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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Functionalized zinc oxide nanorod with ionophore-membrane coating as an intracellular Ca2+ selective sensor
Muhammad Asif,Alimujiang Fulati,Omer Nur,Magnus Willander,Cecilia Brännmark,Peter Strålfors,Sara I. Börjesson,Fredrik Elinder +7 more
TL;DR: The tip of a borosilicate glass capillary with functionalized hexagonal ZnO nanorods was used to make a sensitive electrochemical intracellular Ca2+ sensor.
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Characterization of a near-room-temperature, continuous-wave quantum cascade laser for long-term, unattended monitoring of nitric oxide in the atmosphere.
David D. Nelson,J. Barry McManus,Scott C. Herndon,Joanne H. Shorter,Mark S. Zahniser,Stéphane Blaser,Lubos Hvozdara,Antoine Muller,Marcella Giovannini,Jérôme Faist +9 more
TL;DR: A totally noncryogenic nitric oxide monitor was constructed by integrating this laser with an astigmatic multipass cell and a thermo-electrically cooled infrared detector, capable of continuous unattended monitoring of ambient, atmosphericNitric oxide for several weeks with no operator intervention.
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Uncovering the Intrinsic Variability of Gamma-ray Bursts
TL;DR: In this paper, the authors developed a robust technique to determine the minimum variability timescale for Gamma-ray Burst light curves, utilizing Haar wavelets, and applied their technique to the large sample of Swift GRB Gamma ray light curves and for the first time, due to the presence of a large number of GRBs with measured redshift, determined the distribution of minimum timescales in the source frame.
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A force calibration standard for magnetic tweezers.
Zhongbo Yu,David Dulin,Jelmer Cnossen,Mariana Köber,Maarten M. van Oene,Orkide Ordu,Bojk A. Berghuis,Toivo Hensgens,Jan Lipfert,Nynke H. Dekker +9 more
TL;DR: This work presents a calibration standard for magnetic tweezers consisting of measured forces for four magnet configurations, calibrated for two commonly employed commercially available magnetic microspheres, and calculates forces in both time and spectral domains by analyzing bead fluctuations.
Journal ArticleDOI
Experiments on a semiconductor laser pumped rubidium atomic clock
M. Hashimoto,M. Ohtsu +1 more
TL;DR: In this article, the performance of a semiconductor laser pumped rubidium (87Rb) atomic clock was evaluated using two kinds of Rb gas cells and their performances were compared.
References
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Journal ArticleDOI
An Introduction to Fourier Analysis and Generalized Functions.
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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