The application of dispersion relations (Hilbert transforms) to phase retrieval

Burge, R. E.; Fiddy, Michael A.; Greenaway, A. H.; Ross, G.

doi:10.1088/0022-3727/7/6/101

Cited by 39 publications

(9 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall not address here the general phase retrieval problem (Klibanov et al 1995) but make the minimal phase assumption (Burge et al 1974)…”

Section: Estimation Of the Flare Profilementioning

confidence: 99%

Statistics of superimposed flares in the Taurus molecular cloud

Arzner¹,

Güdel²,

Briggs³

et al. 2007

A&A

View full text Add to dashboard Cite

Context. Stochastically occurring flares provide a possible mechanism of coronal heating in magnetically active stars such as T Tauri objects in star-forming regions. Aims. We investigate the statistics of stellar X-ray light curves from the XMM-Newton Extended Survey of the Taurus Molecular Cloud (XEST). Methods. To this end, the light curve is modeled as superimposed flares occurring at random times and with random amplitudes. The flare shape is estimated non-parametrically from the observations, while the flare amplitude distribution is modeled as a truncated power law, and the flare times are assumed as uniformly distributed. From these model assumptions, predictions on the binned counts are derived and compared with the observations. Results. From a sample of 22 XEST observations matching the above model assumptions we find that the majority of cases have flare amplitude distributions with slopes steeper than two. This favours the role of small flares in coronal heating for 5 targets, of which, however, 4 are foreground or background main-sequence stars.

show abstract

“…We shall not address here the general phase retrieval problem (Klibanov et al 1995) but make the minimal phase assumption (Burge et al 1974)…”

Section: Estimation Of the Flare Profilementioning

confidence: 99%

Statistics of superimposed flares in the Taurus molecular cloud

Arzner¹,

Güdel²,

Briggs³

et al. 2007

A&A

View full text Add to dashboard Cite

show abstract

“…(6) gives the distribution of photographic blackening in a linearly recorded bright-field picture for an ideal weak-phase object. For stronger objects, the squared term (and higher terms) are no longer negligible and computational methods of extracting the image amplitude and phase distributions are essential (e.g., the combined diffraction plane and image plane method of Gerchberg and Saxton (1973), the two-defocus method of Misell (1973a,b) or the Hilbert transform method (Burge, Fiddy, Greenaway, & Ross, 1974). For a pure weak-amplitude object, applying a similar treatment, the image intensity would again be linear, allowing in principle the determination of A(x,y 0 ) as follows:…”

Section: P0695mentioning

confidence: 99%

Imaging with Electrons, X-rays, and Microwaves

Burge

2015

Advances in Imaging and Electron Physics

View full text Add to dashboard Cite

“…Existing methods for the retrieval of the phase of the wave function [11][12][13][14] are based on intensity measurements taken at the location where the phase is retrieved. In the method proposed here, a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Extracting the Green’s function from measurements of the energy flux

Snieder

Douma

Vasconcelos

2012

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

Existing methods for Green’s function extraction give the Green’s function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green’s function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green’s function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green’s function can be retrieved from measurement of the flux of scattered particles through a closed surface.

show abstract

The application of dispersion relations (Hilbert transforms) to phase retrieval

Abstract: A method is given for the retrieval of phase from amplitude information using the Hilbert transform, without the need for evaluating Blaschke factors.

Cited by 39 publications

References 6 publications

Statistics of superimposed flares in the Taurus molecular cloud

Statistics of superimposed flares in the Taurus molecular cloud

Imaging with Electrons, X-rays, and Microwaves

Extracting the Green’s function from measurements of the energy flux

Contact Info

Product

Resources

About