is predicted to grow with field location and
frequency. We note however that the ellipticity is observed to be quite low
even at the edge of the $None$ field of view at the highest frequencies. For
comparison, the mean beam ellipticity of the 100 and
$143\text{\text{-}}\mathrm{GHz}$ channels on Planck was roughly 0.085 and
0.020, respectively [13].

|
---|---
Figure 5: Simulated MFT and HFT beam ellipticity as a function of field angle
for all 10 frequency bands.

###  3.3 Spillover simulation results

Accurate modeling of optical spillover inside the optics tube is necessary for
sensitivity estimates. We can use the physical optics modeling results to
estimate the beam power that misses the secondary and primary lenses and the
aperture stop. By summing up the optical power that misses these optical
elements and comparing it to the pixel beam model input, we can estimate the
fractional cold spillover. Further discussion of this simulation approach is
described in Ref. 12.

As the expected pixel beam response of the proposed detector designs was not
available, these simulations rely on the same Gaussian pixel beam that is used
for analysis described in Section 3.2. Figure 6 shows the predicted edge taper
as a function of focal plane location for the MFT and HFT. For off-axis
pixels, we define the edge taper as azimuthally averaged beam power along the
stop edge. As expected, we see a slight increase in the edge taper as we move
across the focal plane. It is important to note that because of the fixed
pixel diameter assumed for the MFT and HFT, we observe significant shift in
the edge taper as a function of frequency. Consequently, the conservative edge
taper for the high-frequency bands should help reduce sidelobe response.

|
---|---
Figure 6: MFT and HFT edge taper as a function of field angle for all 10
frequency bands.

###  3.4 Inclusion of forebaffle effects

In addition to the dual lens optical path response, the final radiation
pattern is affected by several elements of the MHFT telescopes – e.g.
forebaffle, mHWP, filters, tube with internal absorber, ARC and optical
properties of the lenses among the few – each of them having an impact,
possibly negligible, on different angular ranges. The most off-axis pixels of
the focal plane are characterized by an intrinsic degree of asymmetry which
could magnify the effect of these telescope elements on the beam. Therefore,
we study the impact of each individual item on the resulting beam separately,
in order to assess the angular range which is mainly affected as well as the
relevant intensity in terms of sidelobe levels. An analysis to optimize the
telescope components is also desirable, as it allows for an estimation of the
sensitivity of the beam response to these effects; e.g. the tube diameter, the
properties of the tube internal absorber, forebaffle length, etc.

|
---|---
Figure 7: Left: MFT telescope model used to simulate the forebaffle flare
angle impact on the MFT radiation patterns. The telescope tube is not included
in the simulation, and the forebaffle is assumed to be completely absorbing,
so that only its aperture is considered. Right: the MFT beam former response
is similar to that of a sinuous antenna coupled to a lenslet.

As an example, we now discuss the effect of the forebaffle size on the MFT
beams. We simulated the MFT optics with physical optics, including the feed,
the two lenses, the cold stop aperture and a fully absorbing forebaffle, as
shown in Figure 7. Keeping the total length of the forebaffle fixed to its
nominal value of 270 mm, we varied the flare angle within the range of 10° to
18° (the entrance aperture of the forebaffle is modified accordingly between
395 and 475 mm) to verify the impact on the radiation pattern at the MFT
frequencies of 100, 119, 140, 166 and 195 GHz.

Figure 8 depicts the co-polar beams (phi = 90°) at 100 GHz for the on-axis
pixel. Lower flare angles determine an increase of order of 3.5 dB in the
intermediate sidelobe levels in the angular region between 10 and 15 degrees
and a substantial increase of the far sidelobes at angles larger than $\pm 50$
degrees, still about 80 dB below the main directivity.

The entire analysis includes the co-polar and cross-polar response for on-axis
and off-axis pixels on the focal plane. Similar analyses will be performed for
the different elements of the MHFT telescopes in order to assess their impact
on the final beam, also by combining those components which have a non-
negligible impact on the optical response.

---
Figure 8: Radiation pattern at 100 GHz for the MFT on-axis pixel with varying
forebaffle flare angle.

###  3.5 Feed simulations

The feed beam patterns have been redundantly simulated with mode-matching and
full 3D electromagnetic modeling software. After validating the basic results,
the full-wave software Ansys HFSS has been used to generate a first set of
simulations, thus providing lenslet beam patterns at $89$–$112$ GHz for MFT
and feedhorn beam patterns in the $402$ GHz band of HFT. These feed patterns
have been used so far for preliminary studies of spillover effects. Work is
underway to include these patterns in a full telescope simulation to inform
TOD-based simulations with more realistic beams. A longer-term project
involves therefore the production of the full frequency-dependent set of
lenslet and feed patterns. Such activity is expected to be particularly useful
for the HFT, for which a full system-level numerical simulation is well out of
reach of the available modeling/computing resources.

#### MFT

The MFT focal plane will feature sinuous antenna-coupled detectors with a
silicon AR-coated lenslet[14, 15]. The lenslet diameter is 12 mm for all the
MFT bands. A sketch of the device and the corresponding simulated beam
patterns are shown in Fig. 9.

The MFT detector array consists of seven hexagonal wafers, each of which holds
61 pixels. To observe multiple bands, band-pass filters and multiple TES
detectors are built into multichroic assemblies. The total number of the
detectors in MFT is 2074.

|
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Figure 9: Left: sketch of baseline MFT coupling devices, made of a sinuous
antenna and AR-coated silicon lenslet Right: Beam cuts at $100$ GHz. Copolar
beam cuts are shown at $\phi=0^{\circ}$, $45^{\circ}$ and $90^{\circ}$.
Maximum cross-polarization is shown for $\phi=45^{\circ}$.

#### HFT

The HFT will employ horn-coupled detectors[14]. The horn diameters are 6.6 mm
for the 195 to 338-GHz bands and 5.7 mm for the 402 GHz band. The 6.6-mm horns
make two 127-pixel arrays with planar Ortho-Mode Transducers (OMTs). Each
6.6-mm horn array can observe two bands and two linear polarizations,
simultaneously, so that 254 TESs are employed. The 5.7-mm horns make a 168
pixel monochromatic array with OMT. The total number of the detectors in HFT
is 1354. Two different horn profiles have been proposed for the 402 GHz
detectors. Both are based on Si platelet technology [16] and are shown in the
left panel of Fig. 10. The first profile is a corrugated feedhorn made of
$101$ $150\mu m$–thick platelets, while the second is a spline-profile horn,
adapted to the platelet technology in order to be made of $61$ $250\mu
m$–thick platelets. Nominal performance for both models is excellent, as
summarized in Tab. 2.

Horn type | Corrugated | Spline-profiled
---|---|---
Spillover efficiency avg (max) |  $0.924$ $(0.933)$ |  $0.968$ $(0.986)$
Co-polar beam asymmetry avg (max) |  $0.0037$ $(0.057)$ |  $0.0017$ $(-0.053)$
Cross-polarization avg (max) |  $3.6\cdot 10^{-4}$ $(4\cdot 10^{-3})$ |  $13\cdot 10^{-4}$ $(6\cdot 10^{-3})$
Reflection loss avg (max) |  $-31$dB $(-25$dB$)$ |  $23$dB $(-17$dB$)$
Table 2: Synthetic data for proposed HFT horn geometries. Beam-integrated
quantities refer to a nominal coupling F-number of 2.2. Maximum and average
values refer to the highest HFT frequency channel, with a center frequency of
402 GHz and a 25% bandwidth.

In order to check the consistency of current fabrication and assembly
tolerances of silicon platelet feedhorns with the global coupling requirements
of the HFT, an analysis has been started to investigate the impact of plate-
to-plate misalignment on beam properties. Fig. 11 shows that the copolar and
cross-polar beam patterns are very stable for both horn designs with $3\mu m$
rms displacements between neighboring platelets. This level of alignment has
been achieved in previous silicon platelet horn builds by use of a simple pin
and slot alignment method. The band-averaged HFT spillover efficiency of the
corrugated (spline-profiled) horn is $\sim 93\%$ ($\sim 96\%$), and changes by
no more than $2\%$ over $100$ misalignment realizations for either profile. We
also find that the peak cross-polar response is $<0.7\%$ for all realizations.
These results hold up to the upper edge of the highest HFT band, suggesting
that both designs are suitable for HFT implementation. Additional simulation
work is underway to investigate more extreme or self-correlated misplacement
profiles along the horn.

|
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Figure 10:  Left: Corrugated and spline-profiled feedhorns proposed for the HFT highest frequency baseline channel. Right: Beam cuts of candidate HFT feedhorns at 450GHz. Copolar beam cuts are shown for $\phi=0^{\circ}$, $45^{\circ}$ and $90^{\circ}$. Maximum cross-polarization is shown for $\phi=45^{\circ}$.  |
---|---
Figure 11: Beam cuts of candidate HFT feedhorns for random, $3\mu m\ rms$
platelet misplacements. Copolar beam cuts are shown for $\phi=0^{\circ}$.
Cross-polarization is shown for $\phi=45^{\circ}$. Left: Corrugated feedhorn.
Right: Spline-profiled feedhorn. Colored bands highlight the region containing
68% of realizations.

##  4 Modeling Challenges and mitigating actions

### Optical Ghosts

Telescope ghosts are position-sensitive artifacts originating by field
propagation across the optical system, due to non-ideal behavior of the
optical elements and of supporting/surrounding structures. A few examples are
an imperfect absorption by tube walls, non-ideal AR coatings on HWP and lens
surfaces, with consequent frequency and polarization dependent reflection and
scattering, and an imperfectly matched focal plane coupling. Radiation re-
launched from these effects on optical paths getting it at least partially
refocused on the focal plane will be detected as more or less diffused
structures superimposed over the actual image of the sky, potentially yielding
systematic effects in signal recovery. Preliminary physical optics simulations
have been run to check the ability of common simulation algorithms to capture
some of these effects. As an example, Fig. 12 shows the effects of non-ideal
single-layer ARCs on the 90 GHz beam pattern and field distribution in a
simplified version of the MFT, for a nominal pixel position 40 mm off the
center of the focal plane.

|
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Figure 12:  Left: Optical ghosting at 90 GHz resulting from the combined
effect of non-ideal ARC on MFT lenses and imperfect absorption on the focal
plane, as seen in the telescope far field. Radiation is launched from a focal
plane positon corresponding to a 40 mm off-center detector. Right: Intensity
distribution in the telescope plane for the same combination of effects.

The effort towards a robust modeling and understanding of the relative
contributions of ghosts to the systematic effects is still ongoing. Scattering
effects, in particular, are not easily captured in existing software codes,
especially when system level simulations are performed. This is why a
validation campaign based on experimental measurements on real-life sample
systems is needed to ensure a correct evaluation of the ghosting problem
across the whole MFT and HFT frequency range.

### Polarization Modulator

The continuous rotation by the HWP of the input polarization provides quasi-
simultaneous observations of the I, Q and U Stokes parameter across the focal
plane pixels. In addition, thanks to the HWP modulation, the input
polarization is shifted at higher frequency with reference to the slower
signal fluctuations that are usually associated with any kind of noise coming
from the instrumentation: electronics, cryogenics etc.

However, imperfections of the HWP lead to the modulation of the background
signal which appears to peak at harmonics of the HWP rotation frequency in the
data spectrum. This kind of instrumental noise is known as HWP parasitic
signal (HWPSS) and has been observed in previous experiments, such as Maxima
[17], EBEX [18], NIKA [19]. Methods are available to model this signal and
subtract it in the data analysis step from the TOD of each detector [19].

In addition, any departure from a Gaussian shape of the beam can cause leakage
of the total intensity to polarization, resulting in a beam pattern deformed
in polarization [19]. This effect might be observed in the Stokes Q and U maps
of an unpolarized source and we refer to it as instrumental polarization. The
modelling of this beam pattern is usually more difficult [20] for large arrays
of detectors because each detector might have a slightly different beam. For
this reason the knowledge of the beams and the study of the effect through
simulations and laboratory tests with the full optics, including the HWP, is
crucial to constrain such a systematic in the final data.

### Absorbers

Quasi-optical filters will be designed and implemented to reject unwanted
radiation propagating from the sky all the way down to the focal plane.
Nonetheless, in-band radiation may picked up as a consequence of scattering
off or re-emitted from optical elements or devices along the optical chain. As
already anticipated, this is responsible for excess loading and/or image
artifacts on the focal planes. The use of absorbing coatings and materials,
possibly complemented by a careful shaping of the internal surfaces of the
tube assemblies, is a standard technique to mitigate such issues. Ideally, a
perfect absorber emits an exact blackbody spectrum (in which case the loading
on the focal planes depends only on the absorber temperature), absorbs
efficiently radiation well away from normal incidence, and features a large
thermal inertia, so that the radiating/absorbing properties don’t exhibit
thermal drifts which might ultimately determine dangerous time-constant
effects in the detectors response. In addition, any candidate absorber for the
MHFT tubes must comply with the tight mass allocation constraints and meet the
requirements for space qualification.

A wealth of space-qualified absorbers have been proposed in the past for far-
infrared missions[21, 22]. These are mostly based on dielectric molds loaded
with conductive scattering powders, and their characteristics are available in
the literature down to THz frequencies. Other materials, like Eccosorb CR-110,
have long been known to approach blackbody emissivity down to tens of GHz[23].
Recent work has been devoted to characterize loaded epoxy powders as absorbers
at THz and sub-THz frequencies[24, 25, 26]. Metamaterial-based absorbers,
based on low-frequency adaptations of THz metamaterial designs[27] have also
been recently proposed, even if their readiness for space environment and
actual applicability on non-flat surfaces have yet to be explored. 3D-printed
absorbing structures have also been recently demonstrated in selected bands
below 230 GHz[28].

Regardless of the technology of the adopted solution, MHFT absorbers need to
be carefully measured and modeled to assess their behavior at low temperature
(the MFT and HFT tubes operate at 5K) in terms of incidence-, polarization-
and frequency-dependent reflectance and scattering properties. Most of these
effects cannot be easily implemented in numerical simulations and their
treatment must rely on experimental data for the specific materials involved
at the MHFT frequencies. Absorbers around the cold aperture stop, in
particular, are a source of major concern because of the close vicinity to the
warm PMU mechanism. They are meant to mitigate the excess radiation leaking in
the tube through diffraction and scattering off the edges of the aperture
stop.

The current effort for MFT and HFT absorber studies is twofold:

  * •

Representative subsystem-level simulations are performed to optimize surface
shaping as a function of coating thickness, typical illumination and
likelihood of unwanted pickup.

  * •

A systematic characterization campaign has been started to update the
available information on known materials or molds thorugh dedicated
measurements on samples: spectral/polarimetric room-temperature measurements
of reflectance and scattering will be followed by representative tests in cold
environment.

The results of these studies are meant to inform the tradeoff between
electromagnetic performance and impact on the mass budget, and to inspect the
need for a passive or active thermal control of the most sensitive regions of
the tubes.

##  5 Supporting laboratory measurements

The overall LiteBIRD requirements, dictated by the science goals, translate
into a need in the knowledge of the optical system to unprecedented levels. We
therefore need to rely extensively on dedicated experimental characterisation
in order to verify our assumptions, build and consolidate our models. These
experimental measurements need to happen at different levels, starting from
material characterization to sub-system and system-level performance
assessment. Similarly to any space mission, several models of the instruments
will be developed over the years in order to build our knowledge of the
overall performances of MHFT (typically prototype, qualification model
followed by the flight model). However several fundamental questions need to
be answered very soon in order to gain confidence in the results of our
modelling tools. Questions such as the knowledge of material optical
characteristics at very low temperature, impact of potential in-homogeneity of
the lens material, accuracy of refractive optics modelling, mainly when
polarisation is concerned, still need to be answered to the required accuracy
level. Therefore preliminary characterisations will be performed in parallel,
on materials and on breadboard models, starting from a very simple
configuration (BB1 - BreadBoard 1) evolving then to more complete and complex
optical concepts.
BB1 comprises only one lens coupled to a small array of corrugated feedhorns
(left panel of Fig. 13), allowing to compare predicted and measured co- and
cross-polarisation beams for on-axis and off-axis pixels. The first GRASP
modelling results are presented in the right panel of Fig. 13. Through this
simple concept the accuracy of the modelling will be tested.
BB2 will then be a two lens system, again coupled to corrugated feedhorns in
order to be closer to the MHFT optical design, even if not the same. In
addition to improving the accuracy in the modelling, other tests such as
positioning tolerances between optical components will performed.
While these breadboards will be characterised over the MHFT frequency range,
cryogenics RF characterisation of materials, such as the ones for lenses, or
again potential absorbers will be run in parallel in order to measure their
properties at very low temperature. These tests will rely on Fourier Transform
Spectrometer and quasi optical setups coupled to vector network analysers
measurement systems.

|
---|---
Figure 13: Left: BreadBoard 1 configuration. Right:  Simulated far-field beam
patterns corresponding to BB1. The figure shows co-polarization (ECO) and
cross-polarization (EXP) field amplitude resulting from the illumination of
the lens by on-axis and off-axis pixels for different azimuthal cuts (E- / H-
/ 45°- /135°- planes).

##  6 Concluding remarks.

We have provided an overview of the major optical studies and outstanding
issues related to the Litebird MFT and HFT design. After describing the
general issues of the optical design in relation to the unprecedented
performance requirements of LiteBIRD, and in particular to the use of
continuously rotating PMUs, we have described the baseline optical parameters
along with the main design drivers which helped define the current optical
configuration of MHFT. We have shown preliminary analysis of the optical
configuration for both telescopes and basic physical optics studies of the
telescope properties, including tolerancing studies, forebaffle and spillover
effects. Realistic feed simulations have been separately run to inform the
physical optics studies with more realistic representations of the FPU and
telescope coupling. Sample studies of higher-level effects, related to the
presence of non-ideal HWPs, optical ghosts, imperfectly absorptive structures
have been discussed. We also pointed out the existence of a coordinated effort
towards experimental validation of the adopted modeling tools and methods, in
view of the next generation of optical studies, aimed both at final system
design and optimization, and to the achievement of a more complete and
realistic picture of instrument performance for end-to-end evaluation of
scientific performance.

###### Acknowledgements.

This work is supported in Japan by ISAS/JAXA for Pre-Phase A2 studies, by the
acceleration program of JAXA research and development directorate, by the
World Premier International Research Center Initiative (WPI) of MEXT, by the
JSPS Core-to-Core Program of A. Advanced Research Networks, and by JSPS
KAKENHI Grant Numbers JP15H05891, JP17H01115, and JP17H01125. The Italian
LiteBIRD phase A contribution is supported by the Italian Space Agency (ASI
Grants No. 2020-9-HH.0 and 2016-24-H.1-2018), the National Institute for
Nuclear Physics (INFN) and the National Institute for Astrophysics (INAF). The
French LiteBIRD phase A contribution is supported by the Centre National
d’Etudes Spatiale (CNES), by the Centre National de la Recherche Scientifique
(CNRS), and by the Commissariat à l’Energie Atomique (CEA). The Canadian
contribution is supported by the Canadian Space Agency. The US contribution is
supported by NASA grant No. 80NSSC18K0132. Norwegian participation in LiteBIRD
is supported by the Research Council of Norway (Grant No. 263011). The Spanish
LiteBIRD phase A contribution is supported by the Spanish Agencia Estatal de
Investigación (AEI), project refs. PID2019-110610RB-C21 and AYA2017-84185-P.
Funds that support contributions from Sweden come from the Swedish National
Space Agency (SNSA/Rymdstyrelsen) and the Swedish Research Council (Reg. no.
2019-03959). The German participation in LiteBIRD is supported in part by the
Excellence Cluster ORIGINS, which is funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s
Excellence Strategy (Grant No. EXC-2094 - 390783311). This research used
resources of the Central Computing System owned and operated by the Computing
Research Center at KEK, as well as resources of the National Energy Research
Scientific Computing Center, a DOE Office of Science User Facility supported
by the Office of Science of the U.S. Department of Energy. The European Space
Agency (ESA) has led a Concurrent Design Facility study, focused on the MHFT
and Sub-Kelvin coolers, and funded Technology Research Programmes for “Large
radii Half-Wave Plate (HWP) development” (contract number:
4000123266/18/NL/AF) and for the ‘Development of Large Anti‐Reflection Coated
Lenses for Passive (Sub)Millimeter‐Wave Science Instruments” (contract number:
4000128517/19/NL/AS). In addition, the authors would like to acknowledge the
Ile de France region through its DIM-ACAV programme, the university Paris-
Saclay through a chaire d’excellence, and the OSUPS that have supported the
work presented here.

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