Amplitude and frequency/phase modulated pulses to achieve plane rotations of nuclear spin magnetization vectors with inhomogeneous B1

Claim 1

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field, wherein with the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field Δω to create said effective field B 1 e desired as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to cause a flip in the effective field B 1 e in said matter so that said magnetic spins undergo a plane rotation.

Claim 2

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field, wherein with the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field Δω to create said effective field B 1 e desired as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to cause a flip in the effective field B 1 e in said matter so that said magnetic spins undergo a plane rotation.

Claim 3

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said adiabatic pulse generated to cause said B 1 e field to invert its direction, or flip, during the pulse so that said magnetic spins undergo a plane rotation.

Claim 4

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said adiabatic pulse generated to cause said B 1 e field to invert its direction, or flip, during the pulse so that said magnetic spins undergo a plane rotation.

Claim 7

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; and (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 , said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to include a substantially 180° phase shift in said B 1 field at a time when B 1 substantially equals said effective field B 1 e to flip said effective field B 1 e in said matter to cause said magnetic spins to undergo a plane rotation.

Claim 8

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; and (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 , said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to include a substantially 180° phase shift in said B 1 field at a time when B 1 substantially equals said effective field B 1 e to flip said effective field B 1 e in said matter to cause said magnetic spins to undergo a plane rotation.

Claim 14

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by the said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined (B 1 2 +Δω 2 ) 1/2 , said adiabatic pulse generated to cause said Δω field to invert its direction at a time when B 1 e substantially equals Δω to cause said B 1 e field to flip during said pulse to cause said magnetic spins to undergo a plane rotation.

Claim 15

A method for executing a plane rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by the said coil has components transverse to said B 0 field; (c) energizing said coil to generate an RF adiabatic pulse providing said B 1 field wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined (B 1 2 +Δω 2 ) 1/2 , said adiabatic pulse generated to cause said Δω field to invert its direction at a time when B 1 e substantially equals Δω to cause said B 1 e field to flip during said pulse to cause said magnetic spins to undergo a plane rotation.

Claim 21

A method for executing a plate rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to provide an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to have at least two contiguous segments described by the equations: ##EQU7## ##EQU8## wherein: F 1 and F 2 (t) are functions of time; Δω is defined as (|ω 0 |-|ω(t)|) with ω 0 designating the Larmor frequency of said set of magnetic spins and ω(t) designating the frequency of said adiabatic pulse; v is a parameter which takes into account variations in B 1 magnitude through space and is the ratio of peak B 1 amplitude to the peak frequency modulation amplitude A so that if B 1 changes in space so does v; A is a parameter designating the maximum amplitude of the B 1 field; Δω(t) for segment 2 is a negative relative to Δω(t) for segment 1 at time t 1 to provide for a flip in the B 1 e direction at the time t 1 ; B 1 e =B 1 at the beginning and end of said pulse and B 1 e =Δω when said flip in the B 1 e field is accomplished; and so that said pulse is generated to cause said magnetic spins to undergo a plane rotation.

Claim 22

A method for executing a plate rotation of magnetic spins in matter under the influence of a spin aligning magnetic field B 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to provide an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse generated to have at least two contiguous segments described by the equations: ##EQU7## ##EQU8## wherein: F 1 and F 2 (t) are functions of time; Δω is defined as (|ω 0 |-|ω(t)|) with ω 0 designating the Larmor frequency of said set of magnetic spins and ω(t) designating the frequency of said adiabatic pulse; v is a parameter which takes into account variations in B 1 magnitude through space and is the ratio of peak B 1 amplitude to the peak frequency modulation amplitude A so that if B 1 changes in space so does v; A is a parameter designating the maximum amplitude of the B 1 field; Δω(t) for segment 2 is a negative relative to Δω(t) for segment 1 at time t 1 to provide for a flip in the B 1 e direction at the time t 1 ; B 1 e =B 1 at the beginning and end of said pulse and B 1 e =Δω when said flip in the B 1 e field is accomplished; and so that said pulse is generated to cause said magnetic spins to undergo a plane rotation.

Claim 23

A method for executing a plane rotation of magnetic spins in matter under the influence of spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to provide an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse having at least two contiguous segments described by the equations: ##EQU9## ##EQU10## wherein: F 1 (t) and F 2 (t) are functions of time; Δω is defined as (|ω 0 |-|ω(t)|) with ω 0 designating the Larmor frequency of said set of magnetic spins and ω(t) designating the frequency of said adiabatic pulse; v is a parameter which takes into account variations in B 1 magnitude through space and is the ratio of peak B 1 amplitude to the peak frequency modulation amplitude A so that if B 1 changes in space so does v; A is a parameter designating the maximum amplitude of the B 1 field; B 1 e =B 1 at time t 1 ; B 1 (t) for segment 2 is negative or in other words 180° out of phase relative to B 1 (t) for segment 1 at time t 1 to provide a flip in the B 1 e direction at time t 1 ; B 1 e =Δω at the beginning and end of said pulse; and so that said pulse is generated to cause said magnetic spins to undergo a plane rotation.

Claim 24

A method for executing a plane rotation of magnetic spins in matter under the influence of spin aligning magnetic field B 0 , said magnetic spins having a Larmor frequency ω 0 , said method comprising the steps of: (a) providing a coil responsive to electrical energization to generate a B 1 field; (b) orienting said coil so that the B 1 field generated by said coil has components transverse to said B 0 field; (c) energizing said coil to provide an RF adiabatic pulse providing said B 1 field, wherein when the frequency of said pulse deviates from ω 0 said spins encounter an additional magnetic field of magnitude Δω to create an effective field B 1 e defined as (B 1 2 +Δω 2 ) 1/2 , said pulse having at least two contiguous segments described by the equations: ##EQU9## ##EQU10## wherein: F 1 (t) and F 2 (t) are functions of time; Δω is defined as (|ω 0 |-|ω(t)|) with ω 0 designating the Larmor frequency of said set of magnetic spins and ω(t) designating the frequency of said adiabatic pulse; v is a parameter which takes into account variations in B 1 magnitude through space and is the ratio of peak B 1 amplitude to the peak frequency modulation amplitude A so that if B 1 changes in space so does v; A is a parameter designating the maximum amplitude of the B 1 field; B 1 e =B 1 at time t 1 ; B 1 (t) for segment 2 is negative or in other words 180° out of phase relative to B 1 (t) for segment 1 at time t 1 to provide a flip in the B 1 e direction at time t 1 ; B 1 e =Δω at the beginning and end of said pulse; and so that said pulse is generated to cause said magnetic spins to undergo a plane rotation.