TICRAKRON PRINSENS GADE 13 · DK-1114 COPENHAGEN K DENMARK VAT REGISTRATION NO. DK-1055 8697TELEPHONE +45 33 12 45 72 TELEFAX +45 33 12 08 80 POSTAL GIRO: ACCOUNT NO. 1 19 81 81E-MAIL ticra@ticra.com http://www.ticra.com TICRA FOND REG. NO. 112.467

Author: Per Heighwood Nielsen

RF properties

of the Planck telescope

Designed by ALCATEL

CASE No. 1

November, 1999 S-801-04

TICRAengineering consultantscommunications systems and antennas

TICRA i

TABLE OF CONTENTS

1. INTRODUCTION .............................................. 1

2. VERIFICATION OF CODE V RESULTS ............................ 2

3. OPTIMIZATION OF MIRRORS .................................. 18

4. INFLUENCE OF 10µ SURFACE TOLERANCE ON THE RFPERFORMANCE .............................................. 28

5. REFERENCES ............................................... 37

TICRA 1

1. INTRODUCTION

This report describes the analysis of the RF properties of the

Planck telescope with an aplanatic geometry designed by ALCATEL

and referenced as CASE No. 1. The geometry and the RF

performance of this system are presented in Chapter 2.

In Chapter 3 the ALCATEL design with two elliptical mirrors is

subject to fine-tuning by deforming the mirror surfaces

further. The RF results for two optimizations are presented.

In Chapter 4 the 10µ rms specification for the mirror surfaces

tolerances for all correlation lengths larger than 0.8 mm is

tested by calculating the RF performance at the highest

frequency for different grid densities of a random surface

distortion on the main reflector.

2 TICRA

2. VERIFICATION OF CODE V RESULTS

The geometry of the aplanatic ALCATEL design, denoted CASE No.

1, is defined in ESA Doc. No. PT-DS-07024 and shown in

Figure 2-1. The ellipsoid surface parameters are as follows:

Primary mirror:

Vertex distance, 2a = 22,054.94 mm

foci distance, 2c = 20,564.58 mm

Secondary mirror:

Vertex distance, 2a = 1,641.580 mm

foci distance, 2c = 761.9193 mm

angle of secondary mirror axis 10.10°

The Horn coordinate system is rotated 21.27° in relation to the

secondary mirror coordinate system. The positions and

directions of the horns are provided by ESA and Alcatel, see

Figure 2-2.

The RF performance of the system is calculated for 8 HFI- and 8

LFI horns by the GRASP8 program. The horns are all modelled as

simple Gaussian feeds with the taper given in Table 4.6.a in

the Alcatel Doc. No. PLAS TN 009. The main RF parameters are

given in Table 2.1 and the main reflector illumination in the

major planes is presented in Table 2.2. The values are related

to the “spill over” values in the CODE V program, but the

coordinate system is rotated 180°, meaning that the φ values in

the main reflector coordinate system correspond as 0°(-X), 90°(-

Y), 180°(+X), 270°(+Y). Furthermore, the given values are the

subreflector field illumination rather than the horn taper as

in CODE V. The amplitude of the main reflector aperture field

at 30 GHz is shown in Figure 2-3a.

The rms values and the Strehl ratios in Table 2.1 are

calculated from the phase of the aperture fields, see

Figure 2-3b. The wave front error, WFE, in wavelength is

TICRA 3

deduced from the aperture phase taking into account the

periodic nature of the phase. Then the rms values are

calculated by integration of the WFE over the aperture using

the aperture field amplitude as weight.

The GRASP8 calculations agree very well with the CODE V results

in Table 4.6.a in Doc. No. PLAS TN 009.

The main beams are presented as contour curves in a UV grid in

Figure 2-4 to Figure 2-19, where the centre of each plot is the

beam direction given in Table 2.1. The cross-polar component is

shown for the horn at 857 GHz and 30 GHz in Figure 2-20 and

Figure 2-21, respectively. The contour curves are drawn for the

field levels 3dB, 6dB, 10dB, 20dB and 30dB below peak.

4 TICRA

Primary mirror

Secondary mirror

Xf

Zf

Xo

Zo

Xs

Zs

Figure 2-1 Geometry of aplanatic antenna system.

TICRA 5

Yf

Xf

LFI30-27LFI44-24

LFI70-20

LFI70-18

LFI100-8

LFI100-6

LFI100-4

LFI100-2

HFI100-1

HFI100-2

HFI143-11

HFI143-10

HFI217-12

HFI353-6

HFI545-8 HFI857-1

Figure 2-2 Geometry of horn array.

6 TICRA

GRASP8 Beam data of ALCATEL CASE NO. 1

Freq. Beam direction Peak Spillover Aperture error Angles from peak to Coverage area Angular Power inside

Ghz U V RMS Strehl 3dB [arcmin] 20dB 3dB 20dB Resolut. 3dB 20dB

[dBi] [dB] [%] [lambda] ratio min max min max [steradians] [arcmin] [%]

857-1 0.000 0.004 77.02 0.00 0.00 0.074 0.808 0.75 0.85 1.60 2.47 0.172E-06 0.113E-05 1.61 49.825 98.099

545-8 0.002 0.037 72.11 0.00 0.00 0.115 0.592 1.28 1.56 3.17 4.44 0.516E-06 0.385E-05 2.79 47.921 98.511

353-6 -0.005 0.037 69.23 0.00 0.00 0.075 0.803 1.81 2.13 4.62 5.87 0.102E-05 0.715E-05 3.92 49.081 98.611

217-12 -0.028 0.021 66.63 0.00 0.00 0.047 0.916 2.41 2.95 6.20 7.53 0.190E-05 0.125E-04 5.35 50.371 98.828

143-10 -0.014 0.033 63.60 0.00 0.02 0.038 0.944 3.50 4.12 8.62 10.75 0.384E-05 0.247E-04 7.60 50.663 98.802

143-11 -0.029 0.009 63.77 0.00 0.02 0.033 0.958 3.41 4.14 8.46 10.29 0.374E-05 0.230E-04 7.51 51.312 99.012

100-1 0.028 0.025 60.97 0.00 0.08 0.040 0.938 4.80 5.54 11.49 15.21 0.706E-05 0.450E-04 10.30 50.687 98.695

100-2 0.035 0.008 60.93 0.00 0.07 0.035 0.954 5.02 5.46 12.27 14.75 0.716E-05 0.446E-04 10.38 51.033 98.779

100-L2 -0.052 0.016 60.35 0.00 0.02 0.043 0.929 4.78 6.32 11.72 16.04 0.814E-05 0.519E-04 11.07 50.658 98.930

100-L4 -0.040 0.050 59.86 0.00 0.02 0.069 0.828 4.95 6.67 12.16 17.41 0.895E-05 0.598E-04 11.61 49.842 98.801

100-L6 -0.009 0.058 59.59 0.00 0.01 0.064 0.851 5.35 6.66 13.36 17.60 0.955E-05 0.638E-04 11.98 49.857 98.809

100-L8 0.023 0.058 59.05 0.00 0.01 0.075 0.802 5.80 7.00 14.63 18.82 0.108E-04 0.722E-04 12.72 49.631 98.790

70-L18 0.060 0.052 55.42 0.00 0.01 0.087 0.740 8.82 10.64 22.47 28.28 0.248E-04 0.166E-03 19.30 49.487 98.706

70-L20 0.065 0.011 55.87 0.00 0.00 0.057 0.879 8.57 9.91 21.77 26.20 0.225E-04 0.148E-03 18.39 49.888 98.783

44-L24 -0.069 0.000 54.22 0.01 0.13 0.030 0.965 9.63 13.12 22.29 32.95 0.338E-04 0.205E-03 22.54 51.268 98.778

30-L27 -0.055 0.073 50.71 0.01 0.26 0.049 0.911 14.01 19.95 32.73 51.83 0.748E-04 0.473E-03 33.54 50.636 98.324

Table 2.1 RF characteristics of aplanatic antenna, case no. 1.

TICRA 7

Freq. Incident power in dB at φ Angle

[Ghz] 0°(-X) 90°(-Y) 180°(+X) 270°(+Y)

857-1 -67.16 -61.13 -54.48 -60.30

545-8 -67.19 -62.06 -53.59 -55.45

353-6 -64.57 -62.72 -52.23 -55.65

217-12 -41.99 -49.84 -38.63 -46.95

143-10 -39.76 -42.13 -34.26 -37.99

143-11 -34.98 -42.20 -32.91 -40.87

100-1 -39.56 -30.78 -30.16 -28.42

100-2 -41.60 -30.32 -30.98 -29.34

100-L2 -32.14 -48.62 -34.53 -46.81

100-L4 -37.06 -48.90 -34.96 -42.53

100-L6 -48.27 -48.61 -39.07 -40.52

100-L8 -57.58 -46.89 -43.06 -38.53

70-L18 -63.15 -43.54 -46.53 -36.52

70-L20 -65.87 -42.50 -48.49 -41.06

44-L24 -22.34 -40.34 -26.99 -40.34

30-L27 -27.38 -39.64 -26.52 -33.30

Table 2.2 Illumination of main reflector onaplanatic antenna, case no. 1.

8 TICRA

a) Amplitude in dB below peak

b) Phase in degrees

Figure 2-3 Aperture fields from LFI horn at 30GHz.

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Figure 2-4 Beam from HFI horn no. 1 at 857 GHz.

Figure 2-5 Beam from HFI horn no. 8 at 545 GHz.

10 TICRA

Figure 2-6 Beam from HFI horn no. 6 at 353 GHz.

Figure 2-7 Beam from HFI horn no. 12 at 217 GHz.

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Figure 2-8 Beam from HFI horn no. 10 at 143 GHz.

Figure 2-9 Beam from HFI horn no. 11 at 143 GHz.

12 TICRA

Figure 2-10 Beam from HFI horn no. 1 at 100 GHz.

Figure 2-11 Beam from HFI horn no. 2 at 100 GHz.

TICRA 13

Figure 2-12 Beam from LFI horn no. 2 at 100 GHz.

Figure 2-13 Beam from LFI horn no. 4 at 100 GHz.

14 TICRA

Figure 2-14 Beam from LFI horn no. 6 at 100 GHz.

Figure 2-15 Beam from LFI horn no. 8 at 100 GHz.

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Figure 2-16 Beam from LFI horn no. 18 at 70 GHz.

Figure 2-17 Beam from LFI horn no. 20 at 70 GHz.

16 TICRA

Figure 2-18 Beam from LFI horn no. 24 at 44 GHz.

Figure 2-19 Beam from LFI horn no. 27 at 30 GHz.

TICRA 17

Figure 2-20 Cx pol. at 857 GHz., Max lev. 35.8 dBi.

Figure 2-21 Cx pol. at 30 GHz., Max level 25.5 dBi.

18 TICRA

3. OPTIMIZATION OF MIRRORS

The ALCATEL optimization of the aplanatic antenna in the

previous Chapter is performed using a Geometrical Optic

analysis of an antenna system with two elliptical mirrors. It

may therefore be possible to fine-tune the design by deforming

the mirror surfaces further. Due to the advanced stage of the

horn array construction the positions and directions of the

horns are fixed. The symmetry of the system is retained in the

optimization due to the actually nearly symmetric horn cluster.

The surface shaping is performed using Zernike modes on both

main and subreflector. The maximum order of the Zernike modes

for the main reflector is determined by the most rapid phase

variation of the aperture field. The phase degradation in

Figure 2-3 for the 30 GHz beam demands a Zernike mode with an m

mode of fifth order to compensate for the rotated deformation.

Due to the symmetry constraints only the amplitudes of the

Zernike modes can be varied. Therefore, the rotation can not be

compensated using a rotated astigmatic mode (2,2).

The Zernike modes for the subreflector shaping are limited to a

maximum of m=3, where the m=2 modes are excluded in order to

retain the spillover on the main reflector.

Two optimization goals are investigated. The first is to

improve all 16 beams equally, giving the same RF beam peak

increase in dB. The obtained main RF parameters are given in

Table 3.1 and the main reflector illumination is presented in

Table 3.2. The beam peak increase is largest, 0.1 dB, for the

545 GHz horn, 0.05 dB for the 353 GHz horn and only around 0.01

dB for the other horns. The peak increase is mainly a result of

a generated beam tilt which results in an enlarged effective

aperture. The spillover and main reflector illumination are

unchanged as required.

TICRA 19

The shaping of the main and subreflector is shown in Figure 3-1

and Figure 3-2, respectively.

In the second optimization the aim is to improve especially the

545 GHz beam, being the one with the largest beam loss. The

goal in the optimization is therefore set to the maximum

possible beam peaks. The obtained RF parameters given in Table

3.3 shows that this is obtained. The beam peak is indeed

increased 0.83 dB for the 545 GHz horn, 0.36 dB for the 353 GHz

horn and around 0.1 dB for the LFI horns no. 4 ,6 and 8 at 100

GHz. However, the beam peaks are decreased for all the other

horns up to 0.5dB for the 857GHz horn. The spillover and main

reflector illumination, presented in Table 3.4, are unchanged

as required.

The shaping of the main and subreflector is shown in Figure 3-3

and Figure 3-4, respectively.

20 TICRA

GRASP8 Beam data of ALCATEL CASE NO. 1. Optimisation of all Beam Peaks.

Freq. Beam direction Peak Spillover Aperture error Angles from peak to Coverage area Angular Power inside

Ghz U V RMS Strehl 3dB [arcmin] 20dB 3dB 20dB Resolut. 3dB 20dB

[dBi] [dB] [%] [lambda] ratio min max min max [steradians] [arcmin] [%]

857-1 0.000 0.004 77.02 0.00 0.00 0.077 0.790 0.74 0.87 1.57 2.44 0.176E-06 0.108E-05 1.63 50.900 98.430

545-8 0.001 0.037 72.22 0.00 0.00 0.117 0.584 1.24 1.49 3.05 4.60 0.502E-06 0.377E-05 2.75 47.864 98.473

353-6 -0.005 0.037 69.28 0.00 0.00 0.074 0.805 1.79 2.11 4.57 5.64 0.101E-05 0.705E-05 3.90 49.031 98.615

217-12 -0.028 0.021 66.65 0.00 0.00 0.047 0.917 2.44 2.95 6.11 7.47 0.190E-05 0.124E-04 5.34 50.359 98.877

143-10 -0.014 0.033 63.61 0.00 0.02 0.038 0.944 3.49 4.13 8.51 10.57 0.384E-05 0.246E-04 7.60 50.731 98.833

143-11 -0.029 0.009 63.77 0.00 0.02 0.033 0.958 3.40 4.14 8.34 10.34 0.374E-05 0.230E-04 7.50 51.284 99.035

100-1 0.028 0.025 60.97 0.00 0.08 0.040 0.938 4.82 5.52 11.60 15.10 0.706E-05 0.446E-04 10.30 50.801 98.736

100-2 0.035 0.008 60.94 0.00 0.07 0.035 0.954 5.02 5.46 12.22 14.76 0.716E-05 0.444E-04 10.38 51.093 98.807

100-L2 -0.052 0.016 60.35 0.00 0.02 0.043 0.929 4.81 6.31 11.77 16.07 0.813E-05 0.519E-04 11.06 50.643 98.930

100-L4 -0.040 0.050 59.87 0.00 0.02 0.069 0.829 4.95 6.68 12.15 17.58 0.894E-05 0.596E-04 11.60 49.874 98.809

100-L6 -0.010 0.058 59.60 0.00 0.01 0.064 0.851 5.33 6.68 13.22 17.31 0.951E-05 0.635E-04 11.96 49.825 98.815

100-L8 0.023 0.058 59.06 0.00 0.01 0.075 0.802 5.81 7.00 14.55 18.71 0.107E-04 0.720E-04 12.71 49.657 98.790

70-L18 0.060 0.052 55.43 0.00 0.01 0.087 0.742 8.84 10.63 22.66 28.19 0.247E-04 0.166E-03 19.27 49.464 98.704

70-L20 0.065 0.011 55.89 0.00 0.00 0.057 0.881 8.58 9.95 21.86 26.12 0.224E-04 0.148E-03 18.37 49.899 98.784

44-L24 -0.069 0.000 54.22 0.01 0.13 0.030 0.965 9.65 13.11 22.35 33.01 0.337E-04 0.205E-03 22.53 51.273 98.773

30-L27 -0.055 0.073 50.71 0.01 0.26 0.049 0.911 13.99 19.97 32.67 52.04 0.747E-04 0.473E-03 33.52 50.632 98.327

Table 3.1 RF characteristics of aplanatic antenna optimised on all beam peaks.

TICRA 21

Freq. Incident power in dB at φ Angle

[Ghz] 0°(-X) 90°(-Y) 180°(+X) 270°(+Y)

857-1 -67.20 -61.10 -54.40 -60.27

545-8 -67.23 -62.03 -53.51 -55.43

353-6 -64.60 -62.70 -52.15 -55.62

217-12 -41.95 -49.81 -38.57 -46.93

143-10 -39.75 -42.11 -34.21 -37.97

143-11 -34.95 -42.18 -32.86 -40.85

100-1 -39.62 -30.77 -30.12 -28.40

100-2 -41.67 -30.31 -30.94 -29.33

100-L2 -32.09 -48.60 -34.48 -46.78

100-L4 -37.02 -48.88 -34.91 -42.51

100-L6 -48.28 -48.59 -39.01 -40.50

100-L8 -57.67 -46.88 -43.00 -38.52

70-L18 -63.30 -43.54 -46.48 -36.51

70-L20 -66.04 -42.49 -48.43 -41.05

44-L24 -22.30 -40.31 -26.95 -40.31

30-L27 -27.34 -39.63 -26.48 -33.28

Table 3.2 Illumination of main reflector onantenna optimised for increase of allbeam peaks.

22 TICRA

a) Surface shaping, m.

b) Optimised Zernike modes, mm.

Figure 3-1 Shaping of main reflector

TICRA 23

a) Surface shaping, m.

b) Optimised Zernike modes, mm.

Figure 3-2 Shaping of subreflector

24 TICRA

GRASP8 Beam data of ALCATEL CASE NO. 1. Optimisation of Strehl ratios.

Freq. Beam direction Peak Spillover Aperture error Angles from peak to Coverage area Angular Power inside

Ghz U V RMS Strehl 3dB [arcmin] 20dB 3dB 20dB Resolut. 3dB 20dB

[dBi] [dB] [%] [lambda] ratio min max min max [steradians] [arcmin] [%]

857-1 0.000 0.004 76.50 0.00 0.00 0.115 0.592 0.79 0.91 2.04 2.82 0.190E-06 0.147E-05 1.69 48.823 98.243

545-8 0.002 0.037 72.94 0.00 0.00 0.089 0.732 1.18 1.40 2.71 3.88 0.437E-06 0.300E-05 2.57 49.314 98.385

353-6 -0.005 0.037 69.59 0.00 0.00 0.059 0.872 1.75 2.05 4.14 5.37 0.958E-06 0.637E-05 3.80 49.955 98.588

217-12 -0.028 0.021 66.49 0.00 0.00 0.058 0.876 2.43 3.04 6.51 7.47 0.196E-05 0.130E-04 5.44 50.270 98.540

143-10 -0.014 0.033 63.64 0.00 0.02 0.036 0.950 3.52 4.11 8.66 10.38 0.383E-05 0.240E-04 7.59 50.973 98.725

143-11 -0.029 0.009 63.60 0.00 0.02 0.047 0.915 3.40 4.28 8.69 10.49 0.388E-05 0.239E-04 7.64 51.179 98.773

100-1 0.028 0.025 60.93 0.00 0.08 0.044 0.928 4.82 5.57 11.65 15.14 0.713E-05 0.450E-04 10.36 50.801 98.641

100-2 0.035 0.008 60.77 0.00 0.07 0.047 0.917 5.17 5.51 12.65 15.02 0.740E-05 0.465E-04 10.55 50.846 98.729

100-L2 -0.052 0.016 60.26 0.00 0.02 0.049 0.908 4.78 6.43 12.08 16.18 0.827E-05 0.536E-04 11.16 50.446 98.759

100-L4 -0.040 0.049 59.91 0.00 0.02 0.067 0.836 4.94 6.67 11.95 17.56 0.886E-05 0.591E-04 11.54 49.860 98.751

100-L6 -0.009 0.058 59.74 0.00 0.01 0.057 0.880 5.29 6.57 12.89 17.08 0.926E-05 0.611E-04 11.80 50.062 98.828

100-L8 0.023 0.058 59.18 0.00 0.01 0.069 0.826 5.73 6.86 14.39 18.10 0.105E-04 0.695E-04 12.57 49.856 98.807

70-L18 0.060 0.052 55.38 0.00 0.01 0.089 0.731 8.92 10.55 22.69 28.23 0.250E-04 0.168E-03 19.39 49.501 98.700

70-L20 0.065 0.011 55.75 0.00 0.00 0.064 0.850 8.78 9.90 22.19 26.50 0.231E-04 0.153E-03 18.64 49.803 98.759

44-L24 -0.069 0.000 54.19 0.01 0.13 0.033 0.957 9.63 13.23 22.57 33.12 0.340E-04 0.207E-03 22.61 51.185 98.714

30-L27 -0.055 0.073 50.72 0.01 0.26 0.048 0.914 14.03 19.93 32.75 52.10 0.746E-04 0.470E-03 33.50 50.691 98.326

Table 3.3 RF characteristics of aplanatic antenna optimised for max. Strehl ratios.

TICRA 25

Freq. Incident power in dB at φ Angle

[Ghz] 0°(-X) 90°(-Y) 180°(+X) 270°(+Y)

857-1 -67.12 -61.12 -54.47 -60.29

545-8 -67.16 -62.06 -53.58 -55.44

353-6 -64.54 -62.72 -52.22 -55.63

217-12 -41.97 -49.83 -38.62 -46.93

143-10 -39.74 -42.13 -34.26 -37.97

143-11 -34.96 -42.19 -32.91 -40.86

100-1 -39.54 -30.79 -30.16 -28.42

100-2 -41.57 -30.32 -30.98 -29.34

100-L2 -32.13 -48.61 -34.52 -46.79

100-L4 -37.05 -48.89 -34.96 -42.51

100-L6 -48.26 -48.61 -39.06 -40.50

100-L8 -57.56 -46.90 -43.05 -38.53

70-L18 -63.12 -43.56 -46.53 -36.53

70-L20 -65.83 -42.51 -48.48 -41.07

44-L24 -22.33 -40.32 -26.98 -40.32

30-L27 -27.38 -39.64 -26.52 -33.28

Table 3.4 Illumination of main reflector onantenna optimised for max. Strehlratios.

26 TICRA

a) Surface shaping, m.

b) Optimised Zernike modes, mm.

Figure 3-3 Shaping of main reflector

TICRA 27

a) Surface shaping, m.

b) Optimised Zernike modes, mm.

Figure 3-4 Shaping of subreflector

28 TICRA

4. INFLUENCE OF 10µ SURFACE TOLERANCE ON THE RF PERFORMANCE

The original specification for the mirror surfaces was 10µ rms

from the best-fit paraboloid/ellipsoid on all correlation

lengths larger than .8 mm. To illustrate the implications of

this surface accuracy requirement the RF performance is

calculated at the highest frequency for different grid

densities of a random surface distortion on the main reflector.

The grid spacing, s, defines the correlation length shown in

Table 4.1, c≈2s.

Grid spacing s D/2 D/5 D/15 D/50 D/150 D/500

Correlation length c 1500mm 600mm 200mm 60mm 20mm 6mm

Table 4.1 Minimum correlation lengths.

The surface distortions are shown in Figure 4-1a to Figure

4-6a.

A surface error with large correlation length as in Figure 4-1a

only influences the RF performance near the main beam according

to Ruze equation, TICRA report S-699-02, but, due to the large

phase degradation from the reflector shaping giving a wide main

beam, this RF distortion field is hidden inside the main beam

in Figure 4-1c. For smaller correlation length the distortion

field shows up in Figure 4-2 to Figure 4-6. At the smallest

correlation length, 6 mm, the main beam shape is almost

unchanged, but the field is scattered to the far-out side-

lobes.

The results agree very well with the equations developed in

TICRA report S-699-02, where the maximum envelope error power

for a given θ angle is:

TICRA 29

esin

k2G

2rms

max

θδ

= (4.1)

and the θ angle corresponds to a correlation length of

k c = 2/sin θ. (4.2)

δrms is the root mean square aperture degradation related to the

surface degradation, ε, by:

δrms = 1.4εrms (4.3)

Inserting εrms = 10µ at 857 GHz in equation 4.1 we have

Gmax = -10.3dBi – 20log(sin θ). (4.4)

The envelope is compared with all patterns for different

correlation lengths in Figure 4-7.

Using the peak gain equation

G = η(kD/2)2, (4.5)

where η is the antenna efficiency, in Ruze equation 4.1 the

maximum envelope error gain below peak is given by:

δ

θη= e4

sinDlog10G

2

rms

pm (4.6)

or with η≈.3

Gmp = 87dBi + 20log(sin θ). (4.7)

It is interesting to note that expression (4.6) is independent

of the operating frequency. This means that if the distortion

field generated by the surface distortions is required to be at

a given level below the peak at a given angle from boresight

then the necessary surface accuracy is the same for all

frequencies.

30 TICRA

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-1 Correlation length, ≈1500mm.

TICRA 31

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-2 Correlation length, ≈600mm.

32 TICRA

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-3 Correlation length, ≈200mm.

TICRA 33

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-4 Correlation length, ≈60mm.

34 TICRA

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-5 Correlation length, ≈20mm.

TICRA 35

a) Surface degradation, m.

b) RF performance in φ=0°.

c) Zoomed RF performance in φ=0°.

Figure 4-6 Correlation length, ≈6mm.

36 TICRA

Figure 4-7 Ruze Error envelope compared with fieldpatterns for different correlationlength.

TICRA 37

5. REFERENCES

ALCATEL, 26/07/1999,

"Planck Payload Module Architect Technical Assistance,

Telescope optimisation & RF analysis”. Phase 1 report.

Doc. No. PLAS TN 009.

ESA, 01/09/1999,

Draft report. Doc. No. PT-DS-07024.

TICRA, 1999,

“Design and analysis of the COBRAS/SAMBA telescope”.

Final report S-699-02.