Animation of Simulated Gaussian Jitter to Lorentzian Line Profile

There are two main types of clocks that we work with here at USNO Time Service. They are the cesium-beam clock and the hydrogen maser. The SI-second is defined as 9192631770 periods (Hz) for the measured hyperfine line for the microwave spectra of cesium. The accepted equivalent frequency for hydrogen masers after correction for all known shifts is 1420405751.778 Hz. According to Vanier and Audoin (1989), a typical full-width-half-maximum (FWHM) for the spectral line profile for a passive hydrogen maser is approximately 1 Hz. A 1-Hz shift is equivalent to 704 ps in 1 second.

To simulate a typical H-maser line profile jitter from second to second, the author first generated a standard Lorentzian (also called a Cauchy or Wigner-Breit distribution, depending on specialization area) line profile. We ignore any symmetric and asymmetrical line shape perturbations. The x-units are rather arbitrary units, but one of them is about equal to 400 microhertz in the real world. The FWHM is 2462 x-units, which is equivalent to a real-world 1 Hz for this simulation. The author next generated 100 discrete random Gaussian distributed points which show a 100 x-unit standard deviation (+/-40 millihertz). This is equivalent at this scale of 29 ps of noise from second to second. The standard Lorentzian profile mean was shifted by the discrete Gaussian noise to simulate errors in the measurement of the center frequency of the line profile.

Finally, the shifted line profiles were plotted and a discrete time animation produced, showing the equivalent line profile jitter for the pure white FM case.

Animated loop of simulated hydrogen line spectra centroid jitter. (204 KB)
Time to download
14.4 kbps: 2 m 30 s;
28.8 kbps: 1 m 05 s;
56 kbps: 39 s;
and ISDN: 17 s.

Vanier, J. and Audoin, C. (1989), The Quantum Physics of Atomic Frequency Standards (Adam Hilger, Philadelphia), pp. 1567.