Contains reports on five research projects.National Aeronautics and Space Administration (Grant NsG-419)National Science Foundation (Grant GP-7046)National Aeronautics and Space Administration (Contract NSR-22-009-120)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U, S. Air Force, under Contract DA 28-043-AMC-02536(E)U. S. Navy (Office of Naval Research) under Contract N00014-67-A-0204-000

Barrett, Alan H.

Burke, Bernard F.

Ewing, M. S.

Law, Sara E.

Moran, J. M., Jr.

Neal, R. W.

Papa, D. Cosmo

Papadopoulos, George D.

Reifenstein, E. C., III

Staelin, David H.

Waters, J. W.

Wilson, T. L.

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III. RADIO ASTRONOMYAcademic and Research StaffProf A. H. Barrett Prof. D. H. Staelin O. H. GonzalezProf. B. F. Burke Dr. S. H. Zisk D. C. PapaProf. R. M. Price J. W. Barrett C. A. ZapataGraduate StudentsR. M. Blotky Sara E. Law L. W. Schaper, Jr.M. S. Ewing J. M. Moran, Jr. P. R. SchwartzN. E. Gaut P. C. Myers J. W. WatersW. W. Gebhart G. D. Papadopoulos T. T. Wilheit, Jr.L. P. A. Henckels E. C. Reifenstein III T. L. WilsonH. F. Hinteregger P. W. Rosenkranz W. J. WilsonA. LONG BASELINE INTERFEROMETER EXPERIMENTSAnother very long baseline interferometer experiment was successfully carried outbetween January 28 and 31, 1968. Its purpose was to extend the study of the structureof OH radio sources. The interferometer had 4 elements consisting of the radio tele-scopes at the Haystack Microwave Research Facility of Lincoln Laboratory, M. I. T.,Westford, Mass. , National Radio Astronomy Observatory, Green Bank, West Virginia,University of California Observatory, Hat Creek, California, and Chalmers Univer-sity Observatory, Onsala, Sweden. At each site atomic frequency standards were usedto control the local oscillators and thereby make the system phase coherent. The sig-nals received at each site were sampled and recorded on magnetic tape, the samplingbeing controlled by the frequency standard. The time synchronization at the stationsin Westford, Green Bank, and Sweden was achieved by having all stations monitorthe Loran C transmission of the North Atlantic chain. At Hat Creek the clock wassynchronized to the Hewlett-Packard traveling clock.Figure III-1 shows a complex visibility spectrum on W3 obtained by crosscor-relating the data on tapes taken at Haystack and Onsala, Sweden. The processingtime for this 80-sec integration period was 160 minutes on a CDC-3300 computer.The bulk of this time was taken up with computing the crosscorrelation function,which required performing 4 X 109 1-bit multiplications. The single antenna spec-trum has spectral features at -41. 7, -43. 7 and -45. 1 km/sec. The feature at -45. 1is the strongest but shows low visibility, which implies that it is resolved on thisbaseline. The difference in fringe phase among the features indicates their spatialThis work was supported principally by the National Aeronautics and Space Admin-istration (Grant NsG-419 and Contract NSR-22-009-120); and in part by the Joint ServicesElectronics Programs (U. S. Army, U. S. Navy, and U, S. Air Force, under Con-tract DA 28-043-AMC-02536(E), the U. S. Navy (Office of Naval Research) under Con-tract N00014-67-A-0204-0009, and the National Science Foundation (Grant GP-7046).QPR No. 89(III. RADIO ASTRONOMY)separation. The phase shift across the -41. 7 km/sec feature is probably causedby a change in position of the feature with velocity. The fringe amplitude of the-43. 7 km/sec was computed on each of the 6 baselines by crosscorrelating all pos-sible pairs among the 4 elements. The results (see Fig. III-2) show a systematicdecrease in fringe amplitude with increased baseline, which indicates that the feature80W 3HAYSTACK-ONSALA SWE DEFig. III-1. Visibility spectrum on W3 in rightcircular polarization. Interferom-eter elements were at Haystackand Onsala, Sweden, giving abaseline of 5600 km. The spatialresolution is 0. 007 second of arc,and the velocity resolution is0. 4 km/sec.-41 -42 43 -44 4VELOC TY km/sec1.00.8S0.6S0.4- .004" }SOURCE SIZE\ -. 005" 110 20 30 40D/X x 106Fig. 111-2. Fringe amplitude vs projected baseline length for the -43. 7 km/secfeature in W3. The 6 points were obtained by crosscorrelating the4 data tapes recorded simultaneously with all possible pairs. Thebaselines in order of length are Haystack-NRAO, Berkeley-NRAO,Berkeley-Haystack, Haystack-Onsala, NRAO-Onsala, and Berkeley-Onsala.QPR No. 89(III. RADIO ASTRONOMY)is being resolved. Its diameter is 0. 0045 second of arc if a uniform disk model isassumed or approximately 0. 0025 second of arc between half-power points if a Gaussiandistribution is assumed. The diameter 0. 0045 second of arc corresponds to a lineardistance of approximately 7 A. U. There does not seem to be any great change in fringeamplitude with baseline orientation, which means that this feature is roughly circularin shape.The operation of a multielement interferometer involved no additional developmentof the equipment that was used in the experiments between 2 stations last summer. Theexperiment is important, in that it showed that a multielement system can be operatedsuccessfully without serious coordination problems, thereby making more data availableper tape recording, because of the increased number of possible correlations. Further-more, with 3 or more antenna simultaneously observing, some severe instrumental effectscan be overcome. For example, the effects of phase and frequency uncertainty in theatomic standards can be eliminated to achieve accurate position measurements of the05--491 (L)-43.7 (R)0.0 -. -45.1 (R)- 41.7 (R) -46.4 (L) Fig. III-3. Map of W3 OH source. The0< 5 position separations among, -O -the features were deter-U) mined from the relative;7 fringe-rate information. The0o absolute position of the mapis uncertain to ±5 second of1000 A.U. arc.-1.5- 4 5.5 (L)-2.0-- 44.6 (L)0.5 0.0 -0.5 -1.0 -1.5 -2.0Aa x cos 8 (SECONDS OF ARC)baselines and source position of the order of 0. 001 second of arc, provided the atmo-spheric refraction problems can be solved.We have improved the map of the W3 region that was presented in Quarterly Prog-ress Report No. 88 (page 29). The new map, shown in Fig. 111-3, shows all seven ofthe major features in the W3 spectrum at the 1665-MHz transition. The features at-49. 1(L), -45. 5(L) and -46. 4(L) km/sec have a complex structure of the order ofQPR No. 89(III. RADIO ASTRONOMY)0. 02 second of arc. The -45. 1(R) and -41. 7(R) km/sec features are double, with sepa-rations of the order of 0. 02 second of arc. The feature at -43. 7(R) km/sec is 0. 0045second of arc in size, and approximately circular in shape. The separations among thefeatures were determined by analyzing the difference in fringe rate of the features asa function of local hour angle. The technique is free of ambiguity problems and instru-mental effects, although its sensitivity is rather low. The errors in the positions aretypically ±0. 3 second of arc.J. M. Moran, A. H. Barrett, B. F. BurkeB. RADIO INTERFEROMETERA front-end prototype of the 1. 75-cm radio interferometer has been constructed, andone of the dishes has been used in rudimentary observations of the sun.Slew drives are now being installed in the antenna mounts.The digital interface and phase-lock mechanism are in the final stages of testing.The analog multipliers, as well as the calibration and delay compensation circuits,are currently under construction.G. Papadopoulos, M. S. Ewing, D. C. Papa, B. F. BurkeC. MIT-NRAO RECOMBINATION LINE SURVEYThe MIT-NRAO recombination line survey observations are now complete for theNorthern Hemisphere. We have observed all sources in the NRAO 11-cm survey1 downto an antenna temperature of 1*K at 6 cm on the 140-ft radio telescope. There are120 sources in all, and recombination lines were found in 75 of these. These data arenow being prepared for publication.Our results indicate that except for the Sagittarius sources there are no H II regionsinside the 4-kpc arm. Observations by Costain 2 and Altenhoff 3 indicate that thosesources that have no recombination line are nonthermal. Observation of Helium in M17,Orion, and W49 indicates a Helium/Hydrogen ratio of approximately 9% by number.T. L. Wilson, E. C. Reifenstein, B. F. BurkeReferences1. W. A. Altenhoff and P. G. Mezger, in preparation.2. C. Costain, Private communication, 1968.3. W. A. Altenhoff, Private communication, 1968.QPR No. 89(III. RADIO ASTRONOMY)D. K-BAND OBSERVATIONS OF STRATOSPHERIC WATER VAPORThe microwave spectrum of the terrestrial atmosphere at frequencies within100 MHz of the 22. 235-GHz water-vapor resonance is very sensitive to the abundanceof water vapor at high altitudes. Direct rocket and balloon measurements of the water-vapor content are usually limited to altitudes below 30 km, so microwave measurementscan be valuable in extending the water-vapor profile to higher altitudes.Measurements to detect high-altitude water vapor were made using a 16-channelradiometerl during the period August 1967-January 1968. The radiometer was a super-heterodyne system with IF passband 20-84 MHz without image rejection. Each channelwas 4 MHz wide, and successive channels overlapped at the half-power points. Thetheoretical half-width of the water-vapor line is 42 MHz at 30 km and 3 MHz at 50 km,so the measurements would be most sensitive to water vapor between these altitudes.The measurements were made using 2 microwave horns, each of 15* beamwidth.Reflectors were positioned in front of the horns so that one horn received radiation fromthe sky at 100 from the zenith, and the other horn received radiation at 780 from thezenith. An absorber at ambient temperature was placed partially in the beam of the10' horn in order to approximately equalize the temperature received by the two horns.The data runs consisted in (i) a 4-minute calibration, (ii) 8 integrations of 4 minuteseach, alternating between the two horns, and (iii) another 4-minute calibration. Thedifference in temperature between the two horns was computed and normalized to havea zero mean over the 16 channels. The difference spectrum would be expected to showan emission feature, since the path length through the atmosphere is greater for the780 horn.To minimize the effects of interference in the experimental spectra, data points werediscarded if they showed large rms deviations during a run or if they had valuesdeviating more than 0. 50 K from the mean of the 16 channels. The spectra weresmoothed by computing a weighted average (1-2-2-1) over each set of 4 channels.Figure III-4 shows 4 experimental and theoretical spectra labeled by date. If theerrors are correlated from channel to channel, the larger error bracket is appli-cable, but if the errors are uncorrelated as they should be, then the smaller errorbracket applies. These error brackets represent only the rms receiver noise. Inorder to detect spurious channel-dependent spectral features, each data set wasmade with a difference local-oscillator frequency, as noted in Fig. 111-4. No sucheffects are evident.The theoretical spectra were computed using typical summer temperature andpressure profiles. The theoretical water-vapor profile was based on measurementsof Sissenwine et al. 2 made at Chico, California, for altitudes below 30 km. Thesemeasurements were extrapolated to the 30-60 km region by assuming a constantQPR No. 89(III. RADIO ASTRONOMY)mixing ratio of 1.4 X 10- 5 for this region.the same model atmosphere. They appearUNCORRELATED ERRORCRRELATED ERRORAUGUST'67L.O. 22.185 GHzCHANNEL -HI I-4 MHzSEPTEMBER - OCTOBER'67L .. = 22.220 GHz0.1The 4 theoretical spectra were computed fordifferent because each was folded about theEXPERIMENTALTHEORETICAL WITH H20 CUTOFF AT 60 km--- THEORETICAL WVITH 2 0 CUTOFF AT 30 kmSEPTEMBER - OCTOBER'67L.O. 27.160 GHz0 4 8 12 16CHANNEL - I4 MHzJANUARY'68L.O. - 22.290 GHzCHANNEl8 12 16 0 4 8_1 I- CHANNEL -- I-4 MHz 4 MHz12 16Fig. 111-4. Four experimental and theoretical spectra.appropriate local-oscillator frequency to simulate the effect of double sidebands. Fig-ure III-4 shows good agreement between theoretical and experimental spectra for theAugust 1967 data. The observed spectral feature deviates from a flat spectrum bymore than 2 standard deviations. The theoretical spectrum for no water vapor above30 km is shown for comparison with the August data.The measurements during the September-January period show no features at theexpected frequency larger than 1 standard deviation, and thus one can only concludethat the high-altitude water vapor did not increase significantly during the fall andwinter.These preliminary data support the data of Sissenwine et al.,2 but further measure-ments to confirm these results will be very helpful.Sara E. Law, R. Neal, D. H. StaelinQPR No. 89(III. RADIO ASTRONOMY)References1. D. H. Staelin, R. M. Weigand, and J. M. Waters, "20-channel Microwave Radiom-eter," Quarterly Progress Report No. 86, Research Laboratory of Electronics,M. I. T. , July 15, 1967, pp. 25-26.2. N. Sissenwine, D. D. Grantham, and H. A. Salmels, "Mid-Latitude StratosphericHumidity Regime to 30 km," Interim Notes on Atmospheric Properties No. 73, Pre-sented at AFCRL Scientific Balloon Symposium, Portsmouth, New Hampshire, Sep-tember 14, 1966.E. STATISTICAL INVERSION OF RADIOMETRIC DATAThe statistical data inversion technique presented here is an extension of thatdescribed in previous reports. '1,2 From a set of measurable quantities, representedby a data vector d, one wishes to infer certain parameters represented by a parametervector p. Let p be the inferred value of p. We represent p as a combination of somebasis functions i of the raw data:p = D" (d),where D is a matrix to be determined. No restrictions are placed on the functionsi(d). They may be linear or nonlinear, and need not be orthogonal or complete. Theyare chosen from one's knowledge of the physical relation between p and d. D is foundfrom the statistics of p and d by minimizing the expected mean-square error in p-1D =C(p, ) . C- (4, 4), (1)whereC ij(x,Y) = <xiY>is the correlation matrix. In general, d = do + n, where do represents noiseless data,and n is additive noise. Expanding 4 in a Taylor series yields for the correlationmatrices00Cjp, ) = Cij [P, 4/d)] + i(n. Vd k (dk=l d=doCij(#, #) = Cij[_(d°), _(d°)] + 1 k V d (d) (d-j k! d >k= 1 d=d*where Vd is the del operator in d-space.A problem arises when C( , c) is singular, since then its inverse does not exist andEq. 1 is meaningless. When this occurs one chooses a new set of basis functions 4' forQPR No. 89(III. RADIO ASTRONOMY)which C(4'. 4') is diagonal. Since C is Hermitian, it can be shown that 4' is related to4 by4' = R t,where Rt is the transpose of the matrix formed from the normalized (column) eigen-vectors of C(4, 4). The singularity of C is caused by those functions 4j for whichCjj(4', 4') is zero, or is below the computational noise level. These 4) are discarded,and the remaining 4i are used in the following expression for p :p [C(p, ') C (', ')] (d. (2)Equation 2 gives the value of p which minimizes its expected mean-square error forgiven a priori statistics and basis functions 4(d). This inversion technique is verygeneral and can be applied to a variety of problems. It requires only statistical knowl-edge of the parameters and data or a means of generating these statistics. The physi-cal relationship between parameter and data is not necessarily required.The inversion technique described above has been used in numerical experimentsfor determining tropospheric temperature and water-vapor profiles by microwaveradiometry. Statistical information was computed from radiosonde records obtainedfrom the U. S. Weather Bureau.The results of 100 inversions for total water vapor in various layers of the atmo-sphere are shown in Table III-1. The data vector for these inversions consists of com-puted brightness temperatures as would be observed in emission against a cold sky, byan ideal radiometer at the surface looking toward the zenith. The frequencies were 20. 0and 22. O0 GHz, which are near the 22. 235-GHz resonance of water vapor. Inversionswere performed from noiseless data and from data to which 1°K rms noise had beenadded. Table III-1A gives results for a linear inversion in which the data basis functionvector 4(d) equals the data vector d. Table III-1B shows the improvement obtained byaugmenting the linear basis function vector with the nonlinear function 43 (d) = d 1 d 2 . Alsoindicated are the mean and the standard deviation cr of the parameter. The standarddeviation of the parameter tells how accurately its value can be determined beforemaking a measurement. Comparison of this with the standard deviation in the inversionerrors gives the value of the measurement.Inversions for tropospheric water vapor were also performed from data simulatingthat which would be collected by a radiometer looking down at nadir from an orbitingsatellite. The results are approximately the same as those given in Table III-1 whenthe satellite is over a calm ocean. When the satellite is over land, little informationabout tropospheric water vapor is obtained.Figure III-5 shows the results of 100 linear inversions for tropospheric temperatureprofiles from data simulating that collected by an orbiting radiometer. The dataQPR No. 89Inversion results for water vapor.(Based on 100 radiosonde records. Kwajalein and Tucson, Arizona.)A. Linear InversionReceiverParameter Parameter Statistics Inversion Errors ReceiverSensitivitymean a mean O °K9.5 km gm .04 . 17 0PH0 dh 2 0.42 0.384km 2 cm .02 .18 14 km gm .01 . 13 0H dh 2 0.83 0.552 km 2 cm . 01 . 13 12 km gm -. 02 . 19 0S, PH0 dh 1.94 1. 21~HO 20 2 cm .01 . 21 19.5 km gm .03 .07 0p dh 3. 19 2.032 cm .04 .09 1B. Nonlinear InversionQPR No. 89ReceiverParameter Parameter Statistics Inversion Errors ReceiverSensitivitymean a mean K9.5 km gm -. 01 . 11 04 PH20 dh 2 0.42 0. 384km 2 cm .00 . 16 14 km gm .00 .13 0PH20 dh 2 0.83 0.552km 2 cm .00 .13 12 km gm -. 01 .14 0PH dh 2 1.94 1.212 cm .01 . 20 19.5 km gm .00 .02 0p dh 3.19 2.03H2 cm .00 .08 1Table III-1.(III. RADIO ASTRONOMY)comprised calculated brightness temperatures at three frequencies in the oxygenabsorption band around 60 GHz. The algebraic mean and the standard deviation o- ofFig. I1-5.STANDARD DEVIATION INACTUAL TEMPERATURE PROFILEErrors in inversions for temper-ature profile based on statisticsfrom 100 radiosonde records and100 inversions. Data are calcu-lated brightness temperatures atfrequencies 53. 60, 60. 82, and64. 47 GHz. When looking downat nadir from a 20-km surface,the emissivity is 1. 0. The cal-culations shown here are fornoise-free data.5 10TEMPERATURE (oK)the 100 inversion errors are plotted as a function of altitude. For comparison, the stan-dard deviation in the actual temperature profile is shown. Preliminary investigationsindicate that the results shown in Fig. III-5 are independent of the surface below thesatellite and the statistics used for calculations. From these results, it appears thatthe tropospheric temperature profile can be determined within approximately 30 K bypassive microwave techniques.The results presented in this report should be considered preliminary for tworeasons: the choice of nonlinear basis functions 4(d) has not been fully explored or opti-mized, and some of the matrices that had to be inverted were slightly singular andresults have not yet been obtained by using the method described here for getting aroundthe problem of inverting singular matrices. This work will continue.J. W. Waters, D. H. StaelinReferences1. D. H. Staelin, "Interpretation of Spectral Data," Quarterly Progress Report No. 85,Research Laboratory of Electronics, M. I. T. , April 15, 1967, pp. 15-16.2. N. E. Gaut, A. H. Barrett, and D. H. Staelin, "Results Obtained from the Inversionof Simulated Atmospheric Water-Vapor Spectra," Quarterly Progress Report No. 85,Research Laboratory of Electronics, M. I. T., April 15, 1967, pp. 16-19.QPR No. 89EI 10C)7

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