Tomographic apparatus

Claim 1

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detection means, including a plurality of detector elements surrounding said scanning circle, for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle, and for producing, in response to said radiation, a source fan set of data for various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weighting means for weighting said overlapping data by a smooth function which is complementary in value to said overlapped data sets; convoluter means for performing a convolution of said detector fan sets of data including data weighted by said weighting means without reordering said detector fan data into parallel ray data to derive convoluted data; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 2

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detection means, including a plurality of detector elements surrounding said scanning circle, for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle, and for producing, in response to said radiation, a source fan set of data for various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weighting means for weighting said overlapping data by a smooth function which is complementary in value to said overlapped data sets; convoluter means for performing a convolution of said detector fan sets of data including data weighted by said weighting means without reordering said detector fan data into parallel ray data to derive convoluted data; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 4

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for weighting said overlapping data by a smooth function which is complementary in value to said overlapped data sets; convoluter means for convoluting said detector fan sets with a non-oscillating convolution function; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 5

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for weighting said overlapping data by a smooth function which is complementary in value to said overlapped data sets; convoluter means for convoluting said detector fan sets with a non-oscillating convolution function; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 9

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detection means, including a plurality of detector elements surrounding said scanning circle, for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle, and for producing, in response to said radiation, a source fan set of data for various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weighting means for weighting said overlapped data wherein one of said weights is given as the following: ##EQU30## where L1(φ)=φ+arc sin (S·sin φ/L); L2(φ)=π+2a+φ+arc sin (S·sin φ/L); L3(φ)=φ-arc sin (S·sin φ/L)+2a; and L4(φ)=φ+π-arc sin (S·sin φ/L); φ is the angular orientation of a ray in the detector fan; θ is the angular orientation of the detector elements; "a" is one half the source fan angle; L is the distance between the center of the circle and the source; and S is the distance between the center and the detector elements; convoluter means for performing a convolution of said detector fan sets of data including data averaged by said weighting means without reordering said detector fan data into parallel ray data to derive convoluted data; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 10

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detection means, including a plurality of detector elements surrounding said scanning circle, for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle, and for producing, in response to said radiation, a source fan set of data for various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weighting means for weighting said overlapped data wherein one of said weights is given as the following: ##EQU30## where L1(φ)=φ+arc sin (S·sin φ/L); L2(φ)=π+2a+φ+arc sin (S·sin φ/L); L3(φ)=φ-arc sin (S·sin φ/L)+2a; and L4(φ)=φ+π-arc sin (S·sin φ/L); φ is the angular orientation of a ray in the detector fan; θ is the angular orientation of the detector elements; "a" is one half the source fan angle; L is the distance between the center of the circle and the source; and S is the distance between the center and the detector elements; convoluter means for performing a convolution of said detector fan sets of data including data averaged by said weighting means without reordering said detector fan data into parallel ray data to derive convoluted data; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 11

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for averaging said overlapping data by weights other than zero or one; convoluter means for convoluting said detector fan sets with a convolution function given as the convolution of a desired smoothing function s(φ) and a generalized function hd(φ), said generalized function hd(φ) satisfying the following relationships: hd(φ)=-1λπsin.sup.2 φ) if φ≠0, (i) ##EQU31##

Claim 12

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for averaging said overlapping data by weights other than zero or one; convoluter means for convoluting said detector fan sets with a convolution function given as the convolution of a desired smoothing function s(φ) and a generalized function hd(φ), said generalized function hd(φ) satisfying the following relationships: hd(φ)=-1λπsin.sup.2 φ) if φ≠0, (i) ##EQU31##

Claim 14

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for averaging said overlapping data by weights other than zero or one; convoluter means for convoluting said detector fan sets using convolution function h(mΔφ) where: h(mΔφ)=1/(π·Δφ)·[cot (m+1/2)Δφ-cot (m-1/2)Δφ] where m is an integer and mΔφ equals the detector fan angle; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.

Claim 15

An apparatus for reconstructing a tomographic image of an object positioned within a scanning circle comprising: a source of a fan-shaped beam of radiation having an angle of radiation 2a, said fan-shaped beam rotatable circumferentially about said scanning circle by an angle of π plus 2a; radiation detector means including a plurality of detector elements surrounding said scanning circle for detecting radiation in said beam passing from said source through said scanning circle as said source rotates about said scanning circle and for producing in response to said radiation a source fan set of data for each of various positions of said source as said source rotates, each said source fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from said source; sort means for sorting said source fan sets of data into detector fan sets of data, each said detector fan set of data representing the amount of radiation absorbed by a generally fan-shaped region of said object divergent from a detector element of said radiation detector means, said detector fan sets of data including certain sets which have overlapping data; weight means for averaging said overlapping data by weights other than zero or one; convoluter means for convoluting said detector fan sets using convolution function h(mΔφ) where: h(mΔφ)=1/(π·Δφ)·[cot (m+1/2)Δφ-cot (m-1/2)Δφ] where m is an integer and mΔφ equals the detector fan angle; memory means; back projector means for back projecting and accumulating said convoluted data into said memory means; and display means for displaying an image in response to said data accumulated in said memory means.