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

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ightness distributionoverthecommonfieldofviewof theantennas. Finally,thetwo-dimensional Fouriertransformof themeasured dataistakento getthedesired map.TheproposedVLAsystemwillusethistechnique, calledaperture synthesis. It is obvious that neither of these methods produces a real-time image of the sky. and at an azimuth a will be received by an antenna at x,y with a delay. x sin a +y cos a rr(X,Y) = - sin 8 (36) The greater the resolution desired, the greater is the time required to map a given area of the sky. With the resolution available from the Cyclops array the times are very long indeed. Assume that we have 1000 dishes spread over an area 10 km in diameter, and operating at a wavelength of 10 cm, If we allow 3 dB gain falloff at the edges of each elemental area scanned, the number of resolvable directions is about 1.5 (Ird/X) 2 = 1.5×10 II (see Chap. 6). With an integration time of only 1 sec per elemental area scanned, it would take 1.5× 1011 sec or about 5000 years to map the entire sky. Even to map an object such as M31 (the Andromeda galaxy)would take about 126 eight-hour observing days, or 4 months. But with 1000 elements in the array, we can form I000 independent beams simultaneously, and thus map the whole sky in 5 years, or M31 in an hour. where c is the velocity of light. At the received frequency w r this delay causes a phase shift % = rrW r (37) The delay and, if the spectrum has not been inverted, the phase shift are preserved by all the heterodyning operations and thus are present at the IF outputs. Even with an imaging system, the field of view is limited by the beamwidth of the antenna elements. Moreover, in an array, there are additional grating lobes within this field that confuse the picture and reduce the usable field area by the filling factor. Thus, for the Cyclops array with a filling factor of 1/10, ten times as many fields of view would be needed to synthesize a picture of a given region as would be needed with a single 100-m dish. The advantage of the array is that the final picture contains 10,000 times the detail. Thus, the array with its 1000 dishes is 1000 times more powerful for map ing, as one should expect. In fact, if blurred areas in the map made with the single antenna are resolved into sharp points by the array, the integration time can be reduced, making the array even more powerful. General Principles To simplify our thinking let us initially assume that the Cyclops array is pointed at the zenith. A signal received from the zenith will then produce the same IF output signal at the central station from every antenna element. Let us take Y to be the north-south axis of the array and X to be the east-west axis as shown in Figure 11-I 6a. A signal received at a small angle _ from the zenith SIGNAL PLANE _ V _ ...."_ 0/ IMAGE / PLANE Figure ll-16. (aj Antenna and source coordinate. [b ) Imaging coordinates. Let us imagine the IF outputs to be arranged physically in a plane, forming a small scale map of the array, so that in Figure ll-16b x' = ox andy' = oy where o is the scale factor. Now let us arrange a second lattice of points with coordinates u, v in a second plane, which we will call the image plane, and let us connect each of the IF outputs in the signal plane to every lattice point in the image plane via a transmission path having a phase shift _i = - k(ux + vy) (38) At the image plane point at radius r and at angle a, the phase will be _bi = -k r (u sin a + v cos a) while at the angle Ir + _ the phase will be ¢i = kr (u sin a + v cos _) (39) 142
All the1Fsignalswillarrivein phaseif ¢r + ¢i = 0, that is, if GO/. kr = "-c-" sin 5 (40) and 2nc _r A(6 cos _) = - (46) SGOr s or, since 6
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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
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1. Wewillnothavenough resolving pow
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normalwith the meanat o x/--2. When
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Chapter11 in analyzingthe dataproce
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Therangelimitisthenfoundbyequating_
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TABLE 5-3 PARAMETER Wavelength Tran
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angeanddirectlyasthesquareof antenn
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"_ i i i i i p = STELLAR DENSITY AT
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I-- g u. O >- I--- .d tit (]O 0 0.
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andwidth that will still give near
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acquisitionphasefor otherraces.Supp
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1. They would transmit continuously
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and ¢-Ceti. No signals were detect
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vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
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The price of incomplete sky coverag
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modest size.A largedatabaseontapeor
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THEAUXILIARYOPTICALSYSTEM Althoughn
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edetectedat 20,000light-years byCyc
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feeds must correct for spherical ab
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side of the dish and shade on the o
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TABLE 8-1 UNADJUSTED UNIT COST DATA
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7. Using huge specially designed ji
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9. THE RECEIVER SYSTEM The receiver
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whereP is the radiated power. Divid
Page 103 and 104: SHADOWED AREA SHADOWED AREA // // /
Page 105 and 106: Corrugatedhornssupportingbalancedhy
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: plottedin Figure11-15for various va
Page 157 and 158: x:(1 +x) x 2 - _ -- (53) If we wish
Page 159 and 160: 3's = unitcostof signal planelectro
Page 161 and 162: where0ma x is the maximum value of
Page 163 and 164: Roughestimates of the costs of buil
Page 165 and 166: 12. CYCLOPS AS A BEACON Although th
Page 167 and 168: 13. SEARCH STRATEGY The high direct
Page 169 and 170: distantgalaxies (oraninertialrefere
Page 171 and 172: wouldfollowtheuppermost linein Figu
Page 173 and 174: persquaredegreeof fieldwouldberequi
Page 175 and 176: starsfrom/'18 to G5 could support a
Page 177 and 178: 14. CYCLOPS AS A RESEARCH TOOL Thro
Page 179 and 180: Only a few such galaxies have been
Page 181 and 182: 15. CONCLUSIONS AND RECOMMENDATIONS
Page 183 and 184: perhapsdecadesand possiblycenturies
Page 185 and 186: APPENDIX A ASTRONOMICAL DATA DISTAN
Page 187 and 188: PLANETARY Planet ORBITS Semimajor S
Page 189 and 190: APPENDIX B SUPERCIVILIZATIONS AND C
Page 191 and 192: ABIOLOGICAL CIVILIZATIONS Many writ
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Page 195 and 196: tqOT APPENDIX C OPTIMUM DETECTION A
Page 197 and 198: to rmsnoise.Wenotethatthematchedfil
Page 199 and 200: APPENDIX D SQUARE LAW DETECTION THE
Page 201 and 202: If the output filter is very wide c
Page 203 and 204: 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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