We analyze the polarization properties of the tilted off-axis dual-reflector
submillimeter-wave telescope on the ESA PLANCK Surveyor designed for measuring
the temperature anisotropies and polarization characteristics of the cosmic
microwave background.Comment: 5 pages, 4 figures, 1 tabl

Yurchenko, Vladimir

English

arXiv

Vladimir Yurchenko

Crossref

Measuring CMB polarization with ESA PLANCK subMM-wave telescope

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Measuring CMB Polarization with ESA PLANCK
SubMM-Wave Telescope
Vladimir Yurchenko∗†
∗ Experimental Physics Department, National University of Ireland, Maynooth, Co. Kildare, Ireland
† Institute of Radiophysics and Electronics, National Acad.Sci , 12 Proskura St., Kharkov, 61085, Ukraine
Abstract. We analyze the polarization properties of the tilted off-axis dual-reflector submillimeter-wave tele-
scope on the ESA PLANCK Surveyor designed for measuring the temperature anisotropies and polarization
characteristics of the cosmic microwave background.
INTRODUCTION
The dual-reflector submillimeter-wave telescope on the ESAPL NCK Surveyor is being designed for measuring the
temperature anisotropies and polarization characteristics of the cosmic microwave background (CMB).
Our research is concerned with one of its focal plane instruments, Far-IR High Frequency Instrument (HFI) [1],
which will cover six frequency bands centered at 100, 143,217, 353, 545 and 857GHz providing the sensitivity of
∆T/T ∼ 10−6 and the angular resolution down to 5 arcminutes. The HFI consists of an array of 36 horn antenna
structures (Fig. 1, a) feeding the bolometric detectors which will be cryogenically cooled to a temperature of 100mK.
One objective of the research is the optimization of the HFI optical design and the computation of the HFI beam
patterns. The challenge of the problem is that the telescopeis electrically large (D/λ = 4300 atλ = 350µm) and
consists of two essentially defocused ellipsoidal reflectors providing a very large field of view at the focal plane.
Another objective is the characterization of the polarization properties of the multi-beam telescope system. The
CMB polarization is expected to be at a level of only 10% of thetemperature anisotropy quadrupole, and the success
of the measurements will depend crucially on the precise knowledge of the polarization properties of the telescope.
FORMULATION OF THE PROBLEM
While the performance of the antenna structures can be thoroughly tested in terrestrial conditions, the coupling of the
HFI with the telescope is, basically, optimized through thecomputer simulations.
Among various simulation techniques, physical optics (PO)is the most adequate one for the given purpose.
However, conventional implementations of the technique [2, 3] do not fit the size of the problem. Commercially
available packages are also very limited in their capacity to rigorously answer this sort of questions. For example, even
the best commercial software requires many hours of the full-sca e physical optics computation of the main beam of
the telescope at the relatively low frequency of 143GHz, while all conventional physical optics codes collapse at the
highest frequencies of 545−857GHz.
To solve the problem, we developed a special PO code [1] that allowed us to overcome the limitations of a generic
approach for large multi-reflector systems and perform typical simulations of the telescope in the order of minutes.
Generally, it requires only 1 minute for a polarized Gaussian beam at the frequency of 143GHzand about 30 minutes
for the beam of 30 modes at 857GHzusing a PC Pentium III (500MHz) under the Linux operating system.
We simulated the beams of twelve linearly polarized Gaussian horns operating in the transmitting mode at the nom-
inal frequencies 143, 217, and 353GHz. Each horn is designed for the simultaneous measurement of two orthogonal
linear polarizations, ’a’ and ’b’, of the incoming radiation. The polarization is characterized by the tiltψ of the electric
field at the beam axis in the sky with respect to the local vertical as defined below. The tilt isψa =+45◦ andψb =−45◦
(a) (b)
FIGURE 1. (a) Horn positions on the focal plane as seen from the telescope. (b) Total power of the telescope beam 143-1a
computed for the clipped Gaussian feed model F3 witha= 3.9mm, w= 2.8mm, andL = 120mm( f = 143GHz).
(a) (b)
FIGURE 2. Power pattern of the telescope beam from the enhanced horn HFI-143-1a (ψa = +45◦, feed model F1) at the
frequency (a) 121GHzand (b) 166GHz.
for the horns 143-1, 143-2, 217-5, 217-6, 353-3, and 353-4 (see Fig. 1, a), whileψa = 0◦ andψb = 90◦ for the other
six polarized horns (the angleψ is measured clockwise from the upward vertical direction asseen from the telescope).
We compared three different models of the horn feed, F1, F2 and F3, when the source field is specified in different
manner. The feed model F1 is represented by the far-field power and phase patterns of the actual corrugated horn
in 0◦/45◦/90◦ cuts which are used in a somewhat approximate manner for computing the incident complex-vector
electromagnetic field on the secondary mirror. The feed F2 isspecified by the ’clipped Gaussian’ model distribution of
the horn aperture electric field which is accurately propagated to the secondary mirror and further through the system.
Finally, the feed F3 is represented by the far-field patternssimilar to the model F1 which, however, are computed
precisely from the clipped Gaussian aperture field of the model F2 and then used in an approximate manner identical
to the feed model F1.
The electric field at the aperture of the Gaussian horn in the feed models F2 and F3 is specified as
~E(r) = E0exp(−r
2/w2a)exp(−iqr
2)~e, 0≤ r ≤ a (1)
wherer is the radial coordinate,wa is the beam radius at the horn aperture,a is the horn aperture radius,q= π/λL,
L is the curvature radius of the wavefront at the aperture (approximately,L is the horn slant length), and~e=~ea,b is
the unit polarization vector (~E(r) = 0 if r > a). The aperture model of this kind is quite accurate in representing the
field of real Gaussian horns. In particular, both the power and phase patterns of such a horn computed at the frequency
100GHzcoincide perfectly well with the experimental data available for the model Gaussian horn designed for this
frequency. However, some discrepancies in the sidelobes atthe level of about−30dBappear for the horns specifically
optimized for the higher angular resolution.
The comparison of the feed models F2 and F3 shows that the minor d fferences can only be observed in the
polarization patterns at the periphery of the telescope beam while the power patterns of the main beam are identical
for both models. The beams computed with the feed models F1 and F3 are also very similar when the parameters
of the model F3 are properly adjusted. In this case, also, it is only the polarization at the periphery of the beam that
differs slightly for different models while the power patterns are very similar even at the level below−30dB. Finally,
the orientation of the polarization vector on the beam axis in the sky field is precisely the same for all the feed models,
and the polarization pattern, in general, is rather independent of both the horn pattern and of the fine features of the
propagation model used in the simulations. It proves that the far-field model F1 can safely be used for the simulation
of the telescope beams from the real horns despite the approximations used in the model.
POLARIZATION OF THE GAUSSIAN BEAMS
Fig. 1, b, shows the power pattern of the telescope beam H-143-1 as projected on the plane normal to the telescope
line-of-sight at the(0,0) point (ax anday are the horizontal and vertical axes on the plane, respectively, measured in
degrees). The beam axis is at the pointax =−1.3645◦, ay = 1.1975◦ which is defined as the point of maximum power
of the beam. The pattern is computed for the clipped Gaussianfeed model F3 with adjusted parametersa= 3.9mm,
w= 2.8mm, andL = 120mm, simulating the enhanced horn operating at the frequencyf = 143GHz.
The beam is well shaped down to almost−30dB below the maximum and can be approximated by a Gaussian
function (at this level, the pattern does not depend on polarization) with the full beam width ofWmin = 7.05 arcmin
andWmax= 7.50 arcmin measured at−3dB. The polarization of the beam is generally elliptical except precisely at the
beam axis where it remains linear. In order to achieve the requi d orientation of the polarization pattern in the sky, we
should orient the polarization vector~e properly on the horn aperture [1].
For immediate comparison of polarizations measured by different horns when scanning through the sky, we should
use easily aligned directions in the sky as equivalent reference polarization axes for different beams. Such directions
are the meridians in the spherical frame of the telescope, with the pole being the telescope spin axis tilted byη = 85◦
with respect to the line-of-sight (the meridians define locaverticals at various observation points while the parallels
are local horizontals that constitute the orthogonal directions).
Now, we should define the reference axis for the polarizationvector~e of a tilted horn. We define the reference axis
as the direction of~e in the horn aperture plane that is projected on the vertical axis of the focal plane. The orientation
of~e is specified by the angleφ in the horn aperture plane measured from this reference in a clockwise direction when
looking from the horn to the secondary mirror.
Using these definitions, we have found that the beam of the H-143-1 horn is polarized at its axis at the required
angles of (a)ψa = +45◦ and (b)ψb = −45◦ if the horn polarization vector~e is specified by the angleφa = +42.99◦
andφb =−47.01◦, respectively.
When the polarization vector~e is properly oriented, the cross-polarized component of thear field measured along
the respective orthogonal direction in the sky is minimized. In such a case, the power pattern of the cross-polarized
component is, basically, determined by the power pattern ofthe semi-minor axis of the polarization ellipse at each
observation point of the beam. This pattern is very much the same for any orientation of the polarization vector and
can be approximated as follows
Pcr = Pcr0 [(θ/θ0) sin(ϕ−ϕ0)]p exp[(θ/θ0)q] (2)
wherePcr0, dB, is the maximum power of the minor axis component achieved atthe points specified by the polar angle
θ0 and the azimuthal anglesϕ0±90◦ measured from the center of the pattern which is located at the beam axis (the
values of the parameters in this approximation depend on theposition of the horn considered but the magnitude ofPcr0
is, typically, more than 30dBbelow the maximum value of the total power of the beam).
Since the actual frequency bands of the horns are rather wide(121−166, 182−252, and 295−411GHz), the far-
field patterns of real horns differ essentially at the lower and upper frequencies of each band. It results in somewhat
(a) (b)
FIGURE 3. Deviation of the major axis of polarization ellipse from local vertical in the beam from the enhanced horn HFI-143-1a
(ψa =+45◦, feed model F1) at the frequency (a) 121GHzand (b) 166GHz.
(a) (b)
FIGURE 4. Deviation of the major axis of polarization ellipse from local vertical in the beam from the enhanced horn HFI-143-1b
(ψb =−45◦, feed model F1) at the frequency (a) 121GHzand (b) 166GHz
different power and polarization patterns of the telescopebeam as shown in Figures 2 - 4. Nevertheless, despite these
differences, the polarization angles at the beam axis are the same irrelevant of the horn patterns and of the operating
frequency.
The values of the aperture polarization angleφ computed for all the HFI horns as well as the direction cosines (the
Cartesian components of the unit vector) of the aperture electric field with respect to the coordinate frameM1 of the
primary mirror are summarized in the Table 1.
CONCLUSIONS
A fast physical optics code has been developed for the analysis of the dual-reflector submillimeter-wave telescope
on the ESA PLANCK Surveyor. The code overcomes the limitations f a generic approach for large multi-reflector
quasi-optical systems and can perform typical simulationsof the telescope in the order of minutes.
TABLE 1. Orientation of the Polarization Vector~e of the Aperture Electric Field
HFI horn Aperture Angle Unit Vector of the Aperture Electric Field
φ [degrees] eXM1 eYM1 eZM1
143-1-a 42.99 0.629015 0.679549 0.377562
143-1-b -47.01 0.521115 -0.728982 0.443874
143-2-a 44.17 0.597142 0.696388 0.398076
143-2-b -45.83 0.552563 -0.716862 0.425186
143-3-a 0.82 0.813844 0.014303 0.580907
143-3-b -89.18 0.031357 -0.999321 -0.019324
143-4-a 2.10 0.812137 0.036506 0.582323
143-4-b -87.90 0.080095 -0.995568 -0.049291
217-5-a 42.99 0.661010 0.680077 0.317114
217-5-b -47.01 0.567397 -0.729548 0.381863
217-6-a 44.11 0.634880 0.695677 0.336097
217-6-b -45.89 0.593249 -0.717633 0.364772
217-7-a 0.89 0.869188 0.015525 0.494238
217-7-b -89.11 0.029397 -0.999362 -0.020308
217-8-a 2.01 0.867847 0.034982 0.495598
217-8-b -87.99 0.066276 -0.996754 -0.045699
353-3-a 43.70 0.634926 0.690048 0.347422
353-3-b -46.30 0.571370 -0.722094 0.390020
353-4-a 44.70 0.610581 0.703339 0.364012
353-4-b -45.30 0.594981 -0.710743 0.375289
353-5-a 0.58 0.853206 0.010120 0.521476
353-5-b -89.42 0.020092 -0.999707 -0.013472
353-6-a 1.51 0.852069 0.026308 0.522767
353-6-b -88.49 0.052455 -0.998000 -0.035275
Simulations of the telescope beams from the linearly polarized horns have shown that the far-field of the telescope
is, generally, elliptically polarized except precisely atthe beam axis where the linear polarization is preserved. The
magnitude of the minor semi-axis of the polarization ellipse in the telescope beam remains at the level of−30dB
below the maximum total power of the beam even for the most tilted horns located at the edge of the HFI horn array.
When rotating the polarization vector of the horn field aboutthe horn axis, the major axes of the polarization ellipses
at the central part of the telescope beam rotate virtually bythe same angle about the beam axis while the power patterns
of both the co- and cross-polarized components of the far field remain basically unchanged.
Thus, the orthogonal polarization directions at the beam axis in the sky are transformed into the orthogonal directions
in the focal plane of the telescope. Some deviations from this basic rule which occur mainly at the periphery of the
beam are of minor importance since they virtually do not contribu e to the measured total power of the polarized
component.
ACKNOWLEDGMENTS
The author is grateful to Bruno Maffei for the power and phasepatterns of enhanced horns and to Yuying Longval for
providing the updated positions and aiming angles of the HFIhorns along with the map of the focal plane. The author
would like to acknowledge the support of Enterprise Ireland.
REFERENCES
1. Yurchenko, V., Murphy, J. A., and Lamarre, J. M.,Int. J. Infrared and Millimeter Waves, 22, 173-184 (2001).
2. Diaz, L., and Milligan, T.,Antenna Engineering Using Physical Optics: Practical CAD Techniques and Software, Artech
House, London, 1996.
3. Scott, C.,Modern Methods of Reflector Antenna Analysis and Design, Artech House, London, 1990.


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