Method and apparatus for rapid NMR imaging of nuclear densities within an object

• US 4,318,043 A
• Filed: 02/12/1980
• Issued: 03/02/1982
• Est. Priority Date: 07/20/1978
• Status: Expired due to Term

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Arakawa, Mitsuaki, Crooks, Lawrence E., Hoenninger, John C. III
• Primary Examiner(s): Tokar, Michael J.
• Application Number:
  US06/120,875
• Time in Patent Office: 749 Days
• Field of Search: 324/300, 324/307, 324/309
• US Class Current: 324/309
• CPC Class Codes: G01R 33/54 Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console

Abstract

Densities of resonant nuclei within elemental volumes along a line are measured using the nuclear magnetic resonance phenomenon called "spin echo". A first planar volume of nuclei is selectively excited to nutate spins by approximately 90°. Thereafter a second planar volume of nuclei, transverse to the first planar volume, is selectively excited to nutate spins by approximately 180°. The nuclei in the line volume common to both of the planar volumes thereafter generate characteristic spin echo signals. A magnetic gradient is established along this line volume during the spin echo read out so that the resultant spin echo signals can be processed to determine the respective densities of resonant nuclei along the line volume. Appropriate phasing of the excitations enables interference with the spin echo signals by the free induction decay to be eliminated. To enable rapid development, successive line volumes are read out which do not lie in previously excited planes.

Claims

1. In a method for generating a detectable signal related to the relative densities of nuclei within an object, the method comprising the steps of selectively exciting a predetermined volume by exciting intersecting regions within said object to generate an NMR response, said predetermined volume defined by the intersection of said regions, and repeating said exciting step at least once, the improvement wherein said repeating step further comprises:

repeating said exciting step for further regions defining further predetermined volumes outside of previously excited regions, the last region excitation occurring within the spin-lattice relaxation time of the first predetermined volume excitation.

3. A method as in claim 1 or 2 wherein each of said region exciting steps further comprises the steps of:

generating a carrier having a predetermined frequency;

controllably modulating said carrier so that it has a predetermined frequency bandwidth;

generating a position variant magnetic field having a predetermined strength in said region and only in said region, said predetermined strength causing nuclei in said region to assume a Larmor frequency bandwidth equal to the frequency bandwidth of said modulated carrier; and

irradiating said sample with said modulated carrier.

30. A method as in claim 1, 2, 4 or 24 wherein said spin-lattice relaxation time is five T₁.

33. A method as in claim 1, 2, 4, 11, 24 or 31 wherein said relative density is selected from the group consisting of a relative normal density, a T₁ modified relative density, and a T₂ modified relative density.

2. A method for generating a detectable signal related to the relative densities of nuclei within an object, the method comprising the steps of:

(a) selectively exciting a predetermined volume by exciting intersecting regions within said object to produce a subsequent NMR response, said predetermined volume defined by the intersection of said regions; and

(b) repeating said step (a) at least once for further predetermined volumes, none of said predetermined volumes being disposed within previously excited regions, said step (b) occurring within the spin-lattice relaxation time of the predetermined volume excited in said step (a).

4. A method for generating a detectable signal related to the relative densities of nuclei within an object, the method comprising the steps of:

(a) selectively exciting a first predetermined volume by exciting a first group of intersecting regions of said object, said first predetermined volume defined by the intersection of said first regions, to produce a subsequent NMR response;

(b) repeating said step (a) a plurality of times for first further predetermined volumes, none of said first further predetermined volumes being disposed within previously excited regions, said step (b) occurring within the spin-lattice relaxation time of said first predetermined volume;

(c) selectively exciting a second predetermined volume by exciting a second group of intersecting regions of said object, said second predetermined volume defined by the intersection of said second group of regions, said second predetermined volume being disposed within one of the regions excited in at least one of said step (a) and step (b) to produce a subsequent NMR response; and

(d) repeating said step (c) a plurality of times for second further predetermined volumes, said second further predetermined volumes being disposed outside of regions previously excited in said steps (c) and (d), said step (d) occurring within the spin-lattice relaxation time of the predetermined volume excited in said step (c).

5. A method for generating a detectable signal related to the relative densities of nuclei within an object, said nuclei having nuclear spins, the method comprising the steps of:

(a) selectively exciting one region to produce an NMR response;

(b) reversing the nuclear spins of atoms in another region at a predetermined time interval thereafter, the intersection of said one and another regions defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo signal centered in time at a point after said reversal equal to said predetermined time interval; and

(c) repeating said steps (a) and (b) at least once for further regions defining further predetermined volumes outside of previously excited regions, said step (c) occurring within the spin-lattice relaxation time of said step (b).

6. A method for generating a detectable signal related to the relative densities of nuclei within an object, said nuclei having nuclear spins, the method comprising the steps of:

(a) selectively exciting one region to produce an NMR response;

(b) reversing the nuclear spins of atoms in another region within said object transverse to said one region at a first predetermined time interval thereafter, the intersection of said one and another regions defining a first predetermined volume, whereby the nuclei within said first predetermined volume thereafter generate first spin echo signals at times in accordance with said first predetermined time interval;

(c) repeating said steps (a) and (b) at least once for further regions defining further predetermined volumes outside of previously excited regions, said step (c) occurring within the spin-lattice relaxation time of said step (b);

(d) selectively exciting one of said one and another regions to produce an NMR response;

(e) reversing the nuclear spins of atoms in a third region within said object at a second predetermined time interval thereafter, the intersection of said one of said one and another regions and said third region defining a second predetermined volume, whereby the nuclei within said second predetermined volume thereafter generate second spin echo signals at times in accordance with said second predetermined time intervals; and

(f) repeating said steps (d) and (e) at least once for further regions defining further predetermined volumes outside of regions excited in said steps (d) and (e) and repetitions thereof, said step (f) occurring within the spin-lattice relaxation time of said step (e).

7. A method for generating a detectable signal related to the relative densities of nuclei within an object, the method comprising the steps of:

(a) selectively exciting one planar volume to produce an NMR response;

(b) selectively exciting another planar volume transverse to said one planar volume, at a predetermined time interval thereafter, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval;

(c) repeating said steps (a) and (b) at least once for further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes, said step (c) occurring within the spin-lattice relaxation time of the planar volume excited in said step (b).

8. A method for determining the relative densities of nuclei within an object, the method comprising the steps of:

(a) selectively exciting one planar volume to produce an NMR response;

(b) selectively exciting another planar volume transverse to said one planar volume, at a first predetermined time interval thereafter, the intersection of said one and another planar volumes defining a first predetermined volume, whereby the nuclei within said first predetermined volume thereafter generate first spin echo signals at times in accordance with said first predetermined time interval;

(c) detecting the intensity of said first spin echo signals to obtain a measure of the relative density of nuclei in said first predetermined volume;

(d) repeating said steps (a) through (c) a plurality of times for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, the last planar volume excitation occurring within the spin-lattice relaxation time of the planar volume excited in said step (b);

(e) selectively exciting one of said one and another planar volumes to produce an NMR response;

(f) selectively exciting a third planar volume transverse to said one of said one and another planar volumes, at a second predetermined time interval thereafter, the intersection of said one of said one and another planar volumes and said third planar volume defining a second predetermined volume, whereby the nuclei within said second predetermined volume thereafter generate second spin echo signals at times in accordance with said second predetermined time interval;

(g) detecting the intensity of said second spin echo signals from said second predetermined volume to obtain a measure of the density of nuclei in said second predetermined volume; and

(h) repeating said steps (e) through (g) a plurality of times for further planar volumes defining further predetermined volumes disposed outside of planar volumes previously excited in said steps (e) and (f) and repetitions of said steps (e) and (f), said repetitions of said steps (e) and (f) occurring within the spin-lattice relaxation time of said second predetermined volume.

9. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

(b) reversing the nuclear spins of atoms in another planar volume at a predetermined time thereafter, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate spin echo signals centered in time at a point after said reversal equal to said predetermined time interval;

(c) detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

(d) repeating said steps (a) through (c) at least once for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, said at least once repetition of said step (b) occurring within the spin-lattice relaxation time of said step (b).

10. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

(b) reversing the nuclear spins of atoms in another planar volume within said object transverse to said one planar volume at a first predetermined time interval thereafter, the intersection of said one and another planar volumes defining a first predetermined volume, whereby the nuclei within said first predetermined volume thereafter generate first spin echo signals at times in accordance with said first predetermined time interval;

(c) detecting the intensity of said first spin echo signals to obtain a measure of the relative density of nuclei in said first predetermined volume;

(d) repeating said steps (a) through (c) at least once for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, said repetitions occurring within the spin-lattice relaxation time of said step (b);

(e) selectively exciting one of said one and another planar volumes to nutate the nuclear spins of nuclei in said one of said one and another planar volumes by a second predetermined angle;

(f) reversing the phase of nuclear spins of atoms in a third planar volume within said object at a second predetermined time interval thereafter, the intersection of said one of said one and another planar volumes and third planar volume defining a second predetermined volume, whereby the nuclei within said second predetermined volume thereafter generate second spin echo signals at times in accordance with said second predetermined time intervals;

(g) detecting the intensity of said second spin echo signals to obtain a measure of the relative density of nuclei in said second predetermined volume; and

(h) repeating said steps (e) through (g) at least once for further planar volumes defining further predetermined volumes outside of planar volumes excited in said steps (e) and (f) and repetitions of said steps (e) and (f), said step (h) occurring within the spin-lattice relaxation time of said step (f).

66. A method as in claims 4, 6, 10 and 17 wherein said first and second predetermined volumes are substantially coextensive.

11. In a method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

(b) selectively exciting another planar volume transverse to one said planar volume, at a predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time intervals;

(c) detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volumes; and

(d) repeating steps (a) through (c) at least once, the improvement wherein;

said step (d) further comprises repeating said steps (a) through (c) for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, the last repetition of said step (b) occurring within the spin-lattice relaxation time of said step (b); and

said method further comprises the steps of;

(e) selectively exciting one of said one and another planar volumes to nutate the nuclear spins in nuclei in said one of said one and another planar volumes by a third predetermined angle,

(f) selectively exciting a third planar volume transverse to said one of said one and another planar volumes, at a second predetermined time interval thereafter, to nutate spins of nuclei in said third planar volume by a fourth predetermined angle, the intersection of said one and third planar volumes defining a second predetermined volume, whereby the nuclei within said second predetermined volume thereafter generate second spin echo signals at times in accordance with said second predetermined time interval,

(g) detecting the intensity of said second spin echo signals to obtain a measure of the relative density of nuclei in said second predetermined volume, and

(h) repeating said steps (e) through (g) at least once for further planar volumes defining further predetermined volumes outside of planar volumes previously excited in said steps (e) and (f), and repetitions of said steps (e) and (f), and last repetition of said step (f) occurring within the spin-lattice relaxation time of said step (f).

12. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

(b) selectively exciting another planar volume transverse to said one planar volume, at a predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval;

(c) detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

(d) repeating said steps (a) through (c) at least once for further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes, said step (d), except the last repetition of said step (c), occurring within the spin-lattice relaxation time of said another planar volume excited in said step (b).

14. A method as in claim 12 or 13 wherein said first predetermined angle is 90°

and said second predetermined angle is 180°

.

13. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) generating, during a first time period, a position variant magnetic field across said object, said field having an intensity varying as a function of position along a first direction whereby nuclei in one planar volume perpendicular to said first direction assume nuclear spins at Larmor frequencies within a first predetermined range of frequencies;

(b) selectively irradiating said object, during said first time period, with an electromagnetic signal having a frequency spectrum substantially consisting of components within said first predetermined range of frequencies and an amplitude and duration to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

(c) generating, during a second time period, a position variant magnetic field across said object, said field having an intensity varying as a function of position along a second direction transverse to said first direction whereby nuclei in another planar volume perpendicular to said second direction assume nuclear spins at Larmor frequencies within a second predetermined range of frequencies;

(d) selectively irradiating said object, during said second time period, with an electromagnetic signal having a frequency spectrum substantially consisting of components within said second predetermined range of frequencies, said electromagnetic signal having an amplitude and duration to nutate spins of nuclei in said another planar volume by a second predetermined angle, said step (d) occurring at a predetermined time interval after said step (b), the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval;

(e) detecting, during a third time period, the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

(f) repeating said steps (a) through (e) at least once for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, the last repetition of said step (d) occurring within the spin-lattice relaxation time of said step (d).

15. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) disposing said object in an intense magnetic field to align the nuclear spins of nuclei within said object in accordance with a first predetermined direction;

(b) generating, during a first predetermined time period, a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said position variant magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

(c) irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said nuclei Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said predetermined band such that the nuclear spins of nuclei located in one planar volume of said object are oriented by a first predetermined angle with respect to the previous orientation thereof;

(d) generating, during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined direction transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

(e) irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a second predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volume at a predetermined volume within said object, the nuclei located within said predetermined volume thereafter, during a third time period, generating spin echo signals at the respective Larmor frequencies thereof;

(f) generating during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position such that the Larmor frequencies of the nuclei vary as a function of relative position within said predetermined volume;

(g) determining the relative intensity of the frequency components of said spin echo signals, each of said spin echo signal frequency components being indicative of the relative density of nuclei disposed at an associated position within said predetermined volume; and

(h) repeating said steps (b) through (g) at least once for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, the last repetition of said step (e) occurring within the spin-lattice relaxation time of the said step (e).

16. A method as in claim 8 or 15 wherein planar volumes defining predetermined volumes are not orthogonal with respect to each other.

17. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) disposing said object in an intense first magnetic field to align the nuclear spins of nuclei within said object in accordance with a first predetermined direction;

(b) generating for a first predetermined time period a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said first position varying magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

(c) irradiating said object during said first predetermined period with a first signal having a first frequency spectrum substantially consisting of frequency components corresponding to a first predetermined band of Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said first predetermined band, such that the nuclear spins of nuclei located in one planar volume of said object are reoriented by a first predetermined angle with respect to the previous orientation thereof;

(d) generating during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined direction transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

(e) irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a second predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volume at a first predetermined volume within said object, the nuclei located within said first predetermined volume thereafter, during a third time period, generating first spin echo signals at the respective Larmor frequencies thereof;

(f) generating during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along said first predetermined volume such that the Larmor frequencies of the nuclei vary as a function of relative position within said first predetermined volume;

(g) determining the relative intensity of the frequency components of said first spin echo signals, each of said spin echo signal frequency components being indicative of the relative density of nuclei disposed at an associated position within said first predetermined volume;

(h) repeating said steps (b) through (g) at least once for further planar volumes defining further predetermined volumes outside of previously excited planar volumes, the last repetition of said step (e) occurring within the spin-lattice relaxation time of said step (e);

(i) generating for a fourth predetermined time period a fourth position variant magnetic field to vary the intensity of a magnetic field within said object in accordance with position along one of said second and third predetermined directions, said fourth position variant magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said one of said second and third predetermined directions;

(j) irradiating said object during said fourth predetermined time period with a signal having a third frequency spectrum to selectively excite said nuclei having Larmor frequencies within one of said one and another planar volumes, such that the nuclear spins of nuclei located in said one of said one and another planar volumes are reoriented by a third predetermined angle with respect to the previous orientation thereof;

(k) generating during a fifth predetermined time period subsequent to said fourth time period a fifth position variant magnetic field to vary the magnetic field within said object in accordance with position along a fourth predetermined direction transverse to said one of said second and third predetermined directions such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said fourth predetermined direction;

(l) irradiating said object during said fifth predetermined time period with a fourth signal having a fourth frequency spectrum substantially consisting of frequency components corresponding to a fourth predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in a third planar volume are reoriented by a fourth predetermined angle with respect to the previous orientation thereof, said third planar volume intersecting said one of said one and another planar volumes at a second predetermined volume of intersection within said object, the nuclei located within said second predetermined volume thereafter during a sixth time period generating second spin echo signals at the respective Larmor frequencies thereof;

(m) generating during said sixth time period a sixth position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with a position along a fifth predetermined direction such that the Larmor frequencies of the nuclei vary as a function of relative position within said second predetermined volume;

(n) determining the relative intensity of the frequency components of said second spin echo signals, each of said second spin echo signal frequency components being indicative of the relative density of nuclei disposed at an associated position within said second predetermined volume; and

(o) repeating said steps (i) through (n) at least once for further planar volumes defining further predetermined volumes outside of planar volumes irradiated in said steps (j) and (l) and repetitions of said steps (j) and (l), the last repetition of said step (l) occurring within the spin-lattice relaxation time of said step (l).

18. A method as in claim 17 wherein said first and third predetermined angles are 90°

and said second and fourth predetermined angles are 180°

.

19. A method for determining the relative densities of nuclei within an object, the method comprising the steps of:

(a) selectively exciting one region of said object to generate, for a period of time, a free induction decay signal (FID) having a polarity;

(b) selectively exciting another region transverse to said one region, at a predetermined time interval thereafter, the intersection of said one and another regions defining a predetermined volume, to generate from said predetermined volume a spin echo having a polarity, at times in accordance with said predetermined time interval and within said period of time, so that said FID interferes with said spin echo to produce a spin echo signal having an FID component and a spin echo component;

(c) detecting the intensity of said spin echo signal to obtain a measure of the relative density of nuclei in said predetermined volume;

(d) repeating said steps (a) through (c) at least once for said one and another regions, the phases of excitations in said step (a) and said at least one repetition of said step (a) being such that an arithmetic combination of said polarities of said FIDs is zero, the phases of excitations in said step (b) and said at least one repetition of said step (b) being such that said arithmetic combination of said polarities of said spin echoes is not zero; and

(e) combining corresponding portions of the spin echo signals detected in said step (c) and repetitions of said step (c) with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

20. A method as in claim 19 wherein:

said step (a) comprises the steps of;

(1) generating a position variant magnetic field having a predetermined range of intensity in said one region and only in said one region, and

(2) selectively irradiating said object with a first electromagnetic signal having a frequency range to cause nutation only in said one region, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps

(3) generating a position variant magnetic field across said object, the strength of said field having a predetermined range of values in said another region and only in said another region, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause nutation only in said another region, said second electromagnetic signal having a phase of 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating said step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause nutation only in said one region, said third electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(7) repeating said step (3), and

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause nutation only in said another region, said fourth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity; and

said method further comprises the step of adding corresponding portions of said spin echo signals so that said FID components cancel and said spin echo components do not cancel.

21. A method as in claim 19 wherein:

said step (a) further comprises the steps of;

(1) generating a position variant magnetic field across said object, the intensity of said field having a predetermined range of values in said one region, and only in said one region, and

(2) selectively irradiating said object with a first electromagnetic signal having a frequency range to produce nutation of nuclei only in said one region, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps of;

(3) generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined range of values in said another region, and only in said another region, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause nutation of nuclei only in said another region, the phase of said second electromagnetic signal being 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating said step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause nutation only in said one region, said third electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce an FID having a positive polarity,

(7) repeating said step (3),

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause nutation only in said another region, said fourth electromagnetic signal having a phase of 270°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(9) repeating said step (1),

(10) irradiating said object with a fifth electromagnetic signal having a frequency range to cause nutation only in said one region, said fifth electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(11) repeating said step (3),

(12) irradiating said object with a sixth electromagnetic signal having a frequency range to cause nutation only in said another region, said sixth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(13) repeating said step (1),

(14) irradiating said object with a seventh electromagnetic signal having a frequency range to cause nutation only in said one region, said seventh electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(15) repeating said step (3), and

(16) irradiating said object with an eighth electromagnetic signal having a frequency range to cause nutation only in said another region, said eighth electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity; and

said method further comprises the step of adding corresponding portions of said spin echo signals so that said FID components of said spin echo signals cancel while said spin echo components of said spin echo signals do not cancel.

22. A method as in claim 19 wherein:

said step (a) further comprises the steps of;

(1) generating a position variant magnetic field across said object, the intensity of said field having a predetermined range of values in said one region, and only in said one region, and

(2) selectively irradiating said object with a first electromagnetic signal having a frequency range to produce nutation of nuclei only in said one region, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps of;

(3) generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined range of values in said another region, and only in said another region, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause nutation of nuclei only in said another region, the phase of said second electromagnetic signal being 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause nutation only in said one region, said third electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(7) repeating said step (3),

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause nutation only in said another region, said fourth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(9) repeating said step (1),

(10) irradiating said object with a fifth electromagnetic signal having a frequency range to cause nutation only in said one region, said fifth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce an FID having a positive polarity,

(11) repeating said step (3),

(12) irradiating said object with a sixth electromagnetic signal having a frequency range to cause nutation only in said another region, said sixth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a negative polarity,

(13) repeating said step (1),

(14) irradiating said object with a seventh electromagnetic signal having a frequency range to cause nutation only in said one region, said seventh electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(15) repeating said step (3), and

(16) irradiating said object with an eighth electromagnetic signal having a frequency range to cause nutation only in said another region, said eighth electromagnetic signal having a phase of 90°

with respect to said first electromagnetic signal to produce a spin echo having a negative polarity; and

said method further comprises the steps of;

adding corresponding portions of the spin echo signals detected in step (c) and the first repetition of step (c) to produce a first composite signal wherein said FID components cancel while said spin echo components do not cancel,

adding corresponding portions of the spin echo signals detected in the second repetition of step (c) and the third repetition of step (c) to produce a second composite signal wherein said FID components cancel and said spin echo components do not cancel, and

subtracting corresponding portions of said first composite signal with corresponding portions of said second composite signal to produce a signal having no FID component and a spin echo component.

23. A method as in claim 2, 4 or 19 further comprising the step of initially aligning said spins in said object.

24. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

26. A method as in claim 24 wherein:

said step (a) comprises the steps of;

(1) generating a position variant magnetic field having a predetermined range of intensity in said one planar volume and only in said one planar volume, and

(2) selectively irradiating said object with a first electromagnetic signal to cause said nutation only in said one planar volume, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps of;

(3) generating a position variant magnetic field across said object, the strength of said field having a predetermined range of values in said another planar volume, and only in said another planar volume, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation only in said another planar volume, said second electromagnetic signal having a phase of 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating said step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause said nutation only in said one planar volume, said third electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(7) repeating said step (3), and

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause said nutation only in said another planar volume, said fourth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity; and

said method further comprises the step of adding corresponding portions of said spin echo signals so that said FID components cancel and said spin echo components do not cancel.

27. A method as in claim 24 wherein:

said step (a) further comprises the steps of;

(1) generating a position variant magnetic field across said object, the intensity of said field having a predetermined range of values in said one planar volume and only in said one planar volume, and

(2) selectively irradiating said object with a first electromagnetic signal having a frequency range to produce said nutation of nuclei only in said one planar volume, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps of;

(3) generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined range of values in said another planar volume and only in said another planar volume, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation of nuclei only in said another planar volume, the phase of said second electromagnetic signal being 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating said step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause said nutation only in said one planar volume, said third electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce an FID having a positive polarity,

(7) repeating said step (3),

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause said nutation only in said another planar volume, said fourth electromagnetic signal having a phase of 270°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(9) repeating said step (1),

(10) irradiating said object with a fifth electromagnetic signal having a frequency range to cause said nutation only in said one planar volume, said fifth electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(11) repeating said step (3),

(12) irradiating said object with a sixth electromagnetic signal having a frequency range to cause nutation only in said another planar volume, said sixth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(13) repeating said step (1),

(14) irradiating said object with a seventh electromagnetic signal having a frequency range to cause said nutation only in said one planar volume, said seventh electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(15) repeating said step (3), and

(16) irradiating said object with an eighth electromagnetic signal having a frequency range to cause said nutation only in said another planar volume, said eighth electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity; and

said method further comprises the step of adding corresponding portions of said spin echo signals so that said FID components of said spin echo components cancel while said spin echo components of said spin echo signals do not cancel.

28. A method as in claim 24 wherein:

said step (a) further comprises the steps of;

(1) generating a position variant magnetic field across said object, the intensity of said field having a predetermined range of values in said one planar volume and only in said one planar volume, and

(2) selectively irradiating said object with a first electromagnetic signal having a frequency range to produce nutation of nuclei only in said one planar volume, the phase of said first electromagnetic signal producing an FID having a positive polarity;

said step (b) further comprises the steps of;

(3) generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined range of values in said another planar volume and only in said another planar volume, and

(4) irradiating said object with a second electromagnetic signal having a frequency range to cause nutation of nuclei only in said another planar volume, the phase of said second electromagnetic signal being 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity;

said step (d) further comprises the steps of;

(5) repeating said step (1),

(6) irradiating said object with a third electromagnetic signal having a frequency range to cause nutation only in said one planar volume, said third electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(7) repeating said step (3),

(8) irradiating said object with a fourth electromagnetic signal having a frequency range to cause nutation only in said another planar volume, said fourth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity,

(9) repeating said step (1),

(10) irradiating said object with a fifth electromagnetic signal having a frequency range to cause nutation only in said one planar volume, said fifth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce an FID having a positive polarity,

(11) repeating said step (3),

(12) irradiating said object with a sixth electromagnetic signal having a frequency range to cause nutation only in said another planar volume, said sixth electromagnetic signal having a phase of 0°

with respect to said first electromagnetic signal to produce a spin echo having a negative polarity,

(13) repeating said step (1),

(14) irradiating said object with a seventh electromagnetic signal having a frequency range to cause nutation only in said one planar volume, said electromagnetic signal having a phase of 180°

with respect to said first electromagnetic signal to produce an FID having a negative polarity,

(15) repeating said step (3), and

(16) irradiating said object with an eighth electromagnetic signal having a frequency range to cause nutation only in said another planar volume, said eighth electromagnetic signal having a phase of 90°

with respect to said first electromagnetic signal to produce a spin echo having a negative polarity; and

said method further comprises the steps of;

adding corresponding portions of the spin echo signals detected in step (c) and the first repetition of step (c) to produce a first composite signal wherein said FID components cancel while said spin echo components do not cancel,

adding corresponding portions of the spin echo signals detected in the second repetition of step (c) and the third repetition of step (c) to produce a second composite signal wherein said FID components cancel and said spin echo components do not cancel, and

subtracting corresponding portions of said first composite signal with corresponding portions of said second composite signal to produce a signal having no FID component and a spin echo component.

29. A method as in claim 8 or 24 wherein each of said exciting steps further comprises the steps of:

generating a carrier having a predetermined frequency;

controllably modulating said carrier to have a predetermined range of frequencies;

generating a position variant magnetic field having a predetermined strength in the excited planar volume and only in the excited planar volume, said predetermined strength causing nuclei in said planar volume to assume a range of Larmor frequencies equal to the range of frequencies of said modulated carrier; and

irradiating said sample with said modulated carrier.

25. (a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle, the nuclei within said one planar volume thereafter generating, for a period of time, a free induction decay (FID) having a polarity;

(b) selectively exciting another planar volume transverse to said one planar volume, at a predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo having a polarity at times in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having an FID component and a spin echo component;

(c) detecting the intensity of said spin echo signal to obtain a measure of the relative density of nuclei in said predetermined volume;

(d) repeating said steps (a) through (c) at least once for said one and another planar volumes, the phases of excitations in said step (a) and said at least one repetition of said step (a) being such that an arithmetic combination of the polarities of said FIDs is zero, the phases of excitations in said step (b) and said at least one repetition of said step (b) being such that said arithmetic combination of the polarities of said spin echoes is not zero; and

(e) combining corresponding portions of the spin echo signals detected in said step (c) and repetitions of said step (c) with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

31. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensities of a magnetic field operating thereon, the method comprising the steps of:

(a) selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle, the nuclei within said one planar volume thereafter generating, for a period of time, a free induction decay (FID) having a polarity;

(b) reversing the nuclear spins of atoms in another planar volume within said object transverse to said one planar volume at a predetermined time thereafter, the intersection of said one and another planar volumes defining a predetermined volume, said predetermined volume generating a spin echo centered in time at the point after said reversal equal to said predetermined time interval, and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

(c) detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume;

(d) repeating said steps (a) through (c) at least once for said one and another planar volumes, the phases of excitations in said step (a) and said at least one repetition of said step (a) being such that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

(e) combining corresponding portions of said spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

32. A method for detecting the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) generating, for a first predetermined time period, a first position variant magnetic field within said object, said position variant magnetic field causing the Larmor frequencies of nuclei in said object to vary as a function of the relative positions of said nuclei within said object;

(b) irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said nuclear Larmor frequencies, to selectively excite said nuclei in one planar volume having Larmor frequencies within said predetermined band, such that the nuclear spins of nuclei located in said one planar volume are reoriented by a first predetermined angle, the nuclei within said one planar volume thereafter generating, for a period of time, a free induction decay (FID) having a polarity;

(c) generating, for a second predetermined time period, a second position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position, said position variant magnetic field causing Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei;

(d) irradiating said object during said second predetermined period with a signal having a second frequency spectrum substantially consisting of components corresponding to a second predetermined band of said nuclear Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within another planar volume, transverse to said one planar volume, such that the nuclear spins of nuclei within said another planar volume are reoriented by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

(e) detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume;

(f) repeating said steps (a) through (e) at least once for said one and another planar volumes, the phases of excitations in said step (b) and said at least one repetition of said step (b) being such that an arithmetic combination of the polarities of said FIDs is zero, the phases of excitations in said step (d) and said at least one repetition of said step (d) being such that said arithmetic combination of the polarities of said spin echoes is not zero; and

(g) combining corresponding portions of the spin echo signals detected in said step (e) and repetitions of said step (e) with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

34. A method for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, the method comprising the steps of:

(a) disposing said object in an intense first magnetic field to align the nuclear spins of said atoms in accordance with a first predetermined direction;

(b) generating for a first predetermined time period a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said position variant magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

(c) irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said nuclear Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said predetermined band, such that nuclear spins of nuclei located in one planar volume in said object are reoriented by a first predetermined angle with respect to the previous orientation thereof, the nuclei within said one planar volume thereafter generating, for a period of time, a free induction decay (FID) having a polarity for a period;

(d) generating during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined direction transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

(e) irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a second predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volume at a predetermined volume within said object, the nuclei located in said predetermined volume thereafter, during a third time period, generating a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

(f) generating during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with the position within said predetermined volume such that the Larmor frequencies of the nuclei vary as a function of relative position within said predetermined volume;

(g) determining the relative intensity of the frequency components of said spin echo signals, each of said spin echo signal frequency components being indicative of the relative density of nuclei disposed at an associated position within said predetermined volume;

(h) repeating said steps (b) through (g) at least once for said one and another planar volumes, the phases of said signals in said step (c) and said at least one repetition of said step (c) being such that an arithmetic combination of the polarities of said FIDs is zero, the phases of said signals in said step (e) and said at least one repetition of said step (e) being such that said arithmetic combination of the polarities of said spin echoes is not zero; and

(i) combining corresponding portions of the spin echo signals determined in said step (g) and repetitions of said step (g) with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

39. Apparatus as in claim 34 or 37 wherein each of said means for exciting further comprises:

means for generating a carrier having a predetermined frequency;

means for controllably modulating said carrier to have a predetermined range of frequencies;

means for generating a position variant magnetic field having a predetermined strength in the excited region and only in the excited region, said predetermined strength causing nuclei in said region to assume a range of Larmor frequencies equal to the range of frequencies of said modulated carrier; and

irradiating said sample with said modulated carrier.

35. In apparatus for generating a detectable signal related to the relative densities of nuclei within an object, said apparatus comprising:

(1) means, responsive to a control signal, for selectively exciting a predetermined volume by exciting intersecting regions within said object, said predetermined volume defined by the intersection of said regions, to produce spin echo signals; and

(2) means for generating said control signal, the improvement wherein said generating means further comprises;

means for repetitively generating said control signal a first and at least a second time, said generating means including means for modifying said control signal so that further predetermined volumes disposed outside of previously excited regions are excited, said generating means generating said control signal for said at least a second time within a predetermined period after said first control signal generation so that the last predetermined volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation.

64. Apparatus as in claim 35, 36, 37, 39, 42, 53 or 62 wherein said relative density is selected from the group consisting of relative normal density, T₁ modified relative density, and T₂ modified relative density.

36. In apparatus for determining the relative densities of nuclei within an object, said apparatus comprising:

(1) means, responsive to a first control signal for selectively exciting a predetermined volume by exciting intersecting regions within said object, said predetermined volume defined by the intersection of said regions, to produce spin echo signals;

(2) means, responsive to a second control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

(3) means for generating said first and second control signals, the improvement wherein said generating means further comprises;

means for repetitively generating said first and second control signals in sequence, said generating means including;

first means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying said first control signal so that at said plurality of occasions further regions defining further predetermined volumes disposed outside of previously excited regions are excited, said first means generating said first control signal at said plurality of occasions within a period after said first control signal generation so that the last region excitation occurs within the spin-lattice relaxation time of the first predetermined volume excited, and

second means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying said first control signal so that said second means excites, at the first occasion of the generation of said first control signal, at least one of said regions defining said predetermined volume first excited by said first means, said second means excites, at said plurality of occasions, further regions defining further predetermined volumes disposed outside of regions previously excited in response to control signals generated by said second means, said second means generating said first control signal at said plurality of occasions within a period after said first first control signal generation by said second means so that the last region excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

60. Apparatus as in claim 36, 45 or 53 further comprising means for initially aligning said spins in said object.

62. Apparatus as in claim 36, 37, 53 or 60 wherein said spin-lattice relaxation time is five T₁.

37. Apparatus for generating a detectable signal related to the relative densities of nuclei within an object, the apparatus comprising:

means, responsive to a control signal, for selectively exciting a predetermined volume by exciting intersecting regions of said object, said predetermined volume defined by the intersection of said regions to produce a subsequent NMR response; and

means for repetitively generating said control signal a first and at least a second time, said generating means including means for modifying said control signal so that none of said predetermined volumes are disposed within previously excited regions, said generating means generating said control signal for said at least a second time within a predetermined period after said first control signal generation so that the last predetermined volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation.

38. Apparatus for generating a detectable signal related to the relative densities of nuclei within an object, said apparatus comprising:

means, responsive to a control signal, for selectively exciting a first predetermined volume by exciting intersecting regions in said object, said first predetermined volume defined by the intersection of said regions to produce a subsequent NMR response;

said

means for repetitively generating said control signal, said generating means including;

first means for generating said control signal at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying said control signal so that at said plurality of occasions further predetermined volumes disposed outside of previously excited regions are excited, said first means generating said control signal at said plurality of occasions within a period after said first control signal generation so that the last region excitation occurs within the spin-lattice relaxation time of said first predetermined volume, and

second means for generating said control signal at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying said control signal so that said second means excites, at the first occasion of the generation of said control signal, at least one of said regions defining said first predetermined volume, and said second means excites, at said plurality of occasions, further predetermined volumes disposed outside of planar volumes previously excited in response to said control signals generated by said second means, said second means generating said control signal at said plurality of occasions within a period after said first control signal generation by said second means so that the last region excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

40. Apparatus for generating a detectable signal related to the relative densities of nuclei within an object, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one region to produce an NMR response;

means, responsive to a second control signal, for reversing the nuclear spins of atoms in another region at a predetermined time, thereafter, the intersection of said one and another regions defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo signal centered in time at a point after said phase reversal equal to said predetermined time; and

means for repetitively generating said first and second control signals in sequence a first and at least a second time, said generating means including means for modifying said control signals so that said predetermined volumes are disposed outside of previously excited regions, said generating means generating said control signals for said at least a second time within a predetermined period after said first second control signal generation so that the last predetermined volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation.

41. Apparatus for generating a detectable signal related to the relative densities of nuclei within an object, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one region;

means, responsive to a second control signal, for reversing the nuclear spins of nuclei in another region within said object transverse to said one region at a predetermined time interval thereafter, the intersection of said one and another regions defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval; and

means for repetitively generating said first and second control signals in sequence, said generating means including;

first means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying said first and second control signals so that at said plurality of occasions, further regions defining predetermined volumes disposed outside of previously excited regions are excited, said first means generating said first and second control signals at said plurality of occasions within a period after said first second control signal generation so that the last region excitation occurs within the spin-lattice relaxation time of said another region, and

second means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying said first and second control signals so that said second means excites, at the first occasion of the generation of said first and second control signals, at least one of said one and another regions, and said second means excites, at said plurality of occasions further regions defining further predetermined volumes disposed outside of regions previously excited in response to control signals generated by said second means, said second means generating said first second control signal at said plurality of occasions within a period after said first and second control signals generation by said second means so that the last region excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

42. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

means, responsive to a second control signal, for reversing the nuclear spins of atoms in another planar volume at a predetermined time thereafter, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo signal centered in time at a point after said phase reversal equal to said predetermined time;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

means for repetitively generating said first, second and third control signals in sequence a first and at least a second time, said generating means including means for modifying said first and second control signals so that said predetermined volumes are disposed outside of previously excited planar volumes, said generating means generating said first and second control signals for said at least a second time within a predetermined period after said first second control signal generation so that the last predetermined volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation.

45. Apparatus as in claim 42 or 43 wherein said exciting means further comprises means for exciting planar volumes defining predetermined volumes, each of said planar volumes defining each predetermined volume not being orthogonal with the other of said planar volumes defining each predetermined volume.

58. Apparatus as in claim 45 or 53 wherein said first predetermined angle is 90°

and said second predetermined angle is 180°

.

43. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

means, responsive to a second control signal, for reversing the nuclear spins of nuclei in another planar volume within said object transverse to said one planar volume at a predetermined time interval thereafter, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

means for repetitively generating said first, second and third control signals in sequence, said generating means including;

first means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying said first and second control signals so that at said plurality of occasions further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said first means generating said first second control signals at said plurality of occasions within a period after said first and second control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume, and

second means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying said first and second control signals so that said second means excites at the first occasion of the generation of said first and second control signals, at least one of said one and another planar volumes, and said second means excites, at said plurality of occasions, further planar volumes defining further predetermined volumes disposed outside of planar volumes previously excited in response to control signals generated by said second means, said second means generating said first and second control signals at said plurality of occasions within a period after said first second control signal generation by said second means so that the last planar volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

59. Apparatus as in claim 43 or 53 wherein each of said means for exciting further comprises:

means for generating a carrier having a predetermined frequency;

means for controllably modulating said carrier to have predetermined frequency range;

means for generating a position variant magnetic field having a predetermined strength in the excited planar volume and only in the excited planar volume, said predetermined strength causing nuclei in said planar volume to assume a Larmor frequency range equal to the frequency range of said modulated carrier; and

means for irradiating said sample with said modulated carrier.

44. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

means, responsive to a second control signal, for selectively exciting another planar volume transverse to said one planar volume at a predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echo signals at times in accordance with said predetermined time interval;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume; and

means for repetitively generating said first, second and third control signals in sequence a first time and at least a second time after said first time, said generating means including means for modifying said first and second control signals so that further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said generating means generating said first and second control signals for said at least a second time within a predetermined period after said first and second control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume.

46. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

means, responsive to a second control signal, for selectively exciting another planar volume transverse to said one planar volume, at a first predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one and another planar volumes defining a first predetermined volume, whereby the nuclei within said first predetermined volume thereafter generate first spin echo signals at times in accordance with said first predetermined time interval;

means, responsive to a third control signal, for detecting the intensity of said first spin echo signals to obtain an indication of the relative density of nuclei in said first predetermined volume; and

means for repetitively generating said first, second and third control signals in sequence, said generating means including;

first means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying said first and second control signals so that at said plurality of occasions further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said first means generating said first second control signals at said plurality of occasions within a period after said first second control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume, and

second means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying said first and second control signals so that said second means excites, at the first occasion of the generation of said first and second control signals, at least one of said one and another planar volumes, and said second means excites, at said plurality of occasions, further planar volumes defining further predetermined volumes disposed outside of planar volumes previously excited in response to control signals generated by said second means, said second means generating said first and second control signals at said plurality of occasions within a period after said first second control signal generation by said second means so that the last planar volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

47. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins and Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for generating a position variant magnetic field across said object, said field having an intensity varying as a function of position along a first direction whereby nuclei in one planar volume perpendicular to said first direction assume nuclear spins at Larmor frequencies within a first predetermined range;

means responsive to a second control signal, for selectively irradiating said object with an electromagnetic signal having a frequency spectrum substantially consisting of components within said first predetermined range and an amplitude and duration to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle;

means, responsive to a third control signal, for generating a position variant magnetic field across said object, said field having an intensity varying as a function of position along a second direction transverse to said first direction whereby nuclei in another planar volume perpendicular to said second direction assume nuclear spins at Larmor frequencies within a second predetermined range;

means, responsive to a fourth control signal, for selectively irradiating said object with an electromagnetic signal having a frequency spectrum substantially consisting of components within said second predetermined range, said electromagnetic signal having an amplitude and duration to nutate spins of nuclei in said another planar volume by a second predetermined angle at a predetermined time interval after said second control signal responsive irradiation, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume thereafter generate spin echoes at times in accordance with said predetermined time interval;

means, responsive to a fifth control signal, for detecting the intensity of said spin echo signals to obtain a measure of the density of nuclei in said predetermined volume; and

means for repetitively generating said first, second, third, fourth and fifth control signals in sequence a first time and at least a second time after said first time, said generating means including means for modifying at least one of said first and second control signals and at least one of said third and fourth control signals so that further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said generating means generating said second and fourth control signals for said at least a second time within a predetermined period after said first fourth control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume.

48. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

disposing said object in an intense magnetic field to align the nuclear spins of nuclei in accordance with a first predetermined direction;

means, responsive to a first control signal, for generating, during a first predetermined time period a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said position variant magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

means, responsive to a second control signal, for irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said predetermined band such that the nuclear spins of nuclei located in one planar volume of said object are oriented by a first predetermined angle with respect to the previous orientation thereof;

means, responsive to a third control signal, for generating, during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined position transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

means, responsive to a fourth control signal, for irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volumes at a predetermined volume within said object, the nuclei located within said predetermined volume thereafter, during a third time period, generating spin echo signals at the respective Larmor frequencies thereof;

means, responsive to a fifth control signal, for generating, during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position within said predetermined volume such that the Larmor frequencies of the nuclei vary as a function of relative position within said predetermined volume;

means, responsive to a sixth control signal, for determining the relative intensity of the frequency components of said spin echo signals, each of said spin echo frequency components being indicative of the relative density of nuclei disposed at an associated position within said predetermined volume; and

means for repetitively generating said first, second, third, fourth, fifth and sixth control signals in sequence a first time and at least a second time after said first time, said generating means including means for modifying at least one of said first and second control signals and at least one of said third and fourth control signals so that further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said generating means generating said second and fourth control signals for said at least a second time within a predetermined period after said first fourth control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume.

49. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means for disposing said object in an intense magnetic field to align the nuclear spins of nuclei in accordance with a first predetermined direction;

means, responsive to a first control signal, for generating for a first predetermined time period a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said position varying magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

means, responsive to a second control signal, for irradiating said object during said first predetermined period with a first signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said predetermined band, such that the nuclear spins of nuclei located in one planar volume of said object are reoriented by a first predetermined angle with respect to the previous orientation thereof;

means, responsive to a third control signal, for generating, during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined direction transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

means, responsive to a fourth control signal, for irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a second predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volume at a predetermined volume within said object, the nuclei located at the intersection of said one and another planar volumes thereafter during a third time period, generating spin echo signals at the respective Larmor frequencies thereof;

means, responsive to a fifth control signal, for generating, during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along said predetermined volume such that the Larmor frequencies of the nuclei vary as a function of relative position along said predetermined volume;

means, responsive to a sixth control signal, for determining the relative intensity of the frequency components of said spin echo signals, each of said spin echo signal frequency components being indicative of the relative density of nuclei disposed at an associated position along said predetermined volume; and

means for repetitively generating said first, second, third, fourth, fifth and sixth control signals in sequence, said generating means including;

first means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a first time segment, said first means including means for modifying at least one of said first and second control signals, and at least one of said third and fourth control signals so that at said plurality of occasions further planar volumes defining further predetermined volumes disposed outside of previously excited planar volumes are excited, said first means generating said second and fourth control signals at said plurality of occasions within a period after said first fourth control signal generation so that the last planar volume excitation occurs within the spin-lattice relaxation time of said another planar volume, and

second means for generating said control signals at a first occasion and at a plurality of occasions after said first occasion during a second time segment after said first time segment, said second means including means for modifying at least one of said first and second control signals and at least one of said third and fourth control signals so that said second means excites, at the first occasion of the generation of said second and fourth control signals, at least one of said one and another planar volumes, and, said second means excites, at said plurality of occasions, further planar volumes defining further predetermined volumes disposed outside of planar volumes previously excited in response to control signals generated by said second means, said second means generating said second and fourth control signals at said plurality of occasions within a period after said first fourth control signal generation by said second means so that the last planar volume excitation occurs within the spin-lattice relaxation time of the first predetermined volume excitation in response to control signals generated by said second means.

51. Apparatus as in claim 49 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field having a predetermined intensity in said one region and only in said one region, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to cause nutation only in said one region;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the strength of said field having a predetermined value in said another region, and only in said another region, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause nutation only in said another region;

said generating means generates said control signals a first time and a second time and further comprises means for altering said first and second control signals so that the phase of said first electromagnetic signal said first time produces an FID having a positive polarity, the phase of said second electromagnetic signal said first time is 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity, the phase of said first electromagnetic signal said second time is 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity and the phase of said second electromagnetic said second time is 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity; and

said combining means further comprises means for adding corresponding portions of said spin echo signals so that said FID components cancel and said spin echo components do not cancel.

52. Apparatus as in claim 49 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said field having a predetermined value in said one region, and only in said one region, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to produce said nutation of nuclei only in said one region;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined value in said another region, and only in said another region, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause nutation of nuclei only in said another region;

said control signal generates said generating means control signals a first, second, third and fourth time and further comprises;

means for altering said first control signal said first time to generate said first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said first time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said second time to generate said first electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said second time to generate said second electromagnetic signal having a phase of 270°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said third time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity,

means for altering said second control signal said third time to generate said second electromagnetic signal having a phase of 0°

of with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said fourth time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity, and

means for altering said second control signal said fourth time to generate said second electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity; and

said combining means further comprises means for adding corresponding portions of said spin echo signals so that said FID components of said spin echo signals cancel while said spin echo components of said spin echo signals do not cancel.

53. Apparatus as in claim 49 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said field having a predetermined value in said one region, and only in said one region, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to produce said nutation of nuclei only in said one region;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined value in said another region, and only in said another region, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation of nuclei only in said another region;

said generating means generates said control signals first, second, third and fourth times and further comprises;

means for altering said first control signal said first time to generate said first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said first time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said second time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity,

means for altering said second control signal said second time to generate said second electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said third time to generate said first electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said third time to generate said second electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a negative polarity,

means for altering said first control signal said fourth time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity, and

means for altering said second control signal said fourth time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a negative polarity; and

said combining means further comprises;

means for adding corresponding portions of the spin echo signals detected said first and second times to produce a first composite signal wherein said FID components cancel while said spin echo components do not cancel,

means for adding corresponding portions of the spin echo signals detected in said third and fourth times to produce a second composite signal wherein said FID components cancel and said spin echo components do not cancel, and

means for subtracting corresponding portions of said first composite signal from corresponding portions of said second composite signal to produce a signal having no FID component and a spin echo component.

55. Apparatus as in claim 53 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field having a predetermined intensity in said one planar volume and only in said one planar volume, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to cause said nutation only in said one planar volume;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the strength of said field having a predetermined value in said another planar volume, and only in said another planar volume, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation only in said another planar volume;

said generating means generates said control signals a first time and a second time and further comprises means for altering said first and second control signals so that the phase of said first electromagnetic signal said first time produces an FID having a positive polarity, the phase of said second electromagnetic signal said first time is 90°

with respect to said first electromagnetic signal to produce a spin echo having a positive polarity, the phase of said first electromagnetic signal said second time is 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity, and the phase of said second electromagnetic said second time is 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity; and

said combining means further comprises means for adding corresponding portions of said spin echo signals so that said FID components cancel and said spin echo components do not cancel.

56. Apparatus as in claim 53 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said field having a predetermined value in said one planar volume, and only in said one planar volume, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to produce said nutation of nuclei only in said one planar volume;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined value in said another planar volume, and only in said another planar volume, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation of nuclei only in said another planar volume;

said generating means generates said control signals first, second, third and fourth times and further comprises;

means for altering said first control signal said first time to generate said first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said first time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said second time to generate said first electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said second time to generate said second electromagnetic signal having a phase of 270°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said third time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity,

means for altering said second control signal said third time to generate said second electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said fourth time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity, and

means for altering said second control signal said fourth time to generate said second electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity; and

said apparatus further comprises means for adding corresponding portions of said spin echo signals so that said FID components of said spin echo signals cancel while said spin echo components of said spin echo signals do not cancel.

57. Apparatus as in claim 53 wherein:

said means responsive to said first control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said field having a predetermined value in said one planar volume, and only in said one planar volume, and

means for selectively irradiating said object with a first electromagnetic signal having a frequency range to produce said nutation of nuclei only in said one planar volume;

said means responsive to said second control signal comprises;

means for generating a position variant magnetic field across said object, the intensity of said magnetic field having a predetermined value in said another planar volume, and only in said another planar volume, and

means for irradiating said object with a second electromagnetic signal having a frequency range to cause said nutation of nuclei only in said another planar volume;

said generating means generates said control signals first, second, third and fourth times and further comprises;

means for altering said first control signal said first time to generate said first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said first time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said second time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity,

means for altering said second control signal said second time to generate said second electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a positive polarity,

means for altering said first control signal said third time to generate said first electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce an FID having a positive polarity,

means for altering said second control signal said third time to generate said second electromagnetic signal having a phase of 0°

with respect to said first time first electromagnetic signal to produce a spin echo having a negative polarity,

means for altering said first control signal said fourth time to generate said first electromagnetic signal having a phase of 180°

with respect to said first time first electromagnetic signal to produce an FID having a negative polarity, and

means for altering said second control signal said fourth time to generate said second electromagnetic signal having a phase of 90°

with respect to said first time first electromagnetic signal to produce a spin echo having a negative polarity; and

said combining means further comprises;

means for adding corresponding portions of the spin echo signals detected said first and second times to produce a first composite signal wherein said FID components cancel while said spin echo components do not cancel,

means for adding corresponding portions of the spin echo signals detected said third and fourth times to produce a second composite signal wherein said FID components cancel and said spin echo components do not cancel, and

means for subtracting corresponding portions of said first composite signal from corresponding portions of said second composite signal to produce a signal having no FID component and a spin echo component.

50. Apparatus for determining the relative densities of nuclei within an object, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one region of said object to generate for a period of time a free induction decay signal (FID) having a polarity;

means, responsive to a second control signal, for selectively exciting another region transverse to said one region, at a predetermined time interval thereafter, the intersection of said one and another regions defining a predetermined volume, to generate from said predetermined volume a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume;

means for repetitively generating said first, second and third control signals in sequence a plurality of times, said generating means including means for controlling the phases of said excitations so that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

means for combining corresponding portions of said spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

54. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle, the nuclei within said one planar volume thereafter, for a period of time, generating free a induction decay (FID) having a polarity;

means, responsive to a second control signal, for selectively exciting another planar volume transverse to said one planar volume, at a predetermined time interval thereafter, to nutate spins of nuclei in said another planar volume by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the density of nuclei in said predetermined volume;

means for repetitively generating said first, second and third control signals in sequence a plurality of times, said generating means including means for controlling the phases of said excitations so that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

means for combining corresponding portions of the spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

61. Apparatus for detecting the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for generating a first position variant magnetic field within said object, said position variant magnetic field causing the Larmor frequencies of nuclei in said object to vary as a function of the relative positions of said nuclei within said object;

means, responsive to a second control signal, for irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said nuclear Larmor frequencies, to selectively excite said nuclei in one planar volume having Larmor frequencies within said predetermined band, such that the nuclear spins of nuclei located in said one planar volume are reoriented by a first predetermined angle, the nuclei within said one planar volume thereafter generating for a period of time a free induction decay (FID) having a polarity;

means, in response to a third control signal, for generating for a second predetermined time period a second position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position, said position variant magnetic field causing Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei;

means, in response to a fourth control signal, for irradiating said object during said second predetermined period with a signal having a second frequency spectrum substantially consisting of components corresponding to a second predetermined band of said nuclei Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within another planar volume, transverse to said one planar volume, such that the nuclear spins of nuclei within said another planar volume are reoriented by a second predetermined angle, the intersection of said one and another planar volumes defining a predetermined volume, whereby the nuclei within said predetermined volume generate a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

means, responsive to a fifth control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume;

means for repetitively generating said first, second, third, fourth and fifth control signals in sequence a plurality of times, said generating means including means for controlling the phases of said irradiations so that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

means for combining corresponding portions of the spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

63. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensities of a magnetic field operating thereon, said apparatus comprising:

means, responsive to a first control signal, for selectively exciting one planar volume to nutate the nuclear spins of nuclei in said one planar volume by a first predetermined angle, the nuclei within said one planar volume thereafter generating for a period of time a free induction decay (FID) having a polarity;

means, responsive to a second control signal, for reversing the nuclear spins of nuclei in another planar volume within said object transverse to said one planar volume at a predetermined time thereafter, the intersection of said one and another planar volumes defining a predetermined volume, said predetermined volume generating a spin echo centered in time at the point after said reversal equal to said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

means, responsive to a third control signal, for detecting the intensity of said spin echo signals to obtain a measure of the relative density of nuclei in said predetermined volume;

means, for repetitively generating said first, second and third control signals in sequence a plurality of times, said generating means including means for controlling the phases of said excitations and reversals so that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

means for combining corresponding portions of said spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.

65. Apparatus for determining the relative densities of nuclei within an object, said nuclei having nuclear spins at Larmor frequencies in accordance with the intensity of a magnetic field operating thereon, said apparatus comprising:

means for disposing said object in an intense magnetic field to align the nuclear spins of said nuclei in accordance with a first predetermined direction;

means, responsive to a first control signal, for generating for a first predetermined time period a first position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with position along a second predetermined direction, said position variant magnetic field causing the Larmor frequencies of said nuclei to vary as a function of the relative positions of said nuclei along said second predetermined direction;

means, responsive to a second control signal, for irradiating said object during said first predetermined period with a signal having a first frequency spectrum substantially consisting of components corresponding to a first predetermined band of said nuclei Larmor frequencies, to selectively excite said nuclei having Larmor frequencies within said predetermined bands, such that nuclear spins of nuclei located in one planar volume in said object are reoriented by a first predetermined angle with respect to the previous orientation thereof, the nuclei within said first predetermined plane thereafter generating for a period of time a free induction decay (FID) having a polarity;

means, responsive to a third control signal, for generating during a second predetermined time period subsequent to said first time period, a second position variant magnetic field to vary the magnetic field within said object in accordance with position along a third predetermined direction transverse to said second predetermined direction such that the Larmor frequencies of the nuclear spins of said nuclei within said object vary as a function of the relative position of said nuclei along said third predetermined direction;

means, responsive to a fourth control signal, for irradiating said object during said second predetermined time period with a second signal having a second frequency spectrum substantially consisting of frequency components corresponding to a second predetermined band of Larmor frequencies such that the nuclear spins of nuclei located in another planar volume are reoriented by a second predetermined angle with respect to the previous orientation thereof, said another planar volume intersecting said one planar volume at a predetermined volume within said object, the nuclei located in said predetermined volume thereafter, during a third time period, generating a spin echo at a time in accordance with said predetermined time interval and within said period of time so that said FID interferes with said spin echo to produce a spin echo signal having a polarity and an FID component and a spin echo component;

means, responsive to a fifth control signal, for generating during said third time period a third position variant magnetic field to vary the intensity of the magnetic field within said object in accordance with the position within said predetermined volume such that the Larmor frequencies of the nuclei vary as a function of relative position within said predetermined volume;

means, responsive to a sixth control signal, for determining the relative intensity of the frequency components of said spin echo signals, each of said spin echo signal frequency components being indicative of the relative density of nuclei disposed and an associated position within said predetermined volume;

means for repetitively generating said first, second, third, fourth, fifth and sixth control signals in sequence a plurality of times, said generating means including means for controlling the phases of said irradiations so that an arithmetic combination of the polarities of said FIDs is zero, and said arithmetic combination of the polarities of said spin echoes is not zero; and

means for combining corresponding portions of said spin echo signals with said arithmetic combination so that said FID components cancel while said spin echo components do not cancel.