Computer implementation of image reconstruction formulas

Rowland, Stuart W.

doi:10.1007/3-540-09417-2_2

Cited by 128 publications

(46 citation statements)

References 18 publications

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“…This modification is similar in principle to the deconvolutional techniques used in medical X-ray imaging (Rowland, 1979). The point spread function is estimated by examining the point response of the inversion in various regions of the model domain.…”

Section: Tomographic Methodsmentioning

confidence: 99%

A tomographic image of mantle structure beneath Southern California

Humphreys¹,

Clayton²,

Hager³

1984

Geophysical Research Letters

150

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Abstract. We determined the variations in seismic structure beneath southern California by using a tomographic method of inversion on teleseismic P delays recorded with the Southern California Array. The algorithm employed was a modified form of an Algebraic Reconstruction Technique (ART) used in medical X-ray imaging. Deconvolution with an empirically estimated point spread function was also used to help in focusing the image.The inversion reveals two prominent features beneath the region. The first is a thin, vertical wedge directly beneath the Transverse Ranges that is 2-3% faster than the surrounding region. This feature deepens to the east, attaining a max-

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Section: Tomographic Methodsmentioning

confidence: 99%

A tomographic image of mantle structure beneath Southern California

Humphreys¹,

Clayton²,

Hager³

1984

Geophysical Research Letters

150

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“…There was no significant beam displacement due to the rotation of the half-wave plate, documented by the fact that the maximum displacement 4 of the peak positions in the sensor plane is below 20nm. Measurements for 18 different orientations of the polarization relative to the edge were performed to reconstruct the intensity distribution in the focal plane using the Radon back transformation [23]. For measurements with an annular aperture, a stop is placed directly in front of the microscope objective to block the inner part of the input beam.…”

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confidence: 99%

The focus of light—linear polarization breaks the rotational symmetry of the focal spot

Dorn¹,

Quabis²,

Leuchs³

2003

Journal of Modern Optics

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Abstract:We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc. R. Soc. London A 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing theory.The ability to control and focus light is at the heart of the interdisciplinary field of optics and for many applications an exact knowledge of the structure of the focal field is required. Many areas in optical sciences make use of a tightly focussed light beam such as confocal microscopy [1] and optical data storage [2]. A highly concentrated and well matched field is also a necessary requirement for coupling to small quantum systems [3] and applying light forces to microscopic particles [4]. In the regime of strong focussing the widely used scalar theories are inadequate to describe the focal field. A vectorial focussing theory is required instead. In the concrete example of a beam which is linearly polarized along the y-axis, the rays propagating in the xz-and in the yz-plane, respectively, contribute differently to the focal field (see figures 1(a), (b)). This has two closely related consequences. The effective numerical aperture in the yz-plane is reduced and the focal spot is elongated in the direction of polarization of the input beam because the rays that propagate in this plane do not add up perfectly at the focus. Associated with this elongation, field components in directions orthogonal to the direction of polarization of the input beam arise. These effects are neglected in scalar descriptions [5], which therefore do not predict the correct spot shape and size. All aspects of the field distribution of a tightly focussed linearly polarized light beam have been studied in theory taking into account the vector properties of the field [6,7,8,9]. The theoretical calculations predict pronounced deviations from the results of the scalar theory. Nevertheless, a major part of the intensity 1 is still predicted to be contained in a field 1 In the following, intensity always refers to electric energy density, which is the part of the field energy that couples to standard photodetectors and photosensitive materials. 1Figure 1: Plane wave model for focussing a beam which is linearly polarized parallel to the y-axis. Cross sections for two planes which contain the optical axis, (a) perpendicular and (b) parallel to the direction of polarization, show that the contribution to the total field of the rays propagating under a large angle to the optical axis is weaker in (b). Calculated intensity patterns for the three orthogonal field components (c-e) and total intensity distribution (f). The direction of polariz...

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“…Rowland [1979] So far, filtering has been discussed only for the case of isotropic and homogeneous ray coverage, and the approaches have been exact. When the ray coverage is not isotropic and homogeneous, the general approaches just described may become approximate.…”

Section: Filteringmentioning

confidence: 99%

Adaptation of back projection tomography to seismic travel time problems

Humphreys¹,

Clayton²

1988

J. Geophys. Res.

325

177

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A back projection method of reconstruction is adapted to invert seismic travel time data for velocity structure. Adaptations are made so that the inhomogeneous and anisotropic ray sets and the threedimensional geometries commonly dealt with in seismic experiments can be handled with greater success. Jacobi iteration, deconvolution, and ray weighting work well in augmenting the basic back projection method to produce a well-focused image. These methods succeed by amounts that depend on the quality of the ray coverage. Also, the ability to reconstruct an accurate image when the data include moderate amounts of noise is shown to be good. Comparison of inversions produced with back projection tomography and with damped least squares indicate that the two methods are comparable in their ability to reconstruct an image of the actual structure. The back projection approach, however, is much more computer efficient. In practice, this allows for the construction of more detailed inversions.

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Computer implementation of image reconstruction formulas

Cited by 128 publications

References 18 publications

A tomographic image of mantle structure beneath Southern California

A tomographic image of mantle structure beneath Southern California

The focus of light—linear polarization breaks the rotational symmetry of the focal spot

Adaptation of back projection tomography to seismic travel time problems

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