scholarly journals Carleson's theorem with quadratic phase functions

2002 ◽  
Vol 153 (3) ◽  
pp. 249-267 ◽  
Author(s):  
Michael T. Lacey
Keyword(s):  
Quadratic Phase ◽  
Phase Functions ◽  
Carleson’S Theorem

scholarly journals Edge and Contrast Enhancement Using Spatially Incoherent Correlation Holography Techniques

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 224
Author(s):  
Vijayakumar Anand ◽  
Joseph Rosen ◽  
Soon Hock Ng ◽  
Tomas Katkus ◽  
Denver P Linklater ◽  
...  
Keyword(s):  
Contrast Enhancement ◽  
Coded Aperture ◽  
Optical Technique ◽  
Edge Enhancement ◽  
Coded Aperture Imaging ◽  
Point Spread ◽  
Quadratic Phase ◽  
Spread Function ◽  
Phase Functions ◽  
Spiral Phase

Image enhancement techniques (such as edge and contrast enhancement) are essential for many imaging applications. In incoherent holography techniques such as Fresnel incoherent correlation holography (FINCH), the light from an object is split into two, each of which is modulated differently from one another by two different quadratic phase functions and coherently interfered to generate the hologram. The hologram can be reconstructed via a numerical backpropagation. The edge enhancement procedure in FINCH requires the modulation of one of the beams by a spiral phase element and, upon reconstruction, edge-enhanced images are obtained. An optical technique for edge enhancement in coded aperture imaging (CAI) techniques that does not involve two-beam interference has not been established yet. In this study, we propose and demonstrate an iterative algorithm that can yield from the experimentally recorded point spread function (PSF), a synthetic PSF that can generate edge-enhanced reconstructions when processed with the object hologram. The edge-enhanced reconstructions are subtracted from the original reconstructions to obtain contrast enhancement. The technique has been demonstrated on FINCH and CAI methods with different spectral conditions.

scholarly journals Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Yinghui Guo ◽  
Shicong Zhang ◽  
Mingbo Pu ◽  
Qiong He ◽  
Jinjin Jin ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Simultaneous Detection ◽  
Single Element ◽  
Single Shot ◽  
Single Spin ◽  
Dual Functional ◽  
Angular Momenta ◽  
Quadratic Phase ◽  
Mode Space ◽  
Optical Configuration

AbstractWith inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

Optimal Signal Extraction with Correlated Components

2014 ◽  
Vol 6 (2) ◽  
pp. 237-273 ◽  
Author(s):  
Tucker S. McElroy ◽  
Agustin Maravall
Keyword(s):  
Signal Extraction ◽  
Economic Time Series ◽  
Systematic Treatment ◽  
Finite Samples ◽  
Economic Time ◽  
The Mean ◽  
Phase Functions ◽  
Component Models ◽  
Correlated Components ◽  
Optimal Signal

AbstractWhile it is typical in the econometric signal extraction literature to assume that the unobserved signal and noise components are uncorrelated, there is nevertheless an interest among econometricians in the hypothesis of hysteresis, i.e. that major movements in the economy are fundamentally linked. While specific models involving correlated signal and noise innovation sequences have been developed and applied using state space methods, there is no systematic treatment of optimal signal extraction with correlated components. This paper provides the mean square error optimal formulas for both finite samples and bi-infinite samples and furthermore relates these filters to the more well-known Wiener–Kolmogorov (WK) and Beveridge–Nelson (BN) signal extraction formulas in the case of ARIMA component models. Then we obtain the result that the optimal filter for correlated components can be viewed as a weighted linear combination of the WK and BN filters. The gain and phase functions of the resulting filters are plotted for some standard cases. Some discussion of estimation of hysteretic models is presented, along with empirical results on an economic time series. Comparisons are made between signal extractions from traditional WK filters and those arising from the hysteretic models.

scholarly journals On the scattering behaviour of bullet-rosette and bullet-shaped ice crystals

1996 ◽  
Vol 14 (5) ◽  
pp. 566-573
Author(s):  
B. Strauss
Keyword(s):  
Ray Tracing ◽  
Ice Crystals ◽  
Asymmetry Factor ◽  
Model Calculations ◽  
Geometrical Features ◽  
The Asymmetry ◽  
Particle Length ◽  
Phase Functions ◽  
Tracing Method ◽  
Factor G

Abstract. The scattering behaviour of bullet-rosette and bullet-shaped ice particles is investigated using model calculations (ray tracing method) with special emphasis on the asymmetry factor g. Because the variability of the geometrical features of these particles is very large, some representative shapes are used in the calculations. The model is based on geometrical optics, and particles are assumed to be oriented randomly; a wavelength of 0.56 μm is considered; absorption is neglected. The scattering behaviour of bullet rosettes is compared to that of single branches out of the bullet rosette. It turns out that there are slight differences in the asymmetry factor values, depending on the lengths of the branches (∆g~0.02) and on the angles between the branches (∆g~0.01). Bullets show some special features in their phase functions due to the pyramid. The length of the particle influences the asymmetry factor (∆g~0.10), as does the shape of the pyramid (∆g~0.07). The influence of the pyramidal shape decreases with increasing particle length. Bullets were compared to hexagonally shaped columns. This was done for two columns, one as long as the columnar part of the bullet (length without pyramid), and one for a column as long as the bullet including the pyramid. Asymmetry factor values of bullets with a pyramidal angle of 28° deviate less than ∆g~0.01 from the range given by the two values of the columns.

scholarly journals Dynamically Focused Gaussian Beams for Seismic Imaging

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Robert L. Nowack
Keyword(s):  
Seismic Imaging ◽  
Initial Study ◽  
Gaussian Beams ◽  
Subsurface Scattering ◽  
Local Data ◽  
Quadratic Phase ◽  
Phase Corrections ◽  
Speed Up ◽  
Data Windows ◽  
Slant Stacking

An initial study is performed in which dynamically focused Gaussian beams are investigated for seismic imaging. Focused Gaussian beams away from the source and receiver plane allow the narrowest and planar portions of the beams to occur at the depth of a specific target structure. To match the seismic data, quadratic phase corrections are required for the local slant stacks of the surface data. To provide additional control of the imaging process, dynamic focusing is investigated where all subsurface points are specified to have the same planar beam fronts. This gives the effect of using nondiffracting beams, but actually results from the use of multiple focusing depths for each Gaussian beam. However, now different local slant stacks must be performed depending on the position of the subsurface scattering point. To speed up the process, slant stacking of the local data windows is varied to match the focusing depths along individual beams when tracked back into the medium. The approach is tested with a simple model of 5-point scatterers which are then imaged with the data, and then to the imaging of a single dynamically focused beam for one shot gather computed from the Sigsbee2A model.

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