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National Astronomy and Ionosphere Center Arecibo Observatory
Focal Array Memo Series

Final Feed Selection Study For the

Multi Beam Array System

By: Germñn Cortùs-Medellýn

CORNELL
University

July/19/2002 Rev. 00

National Science Foundation


NAIC INDEX Introduction ................................................................................................................................ 3 Antenna Analysis Methodology ................................................................................................ 3 2.1 Frequency Band ................................................................................................................. 3 2.2 Polarization ........................................................................................................................ 3 2.3 Radiation Patterns .............................................................................................................. 3 2.4 Edge Taper Angle .............................................................................................................. 3 2.5 Antenna Gain and G/T Analysis ........................................................................................ 3 3. Feed Horn Characteristics .......................................................................................................... 3 3.1 CSIRO Coaxial Horn, 22cm Aperture ............................................................................... 3 3.2 CSIRO TE11 Mode Horn, 25cm Aperture.......................................................................... 4 4. Feed Horn Performance ............................................................................................................. 4 4.1 Feed Horn Radiation Patterns ............................................................................................ 4 4.2 Feed Horn 60ÀSpillover Efficiency.................................................................................... 4 5. Optics and Array Layout ............................................................................................................ 5 6. Multi Beam Antenna Performance ............................................................................................ 6 6.1 Feed Horn: CSIRO Coaxial 19.6 cm x 20.4 cm ................................................................ 7 6.2 Feed Horn: CSIRO Coaxial 22.0 cm x 22.8 cm ................................................................ 9 6.3 Feed Horn: Parkes TE11 mode Horn 24 cm x 26.25 cm ................................................. 11 6.4 Feed Horn: CSIRO TE11 mode Horn 25 cm x 26.0 cm .................................................. 13 6.5 Feed Horn: NIAC TE11 mode Horn 26 cm x 26.8 cm ..................................................... 15 7. Comparative Antenna Sensitivity and Aeff/Tsys........................................................................ 16 8. Sky Footprint and Multi-Beam Characteristics ....................................................................... 18 8.1 Feed Motion vs. Antenna Far Field Beam Motion .......................................................... 18 8.2 Antenna Far Field Multi Beam Characteristics ............................................................... 18 8.3 Multi Beam Comatic Levels ............................................................................................ 21 8.4 Total Multi Beam Incoherent Pattern .............................................................................. 22 8.5 Drift Scan Sampling and Multi Beam.............................................................................. 22 9. Conclusions .............................................................................................................................. 26 Appendix A. ..................................................................................................................................... 27 1. 2.

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1. Introduction
This document presents the evaluation of the two CSIRO feed designs for the Arecibo Multi-Beam Array System, namely, a 22cm aperture coaxial horn and a TE11 mode feed horn, with 25cm aperture diameter. We made a comparison of the feed performance of these two designs in the multi beam system with the performance of previously analyzed feed horns1. In addition, a comparison in terms of the imaging characteristics, sky footprint, coma levels, beamoverlapping levels, and drifts scan characteristics for these two feeds is also included.

2. Antenna Analysis Methodology
2.1 Frequency Band
For each horn we analyzed three frequency points in the L-Band: Ç 1.225 GHz Ç 1.375 GHz Ç 1.525 GHz

2.2 2.3 2.4 2.5

Polarization Radiation Patterns Edge Taper Angle Antenna Gain and G/T Analysis

The horns were linearly polarized (VERT or HORZ). Dr. Bird provided radiation patterns at the three specified frequencies in the form of E and H plane cuts with < 180 deg; with both magnitude and phase for each cut. The tertiary reflector edge of the Arecibo Gregorian System is at an angle of 60À with respect the optical axis of the feeds. We obtained a spherical wave expansion of the feed radiation patterns, and we proceeded to perform a complete antenna gain analysis of the Arecibo radio telescope optics by a combination of kinematics and electrodynamics ray tracing, and aperture field integration. Finally, we performed a noise analysis as seen by the feed to obtain the overall G/T, using all previous techniques in conjunction with a detailed Gregorian noise mapping.

3. Feed Horn Characteristics
3.1 CSIRO Coaxial Horn, 22cm Aperture
This feed horn is similar to Lowell's coaxial horn, with a diameter of 22.0 cm, a 4.0 cm inner conductor. The horns have a return loss > 22 dB across the band. The radiation patterns were obtained with the horn located on a 100 cm diameter ground plane.

Germñn Cortùs-Medellýn, "Feed Selection", Arecibo Observatory Focal Array Memo Series, National Astronomy and Ionosphere Center, Cornell University, July 29, 2001.

1

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3.2 CSIRO TE11 Mode Horn, 25cm Aperture
This feed horn design is a stepped TE11 mode horn similar to Parkes, with an aperture diameter of 25.0 cm, and approximately 60 cm in length. The horn design uses four steps and have a return loss > 22 dB across the band. The radiation patterns were obtained with the horn aperture located on an 80 cm diameter ground plane.

4. Feed Horn Performance
4.1 Feed Horn Radiation Patterns
The radiation patterns of these two designs are presented in the Appendix A, along with the radiation patterns of the last 3 feed horns previously analyzed1, namely, Dr. Bird's 19.6 coaxial feed horn, Parkes 24.0 cm TE11 mode Horn, and our 26.0 cm TE11 mode horn.

4.2

Feed Horn 60ÀSpillover Efficiency

Figure 4.1 shows the calculated feed horn 60À spillover efficiency. CSIRO TE11 mode horn 25 cm design has the highest overall spillover efficiency, followed by the 26 cm TE11 mode horn design. Only at the upper end of the band CSIRO Coaxial 22.0 cm design produces a higher value of spillover efficiency. Hence, CSIRO TE11 mode horn 25 cm design it is expected to have a lower noise antenna temperature than CSIRO Coaxial 22.0 cm design all over the band except possibly at the highest end.
Arecibo Multi Beam System
Feed Spillover Efficiency at Taper Angle of 60À
100 98

Feed Spillover Efficiency @ 60À [%]

96 94 92 90 88 86 84 82 80 1.200

CSIRO TE11 25.0 cm NAIC TE11 26.0 cm CSIRO Coax 22.0 cm CSIRO Coax 19.6 cm Parkes TE11 24.0 cm

1.250

1 . 3 00

1.350

1.400

1.450

1.500

1.550

Frequency [GHz]

Figure 4.1 Feed 60À Spillover Efficiency July 19, 2002 4


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5. Optics and Array Layout
Figure 5.1 shows the array layout convention in the focal plane and the orientation of the focal plane in the antenna in Figure 5.2

Figure 5.1 Array Layout in the Focal Plane

Figure 5.2 Coordinate system in the Focal Plane

Figure 5.3 shows the scanning loss of the Arecibo Gregorian System in the focal plane along the x and y axis at 1.375 GHz. The system is symmetrical along the y-axis from y<0 to y>0, but is asymmetrical along the x-axis, with a higher level of scanning loss along x <0.
Arecibo Gregorian System Scanning Losses and Field of View (1.375 GHz)
0.0 -0.2 -0.4 -0.6
Scanning Loss [dB]

-0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Displacement along X/Y Axis [cm]
Along X-Axis Along Y-Axis

Figure 5.3 Scanning Losses in the FOV for the Arecibo Gregorian System

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In order to compensate for this asymmetry, we shift the center position of the multi beam system by a given amount along the x-axis to equalize the scanning losses for all the exterior pixels. Table 5.1 summarizes the feed characteristics as the feed aperture diameter, Do, and center-tocenter separation, D1, and the X-offset used for all the horns in the calculations. Table 5.1 Feed Horn Aperture and Center-to-Center Separation in the Array

Feed Horn Type CSIRO CSIRO Parkes CSIRO NAIC Coax Coax TE11 TE11 TE11 19.6 22.0 24.0 25.0 26.0

Aperture Diameter [cm] 19.60 22.00 24.00 25.00 26.00

Center-to-Center Separation [cm] 20.40 22.80 26.25 26.00 26.80

X-Offset [cm] 1.75 2.40 2.80 2.70 2.60

6. Multi Beam Antenna Performance
We evaluated the antenna performance for five multi beam systems, using each of the horns shown in Table 5.1. In order to further study the astigmatic levels of the Arecibo Gregorian FOV, for the exterior pixels, we calculated the overall antenna performance as a function of angular position, from 0À to 180À, in 30À steps, as indicated in Figure 6.1.



Figure 6.1 Geometry of external feed location as a function of angle in the Focal Plane. We assumed the following gain loss contributions from feeds and the Arecibo Gregorian, Table 6.1 Antenna Contributions to Gain Losses Gain Losses Contributions from Feeds Insertion Losses -0.01 VSWR (Worst Case) 1.300:1 Gain Losses Contribution from Arecibo Gregorian Additional Losses from Physical Optics Cal. -0.30 Scattering and Blockage -0.26 July 19, 2002

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The antenna G/T and antenna system temperature assume the temperature conditions shown in Table 6.2. Table 6.2 System Temperature Contributions Scattering 4K Physical Temperature 300 K Receivers Temperature 8K Sky Temperature (to be convolved with the antenna pattern) 6K Sections 6.1 through 6.5 present the Antenna Sensitivity, Antenna G/T and Antenna System Temperatures for each of the five horns as a function of feed angular position. The performance of Pixel/Horn #0 is also shown in the respective figures superimposed at =0À.

6.1

Feed Horn: CSIRO Coaxial 19.6 cm x 20.4 cm
Arecibo Multi-Beam System Antenna Sensitivity
Horn CSIRO Coaxial 19.6 cm, C-C=20.40cm, X-Offset=1.75cm
12 1.225 GHz 1.375 GHz 1.525 GHz

10
Antenna Sensitivity [K/Jy]

8

6

4

2

0 0 30 60 90 Angle [deg] 12 0 150 180

Figure 6.1.1 Antenna Sensitivity as a function of Feed angular position

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Arecibo Multi-Beam System Antenna G/T
Horn CSIRO Coaxial 19.6 cm, C-C=20.40cm, X-Offset=1.75cm
60 59 58 57
10 Log10 [G/T]

1.225 GHz 1.375 GHz 1.525 GHz

56 55 54 53 52 51 50 0 30 60 90 Angle [deg] 12 0 150 180

Figure 6.1.2 Antenna G/T as a function of Feed angular position
Arecibo Multi-Beam System Antenna System Temperature Horn CSIRO Coaxial 19.6 cm, C-C=20.40cm, X-Offset=1.75cm
45 40

Antenna System Temperature [K]

35 30 25 20 15 10 5 0 0 30 60 90 Angle [deg] 120 150 180 1.225 GHz 1.375 GHz 1.525 GHz

Figure 6.1.3 Antenna System Temperature as a function of Feed angular position

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6.2

Feed Horn: CSIRO Coaxial 22.0 cm x 22.8 cm
Arecibo Multi-Beam System Antenna Sensitivity
Horn CSIRO Coax 22.0 cm, C-C=22.80cm, X-Offset=2.4cm
12 1.225 GHz 1.375 GHz 1.525 GHz

10
Antenna Sensitivity [K/Jy]

8

6

4

2

0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.2.1 Antenna Sensitivity as a function of Feed angular position
Arecibo Multi-Beam System Antenna G/T
Horn CSIRO Coax 22.0 cm, C-C=22.80cm, X-Offset=2.4cm
60 59 58 57
10 Log10 [G/T]

1.225 GHz 1.375 GHz 1.525 GHz

56 55 54 53 52 51 50 0 30 60 90 Angle [deg] 120 150 180

Figure 6.2.2 Antenna G/T as a function of Feed angular position July 19, 2002 9


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Arecibo Multi-Beam System Antenna System Temperature
Horn CSIRO Coax 22.0 cm, C-C=22.80cm, X-Offset=2.4cm
45 40
Antenna System Temperature [K]

1.225 GHz 1.375 GHz 1.525 GHz

35 30 25 20 15 10 5 0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.2.3 Antenna System Temperature as a function of Feed angular position

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6.3

Feed Horn: Parkes TE11 mode Horn 24 cm x 26.25 cm
Arecibo Multi-Beam System Antenna Sensitivity
Horn Parkes TE11 24.0 cm, C-C=26.25cm, X-Offset=2.8cm
12 1.225 GHz 1.375 GHz 1.525 GHz

10

Antenna Sensitivity [K/Jy]

8

6

4

2

0 0 30 60 90 Angle [deg] 120 15 0 180

Figure 6.3.1 Antenna Sensitivity as a function of Feed angular position
Arecibo Multi-Beam System Antenna G/T
Horn Parkes TE11 24.0 cm, C-C=26.25cm, X-Offset=2.8cm
60 59 58 57 1.225 GHz 1.375 GHz 1.525 GHz

10 Log10 [G/T]

56 55 54 53 52 51 50 0 30 60 90 Angle [deg] 120 150 180

Figure 6.3.2 Antenna G/T as a function of Feed angular position

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Arecibo Multi-Beam System Antenna System Temperature
Horn Parkes TE11 24.0 cm, C-C=26.25cm, X-Offset=2.8cm
45 40 1.225 GHz 1.375 GHz 1.525 GHz

Antenna System Temperature [K]

35 30 25 20 15 10 5 0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.3.3 Antenna System Temperature as a function of Feed angular position

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6.4

Feed Horn: CSIRO TE11 mode Horn 25 cm x 26.0 cm
Arecibo Multi-Beam System Antenna Sensitivity
Horn CSIRO TE11 25.0 cm, C-C=26.00cm, X-Offset=2.7cm
12 1.225 GHz 1.375 GHz 1.525 GHz

10

Antenna Sensitivity [K/Jy]

8

6

4

2

0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.4.1 Antenna Sensitivity as a function of Feed angular position
Arecibo Multi-Beam System Antenna G/T
Horn CSIRO TE11 25.0 cm, C-C=26.00cm, X-Offset=2.7cm
60 59 58 57 1.225 GHz 1.375 GHz 1.525 GHz

10 Log10 [G/T]

56 55 54 53 52 51 50 0 30 60 90 Angle [deg] 120 150 18 0

Figure 6.4.2 Antenna G/T as a function of Feed angular position July 19, 2002 13


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Arecibo Multi-Beam System Antenna System Temperature
Horn CSIRO TE11 25.0 cm, C-C=26.00cm, X-Offset=2.7cm
45 40 1.225 GHz 1.375 GHz 1.525 GHz

Antenna System Temperature [K]

35 30 25 20 15 10 5 0 0 30 60 90 Angle [deg] 120 150 18 0

Figure 6.4.3 Antenna System Temperature as a function of Feed angular position

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6.5

Feed Horn: NIAC TE11 mode Horn 26 cm x 26.8 cm
Arecibo Multi-Beam System Antenna Sensitivity
Horn NAIC TE11 26.0 cm, C-C=26.8cm, X-Offset=2.6cm
12 1.225 GHz 1.375 GHz 1.525 GHz

10

Antenna Sensitivity [K/Jy]

8

6

4

2

0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.5.1 Antenna Sensitivity as a function of Feed angular position
Arecibo Multi-Beam System Antenna G/T
Horn NAIC TE11 26.0 cm, C-C=26.8cm, X-Offset=2.6cm
60 59 58 57
10 Log10 [G/T]

1.225 GHz 1.375 GHz 1.525 GHz

56 55 54 53 52 51 50 0 30 60 90 Angle [deg] 120 150 180

Figure 6.5.2 Antenna G/T as a function of Feed angular position July 19, 2002 15


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Arecibo Multi-Beam System Antenna System Temperature
Horn NAIC TE11 26.0 cm, C-C=26.8cm, X-Offset=2.6cm
45 40 1.225 GHz 1.375 GHz 1.525 GHz

Antenna System Temperature [K]

35 30 25 20 15 10 5 0 0 30 60 90 Angle [deg] 120 150 180

Figure 6.5.3 Antenna System Temperature as a function of Feed angular position

7. Comparative Antenna Sensitivity and Aeff/T

sys By averaging the antenna performance in frequency, and for all feeds surrounding the center feed, as a function of azimuth angle as well, we obtained the antenna sensitivity shown in Figure 7.1 The highest antenna sensitivity is a tie between the center pixel/feed of CSIRO Coax 22.0 x 22.8 cm feed and CSIRO TE11 mode 25.0 x 26.0 cm feed. While for the surrounding pixels/feeds CSIRO Coax 22.0 x 22.8 cm feed is slightly better.
The antenna Aeff/Tsys, is shown in Figure 7.2. In particular, for the two candidates we show Aeff/Tsys with and without a full Noise Tertiary Skirt. In both cases, the multi beam with the highest average Aeff/Tsys, is CSIRO TE11 mode 25.0 x 26.0 cm feed. This result is consistent with the feed spillover efficiency shown in Figure 4.1

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Arecibo Multi-Beam System Antenna Sensitivity
14.0
Averaged in Frequency

12.0

Antenna Sensitivity [K/Jy]

10.0

8.0

6.0

Pixel #0 Average[Pixels>0]

4.0 Horn Type: Coax 19.6 cm 0 1 Spacing: x 20.40 cm

Coax 22.0 cm 2 x 22.80 cm

TE11 24.0 cm 3 x 26.25 cm

TE11 25.0 cm 4 x 26.00 cm

TE11 26.0 cm 5 x 26.80 cm

Figure 7.1 Antenna Sensitivity (Aeff in K/Jy) for all feeds (frequency and angle averaged)
Arecibo Multi-Beam System Antenna Aeff/T
32
Averaged in Frequency

31

10xLog10{Aeff/T [mÂ/K]}

30

29

28

27

Pixel #0 Average[Pixels>0] Pixel #0 + Noise Skirt Average[Pix>0] + Noise Skirt

26 Horn Type: Coax 19.6 cm 0 1 Spacing: x 20.40 cm

Coax 22 .0 cm x 22.80 cm

TE11 23 .0 cm 4 x 26.25 cm

TE11 25.0 cm 4 x 26.00 cm

TE11 26.0 cm 5 x 26.80 cm

Figure 5.2 Antenna Aeff/T for all feeds (frequency and angle averaged)

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8. Sky Footprint and Multi-Beam Characteristics
In addition to characteristics section we are Arecibo Multi 25x26cm. antenna sensitivity and G/T (Aeff/T) the multi are also of importance for surveys strategies, sky presenting the imaging characteristics of the two Beam System, namely the Coaxial 22.0x22.8cm beam sky footprint and beam coverage and sampling. In this leading candidate horns for the horn and the TE11 mode horn

8.1

Feed Motion vs. Antenna Far Field Beam Motion

When the feed moves in the focal plane as shown in Figure 8.1, the corresponding beam footprint moves in the sky according with Figure 8.2, Our reference axis, the U-axis goes from the zenith to horizon parallel to Arecibo feed arm.

r

Figure 8.1 Feed motion in the Focal Plane.

Figure 8.2 Beam Motion in the Far Field. (Uaxis is parallel to the feed arm)

8.2

Antenna Far Field Multi Beam Characteristics

We characterize the main antenna beam trough a set of geometric parameters shown in Figure 8.3; these parameters include the beam center2, {rSKY, SKY}, where the angle SKY is measured positive, clockwise with respect to the U-axis3, the beam size, HPBW1 x HPBW2=2ao x 2bo (in the Figure 8.3), since the beam is elliptical due to the antenna optics, and finally, the angle o, between the major semi axis of the ellipse and the U-axis. Based on a non-linear normalized Airy pattern model with elliptical cross section4 we obtained the set of parameters for the multi beam based on the CSIRO Coax 22.0x22.8 cm and CSIRO TE11 mode 25.0x26.0 cm horns shown in Table 8.1, respectively. The first column in the table refers to
2 3

The highest antenna gain point in the pattern in polar coordinates. The antenna optical axis points in the direction of UxV, into the page. , where,

4

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NAIC Pixel #0, (first row in orange), and the following rows correspond to 7 angular positions5 for pixels around the center feed/pixel in the focal plane from 0À to 180À, in steps of 30À.





Figure 8.3 Antenna Far Field Multi-Beam Parameters The values presented in these tables represent a best fit for each individual pattern data down to the -7.0 dB level with respect to the beam maximum. The calculated average beam size for Pixels >0 is 227 x 201 arcsec for the coaxial 22.0 x 22.8 cm feed, and 232 x 204 arcsec for the TE11 25.0 x 26.0 cm feed, respectively. The average distance between Pixels>0 and the central beam is 312 arcsec for the coaxial 22.0 x 22.8 cm feed, and 361 arcsec for the TE11 25.0 x 26.0 cm feed, i.e., 1.46 and 1.66 times the average beam size, for these two feeds respectively. Table 8.1 Far Field Antenna Beam Parameters for a Multi Beam System at 1.375 GHz based on the Coax Horn 22.0x22, on the left, and on the TE11 mode Horn 25.0 x 26.0 cm, on the right
Feed Type Coax Aperture Spacing 22 cm 22.8 cm
Angle

X- Offset 2.4 cm
Position Position rSKY SKY [arcsec] 35.68 371.77 356.59 321.10 290.45 285.02 290.45 304.32 [deg] 0.00 0.00 -24.54 -52.28 -84.99 -119.79 -84.99 180.00

Feed Type TE11

Aperture Spacing 25 cm 26.0 cm
Angle

X- Offset 2.7 cm
Position Position rSKY SKY [arcsec] 39.87 421.46 404.70 364.48 329.95 324.20 338.74 346.55 [deg] 0.00 0.00 -24.72 -52.62 -85.38 -120.14 -151.74 180.00

FPL
Pix 0 0À 30À 60À 90À 120À 150À 180À

HPBW1 HPBW2
[arcsec] [arcsec] 227 198 230 204 228 204 226 204 225 202 226 199 224 202 231 195


[deg] 0 0 3 0 -4 -7 -4 0

FP

L

HPBW1 HPBW2
[arcsec] [arcsec] 230 201 236 206 234 207 229 208 227 206 230 202 234 198 236 197


[deg] 0 0 5 4 -5 -9 -6 0

Pix 0 0À 30À 60À 90À 120À 150À 180À

Figures 8.4 and 8.5 show the sky footprint for the Arecibo multi beam system based on a coaxial 22.0 x 22.8 cm feed and a TE11 25.0 x 26.0 cm feed, respectively.

5

In its standard position, Pixel #1 is at

FPL=30À,

and Pixel #2 is at

FPL

=90À, etc.

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Figure 8.4 Sky Footprint Geometry for a Coax 22.0x22.8cm Horn based Arecibo Multi Beam

Figure 8.5 Sky Footprint Geometry for a TE11 25.0x26.0 cm Horn based Arecibo Multi Beam

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NAIC These figures show the location and shapes of all beams in the standard configuration, as well as when the multi beam is rotated by 30À in the focal plane. The center of the elliptical path is off from the antenna optical axis by 33.73 arcsec in the case of the coaxial 22.0 x 22.8 cm feed and 37.45 arcsec for the TE11 25.0 x 26.0 cm feed. The sky footprint track could be best fitted to an ellipse whose parameters are shown below in Table 8.2. We found that the ellipse size has a linear dependence on the feed center-to-center separation, while the eccentricity remains almost constant. Table 8.2 Parameters of Multi Beam Sky Footprint Ellipse U-Offset Major Minor Eccentricity Feed Type 2xa 2xb U Arcsec arcsec arcsec CSIRO Coax 22.0x22.8 cm 33.73 676.09 578.92 0.5165 CSIRO TE11 25.0x26.0 cm 37.45 768.01 658.12 0.5155

8.3

Multi Beam Comatic Levels

An important parameter for imaging purposes for the Multi Beam in the Arecibo Gregorian optics is the coma level, which is already evident in Figure 8.2. The calculated comatic side lobe level (SLL) for the coaxial 22.0 x 22.8 cm feed, shown in Figure 8.6, varies from -10.5 dB to -8.7 dB, with the minimum value when the feed angular position in the focal plane is at 0À or 180À, and the maximum when is at 90À. The comatic SLL For the TE11 25.0 x 26.0 cm feed vary between -9.5 dB, at 0À or 180À, and -7.7 dB, at 90À. The SLL for the central pixel is very similar for both feed types of the order of -15.8 dB.
Arecibo Multi-Beam System Comatic Side Lobe Level
0 -2 -4 -6 -8 -10 -12 -14 -16 -18 0 30 60 90 Angle In Focal Plane [deg] 120 150 180

Comatic SLL [dB]

TE11 25cm x 26cm Coax 22cm x 22.8cm

Figure 8.6 Comatic Side Lobe Levels for the Arecibo Multi Beam System

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8.4

Total Multi Beam Incoherent Pattern

When we add all the beam patterns incoherently we obtain the picture shown in Figure 8.7 for the coaxial 22x22.8 cm horn, on the left, and for the TE11 mode 25x26 cm horn, on the right. The figure shows the 3 dB contour level for both horns at the center pixel, and power levels at the overlapping points and the highest coma level. Each picture corresponds to a region in the sky of 25-arcmin x 25-arcmin.

Figure 8.7 Total Multi Beam Incoherent Antenna Pattern In average, the overlapping power level is about -4.5 dB for the coaxial 22x22.8 cm horn and -6.5 dB for the TE11 mode 25x26 cm horn.

8.5

Drift Scan Sampling and Multi Beam

Figure 8.8 shows two possible methods for sampling by drift scan; one possibility is to rotate the feed arm to an optimum angle for which the separation between tracks is the same (or almost the same). Another possibility is to rotate the multi beam systems itself, again trying to obtain equal track spacing. It is very likely that a combination of these two methods be used when the multi beam system is operational. By using the differences between track spacing, i.e., d1, d2, ... d6, shown in Figure 8.8, we define the following error function to determine the inequality in the projected track spacing, and which goes to zero when all projected paths are identical.

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Figure 8.8 Drift Scan Sampling Methods: (a). Feed arm rotation, (b). Multi Beam rotation Let us analyze the Feed Arm Rotation method for drift scan sampling: first, in the ideal case of a perfect circular path, the function, f(di) is exactly zero6 at =19.11À, 60ÀÁ19.11À, etc, shown in blue in Figure 8.9. Now, for an elliptical footprint path, such the one shown in Figure 8.10, the function minimums depend on the path eccentricity and beam positions on the path. For the two horns under consideration the function has the first minimum at =22.0À, as shown in Figure 8.9. The other minima are located at 60ÀÁ22.0À, etc, increasing monotonically.
Arecibo Multi Beam System
Optimum Drift Scan Angle
6 Ideal Circle Footprint Coax 22x23 cm TE11 25 x 26 cm



5

{i> max)]Â,

4

3

[|di-dj|/(6xd

2

1

0 0 30 60 90 Feed Arm Angle [deg] 120 150 180

Figure 8.9 Optimum Feed Arm rotation angle for Drift Scan Sampling
Germñn Cortùs, "Maximum Beam Separation for Multi Beam Nyquist Sampling with a Symmetric Elliptical Footprint Path", Arecibo Focal Array Memo Series, NAIC, Cornell University, June 2002.
6

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Figure 8.10 Optimum Feed Arm rotation angle for Drift Scan Sampling with Elliptical path Figure 8.10 shows the geometry for an optimum angle for drift scan sampling in the case of an elliptical path. Other parameter useful in drift scan sampling is the crossover beam level, shown here in Figure 8.11 for CSIRO TE11 25 x26 cm horn, and in Figure 8.12 for CSIRO coax 22 x22.8 cm horn. In the case of CSIRO TE11 25 x26 cm horn, Figure 8.11, the crossover levels vary between 0.8 dB, at the most exterior beams, to 0.5 dB for the beams next to the central beam. For the CSIRO coax 22 x22.8 cm horn, Figure 8.12, the crossover levels are between 0.6 dB, between exterior beams, and 0.3 dB between interior beams and the central beam.

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Arecibo Multi Beam System
Crossover Levels for Drift Scan at Optimum Angle
0 TE11 25x26cm

-1

Relative Power Level [dB]

-2

-3

-4

-5 -600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

FOV angle [arcsec]

Figure 8.11 Projected patterns and Crossover levels for CSIRO TE11 25 x26 cm Horn
Arecibo Multi Beam System
Crossover Levels for Drift Scan at Optimum Angle
0 Coax 22x22.8cm

-1

Relative Power Level [dB]

-2

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-5 -600

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FOV angle [arcsec]

Figure 8.12 Projected patterns and Crossover levels for CSIRO coaxial 22 x22.8 cm Horn

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9. Conclusions
We have analyzed two feed horn designs from CSIRO for the Arecibo Multi Beam System, namely, a coaxial horn with 22.0 cm aperture and a center-to-center spacing of 22.8 cm, and a stepped TE11 mode horn of 25 cm aperture and center-to-center spacing of 26.0 cm The overall study concludes that the TE11 mode horn of 25 x26 cm has better performance in terms of spillover efficiency, antenna noise temperature, Aeff/Tsys, with and without the full tertiary Noise skirt. In terms of antenna sensitivity both feed horns perform equally well for the central pixel, and the coaxial feed horn slightly better performance for the peripheral pixels. Even though, G/T (or Aeff/Tsys ) for the coaxial 22x22.8cm improves with the tertiary Noise Skirt in place, its performance is still lower than for the TE11 mode 25 x26 cm horn. We also studied the far field imaging characteristics of both arrays, the sky footprint, beam size, coma levels. We obtained the overlapping power level between beams, as well the crossover levels for drift scan sampling. We found that the beam spacing for these two feeds is 1.46 times the beam size for the coaxial 22.0 x 22.8 cm feed, and 1.66 times the average beam size, for TE11 mode 25 x26 cm feed respectively, in both cases larger than the Nyquist sampling spacing. We obtained that the path followed by the beams in the sky, as the array rotates in the focal plane, is elliptical. Its size depends linearly on the feed spacing in the focal plane, but these ellipses have almost constant eccentricity. We obtained that the optimum feed arm rotation angle for drift scan sampling for these two feeds is approximately 22À. Considering all aspects of feed horn, plus antenna performance, including perceived technical risks for the two designs, we have concluded the TE11 mode horn of 25 cm aperture and 26 cm centerto-center spacing is preferred for the Arecibo multi beam feed array.

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Appendix A.

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A.1 Feeds Far Field Radiation Patterns
Figures A.1 through A.9 show the far field radiation patterns for Dr. Bird's 19.6cm coaxial horn, Parkes 24.0cm TE11 mode horn, our 26.0cm TE11 mode horn, and Dr. Bird's 25cm TE11 mode horn. For each horn we are presenting amplitude and phase pattern cuts at the following frequencies: 1.225 GHz, 1.375 GHz, and 1.525 GHz. Due to the rotationally symmetry of the feeds, only two cuts of the feed's radiation pattern are necessary to analyze the overall antenna performance. Nevertheless, for completeness in this document, an additional cut at 45À is also included here, in the field amplitude figures, to show cross-polar levels.

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NAIC Dr. Bird's Coaxial feed Horn (19.6 cm diameter.)

Figure A.1 Bird's Coax feed (19.6 cm diameter) Radiation Pattern, 1.225 GHz July 19, 2002 29


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Figure A.2 Bird's Coax feed (19.6 cm diameter) Radiation Pattern, 1.375 GHz July 19, 2002 30


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Figure A.3 Bird's Coax feed (19.6 cm diameter) Radiation Pattern, 1.525 GHz July 19, 2002 31


NAIC CSIRO Coaxial feed horn (22.0 cm diameter.)

Figure A.4 CSIRO Coaxial Horn (22.0 cm diam) Radiation Pattern at 1.225 GHz July 19, 2002 32


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Figure A.5 CSIRO Coaxial Horn (22.0 cm diam) Radiation Pattern at 1.375 GHz July 19, 2002 33


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Figure A.6 CSIRO Coaxial Horn (22.0 cm diam) Radiation Pattern at 1.525 GHz July 19, 2002 34


NAIC Parkes TE11 mode feed horn (24.0 cm diameter.)

Figure A.7 Parkes TE11 feed (24.0 cm diam) Radiation Pattern at 1.225 GHz July 19, 2002 35


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Figure A.8 Parkes TE11 feed (24.0 cm diam) Radiation Pattern at 1.375 GHz July 19, 2002 36


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Figure A.9 Parkes TE11 feed (24.0 cm diam) Radiation Pattern at 1.525 GHz July 19, 2002 37


NAIC CSIRO TE11 mode feed horn (25.0 cm diameter.)

Figure A.10 CSIRO TE11 mode Horn (25.0 cm) Radiation Pattern at 1.225 GHz July 19, 2002 38


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Figure A.11 CSIRO TE11 mode Horn (25.0 cm) Radiation Pattern at 1.375 GHz July 19, 2002 39


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Figure A.12 CSIRO TE11 mode Horn (25.0 cm) Radiation Pattern at 1.525 GHz July 19, 2002 40


NAIC TE11 mode feed horn (26.0 cm diameter.)

Figure A.13 TE11 Mode Horn (26.0 cm diam) Radiation Pattern at 1.225 GHz July 19, 2002 41


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Figure A.14 TE11 Mode Horn (26.0 cm diam) Radiation Pattern at 1.375 GHz July 19, 2002 42


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Figure A.15 TE11 Mode Horn (26.0 cm diam) Radiation Pattern at 1.525 GHz

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