Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
Fucai Zhang ◽  
Giancarlo Pedrini ◽  
Wolfgang Osten
Keyword(s):  
Phase Retrieval ◽  
Valued Fields ◽  
Arbitrary Complex ◽  
Complex Valued

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

scholarly journals A MLMVN with Arbitrary Complex-Valued Inputs and a Hybrid Testability Approach for the Extraction of Lumped Models Using FRA

2019 ◽  
Vol 9 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Igor Aizenberg ◽  
Antonio Luchetta ◽  
Stefano Manetti ◽  
Maria Cristina Piccirilli
Keyword(s):  
Neural Network ◽  
Frequency Response ◽  
Learning Algorithm ◽  
Repeated Measurements ◽  
Distributed Parameter ◽  
Response Analysis ◽  
Frequency Response Analysis ◽  
Arbitrary Complex ◽  
Lumped Models ◽  
Complex Valued

Abstract A procedure for the identification of lumped models of distributed parameter electromagnetic systems is presented in this paper. A Frequency Response Analysis (FRA) of the device to be modeled is performed, executing repeated measurements or intensive simulations. The method can be used to extract the values of the components. The fundamental brick of this architecture is a multi-valued neuron (MVN), used in a multilayer neural network (MLMVN); the neuron is modified in order to use arbitrary complex-valued inputs, which represent the frequency response of the device. It is shown that this modification requires just a slight change in the MLMVN learning algorithm. The method is tested over three completely different examples to clearly explain its generality.

Robust phase retrieval of complex-valued object in phase modulation by hybrid Wirtinger flow method

2017 ◽  
Vol 56 (09) ◽  
pp. 1
Author(s):  
Zhun Wei ◽  
Wen Chen ◽  
Tiantian Yin ◽  
Xudong Chen
Keyword(s):  
Phase Modulation ◽  
Phase Retrieval ◽  
Flow Method ◽  
Complex Valued

Tensor Bogolyubov representations of the renormalized square of white noise (RSWN) algebra

2019 ◽  
Vol 22 (04) ◽  
pp. 1950025
Author(s):  
Habib Rebei ◽  
Luigi Accardi ◽  
Hajer Taouil
Keyword(s):  
White Noise ◽  
Lebesgue Measure ◽  
Absolutely Continuous ◽  
First Order ◽  
Commutation Relations ◽  
Hyperbolic Sine ◽  
Arbitrary Complex ◽  
Borel Functions ◽  
Complex Valued

We introduce the quadratic analog of the tensor Bogolyubov representation of the CCR. Our main result is the determination of the structure of these maps: each of them is uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text] into itself whose inverses induce transformations that map the Lebesgue measure [Formula: see text] into measures [Formula: see text] absolutely continuous with respect to it. Furthermore, the Radon–Nikodyn derivatives [Formula: see text], of these measures with respect to [Formula: see text], must satisfy the relation [Formula: see text] for [Formula: see text]-almost every [Formula: see text]. This makes a surprising bridge with the hyperbolic sine and cosine defining the structure of usual (i.e. first-order) Bogolyubov transformations. The reason of the surprise is that the linear and quadratic commutation relations are completely different.

scholarly journals Encoding complex valued fields using intensity

2016 ◽  
Vol 24 (20) ◽  
pp. 23186 ◽  
Author(s):  
Edoardo De Tommasi ◽  
Luigi Lavanga ◽  
Stuart Watson ◽  
Michael Mazilu
Keyword(s):  
Valued Fields ◽  
Complex Valued

Applications of the Karhunen-Loève Decomposition to Quantum Dynamical Problems

2002 ◽  
Vol 216 (3) ◽  
Author(s):  
H. Dietz ◽  
M. Marek ◽  
A.F. Münster ◽  
V. Engel
Keyword(s):  
Bound State ◽  
Efficient Tool ◽  
Straightforward Manner ◽  
Time Resolved ◽  
Pump Probe ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
Arbitrary Complex ◽  
Long Time ◽  
Complex Valued

The Karhunen-Loève (KL)-decomposition is a standard method to analyze spatiotemporal patterns which are characteristic for non-linear chemical dynamics on surfaces. We apply the KL-decomposition to quantum dynamical problems. Using a variational principle it is shown how to arrive at the KL-expansion of an arbitrary complex valued function. In the case of an one-dimensional bound state motion, the KL-decomposition yields the eigenstates of the system in a straightforward manner. The time-resolved spectroscopy of an atom-molecule collision serves as another application. We demonstrate that the orthonormal decomposition into KL-modes provides an efficient tool to calculate long-time pump-probe signals.

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