Diffraction tomography systems and methods with fixed detector arrays
First Claim
1. A method for the tomographic reconstruction of a subsurface geological formation which has diffracted at least one wave of energy interacting with it, comprising the steps of:
- (a) obtaining one or more signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation;
(b) preprocessing said obtained signals, wherein said preprocessing includes the step of scaling and phase correcting signals; and
(c) converting said preprocessed signals by means of a filtered backpropagation technique into an array representing the partial reconstruction profile of the formation.
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Abstract
Diffraction tomography systems and methods are disclosed for the reconstruction of physical properties of two- and three-dimensional objects from information collected by detector arrays which are fixed in space. Improved preprocessing procedures and an optimal filtered backpropagation technique are disclosed for both geophysical and ultrasonic diffraction tomography systems and methods. A novel method for reconstructing properties of three-dimensional objects and slices thereof in real time is also disclosed. An optimal filtered backpropagation technique for the backscatter mode is further disclosed.
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Citations
28 Claims
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1. A method for the tomographic reconstruction of a subsurface geological formation which has diffracted at least one wave of energy interacting with it, comprising the steps of:
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(a) obtaining one or more signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; (b) preprocessing said obtained signals, wherein said preprocessing includes the step of scaling and phase correcting signals; and (c) converting said preprocessed signals by means of a filtered backpropagation technique into an array representing the partial reconstruction profile of the formation. - View Dependent Claims (2, 3)
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4. A method for the tomographic reconstruction of a subsurface geological formation comprising:
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(a) directing at a phase tilt one or more waves of energy toward said geological formation; (b) detecting as a function of time, the one or more fields produced by said one or more waves; (c) producing one or more signals which are functions of said one or more detected fields; (d) preprocessing said produced signals wherein said preprocessing includes the step of scaling and phase correcting signals; and (e) filtering said scaled and phase corrected preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of said geological formation. - View Dependent Claims (5, 6, 7, 8, 9, 10, 11)
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12. A method for the reconstruction of a three-dimensional object which has diffracted waves of energy propagating through it at at least one view angle on a plane for at least one planar orientation, comprising the steps of:
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(a) obtaining signals which are a function of at least one of the phase and amplitude of each propagating wave after said wave has interacted with said object; (b) preprocessing and separating said obtained signals to obtain sets of preprocessed signals, each set representing the signals obtained from the propagation of an energy wave at a separate view angle, said preprocessing and separating including the step of scaling and phase correcting signals. (c) converting said sets of preprocessed signals by means of a filtered backpropagation technique into arrays representing the partial reconstruction of the the object; and (d) interpolating each partial reconstruction onto a master array to obtain a two-dimensional reconstruction of a planar projection of the object. - View Dependent Claims (13)
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14. A method for tomographic reconstruction of a three-dimensional object comprising:
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(a) directing at a view angle on a plane one or more waves of energy toward an object being examined; (b) detecting as a function of time the one or more fields produced by said one or more waves; (c) producing one or more signals which are functions of said one or more detected fields; (d) preprocessing said produced signals wherein said preprocessing includes the step of scaling and phase correcting signals; and (e) filtering said preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of the object. - View Dependent Claims (15, 16, 17, 18, 19, 20)
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21. A method for tomographic reconstruction of a three-dimensional object comprising:
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(a) directing at a view angle on a plane one or more waves of energy toward an object being examined; (b) detecting as a function of time the one or more fields produced by said one or more waves; (c) producing one or more signals which are functions of said one or more detected fields; (d) preprocessing said produced signals wherein said preprocessing includes, converting said produced signal from analog to digital form; transforming said digital signals over time with a Fourier transform; normalizing said transformed signals; complex phase converting said normalized signals; phase unwrapping said complex phase converted signals scaling and phase correcting said phase unwrapped signals; (e) filtering said preprocessed signals according to a filtered backpropagation technique; (f) changing said view angle on said plane; (g) changing said plane on which said waves of energy are directed at a view angle; and (h) repeating steps a-g at a sufficient number of different planar orientations such that a full three-dimensional reconstruction of the object profile can be obtained. - View Dependent Claims (22, 23, 24)
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25. A system for the tomographic reconstruction of a subsurface geological formation which has diffracted at least one wave of energy interacting with it comprising:
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(a) obtaining means for obtaining one or more signals which are a function of at least one of the phase and amplitude of the diffracted propagating wave after said wave has interacted with said formation; (b) preprocessing means for preprocessing said signals obtained by said obtaining means, wherein said preprocessing means includes means for scaling and phase correcting signals; and (c) filtering means for converting said preprocessed signals by means of a filtered backpropagation technique into an array representing the partial reconstruction profile of the formation.
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26. A system for the tomographic reconstruction of a subsurface geological formation comprising:
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source means for directing at a phase-tilt one or more waves of energy toward said geological formation; (b) detecting means for detecting as a function of time, the one or more fields produced by said one or more waves and for producing one or more signals which are functions of said one or more fields wherein said detecting means is located on the same line as said source means; (c) preprocessing means for preprocessing said produced signals wherein said preprocessing means includes means for scaling and phase correcting signals; and (d) filtering means for filtering said scaled and phase corrected preprocessed signals according to a filtered backpropagation technique to generate a two-dimensional array representing the partial reconstruction of said geological formation.
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27. A system for tomographic reconstruction of a three-dimensional object comprising:
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(a) source means for directing at a view angle on a plane one or more waves of energy directed toward an object being examined; (b) detecting means for detecting as a function of time the one or more fields produced by said one or more waves, and producing one or more signals which are functions of said one or more fields; (c) converting means for correcting said produced signals from analog to digital form; (d) transforming means for Fourier transforming said digital signals over time; (e) normalizing means for normalizing said transformed signals; (f) complex phase converting means for complex phase converting said normalized signals; (g) phase unwrapping means for phase unwrapping said complex phase converted signals to produce a two-dimensional array; (h) scaling and phase converting means for scaling and phase converting said phase unwrapped signals; (i) filtering means for filtering said scaled and phase converted signals according to a filtered backpropagation technique
space="preserve" listing-type="equation">H.sub.q,m,n =h.sup.m,n (S.sub.o)e.sub.-iks o.sup..r e.sup.iγ
.sbsp.m,n.sup.(z-l.sbsp.o.sup.)wherein Hq,m,n is a filtered backpropagation technique for object depth zq, and n and m index sample values of preprocessed signals; hm,n is a deblurring filter;
##EQU19## where M and N are the number of detector rows and columns used in detecting said wave;k is the wavenumber associated with the frequency of said directed waves; zq is the distance of the investigated object depth q from the axis of rotation of said object; and .sub. o is the distance between the axis of rotation of said object and the detector array. s0.r is a scalar product between the unit propagation vector s0 =sin θ
0 cos φ
0 sin θ
0 sin φ
0 cos θ
0) and the position vector r;θ
n is the view angle; andφ
n is the planar orientation. - View Dependent Claims (28)
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Specification