Project Cyclops, A Design... - Department of Earth and Planetary ...

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Wealsofindfromequation(7)that = 2I logcos(0o/2)12 r/ [sin(0 o/2)tan(0o/2)J (16) Figure 9-6 shows a plot of I/Io vs. 0 and of mf/d and 77vs. 0o. We see that even for values of 0o as high as 70 °, where the illumination intensity at the rim has fallen to 45% of its central value, the efficiency is still almost 99%. If the f/d ratio of the primary mirror is 0.25 (which places the focus in the plane of the rim), and the magnification m = 3, then mf/d = 0.75 and at the Cassegrain focus 0o = 37 °. At this angle I/Io = 0.81 and r/_l. transmission mode, generates (with reversed E X H) the diffraction pattern produced in the image plane by an infinitely distant point source. This is illustrated schematically by feed horn A in Figure 9-7. The second is to make a large feed horn that, in the transmission mode, generates (with reversed E X H) the spherical wavefront produced by the same distant source many wavelengths "upstream" from the focal plane. This is illustrated by feed horn B in Figure 9-7. 2.O I.O 1.8 .9 FEED HORN , HORN "B" 1.2 fld 1.0 .8 f d V-- "A" ! _>_HERICAL _._.'" V*AVEFRONT Vl ONOARY.- ,_\ '\IMAGE _REFLECTOR PLANE PRIMARY / / ,I i i J i IO 20 30 40 0 ond 8 0 'o ' o 5 60 70 Figure 9-6. Illumination of a isotropic feed. paraboloid by an Figure 9-7. Two methods of feeding a Cassegrainian antenna. We conclude that with a properly designed Cassegrainian system there is very little reason to attempt to increase the off-axis radiation of the feed to compensate for the illumination falloff given by equation (13). It is far more important to achieve as abrupt a decrease in illumination at the rim and as little spillover as possible. There appear to be two distinct approaches that can be used. The first is to make a feed that, in the Minnett and Thomas (ref. 1) have investigated the fields in the vicinity of the focal plane, and have shown that they are composed of HEwn balanced hybrid modes. Such modes can be propagated in waveguides and horns whose inner surfaces are corrugated-that is, carry circumferential grooves having a spacing less than about X/10 and a depth of X/4 at the center of the band. 92
Corrugatedhornssupportingbalancedhybridmodes hav equalE-plane and H-plane patterns with zero cross polarization component and are therefore well suited for illuminating reflectors having axial symmetry (refs. 2-4). In the focal plane the field amplitude as a function of radius is very nearly given up by the classical Airy distribution Zll(2gOop/X) u@) = Uo (17) 2_OoP/_ the wave off axis, increases the convexity of the wavefront at the axis and thus serves to guide the energy flow away from the axis. Since all transitions can be many wavelengths long, very low standing wave ratios should be expected. The major problem with such a horn might be the loss of the dielectric and the consequent elevation of the noise temperature. If this proves to be the case, artifical dielectrics might be preferable. for values of the (maximum) convergence angle/9o from zero to 30° . For /9o > 30° the energy in the rings increases at the expense of energy in the central spot. In addition, for Oo _ 60 ° regions of reversed energy flow appear in what, for lower values of 0o, were the dark rings. Thus for wide angle feeds the focal plane matching must include severalrings to obtain high efficiencies. Thomas (refs. 5, 6) has shown that it is possible to match the focal plane fields of a reflector having 8o = 63°, and to obtain efficiencies within 0.1% of the theoretical values of 72.4%, 82.8%, 87.5%, 90.1% and 91.9% for feed diameters capable of supporting one to five hybrid modes, respectively. The match requires that the relative amplitudes of the modes of different orders be correct. Mode conversion can be accomplished in various ways such as by irises or steps in the waveguide or horn. Whether the ratios between the mode amplitudes can be made to vary in the appropriate fashion to preserve the distribution of equation (17) as X varies is another question. The efficiencies cited above assume that the guide radius at the mouth equals the radius of the first, second, third, fourth or fifth null of equation (16), a condition that is only possible at discrete frequencies. Thus, although bandwidth ratios of 1.5 to 1 have been reported (ref. 7) for single mode horns, it is not clear that multimode horns designed to match focal plane fields over several rings of the diffraction pattern can achieve high performance over such bandwidths. For broadband operation the second approach of generating a spherical cap of radiation several wavelengths in diameter to match the field some distance in front of the focal plane appears more promising. Higher order modes are involved here also, but since their role now is simply to maintain the field at a nearly constant value over the wavefront at the mouth of the horn, the higher order mode amplitudes are less than in the focal plane horn where field reversals are required. Thus the mode conversion process is less critical and might take the form of a dielectric cone lining the horn as shown purely schematically in Figure 9-8. The dielectric slows Figure 9-8. Dielectric loaded corrugated feed horn. With this type of feed horn, the spherical cap of radiation illuminates the secondary mirror in the same way that the spherical cap of radiation generated by the secondary illuminates the primary mirror, except that for the feed horn the cap dimensions are less and the secondary spillover is therefore greater for a given illumination at the rim. However, the secondary spillover represents side lobe response aimed at the sky, so the effect on noise temperature is negligible. The reradiation reflected in the transmission mode by the secondary onto the primary in the shadow region of the secondary is reflected off the primary as a parallel wavefront that is intercepted by and re-reflected by the secondary. After this second reflection off the secondary, most of this radiation is refected by the primary to a distant focus on the beam axis after which the radiation diverges. The net result is a general rise in the side lobe level at modest off axis angles. By applying spherical wave theory to the design of Cassegrainian systems, Potter (ref. 8) has shown that it is possible to shape the secondary mirror near the vertex so that the radiation that would normally be reflected into the shadow region is redirected into the unshadowed region where it combines constructively with the rest of the radiation. This reduces the shadowing loss and improves the side lobe pattern. 93
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(NASA-CR- 11_5) PROJECT CYCLOPS: A
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CR 114445 Available to the public A
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At this very minute, with almost ab
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ACKNOWLEDGMENTS The Cyclops study w
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COMMUNICATION BY ELECTROMAGNETIC WA
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APPENDIX A - Astronomical Data ....
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t _ 2
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of the living beings evolved by the
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Figure2-1. M3I,the great galaxy in
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self.Thus,wecaninterpretFigure2-2as
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magnitude (low brightness) end, the
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Red Giant. The transition from main
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tion, as the central part of the cl
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TABLE 2-4 SELECTED NEARBY STARS WIT
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tideraisingforcesasr--_ where ,v =
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3. Is it possible that living syste
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lawsof natural selection, more like
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starsthroughout the Galaxyhave also
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if the longevity of that life is ty
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The imaginative reader will have no
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Lookingfar ahead,supposewe aresucce
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usuallyterritorial expansion by the
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IOO IO 1 [ [ J [ J I J i [ i I i I
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order with what Morrison has descri
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The quantity gtPt is often called t
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which might result from synchronous
Page 54 and 55: 1. Wewillnothavenough resolving pow
Page 56 and 57: normalwith the meanat o x/--2. When
Page 58 and 59: Chapter11 in analyzingthe dataproce
Page 60 and 61: Therangelimitisthenfoundbyequating_
Page 62 and 63: TABLE 5-3 PARAMETER Wavelength Tran
Page 64 and 65: angeanddirectlyasthesquareof antenn
Page 66 and 67: "_ i i i i i p = STELLAR DENSITY AT
Page 68 and 69: I-- g u. O >- I--- .d tit (]O 0 0.
Page 70 and 71: andwidth that will still give near
Page 72 and 73: acquisitionphasefor otherraces.Supp
Page 74 and 75: 1. They would transmit continuously
Page 76 and 77: and ¢-Ceti. No signals were detect
Page 79 and 80: vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
Page 81 and 82: The price of incomplete sky coverag
Page 83 and 84: modest size.A largedatabaseontapeor
Page 85 and 86: THEAUXILIARYOPTICALSYSTEM Althoughn
Page 88 and 89: edetectedat 20,000light-years byCyc
Page 90 and 91: feeds must correct for spherical ab
Page 92 and 93: side of the dish and shade on the o
Page 94 and 95: TABLE 8-1 UNADJUSTED UNIT COST DATA
Page 96 and 97: 7. Using huge specially designed ji
Page 99 and 100: 9. THE RECEIVER SYSTEM The receiver
Page 101 and 102: whereP is the radiated power. Divid
Page 103: SHADOWED AREA SHADOWED AREA // // /
Page 107 and 108: o 50 ----- - _ T i 20 _,o 5 ,,,5 09
Page 109 and 110: TABLk ?- I A COMPARISON OF VARIOUS
Page 111 and 112: CENTRAL POINT STATION LSB LINE FREQ
Page 113 and 114: A02 .... + No (25) (i C 1 where No
Page 115 and 116: COAXIAL LINE DIRECTIONALCOUPLER FRE
Page 117 and 118: DeJager, J.T.:IEEETrans.onMicrowave
Page 119 and 120: pR_ING PA6E BLANK HOT FILMF_ 10. TR
Page 121 and 122: o-------------o_ _ o o o o ing of t
Page 123 and 124: addedto theother IF channel. The tw
Page 125 and 126: INPUT MHZ _PF 500 MHZ i : 575 T1 92
Page 127 and 128: azimuth _) has a delay (2a/c)sin 0
Page 129 and 130: stripline. For 2 _< k _< 6, appropr
Page 131 and 132: mation are common to all antennas i
Page 133 and 134: A cable pair costs about 20 cents/m
Page 135 and 136: 11. SIGNAL PROCESSING The Cyclops s
Page 137 and 138: 1.0 T t t I I r .9 -8 asynchronousl
Page 139 and 140: collimated coherent light. A simple
Page 141 and 142: power of the film and associated op
Page 143 and 144: samples simultaneously onto the sam
Page 145 and 146: outputs is assumed. COMPOSITE SIGNA
Page 147 and 148: SPECTRUM I n LINES M n LINES U SPEC
Page 149 and 150: signal andyet have a tolerable fals
Page 151 and 152: i --_- i i i i large values of n. T
Page 153 and 154: plottedin Figure11-15for various va
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All the1Fsignalswillarrivein phasei
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x:(1 +x) x 2 - _ -- (53) If we wish
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3's = unitcostof signal planelectro
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where0ma x is the maximum value of
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Roughestimates of the costs of buil
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12. CYCLOPS AS A BEACON Although th
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13. SEARCH STRATEGY The high direct
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distantgalaxies (oraninertialrefere
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wouldfollowtheuppermost linein Figu
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persquaredegreeof fieldwouldberequi
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starsfrom/'18 to G5 could support a
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14. CYCLOPS AS A RESEARCH TOOL Thro
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Only a few such galaxies have been
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15. CONCLUSIONS AND RECOMMENDATIONS
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perhapsdecadesand possiblycenturies
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APPENDIX A ASTRONOMICAL DATA DISTAN
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PLANETARY Planet ORBITS Semimajor S
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APPENDIX B SUPERCIVILIZATIONS AND C
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ABIOLOGICAL CIVILIZATIONS Many writ
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182
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tqOT APPENDIX C OPTIMUM DETECTION A
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to rmsnoise.Wenotethatthematchedfil
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APPENDIX D SQUARE LAW DETECTION THE
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If the output filter is very wide c
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if B/2 > T we can start instead wit
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Let us now introduce the normalized
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where h-- = expectation count of si
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APPENDIXE RESPONSE OF A GAUSSIAN FI
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APPENDIXF BASE STRUCTURES AZ-EL BAS
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ack,it shouldnotbenecessary to prov
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204
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206 i
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PAGE BLANK NOT APPENDIX H POLARIZAT
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APPENDIX I CASSEGRAINIAN GEOMETRY C
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APPENDIXJ PHASINGOFTHE LOCALOSCILLA
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APPENDIXK EFFECTOF DISPERSION IN CO
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APPENDIX L TUNNEL AND CABLE LENGTHS
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where r = "Ym/'rs- If we let o-_--o
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L-4 we see that the length of IF ca
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APPENDIX M PHASING AND TIME DELAY A
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andobtain V = 2 (Ps [! + _(Ar)] +Pn
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L" D 226
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APPENDIX N SYSTEM CALIBRATION The p
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APPENDIXO THE OPTICAL SPECTRUM ANAL
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232
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APPENDIX P LUMPED CONSTANT DELAY LI
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Thevalueofthefinalcoilonthelineis =
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APPENDIXQ CURVES OF DETECTION STATI
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I I I I LE :E oo
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APPENDIX R RADIO VISIBILITY OF NORM
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io 3 - l rlrllll I I I ]l+,ll_ I _f
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