Study of systematic errors in VLBI caused by spurious phase calibration signals



MARK-III system injects a phase calibration signal in a feed horn in order to trace changes in phase of the signal propagated from feed horn to the formatter. This signal is written in tape together with signal from the source and is extracted during correlation. Phase calibration is a rail of narrow-band signals with frequencies to be multiple to 1 MHz. Two phase calibration signals are written in one channel, but MARK-III correlator extracts only one. It multiplies data stream from the station by sine and cosine of the signal with the same frequency as phase calibration and filter out high frequency component. Phase of phase calibration signal is found as arctan of ration sine and cosine components.

Ideally this system would provide accuracy oh phase calibration better than 0.2 degree. However, in reality phase calibration system is subjected by various systematic effects which distort measurements. Different parts of data acquisition system may generate and, alas, generates signals which have the same frequency as phase calibration and coherent with it. Such signals are called spurious signals (or, in interests of brevity, "spurs")
[1]. They were discovered in earlier 80-s and it was shown [2] that they may substantially affect measurements of group delay. At the same time it was shown that 1) they can be eliminated or at least reduced; 2) group and phase delays may be calibrated for their presence. Strange, but this technique didn't become routine in processing VLBI observations.

Spurious signals with amplitude 10% of true phase calibration signal may introduce errors in determination of group delays up to 50psec. Unfortunately, cases of such strong spurious signals are not rare.


The general aim is to reduce the level of instrumental errors and improve precision and accuracy of estimation of the targeted parameters: station coordinates, source coordinates, Earth orientation parameters and others quantities.

The objectives of the study is:


As T. Herring noticed [2] phase calibration amplitude may be used in diagnostic purposes. Since the amplitude of injected phase calibration is constant therefore the amplitude of extract phase cal should be also constant. In reality phase cal amplitude is not a constant due to
  1. Changes in system temperature.

  2. Presence of spurious signals.

  3. Probably some other reasons.

Extracted phase calibration amplitude is reciprocal to SQRT(Tsys). At the absence of spurious signal normalized extracted phase calibration amplitude Amp*SQRT(Tsys) should be constant.

Normalized sine and cosine component of extracted phase calibration signal (S and C) can be expressed as

S = Ap sin ( Omega*t + phi ) + As sin ( Omega*t + teta )
C = Ap cos ( Omega*t + phi ) + As cos ( Omega*t + teta )

where Ap is a normalized amplitude and phi is a phase of true phase calibration signal and As, teta are normalized amplitude and phase of spurious signal.

Normalized amplitude of extracted signal SQRT(S2 + C2) is then expressed as

An = SQRT ( Ap2 + As2 + 2 ApAscos(phi - teta) )

Assuming that the amplitude of spurious signal is much smaller than the amplitude of the true phase cal signal and introducing a small parameter

a=As/Ap we can reduce this expression by neglecting terms proportional to a2 to

An = Ap(1 + a cos(phi - teta) )

Tangent of extracted phase is expressed as

tan(phie) = tan(phi) * (1 + a*sin(omega*t+teta)/sin(omega*t+phi) - cos(omega*t+teta)/cos(omega*t+phi) )

If we plot normalized extracted amplitude versus extracted phase and assuming that 1) we can neglect the fact that phie is not exactly the same as phi ; 2) a=const; 3) we can neglect terms proportional to a2 we may have several cases:

A teta=const phase of spurious signal is constant periodicity with frequency 1.00 cycle
B teta=-phi spurious signal arise from imaginary band periodicity with frequency 2.00 cycle
C teta=1/4 phi phase of spurious signal at X-band arises from phase cal at S-band periodicity with frequency 0.75 cycle
D teta=-1/4 phi phase of spurious signal at X-band arises from imaginary band of phase cal at S-band periodicity with frequency 1.25 cycle
E teta=4 phi phase of spurious signal at S-band arises from phase cal at X-band periodicity with frequency 3.00 cycle
F teta=-4 phi phase of spurious signal at S-band arises from imaginary band of phase cal at X-band periodicity with frequency 5.00 cycle

Examples of spurious signals

Plots of normalized amplitude of phase calibration signal versus phase of phase calibration signal are presented here. The phase calibration amplitude is a dimensionless quantity -- a share of system noise; phase is expressed in phase turns. Normalized amplitude An is calculated as

An = Ae * SQRT( Tsys(obs) )/ SQRT( Tsys(zen,mean) )

where -- Ae extracted phase calibration amplitude, Tsys(obs) -- modeled system temperature for this scan, Tsys(zen,mean) -- mean system temperature in zenith direction.
  1. A Constant spurious signal. Alas, common case.

  2. B Influence of imaginary band. Fortunately, rare case.

  3. C Influence of phase cal at S-band on phase cal at X-band. Found at MATERA and HARTRAO.

  4. E Influence of phase cal at X-band on phase cal at S-band. Found at GILCREEK.

  5. X Unrecognized spurious signal. No comments...

  6. Z No spurious signal. When all stations will give only this picture??

Specific cases of spurious signals

    Spurious signals at MATERA and further discussion related to this issue.


Phase_Doctor has been developed. It creates a lot of plots and tables related to phase-cal and allows to detect spurious signals, to apply a model of phase-cal, to compute contributions of purious signal inphase-cal to group and phase delay and finally to write these contriobution in the form whcih can be used directly by software for VLBI processing SOLVE.


I don't have yet...


1. B. Corey, "Spurious phase calibration signals: how to find them and how to cure them", Proceedings of VLBI chief meetings held in Haystack Observatory on 11 May 1998.
Abstract Full text (PS + gzip, 31Kb )
2. T.A. Herring "Precision and accuracy of intercontinental distance determination using radio interferometry", Ph.D. Thesis, Hanscom AFB, Massachusetts 01731, 442 p. 1983
3. L. Petrov: "Instrumental errors of geodetic VLBI" (submitted to the Proceedings of the 1-st IVS General meeting, ed. by N. Vandenberg, 2000)
Abstract Full text (PS + gzip, 88Kb )

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Last update: 31-MAR-2000 19:16:34