the nrao tape-recorder interferometer system

8
1242 PROCEEDINGS OF TFIE IEEE, VOL. 61, NO. 9, SEPTEMBER 1913 The observation of the OH source in W3(OH) with the Haystack and NRAO antennas provides an example of the foregoing analysis. The parameters are D -845 km, w/2r = 1665 MHz, SB= -24’, and 6s=6l0. Thus SO-4.7 X10” and s0-~=0.213X1W rad=O‘.044, the minimum fringe spacing. If we take TB = 250 K, TA = 1 K, B = 1 kHz, N= 24, and 71500 s, we get u,=0.25 rad, uf= 1.7 X 10-* rad/s -0.27 mHz, and position errors from the fringe-rate analysis of u% = 0”.052 and uh = 0“.060. The first bothersome sidelobe or possible position ambiguity occurs at 8-~12/(rS0 cos 6 ~ ) 4.18, or about three times the coordinate error. Hence the analysis of thephasedata gives an unambiguous relative position with errors u0~’~~0,,’-0“.006. ACKNOWLEDGMENT The author wishes to thdk J. A. Ball, B. G. Clark, and A. E. E. Rogers for their helpful discussions of this paper. REFERENCES [l] B. G. Clark, ‘The NRAO tape-recorder interferometer system,” [2] J. H. Van Vleck and D. Middleton, “The spectrum of clipped noise,” Proc. IEEE, this issue, pp. 1242-1248. Proc. IEEE, vol. 54, pp. 2-19, Jan. 1966. [3] B. G. Clark, K. 1. Kellermann, C. C. Bare, M. H. Cohen, and D. L. Jauncey, “High resolution observatiom of small diameter radio sources at 18 centimeter wavelength,” Astrophys. J., vol. 153, pp. [4] A. E. E. Rogers, Very long baseline interferometry with large ef- fective bandwidth for phase delay measurements,” Radio Sci., vol. [5] A. Papoulis, Probability, Random Variables and Sbchmtic Procuscs. [6] M. Vinokur, “Optimisation dam la recherche d’unesinusoide de New York: McGraw-Hill, 1965, pp. 498-502. periode connue en presence de bruit,” Awn. Astrophys., vol. 28, pp. 41245,1965. [7] W. B. Davenport and W. L. Root, An Zwtrodudion to the Theory of Random Signals and Noise. New York: McGraw-Hill, 1958, pp. [8] R. Hanbury Brown and R. Q. Twiss, “A new type of interferometer for use in radio astronomy,” Phil. Mag., vol. 45, pp. 663-682, July 1954. [9] B. G. Clark, “Radio interferometers of intermediate type,” ZEEE Trans. Awknrros Propara!. (Commun), vol. AP-16, pp. 143-144, Jan. 1968. [lo] J. M. Moran et al., ‘The structure of the OH source in W3,” As- [ll] I(. J. Johnston et d., ‘An interferometer map of the water-vapor trophys. J. (Lett.), vol. 152, pp. L97-L101, May 1968. sourcea in W49,” Astrophys. J. (Lett.), vol. 166, pp. L21-L26, May 15, 1971. [12] R. N. Bracewell, “Radio interferometry of discrete sources,” Proc. IRE, vol. 46, pp. 91-105, Jan. 1958. 1131 J. A. Ball, “Okmatiom of OH radio emission sources,” M.I.T. Lincoln Lab., Lexington, Mass., Tech. Rep. 458, May 23, 1969. 705-714, Sept. 19:s. 5, pp. 1239-1247, Oa. 1970. 322-332. The NRAO Tape-Recorder Interferometer System BARRY G. CLARK Abstroct-Severnl t.pbmordu interferometer systems have been constructed in the last few yeanr These bystems are used for carmeeting existing radio-telescope systems into interferometers, with baselines ranging from a few kilometers to ndy the diameter oftheearth. The NRAO Mark 11 interferometer -em is in wide use. This, and the fact that its properties are typical of those of such systems in general, jnsMes a detailed desaiption of the system. The system is based on atelevision-typerotating-headvideo der. Onebit sampled data are recorded at a 4-Mb rate. After recovery, the data sue processed in rpedal-porpose digital devices and generrl-parpose digital computer8 to complete the interferometer system. For puqbsea of this descriplion, the mftware is regarded M an intrinsic part of the aystem. ‘R 1. INTRODUCTION AD10 INTERFEROMETERS of all the various sorts which have been built by radio astronomers have a strong generic resemblance, and differ more in con- structional details than in principle. They differ strongly in appearancefrommostinterferometers used at visible-light wavelengths, chiefly because the radio engineer prefers to construct a local oscillator (LO) at each of the interferometer Manuscript received February 19,1973. The National Radio Astron- omy Observatory is operated by W t e d Universities, Inc, under Contract with the National Science Foundation. Charlottesville, Va. 22901. The author in with *e National Radio Astronomy Obeervatory, elements, and to perform the correlation in an efficient fashion at a convenient intermediate frequency (IF). In recent years, the desire of the radio astronomer for even longer baselines. has outdistanced the capability of.construct- ing economically feasible cable- or microwave-link-connected interferometers. T o meet this need, interferometers have been constructed which eliminate all physical connection between elements, replacing the conventional LO link with inde- pendent LO’S, andtheconventional I F link with tape re- cordings carried physically from one interferometer element to the other. These interferometers have been used on many baselines, ranging from a few kilometers to nearly the diame- ter of the earth [l]. Even such a strong variant as thetape-recorderinter- ferometer, however, differs very little from the conventional cable- or microwave-link-connected interferometer. The more conventional I F transmission and delay systems’ are merely replaced by the tape-recorder system. The main remarkable property of the tape recorders as a transmissionsystem is their long transmission delay, measured in days or weeks, but no different in principle than delays of microseconds or nanoseconds encountered in conventional transmission sys- tems. Because the tape-recorder interferometer system is similar to the conventional radio interferometer, it will be found that a firm grounding in either system permits immediate under-

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Page 1: The NRAO tape-recorder interferometer system

1242 PROCEEDINGS OF TFIE IEEE, VOL. 61, NO. 9, SEPTEMBER 1913

The observation of the OH source in W3(OH) with the Haystack and NRAO antennas provides an example of the foregoing analysis. The parameters are D -845 km, w/2r = 1665 MHz, SB= -24’, and 6s=6l0. Thus SO-4.7 X10” and s0-~=0 .213X1W rad=O‘.044, the minimum fringe spacing. If we take TB = 250 K, TA = 1 K, B = 1 kHz, N = 24, and 7 1 5 0 0 s, we get u,=0.25 rad, uf= 1.7 X 10-* rad/s -0.27 mHz, and position errors from the fringe-rate analysis of u% = 0”.052 and uh = 0“.060. The first bothersome sidelobe or possible position ambiguity occurs at 8-~12/(rS0 cos 6 ~ ) 4 . 1 8 , or about three times the coordinate error. Hence the analysis of the phase data gives an unambiguous relative position with errors u0~ ’~~0 , , ’ -0“ .006 .

ACKNOWLEDGMENT The author wishes to t h d k J. A. Ball, B. G. Clark, and

A. E. E. Rogers for their helpful discussions of this paper.

REFERENCES [l] B. G. Clark, ‘The NRAO tape-recorder interferometer system,”

[2] J. H. Van Vleck and D. Middleton, “The spectrum of clipped noise,” Proc. IEEE, this issue, pp. 1242-1248.

Proc. IEEE, vol. 54, pp. 2-19, Jan. 1966.

[3] B. G. Clark, K. 1. Kellermann, C. C. Bare, M. H. Cohen, and D. L. Jauncey, “High resolution observatiom of small diameter radio sources a t 18 centimeter wavelength,” Astrophys. J . , vol. 153, pp.

[4] A. E. E. Rogers, Very long baseline interferometry with large ef- fective bandwidth for phase delay measurements,” Radio Sci., vol.

[5] A. Papoulis, Probability, Random Variables and Sbchmtic Procuscs.

[6] M. Vinokur, “Optimisation dam la recherche d’une sinusoide de New York: McGraw-Hill, 1965, pp. 498-502.

periode connue en presence de bruit,” Awn. Astrophys., vol. 28, pp. 41245,1965.

[7] W. B. Davenport and W. L. Root, An Zwtrodudion to the Theory of Random Signals and Noise. New York: McGraw-Hill, 1958, pp.

[8] R. Hanbury Brown and R. Q. Twiss, “A new type of interferometer for use in radio astronomy,” Phil. Mag., vol. 45, pp. 663-682, July 1954.

[9] B. G. Clark, “Radio interferometers of intermediate type,” ZEEE Trans. Awknrros Propara!. (Commun), vol. AP-16, pp. 143-144, Jan. 1968.

[lo] J. M. Moran et al., ‘The structure of the OH source in W3,” As-

[ l l ] I(. J . Johnston et d., ‘An interferometer map of the water-vapor trophys. J . (Lett.), vol. 152, pp. L97-L101, May 1968.

sourcea in W49,” Astrophys. J . (Lett.), vol. 166, pp. L21-L26, May 15, 1971.

[12] R. N. Bracewell, “Radio interferometry of discrete sources,” Proc. IRE, vol. 46, pp. 91-105, Jan. 1958.

1131 J. A. Ball, “ O k m a t i o m of OH radio emission sources,” M.I.T. Lincoln Lab., Lexington, Mass., Tech. Rep. 458, May 23, 1969.

705-714, Sept. 19:s.

5, pp. 1239-1247, Oa. 1970.

322-332.

The NRAO Tape-Recorder Interferometer System

BARRY G. CLARK

Abstroct-Severnl t.pbmordu interferometer systems have been constructed in the last few yeanr These bystems are used for carmeeting existing radio-telescope systems into interferometers, with baselines ranging from a few kilometers to n d y the diameter oftheearth.

The NRAO Mark 11 interferometer -em is in wide use. This, and the fact that its properties are typical of those of such systems in general, jnsMes a detailed desaiption of the system.

The system is based on a television-type rotating-head video der. Onebit sampled data are recorded at a 4-Mb rate. After recovery, the data sue processed in rpedal-porpose digital devices and generrl-parpose digital computer8 to complete the interferometer system. For puqbsea of this descriplion, the mftware is regarded M an intrinsic part of the aystem.

‘R 1. INTRODUCTION

AD10 INTERFEROMETERS of all the various sorts which have been built by radio astronomers have a strong generic resemblance, and differ more in con-

structional details than in principle. They differ strongly in appearance from most interferometers used at visible-light wavelengths, chiefly because the radio engineer prefers to construct a local oscillator (LO) at each of the interferometer

Manuscript received February 19,1973. The National Radio Astron- omy Observatory is operated by W t e d Universities, Inc, under Contract with the National Science Foundation.

Charlottesville, Va. 22901. The author in with *e National Radio Astronomy Obeervatory,

elements, and to perform the correlation in an efficient fashion at a convenient intermediate frequency (IF).

In recent years, the desire of the radio astronomer for even longer baselines. has outdistanced the capability of.construct- ing economically feasible cable- or microwave-link-connected interferometers. T o meet this need, interferometers have been constructed which eliminate all physical connection between elements, replacing the conventional LO link with inde- pendent LO’S, and the conventional I F link with tape re- cordings carried physically from one interferometer element to the other. These interferometers have been used on many baselines, ranging from a few kilometers to nearly the diame- ter of the earth [l].

Even such a strong variant as the tape-recorder inter- ferometer, however, differs very little from the conventional cable- or microwave-link-connected interferometer. The more conventional I F transmission and delay systems’ are merely replaced by the tape-recorder system. The main remarkable property of the tape recorders as a transmission system is their long transmission delay, measured in days or weeks, but no different in principle than delays of microseconds or nanoseconds encountered in conventional transmission sys- tems.

Because the tape-recorder interferometer system is similar to the conventional radio interferometer, it will be found that a firm grounding in either system permits immediate under-

Page 2: The NRAO tape-recorder interferometer system

CLARK: TAPE-RECORDER INTERFEROMETER SYSTEM 1243

standing of the other. Any principle found useful in utilizing or in describing the behavior of one system will also find application in the other. Minor differences arise because the behavior of the instrument may be dominated by one term in one case and by another term in another case, but it is found in practice that if an effect needs to be taken into account for the tape-recorder interferometer, there arise cases for con- ventional interferometers in which i t is also important, and vice versa.

With very little difference in principle between the various classes of radio interferometers, it is clear that the differences among the tape-recorder interferometers wiil be smaller yet. Indeed, since the designers of the various recorder systems are all motivated by the same desire to reduce the cost of the recording medium by maximizing the amount of information which can be stored on a square centimeter of tape, the vari- ous systems tend to encounter a very similar set of problems. The various systems differ only in details, and the compari- son of them rests on secondary considerations, such as the reliability of the recorders, the convenience of the recording and reproduction processes, and the adaptability of the sys- tem to requirements not originally built into it.

Since the NRAO Mark I1 tape-recorder interferometer system is more or less typical of those in use, its special fea- tures will be described in detail as typical of the way technical problems may be handled.

Because of the complexity of any interferometer with a baseline more than a few hundred wavelengths, the use of digital computers tends to be an intrinsic part of the design. The NRAO Mark I1 system is no exception. At every step of the design i t was carefully considered whether a given func- tion could best be performed by analog hardware, special- purpose digital hardware, or software in a general-purpose digital computer. As a result, the mixture of hardware and software is so intimate that someone using the equipment for the first time may not realize with which he is dealing, and no clear distinction between them will be made in this paper.

11. PRINCIPLES OF DIGITAL I F INTERFEROMETRY In order to make the recording and playback systems as

reliable as possible, the decision was made to record a digitized version of t he IF voltages rather than the voltages themselves. Given that we record binary digits, it can be shown that single bit (1-b) digitization conveys more information per bit than any multilevel scheme. That is, a 2-b digitization pro- duces less increase in signal-to-noise ratio (SNR) than does using the second bit to double the bandwidth of the 1-b digitized signal.

Although the use of 1-b digitized IF'S has been extensively discussed in relation to spectroscopy, and has become a standard technique in radio astronomy [2]-[4], it still perhaps warrants a few words of comments with respect to its use in interferometers [SI, [6]. In this connection, the digitization does not introduce as much complication as one might sup- pose. The relation between the correlation of two 1-b digitized signals, and the correlation of the signals without digitization has, for Gaussian distributed random signals, long been known [7]. In this connection, it turns out that the sampling of the signals, though done at a sufficiently high rate to avoid information loss, introduces more complexity than the trun- cated digitization. For example, consider the case of a signal with a flat power spectrum extending from zero tofo, sampled at a rate 2f0 so that all samples are uncorrelated. Tha t is, the autocorrelation function of the signals has zeros at the

sample intervals. Cross-correlating the signals, however, is not quite the same process, because an arbitrary phase shift can be, and usually is, introduced in the signals before corre- lation. If, for instance, a phase shift of 90" is introduced, the cross-correlation function has a zero at zero lag, because the sine and cosine components of a noise-like signal are inde- pendent random variables. However, at k one lag, the corre- lation is no longer zero, but has a positive value at one point and a negative value at the other. Because of this phase effect, i t is convenient to speak of the complex correlation function, which is the complex function obtained by adding j times the cross-correlation function with 90" phase shift to that with zero phase shift. This complex cross-correlation function does not have zeros at multiples of the sampling interval, but at multiples of twice the sampling interval.

This gives rise to an interesting problem. The cross-corre- lation function at lag n bears information about those at lags n - 1 and n+l . Since the noise on these different lags is independent, to find the best estimate of the cross-correlation function at lag n, one must combine the measured cross- correlation function at all other lags, but principally a t lags n- 1 and n+l . The proper procedure of estimating the delay and magnitude of the cross-correlation function is therefore a rather complex one. Rogers [8] describes the maximum likelihood approach to the problem, and this approach should be used in difficult cases. In most practical cases, however, a much simpler least squares approach may be used without significant loss of SNR.

When the interferometer is used for observations of dis- crete atomic or molecular line radiation, the observer is usually interested in the frequency structure of the radiation as well as its simple cross-correlation coefficient. In the digital interferometer it is easiest to calculate the cross power spec- trum from the observed cross-correlation function by way of a Fourier transform. I t is easily shown that the fundamental principles of autocorrelation-function spectroscopy can be extended in this simple fashion to give the cross power spec- trum, identical to the one that would be measured by inserting a filter bank in front of the correlators, and measuring the complex correlation function as a function of frequency.

The fact previcusly discussed, i.e., that the cross-correla- tion function goes to zero at twice the sample spacing, is demonstrated in an interesting fashion in the line case. If only the real part of the correlation function is measured, then clearly the Fourier transform will, in general, be complex and Hermitian. That is, the complex cross power spectrum will be determined from these measurements of the real part only of the correlation function. Further, the spectrum is redundant; half the spectrum, say, the half at negative fre- quencies, may be discarded without loss of information. If the true complex cross-correlation function is measured, when we take its Fourier transform we find that the useful informa- tion is still present in only one half of the spectrum, and the other half may usually be discarded as containing only noise.

111. THE NRAO MARK I1 TAPE-RECORDER SYSTEM-TEE RECORDING SYSTEM

The block diagram of the tape-recorder interferometer recording system is shown in Fig. 1. As usual for an inter- ferometer, the feed of the radio telescope comprising an inter- ferometer element is connected to a low-noise preamplifier. The signal is then mixed to an IF, using an LO signal which is sufficiently nearly identical to the LO signal in use at the other element of the interferometer. In the tape-recorder inter-

Page 3: The NRAO tape-recorder interferometer system

1244 P~OCEEDINGS OF TEE IEEE, SEPTEMBER 1973

mercial TV (it is a popular choice for implementing “instant slow motion replay” at sports events) and in academic envi- ronments. The VR 660 C has slightly enhanced frequency response. This transport has two video recording heads mounted at diametrically opposite points on a horizontal wheel which spins at 30 r/s. The recording tape is wrapped around this wheel in a single turn helix, and is in contact with the headwheel for half a turn, so that one head is in contact with the tape at all times.

The tape is drawn past the headwheel assembly a t a rate of 3.7 in/s. The combination of this tape motion with the motion of the wheel results in each head tracing a diagonal line from one edge of the tape to the other. The separation of the video tracks is about 0.06 in along the length of the tape, or 0.010 in perpendicular to their length. The layout of data on the tape is shown in Fig. 2. The rotation of the headwheel results in an effective head-to-tape speed of about 650 injs. In the Mark I1 system, where digital data are recorded at 4 mil- lion b/s, the effective packing density is about 60oO b/in along the video tracks, and the area density is about 800 b/mm*, much the same information density as on astronomical photo- graphic plates.

The digitized data stream, sampled at 4 MHz, has essen- tial information spread over the frequency range from near zero to about 2 MHz. The video recording system cannot be sufficiently accurately compensated for the recording satura- tion effects and the head impedance effects over a very wide percentage bandwidth. In usual TV recording practice, this problem is avoided by using an FM modulation scheme to reduce the frequency range recorded to one or two octaves. For digital data, we may use a close equivalent of FM modu- lation, digital diphase coding. This code is illustrated in Fig. 3. The first line shows the input data, in non-return-to-zero format. In the second line, which is the diphase coding, there is always a transition, from positive to negative or vice versa, at the beginning of every bit time (for 4-Mb data, a bit time is a 250-ns interval). When the data are binary ones, there are, in addition, transitions in the center of the bit time. The re- sulting code string can be decoded and both clock and data can be extracted from it. The spectrum of an encoded bit string would show most of the power between 2 and 4 MHz. If this band is reproduced with reasonable fidelity, the data and clock are reproduced with high reliability.

As previously stated, it is necessary to label some bits explicitly with the time, to fix the time at which i t and all succeeding bits were recorded. This is done at the natural interval of the recorder. A new head comes in contact with the tape every sixtieth of a second. At this time, a unique sync pattern is written, one which can never occur in data, followed by a binary number giving the number of sixtieths of a second that have elapsed since the last integer second, expressing the time exactly of a given data bit.

The more significant bits of time and date are written on one of the two audio tracks of the tape recorder, also in di- phase coding. Therefore, the first bit of the track on tape was recorded at a time corresponding to the days, hours, minutes, and seconds recorded on the audio track, and to the number of sixtieths of a second recorded on the video track itself.

Y

Y t +--= S T U q A R D I VIDEO COmERTER rlEquEwcr

ONE-BIT D I c I T I U T 1 O N ;

n I I

INSERT F O W T CDllpARISoW

LORAN INFO; ENCOOE

- T l l F KEEPING - EQUl PlYNT -

t I i

Fig. 1. Tape-recorder interferometer system block diagram-record time portion.

ferometer this is accomplished by the use of an atomic- frequency standard to generate nearly perfect sine waves at both antenna elements. The preamplifier has sufficient fre- quency discrimination to reject the unwanted sideband of the mixer. The IF signal resulting from this mixing is further amplified to a conveniently high level. Then, to simplify the sampling procedure, t he IF is converted to a square bandpass with one edge of the bandpass a t zero frequency. The Mark I1 converter has a great deal of flexibility in choice of t he IF frequency, due primarily to the use of a wide-band quadrature mixer [9] to reject the unwanted sideband of the second LO used for conversion to video.

The 1-b digitization is simple clipping, done by very fast saturating amplifiers. The clipped signal is then sampled in a diode bridge driven by a very narrow pulse, and the sampled signal strobed into a T T L integrated circuit flip-flop. Sam- pling is done at a 4 M H z rate.

In the tape-recorder interferometer, each bit of data must be precisely labeled with its time of arrival at the element, either implicitly or explicitly. In the Mark I1 system, some bits are labeled explicitly, and others are labeled implicitly by counting bits from the occurrence of the labeled bits. Explic- itly labeled bits occur 60 times/s. In order for time keeping to be consistent between the two elements of the interferometer, the usual practice is to set clocks at both to universal time coordinated (UTC). There is a fairly elaborate set of time- keeping equipment to keep UTC time, and to generate all of the necessary timing signals necessary in the system (for in- stance, the tape recorders, operating at 60 frames/s, need a 60-Hz input signal). The time is compared with a known UTC either by the transportation of a running clock or by the com- parison with the Loran navigation signals, many of which are emitted at known UTC times with a precision of a few micro- seconds.

The NRAO Mark I1 system is based on the Ampex VR 660 C videotape transport. This transport is a rotating-head helical-scan television-type tape recorder, which records on 2-in wide videotape. The VR 660 B is extensively used in com-

IV. THE MARE I1 SYSTEM-THE REPRODUCTION SYSTEM A block diagram of the Mark I1 tape-recorder interferom-

eter reproduction system is shown in Fig. 4. The block dia- gram falls nicely into two parts. The upper three levels show

Page 4: The NRAO tape-recorder interferometer system

CLARK: TAPE-RECORDER INTERFEROMETER SYSTEM 1245

GUARD AL7)IO L).\A7) KO. 2 Rwn 0.015

xo, 1 0.043 0.093 0.043

GUARD A l Q 1 0

I . I

# A M I 0 2 A LDIO 1

2.000

LOTI?: ALL DINEhWOKS IS ISCIlES

v*oeo

VR-660CRecortlcd Tapc Track W!tcru

Fig. 2. Layout of data on videotape.

I l O l O O l O

Ma

I

Fig. 3. Illustration of digital diphaw code. First line-typical data, non-return-to-zero format. Second line-digital diphase coding of the same data.

RECORDER A DECODER DECODER RECORDER B - VIDEO I V I D E 0

5 511 DECODER

LOCAL CLOCK !I

DECODER 2,: 4 mr

l e

t I t - BUfFER

T I M l W RELATIVE - LAG . BUFFER -

Fig. 4. Tape-recorder interferometer system block diagram-playback time portion.

the equipment necessary to reproduce the IF signals exactly as they were recorded. The output of this part of the system is two streams of digitized data, both delayed by some very large time, but in relative synchronism. Tha t is, the data samples which were sampled and recorded at the same time are now being reproduced at the same time.

The lower three levels of the diagram show those parts of the interferometer which operate on these data streams to

produce the cross-correlation function output, and are things which might be desirable to have on any interferometer, irre- spective of the form of i t s IF transmission system.

As previously mentioned, the data are recorded in digital diphase coding on the video tracks of the tape. After repro- duction, the signal is clipped and used to derive both the data stream and the clocking pulses. In practice i t is not as difficult to recover a given bit (that is, determine if i t is a '0" or a '1") as i t is to determine where in the time sequence it belongs. The data need only to have a reliability exceeding 99 percent to contribute negligibly to the error budget of the interferometer, but the clock must be so reliable that it has a small probability of inserting an extra pulse, or deleting a pulse, in the interval between fiducial marks, a period of about 66 OOO pulses.

In the Mark I1 system, several procedures are used to recover a reliable clock. First, the recovered clock is not used directly, but is used to run a 'flywheel," such that the fly- wheel inserts any missing pulses and deletes any extra pulses. This flywheel effect is provided by an L-C filter of fairly low Q, which, nonetheless, stores the energy equivalent of several pulses, and whose output therefore is not much affected by a single input pulse. This device enables the clock to coast across 'dropouts"-tiny holes in the magnetic coating of the recording tapes-if they are not too large.

A second level of clock protection is provided by inserting into the data a short check pattern every 512 ps. This pattern consists of seven zeros and a one. At playback time this pat- tern is used to reset the clock counter if i t has gained or lost one or two pulses since the last previous pattern.

There are two parts to the data stream reproduction pro- cess. The first is the recovery of the data bits and the appro- priate clock information as previously discussed. The second is the problem of restoring the bit streams to an appropriate relative timing. In the end, we wish to have at the center of our measured correlation function not the correlation of the bits which were sampled at the same time, according to the clocks at the two elements of the interferometer, but those bits which are samples from the same wavefront of the radio-

Page 5: The NRAO tape-recorder interferometer system

1246 PROCEEDINGS OF THE IEEE, SEPTEMBER 1973

source radiation. Therefore, the apparent times on the two bit 4 = wor (4) streams should differ by the relative clock error of the two recording station clocks, and also by a geometric term arising where WO is the Lo frequency, or, in the Lo case, the from the different tirne of arrival of a given wavefront at the signed sum Of Lo frequencies* The part Of this arising from two elements of the interferometer. This geometric term is the geometric part Of the given appioximately (neglecting relativistic terms) by +,, = w0D.S ( 5 )

rg = Des. (1)

Where the source vector S is a vector of unit length directed toward the radio source, and is, in rectangular coordinates fixed in the earth,

S = (cos 6 cos H, cos 6 sin H, sin 6) (2)

and D is the baseline vector, measured in time units,

VI and Vt are the vector locations of the interferometer ele- ments, and 6 is as usual the declination of the radio source. The reference hour angle, H , is defined as the sidereal time on the x axis of the coordinate system minus the right ascension of the source.

This term may be quite large. In the extreme case, D e S may be as large as one earth radius-approximately 21 ms. The tape-recorder interferometer has an additional source of relative delay-the reproduction instability of the recorders. The time that a given bit comes out of the recorder is deter- mined chiefly by the rotation of the headwheel, since that bit is reached a t a given angle of the headwheel. The headwheel is servo controlled to an angle uniformly increasing with time, but i t is a heavy object, and subject to various mechanical disturbances. In practice, the intrinsic time stability of the VR 660 C is about 100 ps.

In the conventional radio interferometer the geometric term and the station clock errors are compensated by an I F delay system, consisting of cable, lumped constant circuits, or acoustic delays which can be inserted into an I F line as needed. Such a solution would also be possible for the tape- recorder interferometer.

In the Mark I1 interferometer, however, these various sources of relative delays between the bit streams are compen- sated for by a delay line comprised of a relatively small semi- conductor memory. The semiconductor memories for the two recorders are unloaded in synchronism by a local clock in such a fashion that the record time difference of the 2 b coming from the two buffers is strictly controlled; that is, the time difference between the two record time clocks at the time that the 2 b were recorded is strictly controlled by the playback terminal on-line computer, which calculates the approximate value of this time difference from (1) and known clock errors, with parameters supplied by the observer. The memory may be relatively small because long delays are compensated for by a mechanical relative rotation of the recorder headwheels i n response to timing signals from the memories.

In an idealized interferometer system, and perforce in optical wavelength interferometers, the delay called for by (1) should be applied at R F frequency rather than at IF. If this is done, all effects of the delay are removed, and the inter- ferometer operates as if the elements were fixed in space rela- tive to the radio source, rather than being mounted on a rotat- ing earth. I t is clear that a delay line operating a t t h e R F frequency is equivalent to a delay line operating at the IF frequency with an additional phase shift

is called the natural fringe phase, and its derivative, the natural fringe rate. This phase rotation may be thought of as the relative Doppler shift of the two ends of the interferometer with respect to the radio source.

In long-baseline interferometry very high natural fringe rates are often encountered. One earth radius baseline at 3-cm wavelength has a maximum natural fringe rate slightly greater than 15 kHz. This phase rotation must be removed before the data are eventually presented to the observer. One possibility of doing this is to alter the LO phase at record time in such a fashion that it tracks the expected geometric phase. However, in the design of the Mark I1 system, i t was felt that as much as possible, complicated functions which either require com- plex and expensive equipment, or in which i t is possible that a tiRd observer might make an unrecoverable mistake, should, if possible, be done a t playback time rather than at record time. Therefore, the natural fringe rate is removed by phase rotation of the recovered I F at playback time. I t may at first seem unnatural to talk about phase rotation of a n I F consist- ing of a stream of 1-b samples of the signal, but it is accom- plished in a rather conventional fashion. The expected fringe function (cosine of the phase +,-nearly a sine wave) is calcu- lated in special-purpose digital hardware and is mixed with the bit stream in a quadrature mixer phased to produce a single- sideband output. This output has the phase of the input signal plus the phase of the supplied “local-oscillator” signal. The expected fringe function is approximated by a square wave generated with appropriate phase &. Both in-phase and quad- rature componen% are produced. These are used to multiply the data stream from one recorder in the one bit sense (also called “exclusive-OR”). In the correlation function computer, the two resulting data streams are again multiplied by the data stream from the other recorder, and the product is inte- grated. Multiplication is inhibited for a short time near the transitions of the expected fringe function, making the multi- plication in the quadrature mixer essentially into a three-level scheme, -1, 0, 1 rather than the two-level scheme natural with binary logic. The resultant is a small saving in SNR. At any one lag, two quantities are now accumulating. One is re- garded as the real part of a complex fringe amplitude, and the other as the imaginary part. This completes the phasing of the quadrature mixer.

The phase of the expected fringe function is calculated by linear interpolation by a programmable fractional divider, whose rate is set by the on-line computer. Ten times per second a new starting phase, also set by the computer, is strobed into the phase register at the exact tenth of a second, according to the clock recorded on the “A” recorder. I t is sufficiently often that the second derivative term in the Tay- lor expansion of the expected fringe function will be negligible for any earth-based interferometer with nonmobile elements.

The correlation function computer is comprised of inte- grated-circuit cards developed for the NRAO autocorrelation function spectrometers, which operate at bit rates up to 20 Mb/s. The present functions do not require such performance, bu t i t was felt that the cost of developing a less capable pack-

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CLARK: TAPE-RECORDER INTERFEROMETER SYSTEM 1241

TABLE I PLAYBACK TERMINAL EVENTS

Recurrence Event

0.25 ps new bit is recovered from each recorder output; new bit is unloaded from each buffer; 95-channel cross-correlation function is calculated for that bit and added to store;

4 ps (max) deasion is made whether to advance phase of predicted

512 data from recorder are checked for timing; buffer counter fringe function by one-eighth turn;

16f ms unique sync pattern and binary clock read from each re- reset if necessary;

corder; decision is made whether to adjust relative delay of the 2-b streams by 1-b time; correlation function dis-

0 . 1 s play is refreshed;

new predicted fringe function phase is calculated and strobed into fringe function generator;

0 . 2 s cross-correlation function is transferred from semiconductor memory to computer core and thence to computer read- able magnetic t a p e ;

12.8 s minimum data length for post-processing programs averag- ing;

20-500 s typical fringe coherence times.

Fig. 5. Correlator output, real-time display. Radio source is 3C273, frequency 8430 MHz, 10 000-km baseline.

age would exceed the amount to be saved by using slower logic and l e s s compact packaging. The cross-correlation func- tion is calculated for 9 5 channels simultaneously. The lag be- tween channels may be adjusted in steps of a factor of two from 0.25 to 32 ps. In observations of continuum sources of radio radiation, the correlator is normally used to calculate only 31 channels of cross-correlation function, allowing room for a possible -53.5 ps of error in the preestimated delay for the source, which might arise from uncertainties in the source position, uncertainties in the interferometer baseline, or errors in the record time clocks.

For observations of the interstellar maser signals, such as those of OH or water, the entire 9 5 channels are used, operat- ing as a cross-correlation function spectrometer, giving about 47 independent frequency channels in a total bandwidth, determined by the lag between channels of the correlation function, of 2 MHz, 1 MHz, etc., down to 16 kHz.

At 0.2-s intervals, the cross-correlation function is trans- ferred from the special-purpose digital cross-correlation func- tion computer to the general-purpose minicomputer which serves as a controller for the playback devices. I t is then writ- ten on an IBM compatible magnetic tape for further process- ing in a Iarger general-purpose computer.

As an on-line display, in order for the observer to be able to tell (on strong sources, at least) that the reproduction ma- chinery is functioning properly, the real part of the center 12 channels of the cross-correlation function is displayed as a function of time, on a memory oscilliscope. This real part may be preintegrated with a 0.2-, 1-, or 5-s integration time. An example of such a display is shown in Fig. 5 . The fringes have a typically sinusoidal appearance. This is due to the fact that the estimated source position or baseline description was in error, so that the estimated fringe function, given by ( 5 ) , is in error. The error is sufficiently small and slowly varying that i t may be approximated as a linear increase in phase with time, and hence a sinusoidal variation of the real part of the cross- correlation function.

The display of Fig. 5 was produced by observations of the radio source 3C273 at a frequency of 8430 MHz on a baseline between the 64-m telescope in Goldstone, Calif., and the 22-m radio telescope near Simeis, Crimea, USSR.

In the preceding discussion, i t has been made clear that a great many events are occurring in the playback mechanism, each with its own characteristic period of recurrence. To aid in summarization, many of the major events are listed in Table I.

V. THE CONTINUUM INTERFEROMETER SOFTWARE SYSTEM An important part of the processing occurs after the initial

data recording at 0.2-s intervals. This is illustrated 'by the relative data compression of the two stages. For the con- tinuum, the playback processor reduces the lo6 b recorded in 0.2 s to 31 channels of complex cross-correlation function data, a total of about lo8 b, so that the total compression is by a factor of l(r. The machine-performed part of the post pro- cessing must reduce these data to an amount comprehensible to a human being. In practice, this normally means perhaps two numbers (fringe amplitude and rate, say) at 5-min inter- vals. This represents a further compression of the data by a factor of about 5 X 10'.

A set of programs has been developed to process con- tinuum data with a great deal of flexibility and power. These programs may properly be considered to be a part of the tape- recorder interferometer system, along with the hardware and on-line software.

In discussing the processing of data beyond the 0.2-s outputs from the playback processor, 1 shall occasionally refer to the 'coherence time" of the LO'S. The definition of coherence time that is useful in this connection differs some- what from the standard one. Because we are never extremely certain of our baseline parameters or source positions, we usually have a residual fringe rate, of the sort shown in Fig. 5 and previously discussed. These residuals, which to a good approximation are taken locally to be a linear phase drift, must be taken into account in whatever processing we do. Therefore, we do all further processing for many such phase drifts-offset frequencies-in parallel. In taking into account the residual offset frequencies in this way, we have also taken into account any linear drift of the two LO systems. We there- fore define the coherence time of the oscillators to be the longest time over which their relative phase differs from the best linear drift in that time by l e s s than a radian.

A priori we only know within what limits to expect the residual offset frequency to lie. These are usually much wider

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1248 PROCEEDINGS OF THE IEEE, SEPTEMBER 1913

limits than the reciprocal of the time for which we wish to average to be sure of detecting the (often weak) radio source. We therefore wish to average the data, in parallel, for all of the possible residual offset frequencies within that range. Adding together complex numbers with various linear phase rates which multiply them is precisely the function performed by a Fourier transform. Therefore, the post-processing pro- grams include one which takes the Fourier transform of all of the 31 delay channels, and prints a display of amplitude as a function of delay and of fringe frequency.

This, however, is a very inefficient procedure. A much more efficient process is to take only discrete Fourier trans- forms in the immediate neighborhood of the delay and rate at which one expects fringes from the source to appear. This estimated delay and rate are produced by the program which takes complete Fourier transforms on a small percentage of the data. Rogers [8] has shown that the best estimate of cor- relation at a given lag is computed by the use of several adja- cent lags. For equally spaced points in the correlation function and a square bandpass of width B , an interpolation formula of the form

may be used to add together estimates of the correlation at a given lag. The three largest terms of this formula are used in this program to estimate the fringe amplitude.

T o make the program set simple to run and to save com- puter time, the Fourier transform program does not accept an arbitrary number of input points. To do so would require excessive amounts of storage. One usually has a rather better knowledge of where to expect the fringe frequency of a given source than the 5-Hz range implied by the 0.2-s sampling time of the correlation function. Therefore, one may pre- average the data to a longer sampling time. A program is written to do this. I t has provision for altering the fringe rate before applying the averaging procedure, so that in the rare cases when the entire range needs to be covered, i t can be handled by repeatedly applying the program with different rate offsets. The output of this program is identical in format to its input, so i t may be processed by any of the other pro- grams in the set.

In processing data, one may average only up to the coher- ence time of the LO’S. T o a rough approximation, the coher- ence properties of the LO simply multiply those of the radio- source radiation, which we want to measure. In averaging beyond the coherence time, we degrade the quantity we are seeking. However, one may do further averaging in a different way, by breaking coherence. T o break coherence means to discard phase information. One procedure for discarding phase information is simply to convert the complex number de- scribing the correlation coefficient, averaged over a time short compared to the coherence time, into the magnitude-phase format, and ignore the phase. These averaged amplitudes then give an estimate of the correlation coefficient averaged over the whole interval. I t is well known that this estimate is too large by about a factor of

SN R-2 2

1+-*

Operationally, it turns out to be convenient to use the above form of broken coherence averaging only for cases where the SNR is somewhat greater than 1. For very weak

sources, i t is more convenient to Fourier transform the original time sequence of cross-correlation coefficients over a time rather longer than the coherence time, and to square the re- sulting spectrum. This squared spectrum (with no phase and therefore with broken coherence) can then be averaged for the duration of the observation. In the end, one can average this fringe power spectrum over a bandwidth reciprocally related to the LO coherence time.

In any broken coherence procedure (including the most classical, the post detection correlation interferometer [lo], [ l l ] ) the limiting sensitivity of the instrument decreases as the fourth root of the observing time, instead of the square root as i t does in the case of the coherent averaging. If the coherence time is short compared to the length of the observa- tions, the sensitivity of the interferometer can be significantly increased by this procedure.

VI. SUMMARY The NRAO Mark I1 system is a flexible tape-recorder

interferometer system, which records 1-b digitized I F volt- ages on magnetic tape for later reproduction and correlation. The maximum data rate is 4 Mb/s (2-MHz bandwidth). The data density on the magnetic recording medium is quite high, about 800 b/mmz. The record time equipment is relatively simple, deferring all complex operations until reproduce time. The reproduce controller, because of the incorporation of a minicomputer, is a fairly flexible device, with capabilities for continuum observations, pulsar observations, multiple an- tenna obseruations, and line observations (47 instantaneous frequency channels). The system is now, or will be shortly, in use at about ten radio astronomy observatories.

ACKNOWLEDGMENT Many people have participated in the design and con-

struction of the Mark I1 system. The initial design was done by Leach Corporation, based on their H D D R recording techniques. Further perfection of the recording system was done by R. Weimer and R. Hallman. Other system elements were designed or built by R. Mauzy, A. Shalloway, and S. Weinreb. The spectral uses of the system have been developed by S. Knowles and J. Moran.

REFERENCES [ l ] M. H. Cohen, “Introduction to very-long-baseline interferometry,”

this issue, pp. 1192-1 197. [2] S. Weinreb, “A digital spectral analyeis technique and ita applica-

tion to radio astronomy,” M.S. thesis, Massachuaetta Institute of

[3] R. D. Davies, J. E. B. Ponsonby, L. Pointon, and C. de Jager, ‘Th: Technology, Cambridge, 1963, pp. 1-157.

Jodrell bank radiofrequency digital autocorrelation spectrometer, Ndurc, vol. 222, pp. 933-937, June 1969.

[4] B. F. C. Cooper, “Correlators with tw-bit correlatlon,” A W L 1.

[SI A. E. E. Rogers el d., “Poeitions and angular extent of OH emissio; a d a t e d with the HI1 regions W3, W24, and NGC 6334, 369,

[a] M. C. H. Wright, B. G. Clark, C. H. Moore, and J. Coe, “Hydrogen Astrophys. J. , vol. 147, pp. 369-377, 1967.

line aperature synthesis at NRAO-Techniques and data reduction,”

Phys., VOI. 23, pp. 521-527, 1970.

[71 J. H. Van Vleck and D. Middeton. ‘The spectrum of clipped noise,” Rudwsci., in press.

. . . Proc. IEEE, vol. 54, pp. 2-19, Jan. 1966.

[SI A. E. E. Rogers, “Very long baseline interferomentry with large dec- tive bandwidth for phasedelay measurements, Radio Sci., vol. 5,

[9] -, “Broad-band passive 90° RC hybrid with low component sensitivity for use in the video range of frequenaes,” Proc. IEEE

[lo] R. Brown and R. Q. Twisa. ‘A new type of interferometer for w e in radio astronomy,” PkU. Mor., vol. 45, pp. 663-682, July 1954.

Ill] B. G. Clark, “Radioinkrferorneters of intermediate type,” IEEE Trans. A u f n r w Propogut. (Commun.), vol. AP-16, pp. 143-144, Jan. 1968.

~~

pp. 1239-1247, Oct. 1970.

(Lett.), VOI. 59, pp. 1617-1618, NOV. 1971.

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