Abstract: The purpose of this memo is to answer the questions: what kind of time measurements takes place in VLBI and to which time scale the observed VLBI delay is related.
Let's consider the simplified model of VLBI observations: 1) interferometer consists of two telescopes; 2) two-level of quantization is used in recording the signal; 3) change of time delay is negligible during the time of observation; 4) measurements are done in one channel. The simplified scheme of the VLBI equipment is shown in this figure.
GPS-receiver
|
|
v
H-maser --> Formatter <--- Reciever <--- Phase center <--- Source
| of the antenna
v
Tape
The signal from the source travels billions years till it reaches the phase
center of the antenna, reflects from the surface(s), reaches the receiver,
travels through the waveguides and cables and finally arrives to the part
of the data acquisition terminal called "formatter". Formatter receives also
the signal from an H-maser located in the thermostabilized room within
3-300 meters from it. H-maser generates the highly stable 5 MHz signal.
The formatter divides this frequency to the so-called sampling frequency
which is specified by the principle investigator of the VLBI experiment.
The typical value of sampling frequency for geo-VLBI is 4MHz.
The formatter has also a counter which counts the number of cycles of the sampling frequency. H-maser and this counter forms a so-called formatter clock. Formatter clocks are synchronized with UTC before VLBI experiment, although not necessarily before each experiment, provided no changes in equipment has been done. It means that during synchronization the formatter initializes the counter and saves the UTC time tag at the moment of synchronization when the counter iz set to zero. All VLBI stations are equipped by the GPS receiver and special hardware and software called Totally Accurate Clock (TAC) [1]. TAC makes makes coordinate synchronization and computes the difference between formatter clock and GPS clock. After applying the difference GPS clock minus UTC available in USNO, the difference UTC minus formatter clock is available. The accuracy of TAC located at the stations is about 30-300 nsec, although Tom Clark reported recently that the accuracy 0.5-1.0 nsec can be achieved with using a new type of receivers and taking advantage of switching off selected availability at GPS satellites. Thus, initially formatter clocks are set to the UTC time with accuracy 30-300 nsec.
During the observations the signal from the receiver and from the generator of sampling frequency arrives to the formatter. When the phase of sampling rate is becoming zero a trigger activates and it generates the impulse which writes a bit to the buffer: zero if voltage of the signal is negative and 1 otherwise. When the buffer is filled, usually 20000 bits, it is written in tape. This portion of information is called "frame". When formatter writes the first bit into the buffer it also creates the frame header which in particularly has the value of the sampling frequency counter at the moment when the first bit was put into the buffer and the UTC tag at the moment when the formatter counter was set to zero. Therefore, each recorded bit has a time tag: the integer number of sampling frequency cycles elapsed from the formatter counter initialization. These time tags can be considered as imlpementation of formatter clocks. However, each bit is NOT syncronized with UTC or whatever global timescale, only the event of formatter counter initialization is synchronized with UTC time coordinate. Stability of formatter clock is determined by stability of the H-maser.
VLBI observing session, usually of 24 hours long, consists of recording the signals form one source during 30-600 sec -- this operation is called source scanning, then slewing antenna to another source, and again scanning. Software which runs at the control computer of the VLBI station called "Field System" [2], requests TAC before and after each scan, records the difference UTC minus formatter time and writes these differences in the log file. Therefore, the time series of UTC minus formatter time during a VLBI session is available. H-maser has a superior stability at the time scale 10-3 -- 105 seconds, but its stability at time scales days and months is worse than stability of cesium standard. Besides, formatter clock may have "jumps" due to malfunction of the electronics and therefore the formatter clocks should be checked.
Correlator reads the tapes, extract frames and extracts the time tags. In addition software reads log files, extracts the time series of UTC-FMT and build the polynomial model of UTC-FMT differences. Usually linear model is adequate, but quadratic term and clock jumps may be added if necessary. Then correlator software computes the theoretical model of time delay. Time delay within scanning time (30-600 seconds) is represented by a polynomial of the 5-th degree refeerred tio some moment within scan called Fringe Reference Time (FRT). The correlator's model has also the clock function which is computed as UTC-FMT(1) - UTC-FMT(2). The theoretical delay is divided by the sampling rate and the bit stream of the second, slave or Y station, is shifted by this amount of bits. The complex cross correlation finction is computed for this shift as well as -15, -14,..., 0, 1,...16 bits around this shift: shifted bit stream is multiplied and the sum is written.
Further analysis is done by post-correlator software. We omit here details. Results of this analysis gives us a non-integer correction to the theoretical bits shoft of the bits stream from the second station with respect tot the bits stram of the first station which provides the maximum of cross-correlation.
Fxxx|011101010100101011110 1-st station
Fyyy| shift .... |011101010100101011110 2-nd station
This quantity divided by the sampling rate is residual delay. Residual delay
plus theoretical delay minus correlator clock model, UTC-FMT(1) - UTC-FMT(2),
is total delay. It is just the quantity which is later used in scientific
analysis of the observation. Now we can lift the condition that time delay is not changing during the scan time. In reality time delay can change as much as 10-4 sec during scan time due to the Earth rotation. To overcome this problem, correlator's model represents theoretical delay as a polynomial of the fifth degree and the scan interval is divided onto shorter intervals called accumulation periods of 0.5-5 seconds long. Post-correlator software computes residual delay, delay rate, delay acceleration and the computes delay and delay rate for the entire scan. More details can be found in [3] Time delay now is represented by the linear function. What is the argument of this function? Initially, correlator computes delay as a function of formatter time. Then it computes the value of function UTC-FMT(1) for nominal start of the scan. Having these two functions, post-correlator software computes delay on the specific moment within the scan, called Fringe Reference Time, on time scale UTC.
Modern correlators, like Mark-4, VLBA, are station-based. In station-based correlators both data streams are shifted to the amount which would be equal to the time propagation to some common reference point which approximates predicted position of the geocenter based on apriori position of observing stations. Therefore, the station-based correlator relates the raw delay to the moment of time when the wave front would reach the reference point near the geocenter. The post-correlator software transfers the raw delay back to the time of the signal arrival to the first station, using exactly the same apriori model which the correlator used. Details of this mathematical procedure can be found in [4].
Frequency of the H-maser is checked against cesium primary frequency standard by a manufacturer. Analysis of VLBI observations allows to determine relative frequency drift of one formatter clock against another. Relative frequency drift has typical values 10-13-10-14 and does not exceed 10-12. Therefore, we can conclude that the frequency of each station does not divert from the nominal value by more than 10-12. Thus, formatter clock provides an implementation of the concept of proper time.
Taken into account mentioned aboove consideration we can give the following definition of VLBI delay. "The VLBI delay is the difference of two intervals: 1) the interval of proper time at the second station between the events: arrival of the radio signal from the source to the formatter of the second station and clock synchronization; 2) the interval of proper time at the first station between the events: arrival of the radio signal from the source to the formatter of the first station and clock synchronization. Reported time delay is the function of the UTC time argument at the moment of arrival the signal at the formatter of the first antenna".
It should be noted that since group and phase delays computed by post-processing software are determined up to an unknown number group or phase delay ambiguity estimation of clock ofcset is unavoidable even if the clock could be synchronized with precision better than delay measurements.
Typical values of clock rate are 10-12 -- 10-14, clock acceleration are 10-17 -- 10-20 sec-1 and these conditions are met.
VLBI system reports the difference of UTC minus formatter time. The VLBI delay model computes time delay to the reference point of the antenna, the point of projecting the moving axis to the fixed antenna axis. Time delay between the reference antenna point to the formatter may be of several microseconds and should be taken into account in computing time tag.
VLBI stations are equpped by the system of phase calibration. Calibarting signal is inserted at the receiver and its phase is determined during post-processing analysis. Postprocessing software subtracts phase calibration phases and group and "observed" phase delays are reported with this correction applied. Thus, reported delay are reduced to the delay in the cable between the point of injection of phase calibration singal and the formatter.
Last update: 14-MAY-2002 16:30:04