Measurement Of Coherence Function Research Articles

Investigation of 1/f noise sources with the coherence function

We demonstrate the application of the coherence function to analyze the 1/f noise sources in a planar semiconductor structure with multiple electrical contacts. This article includes noise and coherence function measurements, the 1/f noise model for the transmission-line-model (TLM) sample, theoretical calculations of the coherence function, and a comparison of theoretical and experimental values. In the developed noise model, bulk semiconductor noise and metal–semiconductor contact noise are considered noise sources. It was shown that the experimental results of coherence measurements are well explained by the model, which assumes 1/f noise from contacts and no 1/f noise from a bulk semiconductor. The presented method can be used to find dominant noise sources originating from bulk semiconductor or metal–semiconductor contacts in planar structures. The strength of the method, in comparison with models based only on power spectral density, is straightforward interpretation and the lack of sophisticated model parameters.

Lasing action in low-resistance nanolasers based on tunnel junctions

We experimentally demonstrate the lasing action of a new nanolaser design with a tunnel junction. By using a heavily doped tunnel junction for hole injection, we can replace the p-type contact material of a conventional nanolaser diode with a low-resistance n-type contact layer. This leads to a significant reduction of the device resistance and lowers the threshold voltage from 5V to around 0.95V at 77K. The lasing behavior is verified by the light output versus the injection current (L-I) characterization and second-order coherence function measurements. Because of less Joule heating during current injection, the nanolaser can be operated at temperatures as high as 180K under CW pumping. The incorporation of heavily doped tunnel junctions may pave the way for other nanoscale cavity design for improved heat management.

Measurement and characterization of the three-dimensional coherence function in neutron interferometry.

The spatial coherence function in all three orthogonal directions has been measured by means of perfect crystal neutron interferometry. It has been demonstrated that the coherence function is given by the Fourier transform of the related momentum distribution, which in turn is determined by the collimation and monochromatization of the beam incident upon and traversing the interferometer. Thus, a measurement of the coherence function can replace a measurement of the momentum distribution in certain cases. Retrieval of the coherence can be accomplished by phase echo and/or postselection methods. A complete retrieval of the coherence is impossible in principle due to unavoidable loss factors.

High-bandwidth method for measurement of coherence function of laser source

The coherence properties of a laser source are derived from high bandwidth (with respect to the source linewidth) measurements of the instantaneous output intensity at the output of a two-beam optical interferometer. This technique saves the need to compensate for polarisation and wavefront mismatches and for unequal power splitting between the two interfering beams.

Resolution bias errors in spectral density, frequency response and coherence function measurements, VI: Non-white noise at the input

The general theory of spectral estimation presented in a previous part of this series of papers is applied exemplarily to the case of a non-white (1/ f 2 )-noise excited RC-low-pass filter. It is shown that the differences compared to the case of white noise excitation observed in the frequency response and coherence estimates are small if the Hanning (or another continuous) window is used, but that they can become drastic for the rectangular window. Experimental results are in accord with the theoretical prediction. Further experiments with an electrical LRC-resonance circuit (second-order system) show that the same applies in this case.

Resolution bias errors in spectral density, frequency response and coherence function measurements, IV: Time delay bias errors

The problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part. It is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively. Experimental results for the rectangular and Hanning windows are in accord with the theoretical predictions. The theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function.

Resolution bias errors in spectral density, frequency response and coherence function measurements, V: Comparison of different frequency response estimators

Three different types of frequency response estimators are considered and compared with each other with respect to the inherent resolution bias errors. The behavior of these estimators is shown to differ considerably, especially with respect to peak estimation in resonance systems such as a simple spring-mass system. One of these estimators is shown to exhibit almost no peak bias error at resonance under noise-free measurement conditions whereas the peak bias error of the estimator most commonly used is maximum. However, aside from resonance, the peak-bias-free estimator proves to be the worst of the three estimators. The theoretical predictions are accurately verified by experiments with an electrical LRC-resonance circuit.

Resolution bias errors in spectral density, frequency response and coherence function measurements, II: Application to first-order systems (white noise excitation)

Resolution bias errors in spectral density, frequency response and coherence function measurements, II: Application to first-order systems (white noise excitation)

Resolution bias errors in spectral density, frequency response and coherence function measurements, I: General theory

A general theory of resolution bias errors inherent in the usual ensemble (segment) averaging estimation procedure for spectral density, frequency response and coherence functions has been developed. It is shown that the estimation procedure is mathematically equivalent to a situation where the true correlation functions would be modified in a specified manner: that is, they would be multiplied with the normalized autocorrelation function of the window function and transformed into the frequency domain to yield the spectral density estimates. The theory is worked out for an arbitrary ideal, linear, and time-invariant system which is driven by a stationary stochastic input and for an arbitrary window function. Specifically, the rectangular and Hanning windows are compared with each other and the theoretical results are verified experimentally to great accuracy by using electrical RC- and LRC-circuits and a true random noise generator (see later parts of this series of papers). Furthermore, as an application of the theory, approximate formulas for the bias errors of spectral estimators are derived and discussed, thus extending some older results given in the literature.

Resolution bias errors in spectral density, frequency response and coherence function measurements, III: Application to second-order systems (white noise excitation)

A general theory of spectral estimation given in a previous paper is applied to second-order systems such as a simple spring-mass system where either the displacement, velocity or acceleration of the vibrating mass may be considered as the output signals. By means of approximate formulas, an extensive bias error discussion of frequency response, output power spectral density and coherence estimates is given, which clarifies characteristic differences between spectral estimators obtained with the rectangular window on the one hand and the Hanning window (or another continuous window) on the other hand. In particular, characteristic coherence notches in the measurement of resonance systems, as reported in the literature, are explained from first principles. All of the theoretical predictions are verified experimentally to great accuracy by using electrical LRC-resonance circuits which are equivalent to the respective mechanical systems.

Statistical errors in measurement of coherence functions and input/output quantities

Practical statistical error analysis formulas are developed for evaluating ordinary, partial and multiple coherence function estimates, and associated quantities which occur in analysis of single input/output problems and in multiple input/output problems. These include estimates of coherent output spectra and estimates of gain and phase factors of related frequency response functions. Models are either single input/output models or conditioned input/output models, where the latter models can be created from arbitrary measured multiple input/output data. Guidelines are presented to reduce statistical errors in such computed quantities. These results are essential for applications to identify different multiple noise sources, to determine multiple system properties, to measure response effects due to the sources acting singly or in various combinations, to simulate multiple random environments, and to predict system failures from response measurements only.

Interpretation of Coherence Function Measurements in Zero-Power Coupled-Core Reactors

New techniques for inferring several reactor kinetic parameters from frequency-domain noise analysis measurements in coupled-core reactors are developed and utilized. These parameters are the eigenvalue separation, delayed-neutron fraction, and, independently, the prompt-neutron lifetime. Reactor characteristics and detector placement criteria necessary for obtaining the parameters are discussed. Comparison with other time-domain noise techniques is undertaken and the merits and shortcomings of each are reviewed.