Time symmetric pulse to uniformly rotate magnetization vectors by an arbitrary angle in the presence of large B1 inhomogeneities and resonance offsets

Claim 1

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having B 1 components transverse to said B 0 field wherein said pulse introduces a field Δω in said matter equal to the time dependent difference of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to be symmetrical in amplitude and phase about is center and to include a pair of discontinous phase shifts φ 1 , φ 2 in B 1 of substantially equal and opposite sign symmetrically positioned in said pulse, each phase shift executed concomitantly with an inversion in Δω to cause a flip in B e in the frequency modulated frame of reference so that said pulse achieves a plane rotation of said spins with a high degree of insensitivity to off-resonance effects.

Claim 2

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having B 1 components transverse to said B 0 field wherein said pulse introduces a field Δω in said matter equal to the time dependent difference of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to be symmetrical in amplitude and phase about is center and to include a pair of discontinous phase shifts φ 1 , φ 2 in B 1 of substantially equal and opposite sign symmetrically positioned in said pulse, each phase shift executed concomitantly with an inversion in Δω to cause a flip in B e in the frequency modulated frame of reference so that said pulse achieves a plane rotation of said spins with a high degree of insensitivity to off-resonance effects.

Claim 3

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having with B 1 field wherein said pulse introduces a field, Δω, in said matter aligned with B 0 equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first segment to cause B e to rotate substantially 90°; ii) a first discontinuous phase shift of φ 1 in B 1 after said first segment; iii) an inversion of Δω occurring concomitantly with said first discontinuous phase shift to cause B e to flip in the frequency modulated (FM) frame of reference; iv) a second segment following said first phase shift and Δω inversion to to rotate substantially 180° in the FM frame of reference; v) a second discontinuous phase shift of φ 2 in B 1 after said second segment with φ 2 of substantially equal but opposite sign to φ 1 ; vi) a second inversion of Δω occurring concomitantly with said second discontinous phase shift to cause B e to flip in the FM frame of reference; vii) a third segment following said second phase shift and Δω inversion to cause B e to rotate substantially 90° in the FM frame of reference; and wherein said pulse is generated so that it is symmetric in amplitude and phase about its center whereby a plane rotation of said spins is achieved with insensitivity to off-resonance effects.

Claim 4

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having with B 1 field wherein said pulse introduces a field, Δω, in said matter aligned with B 0 equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first segment to cause B e to rotate substantially 90°; ii) a first discontinuous phase shift of φ 1 in B 1 after said first segment; iii) an inversion of Δω occurring concomitantly with said first discontinuous phase shift to cause B e to flip in the frequency modulated (FM) frame of reference; iv) a second segment following said first phase shift and Δω inversion to to rotate substantially 180° in the FM frame of reference; v) a second discontinuous phase shift of φ 2 in B 1 after said second segment with φ 2 of substantially equal but opposite sign to φ 1 ; vi) a second inversion of Δω occurring concomitantly with said second discontinous phase shift to cause B e to flip in the FM frame of reference; vii) a third segment following said second phase shift and Δω inversion to cause B e to rotate substantially 90° in the FM frame of reference; and wherein said pulse is generated so that it is symmetric in amplitude and phase about its center whereby a plane rotation of said spins is achieved with insensitivity to off-resonance effects.

Claim 10

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field utilizing a composite pulse having B 1 components transverse to said B 0 field and wherein said pulse introduces a field in said matter equal to the difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said pulse to include: i) a first segment to cause magnetization to rotate by an effective angle substantially equal to 90° in a rotating frame of reference; ii) a discontinuous phase shift of φ 1 in B 1 after said first segment; iii) a second segment following said first phase shift to cause magnetization to rotate by an effective angle substantially equal to 180° in the rotating frame of reference; iv) an additional discontinuous phase shift of φ 2 of said second segment of substantially equal but opposite sign to φ 1 ; v) a third segment following said second phase shift to cause magnetization to rotate by an effective angle substantially equal to 90° in the rotating frame of reference and so that said pulse is generated so that it is symmetric in amplitude and phase about its center whereby a plane rotation of said spins is achieved with a high degree of insensitivity to off-resonance effects.

Claim 11

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field utilizing a composite pulse having B 1 components transverse to said B 0 field and wherein said pulse introduces a field in said matter equal to the difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said pulse to include: i) a first segment to cause magnetization to rotate by an effective angle substantially equal to 90° in a rotating frame of reference; ii) a discontinuous phase shift of φ 1 in B 1 after said first segment; iii) a second segment following said first phase shift to cause magnetization to rotate by an effective angle substantially equal to 180° in the rotating frame of reference; iv) an additional discontinuous phase shift of φ 2 of said second segment of substantially equal but opposite sign to φ 1 ; v) a third segment following said second phase shift to cause magnetization to rotate by an effective angle substantially equal to 90° in the rotating frame of reference and so that said pulse is generated so that it is symmetric in amplitude and phase about its center whereby a plane rotation of said spins is achieved with a high degree of insensitivity to off-resonance effects.

Claim 13

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing a composite pulse having B 1 components transverse to said B 0 field and wherein said pulse introduces a field in said matter equal to the difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said composite pulse to be symmetrical about its center and in the following form: Θ.sub.0 Θ.sup.-1.sub.(β/2) Θ.sub.(180°+β/2) Θ.sup.-1.sub.180° where β is the desired rotation angle to be achieved by the pulse in a rotating frame of reference, Θ 0 is one or more square pulses, (i.e. having constant phase and amplitude) which together produce a substantially 90° rotation of the magnetization vectors, and Θ -1 .sub.(β/2) is the inverse of Θ 0 with β/2 added to phases of all the pulses, and wherein the inverse of Θ 0 , (Θ 0 -1 ) is generated by adding 180° to the phases of the square pulse(s) composing Θ 0 and executing these pulses in reverse order, and further wherein Θ -1 180 ° is the inverse of Θ.sub.(180°+β/2) with β/2 subtracted from the phases of the square pulse(s).

Claim 14

A method for achieving plane rotations of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 utilizing a composite pulse having B 1 components transverse to said B 0 field and wherein said pulse introduces a field in said matter equal to the difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said composite pulse to be symmetrical about its center and in the following form: Θ.sub.0 Θ.sup.-1.sub.(β/2) Θ.sub.(180°+β/2) Θ.sup.-1.sub.180° where β is the desired rotation angle to be achieved by the pulse in a rotating frame of reference, Θ 0 is one or more square pulses, (i.e. having constant phase and amplitude) which together produce a substantially 90° rotation of the magnetization vectors, and Θ -1 .sub.(β/2) is the inverse of Θ 0 with β/2 added to phases of all the pulses, and wherein the inverse of Θ 0 , (Θ 0 -1 ) is generated by adding 180° to the phases of the square pulse(s) composing Θ 0 and executing these pulses in reverse order, and further wherein Θ -1 180 ° is the inverse of Θ.sub.(180°+β/2) with β/2 subtracted from the phases of the square pulse(s).

Claim 15

A method for achieving spectral editing by selectively generating signals from selected nuclei engaged in spin-spin coupling in matter under the influence of a spin aligning magnetic field utilizing an adiabatic pulse having B 1 components transverse to said wherein said pulse introduces a field Δω in said matter equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first, second and third segment to cause B e to rotate substantially 90°, substantially 180°, and substantially 90°, respectively, in the frequency modulated (FM) frame of reference; ii) a delay τ between said first and second segments and said second and third segments, said delay τ substantially equal to 1/(8J) where J is the spin-spin coupling constant in Hz units of the selected spins, so that the selected spins undergo effective phase shifts of φ 1 and φ 2 , respectively, where φ 1 =2π(νπ+(1/8)) and φ 2 =2π(ντ±(1/8)), and where ν is the spin precessional frequency in the FM frame of reference in the absence of spin-spin coupling; iii) a 180° discontinuous phase shift implemented concomitantly with an inversion to Δω to cause B e in the FM to flip at the end of each said delay τ; whereby J-filtering can be achieved.

Claim 16

A method for achieving spectral editing by selectively generating signals from selected nuclei engaged in spin-spin coupling in matter under the influence of a spin aligning magnetic field utilizing an adiabatic pulse having B 1 components transverse to said wherein said pulse introduces a field Δω in said matter equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e in said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first, second and third segment to cause B e to rotate substantially 90°, substantially 180°, and substantially 90°, respectively, in the frequency modulated (FM) frame of reference; ii) a delay τ between said first and second segments and said second and third segments, said delay τ substantially equal to 1/(8J) where J is the spin-spin coupling constant in Hz units of the selected spins, so that the selected spins undergo effective phase shifts of φ 1 and φ 2 , respectively, where φ 1 =2π(νπ+(1/8)) and φ 2 =2π(ντ±(1/8)), and where ν is the spin precessional frequency in the FM frame of reference in the absence of spin-spin coupling; iii) a 180° discontinuous phase shift implemented concomitantly with an inversion to Δω to cause B e in the FM to flip at the end of each said delay τ; whereby J-filtering can be achieved.

Claim 18

A method for achieving spectral editing by selectively generating signals from selected nuclei engaged in spin-spin coupling in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having B 1 components transverse to said B 0 field wherein said pulse introduces a field Δω in said matter equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first, second and third segment to cause B e to rotate substantially 90° substantially 180°, and substantially 90°, respectively, in the frequency modulated (FM) frame of reference; ii) a delay τ between said first and second segments and said second and third segments, said delay τ substantially equal to 1/(2J) where J is the spin-spin coupling constant in Hz units; iii) a 180° discontinuous phase shift implemented concomitantly with an inversion of Δω to cause B e to flip in the FM frame of reference at the end of each said delay τ; iv) a second adiabatic inversion pulse, 180° as , applied during the middle of the said first (or second) τ delay at a frequency to invert the spin state of a second homo or heteronucleus which is engaged in spin-spin coupling with the first spin experiencing the processes described in i-iii above so that the selected first spins undergo the phase shifts, φ 1 and φ 2 , respectively, φ 1 =2π(νπ±(1/4)) and φ 2 =2πντ (or φ 1 =2πντ and φ 2 =2π(ντ±(1/4))), where ν is the spin precessional frequency of reference in the absence of spin-spin coupling; whereby spectral editing can be achieved.

Claim 19

A method for achieving spectral editing by selectively generating signals from selected nuclei engaged in spin-spin coupling in matter under the influence of a spin aligning magnetic field B 0 utilizing an adiabatic pulse having B 1 components transverse to said B 0 field wherein said pulse introduces a field Δω in said matter equal to the time dependent difference between the frequency of the pulse and the Larmor frequency of the spins and wherein the vector sum of B 1 and Δω/γ introduce an effective field B e said matter, where γ is the gyromagnetic ratio, said method comprising generating said adiabatic pulse to include: i) a first, second and third segment to cause B e to rotate substantially 90° substantially 180°, and substantially 90°, respectively, in the frequency modulated (FM) frame of reference; ii) a delay τ between said first and second segments and said second and third segments, said delay τ substantially equal to 1/(2J) where J is the spin-spin coupling constant in Hz units; iii) a 180° discontinuous phase shift implemented concomitantly with an inversion of Δω to cause B e to flip in the FM frame of reference at the end of each said delay τ; iv) a second adiabatic inversion pulse, 180° as , applied during the middle of the said first (or second) τ delay at a frequency to invert the spin state of a second homo or heteronucleus which is engaged in spin-spin coupling with the first spin experiencing the processes described in i-iii above so that the selected first spins undergo the phase shifts, φ 1 and φ 2 , respectively, φ 1 =2π(νπ±(1/4)) and φ 2 =2πντ (or φ 1 =2πντ and φ 2 =2π(ντ±(1/4))), where ν is the spin precessional frequency of reference in the absence of spin-spin coupling; whereby spectral editing can be achieved.