II. __MEASUREMENT METHODS COMPARISON__

When making measurements between a pair of
frequency standards or clocks, it is desirable
to have less noise in the measurement system
than the composite noise in the pair of standards
being measured. This places stringent requirements
on measurement systems as the state-of-the-art
of precision frequency and time standards
has advanced. As will be shown, perhaps one
of the greatest areas of disparity between
measurement system noise and the noise in
precision standards is in the area of time
difference measurements. Commercial equipment
can measure time differences to about 10^{-11} s, but the time fluctuations second to second
of state-of-the-art standards is as good
as 10^{-13} s.

The disparity is unfortunate because if time
differences between two standards could be
measured with adequate precision then one
may also know the time fluctuations, the
frequency differences, and the frequency
fluctuations. In fact, one can set up an
interesting hierarchy of kinds of measurement
systems: 1) those that can measure time,
x(t); 2) those that can measure changes in
time or time fluctuations d x(t); 3) those that can measure frequency,
n (y / (n -n _{0})/n _{0}); and 4) those that can measure changes
in frequency or frequency fluctuations, d n (d y / d n /n _{0}). As depicted in table 2.1, if a measurement
system is of status 1 in this hierarchy,
i.e., it can measure time, then time fluctuations,
frequency and frequency fluctuations can
also be deduced. However, if a measurement
system is only capable of measuring time
fluctuations (status 2 - table 2.1), then
time cannot be deduced, but frequency and
frequency fluctuations can. If frequency
is being measured (status 3 - table 2.1),
then neither time nor time fluctuations may
be deduced with fidelity because essentially
all commercial frequency measuring devices
have "dead time" (technology is at a point
where that is changing with fast data processing
speeds that are now available). Dead time
in a frequency measurement destroys the opportunity
of integrating the fractional frequency to
get to "true" time fluctuations. Of course,
if frequency can be measured, then trivially
one may deduce the frequency fluctuations.
Finally, if a system can only measure frequency
fluctuations (status 4 - table 2.1), then
neither time, nor time fluctuations, nor
frequency can be deduced from the data. If
the frequency stability is the primary concern
then one may be perfectly happy to employ
such a measurement system, and similarly
for other statuses in this measurement hierarchy.
Obviously, if a measurement method of status
1 could be employed with state-of-the-art
precision, this would provide the greatest
flexibility in data processing. From section
1, the dual mixer time difference system
is such a method.

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Summary and Introduction
I
II
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IV
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VI
VII
VIII
IX
X
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XII
Conclusion
References