Journal ArticleDOI
Statistics of atomic frequency standards
David W. Allan
- Vol. 54, Iss: 2, pp 221-230
TLDR
In this paper, a theoretical analysis of the relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of a standard deviation is presented.Abstract:
A theoretical development is presented which results in a relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of the standard deviation, which provides an invariant measure of an important quality factor of a frequency standard. A practical and straightforward method of determining the power spectral density of the frequency fluctuations from the variance of the frequency fluctuations, the sampling time, the number of samples taken, and the dependence on system bandwidth is also developed. Additional insight is also given into some of the problems that arise from the presence of "flicker noise" (spectrum proportional to |ω|-1) modulation of the frequency of an oscillator. The theory is applied in classifying the types of noise on the signals of frequency standards made available at NBS, Boulder Laboratories, such as: masers (both H and N15H 3 ), the cesium beam frequency standard employed as the U. S. Frequency Standard, and rubidium gas cells. "Flicker noise" frequency modulation was not observed on the signals of masers for sampling times ranging from 0.1 second to 4 hours. In a comparison between the NBS hydrogen maser and the NBS III cesium beam, uncorrelated random noise was observed on the frequency fluctuations for sampling times extending to 4 hours; the fractional standard deviations of the frequency fluctuations were as low as 5 parts in 1014.read more
Citations
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Journal ArticleDOI
Self-Mixing Interferometer With a Laser Diode: Unveiling the FM Channel and Its Advantages Respect to the AM Channel
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Characterization of the global network of optical magnetometers to search for exotic physics (GNOME)
S. Afach,Dmitry Budker,Dmitry Budker,Dmitry Budker,G. DeCamp,Vincent Dumont,Zoran D. Grujić,Hong Guo,D. F. Jackson Kimball,T.W. Kornack,Victor Lebedev,Wenhao Li,Hector Masia-Roig,S. Nix,Mikhail Padniuk,Christopher Palm,Chris Pankow,Alexander Penaflor,Xiang Peng,Szymon Pustelny,Theo Scholtes,Joseph A. Smiga,Jason Stalnaker,Antoine Weis,Arne Wickenbrock,David Wurm +25 more
TL;DR: The Global Network of Optical Magnetometers to Search for Exotic Physics (GNOME) as mentioned in this paper is a network of geographically separated, time-synchronized, optically pumped atomic magnetometers that is being used to search for correlated transient signals heralding exotic physics.
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International Comparison of Iodine-stabilized Helium-neon Lasers at λ = 633 nm Involving Seven Laboratories
J. M. Chartier,Lennart Robertsson,M Sommer,J Tschirnich,V Navratil,R Gata,B Pucek,J. Blabla,J. Smydke,M. Ziegler,V Zeleny,F Petru,Z Vesela,K Tomanyiczka,E Banreti,Yu G Zakharenko,L. Vitushkin +16 more
TL;DR: In this article, an international comparison of the frequencies of stabilized He-Ne lasers using intracavity saturated absorption of 127I2 at λ = 633 nm in Bratislava (Czechoslovakia).
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On the application of fiber optic gyroscopes for detection of seismic rotations
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Fundamental Sensitivity Limitations of Nanomechanical Resonant Sensors Due to Thermomechanical Noise
Alper Demir,M. Selim Hanay +1 more
TL;DR: A precise, first-principles based theory is presented for the analysis of PLL based resonator tracking systems and the results that are deduced are in complete agreement with the ones obtained from extensive, carefully run stochastic simulations of a PLLbased sensor system.
References
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Journal ArticleDOI
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R. A. Kunze,M. J. Lighthill +1 more
TL;DR: The theory of generalised functions and their Fourier transforms is discussed in this paper. But the analysis of Fourier transform is limited to the case of generalized functions, and it is not suitable for generalised function analysis.
Journal ArticleDOI
Some aspects of the theory and measurement of frequency fluctuations in frequency standards
Leonard S. Cutler,C. L. Searle +1 more
TL;DR: In this article, the effects of finite observation time on the frequency and phase stability of a servo-controlled oscillator with respect to a given quartz oscillator and an atomic reference are analyzed.
Journal ArticleDOI
Atomic timekeeping and the statistics of precision signal generators
TL;DR: In this paper, a detailed analysis of the calibration procedure showed that the third finite difference of the phase is closely related to the clock errors and that quartz crystal oscillators exhibit a "flicker" or |ω|-1type of noise modulating the frequency of the oscillator.
Atomic timekeeping and the statistics of precision signal generators
TL;DR: The method of finite differences of the phase is shown to be a powerful means of classifying the statistical fluctuations of thephase and frequency for signal generators in general and by employing finite differences it is possible to avoid divergences normally associated with flicker noise spectra.
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