RF properties. of the Planck telescope. Designed by ALCATEL. CASE No. 1. Per Heighwood Nielsen

Transcription

1 TICRA engineering consultants communications systems and antennas RF properties of the Planck telescope Designed by ALCATEL CASE No. 1 November, 1999 S Author: Per Heighwood Nielsen TICRA KRON PRINSENS GADE 13 DK-1114 COPENHAGEN K DENMARK VAT REGISTRATION NO. DK TELEPHONE TELEFAX POSTAL GIRO: ACCOUNT NO ticra@ticra.com TICRA FOND REG. NO

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3 TICRA i TABLE OF CONTENTS 1. INTRODUCTION VERIFICATION OF CODE V RESULTS OPTIMIZATION OF MIRRORS INFLUENCE OF 10µ SURFACE TOLERANCE ON THE RF PERFORMANCE REFERENCES... 37

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5 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.

6 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 and shown in Figure 2-1. The ellipsoid surface parameters are as follows: Primary mirror: Vertex distance, 2a foci distance, 2c = 22, mm = 20, mm Secondary mirror: Vertex distance, 2a = 1, mm foci distance, 2c = mm angle of secondary mirror axis The Horn coordinate system is rotated 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

7 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.

8 4 TICRA X o Primary mirror Z o X f Z s X s Z f Secondary mirror Figure 2-1 Geometry of aplanatic antenna system.

9 TICRA 5 X f LFI70-18 LFI70-20 HFI100-1 HFI100-2 LFI100-8 Y f HFI545-8 HFI857-1 LFI100-6 HFI353-6 HFI HFI HFI LFI100-4 LFI100-2 LFI30-27 LFI44-24 Figure 2-2 Geometry of horn array.

10 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] [%] E E E E E E E E E E E E E E E E L E E L E E L E E L E E L E E L E E L E E L E E Table 2.1 RF characteristics of aplanatic antenna, case no. 1.

11 TICRA 7 Freq. Incident power in db at φ Angle [Ghz] 0 (-X) 90 (-Y) 180 (+X) 270 (+Y) L L L L L L L L Table 2.2 Illumination of main reflector on aplanatic antenna, case no. 1.

12 8 TICRA a) Amplitude in db below peak b) Phase in degrees Figure 2-3 Aperture fields from LFI horn at 30GHz.

13 TICRA 9 Figure 2-4 Beam from HFI horn no. 1 at 857 GHz. Figure 2-5 Beam from HFI horn no. 8 at 545 GHz.

14 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.

15 TICRA 11 Figure 2-8 Beam from HFI horn no. 10 at 143 GHz. Figure 2-9 Beam from HFI horn no. 11 at 143 GHz.

16 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.

17 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.

18 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.

19 TICRA 15 Figure 2-16 Beam from LFI horn no. 18 at 70 GHz. Figure 2-17 Beam from LFI horn no. 20 at 70 GHz.

20 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.

21 TICRA 17 Figure 2-20 Cx pol. at 857 GHz., Max lev dbi. Figure 2-21 Cx pol. at 30 GHz., Max level 25.5 dbi.

22 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.

23 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.

24 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] [%] E E E E E E E E E E E E E E E E L E E L E E L E E L E E L E E L E E L E E L E E Table 3.1 RF characteristics of aplanatic antenna optimised on all beam peaks.

25 TICRA 21 Freq. Incident power in db at φ Angle [Ghz] 0 (-X) 90 (-Y) 180 (+X) 270 (+Y) L L L L L L L L Table 3.2 Illumination of main reflector on antenna optimised for increase of all beam peaks.

26 22 TICRA a) Surface shaping, m. b) Optimised Zernike modes, mm. Figure 3-1 Shaping of main reflector

27 TICRA 23 a) Surface shaping, m. b) Optimised Zernike modes, mm. Figure 3-2 Shaping of subreflector

28 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] [%] E E E E E E E E E E E E E E E E L E E L E E L E E L E E L E E L E E L E E L E E Table 3.3 RF characteristics of aplanatic antenna optimised for max. Strehl ratios.

29 TICRA 25 Freq. Incident power in db at φ Angle [Ghz] 0 (-X) 90 (-Y) 180 (+X) 270 (+Y) L L L L L L L L Table 3.4 Illumination of main reflector on antenna optimised for max. Strehl ratios.

30 26 TICRA a) Surface shaping, m. b) Optimised Zernike modes, mm. Figure 3-3 Shaping of main reflector

31 TICRA 27 a) Surface shaping, m. b) Optimised Zernike modes, mm. Figure 3-4 Shaping of subreflector

32 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 , 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 sidelobes. The results agree very well with the equations developed in TICRA report S , where the maximum envelope error power for a given θ angle is:

33 TICRA 29 G max = 2k δrms sin θ 2 e (4.1) and the θ angle corresponds to a correlation length of k c = 2/sin θ. (4.2) δ rms is the root mean square aperture degradation related to the surface degradation, ε, by: δ rms = 1.4ε rms (4.3) Inserting ε rms = 10µ at 857 GHz in equation 4.1 we have G max = -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: 2 p D sin θ G m = 10 log η e (4.6) 4δrms or with η.3 G m p = 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.

34 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.

35 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.

36 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.

37 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.

38 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.

39 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.

40 36 TICRA Figure 4-7 Ruze Error envelope compared with field patterns for different correlation length.

41 TICRA 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 TICRA, 1999, Design and analysis of the COBRAS/SAMBA telescope. Final report S