Sixia Yu · Physical Review Letters · 1997
A quantum description for the phase difference between two harmonic oscillators is proposed. Being represented by a Hermitian operator, phase difference displays two striking quantum features. First, its eigenvalues form a new type of quantized value which is countable and dense in a $2\ensuremath{\pi}$ window. Second, because quantized phase difference cannot be defined as a difference of phases, it obeys a quantum addition rule which may not be commutative.
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Jonas Söderholm, Alexei Trifonov, Tedros Tsegaye et al. · Kluwer Academic Publishers eBooks · 2005
From the experimentalist’ spoint of view, it is natural to think of aphase measurement as a measurement that involves a reference time. As a part of the system, the reference time generating “clock” must be taken into account in the quantum treatment of the measuring process. This could be argued to be the reason why there does not exist any observable corresponding to the absolute phase in the unrestricted Hilbert space.Luis and Sánchez-Soto [Phys. Rev. A 48, 4702 (1993)] have investigated the case where the “clock” is another harmonic oscillator and defined a Hermitian phase-difference operator, which is valid in the infinite Hilbert space.In the present work we propose and experimentally demonstrate a setup for direct measurement of the phase-difference. We derive the phase-difference distributions for some two-mode states and compare them with the experimental results.
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2009
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Oscar W. Richards · Nature · 1944
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Luis Aina, Alfredo, Sánchez Soto, Luis Lorenzo · Library Open Repository (Universidad Complutense Madrid) · 1993
We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields.
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M. J. Reina Lamothe, Brian K. Rutt · Journal of Magnetic Resonance Imaging · 1997
A new technique for multistep phase-contrast image processing is presented. The N-step method consists of simply forming the linear average of the N-1 adjacent phase-difference signals. It has similar noise reduction properties as other multistep techniques, but the simplicity of the noise variance of the N-step technique allows intuitive insight into phase-difference phase-contrast processing and noise reduction, which can aid in the design of efficient and improved phase-contrast imaging sequences. As well, the computational simplicity of the N-step phase-difference technique compared with any other known multistep technique is advantageous. Like other multistep techniques, it has far more efficient noise reduction properties than simple two-step, multiple average phase-contrast imaging, even when normalized for total scan time. A three-step phase-difference velocity image has 50% less variance than an image acquired with two steps and two scans averaged but is obtained in 25% less scan time. Given its advantages, it should now be the chosen technique for increasing velocity-to-noise and contrast-to-noise ratios in all phase-difference phase-contrast clinical applications.
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G. Fornaro, Antonio Pauciullo, E. Sansosti · IEEE Transactions on Image Processing · 2005
This work addresses the derivation of the phase difference-based maximum likelihood (ML) phase unwrapping algorithm. To this end, we derive the joint statistics of the phase differences on a two-dimensional grid for the multichannel case, where several scaled wrapped phase values are available. Subsequently, we determine and study the structure of the phase difference-based ML estimator and compare it to known phase unwrapping techniques. This work allows us to frame single and multichannel algorithms in a common formulation. Moreover, among the known single-channel phase difference-based procedures, we identify those attaining an ML solution. We also show that multichannel phase difference-based and, recently proposed, phase-based ML algorithms achieve equivalent solutions.
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Raúl J. Martín‐Palma · SPIE eBooks · 2021
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Gunnar Björk, Jonas Söderholm · Journal of Optics B Quantum and Semiclassical Optics · 1999
We discuss phase-difference measurements of two bosonic modes and propose an experimental realization of the phase-difference operator by Luis and S?nchez-Soto (1993 Phys. Rev. A 48 4702). We show that a measurement of a two-mode state will collapse any state into a phase-difference eigenstate. We also show that the phase-difference number-difference commutator can be expressed in the phase-difference distribution. Finally, we discuss the associated minimum uncertainty states.
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NCSU Libraries Repository (North Carolina State University Libraries) · 2008
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哲也 米田, Tomoyo Ideta, Yasuhiro Hiai · Kumamoto University Repository (Kumamoto University) · 2008
The phase image of MRI has a much high diagnosis potential. Susceptibility or another properties of tissue directly or indirectly affect on phase differences in the phase image. Therefore, it is possible to enhance a tissue's physical properties via phase differences. These enhanced images are great of use for discriminating the different tissues and further clinical applications. In this paper, we report on new imaging technique "PhAse DiffeRence Enhanced imaging (PADRE)" as an application of using the phase information in which we use a phase difference between tissues. This new technique can enhance the phase difference on the magnitude image, which corresponds to the local magnetic field difference caused by susceptibility difference, physical dynamics and so on. For comprehensive understanding of PADRE, a simple model is to be examined. The enhanced tissue makes a higher contrast between different tissues, which is going to support the diagnosis of problems. We examine an improvement of contrast by using the PADRE thorough a comparison between a CNR of experimental data and theory which we introduced. Discussions and results of this paper determine the best imaging parameters. We can see wonderful appearance of small vessels in the brain by using these parameters.
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Oana Panazan (20765749), Catalin Gheorghe (20765752) · Figshare · 2025
<div> This study conducts a comparative analysis of how geopolitical risk (GPR) and innovation impact stock returns in the defense industry based on data from 75 defense companies across 17 countries and 4 continents. With daily datasets spanning from January 1, 2014 to March 29, 2024, wavelet coherence and wavelet phase differences were used to conduct the analysis. The results revealed that innovation had a greater and more pronounced impact during the entire analysis period compared with the influence of GPR events. GPRs exerted an uneven and heterogeneous impact on global defense stocks and had a concentrated impact during events that generated uncertainty. Overall, we found significant time-varying dependence across a large number of companies at different time frequencies. The COVID-19 pandemic did not have a major impact on companies in the defense industry. Further, GPR events led to increased volatility during the Russia–Ukraine war, leading to increased uncertainty. In addition to the dominant role they play in the world defense market, US companies served as a robust hedge, especially from 2021 to 2022. Defense companies in the UK are more sensitive to both GPR events and innovation, followed by companies in Germany and France. Comparative analysis of the scalograms of China reveals a greater influence of innovation compared with GPR events. Thus, diversification opportunities have been extended from the defense industry in China, offering investors a promising way to capitalize on refuge opportunities during periods of disruption. To mitigate the global rearmament trend, we suggest alternative investment opportunities for different time horizons. </div>
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Heinonen, T., Lahti, P., Pellonpaa, J. -P. · arXiv (Cornell University) · 2002
Covariant phase difference observables are determined in two different ways, by a direct computation and by a group theoretical method. A characterization of phase difference observables which can be expressed as difference of two phase observables is given. Classical limit of such phase difference observables are determined and the Pegg-Barnett phase difference distribution is obtained from the phase difference representation. The relation of Ban's theory to the covariant phase theories is exhibited.
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Liu Sheng-dian, Xiong Zhang, Hou Guang et al. · Communications in Theoretical Physics · 1999
In this paper, from the index theorem, we present the Hermitian phase operator for fermion, give its eigenvalues and orthogonal, normalized and complete eigenstates. Furthermore, we also get the phase difference operator for two fermions and discuss its quantum properties.
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G. Fornaro, Antonio Pauciullo, E. Sansosti · 2004
This work addresses the derivation of a phase-difference (gradient) based maximum likelihood (ML) phase unwrapping algorithm. In particular, we determine and study the structure of the ML phase unwrapping on a 2D grid in the multi-channel case and compare it with existing phase unwrapping algorithms. This allows us first to frame single-channel, phase based phase unwrapping algorithm in a general formulation. Second, among the known single-channel, phase-difference based phase unwrapping algorithms we identify those achieving a ML solution. Although achieving results similar to existing phase-based ML phase unwrapping algorithm in the multi-channel case, our approach allows to easily incorporate possible a priori knowledge about the absolute phase variation dynamics.
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В. Е. Куницын, E. S. Andreeva, O.G. Razinkov et al. · International Journal of Imaging Systems and Technology · 1994
Abstract Variants of ray ionospheric radiotomography (RT) are considered: the phase RT based on measuring the absolute phase or the total electron content and the phase‐difference RT based on measuring the phase‐difference RT based on measuring the phase difference or Doppler frequency. The phase technique is shown to give poor results with typical errors in determining the absolute phase. The previously developed technique of the phase‐difference RT is presented.©1994 John Wiley & Sons Inc
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Matt A. Bernstein, Yoshikazu Ikezaki · Journal of Magnetic Resonance Imaging · 1991
The two main phase-contrast reconstruction methods are phase difference and complex difference. The signal-to-noise ratio properties and relative advantages of the two techniques are discussed. It is argued that each processing method has applications in which it is superior, and guidelines are provided to determine those applications. It is demonstrated theoretically and experimentally that only the complex-difference method is well suited for processing phase-contrast slabs with use of a projection dephaser gradient.
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R.S.MacKay · TIB Data Manager · 2024
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Lee, Daesoo · Figshare · 2025
Self-contained jupyter notebook for the phase-difference prediction model from [1].---[1] Fernandez, Andres, et al. "Efficient Neural and Numerical Methods for High-Quality Online Speech Spectrogram Inversion via Gradient Theorem." <i>arXiv preprint arXiv:2505.24498</i> (2025).
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Daniel Smith · Society of Photo-Optical Instrumentation Engineers eBooks · 2013
This excerpt gives a succinct explanation of the phase difference between parallel reflections.
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