Methods of using combined forward and backward sampling of nuclear magnetic resonance time domain for measurement of secondary phase shifts, detection of absorption mode signals devoid of dispersive components, and/or optimization of nuclear magnetic resonance experiments
View Patent ↗The present invention relates to a method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by the use of forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure time domain amplitudes and secondary phase shifts. The present invention also relates to methods of conducting an N-dimensional NMR experiment in a phase-sensitive manner by the use of dual forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image signal components arising in the frequency domain from secondary phase shifts.
1. A method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by use of forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure time domain amplitudes and secondary phase shifts, said method comprising:
providing a sample;
applying radiofrequency pulses for an N-dimensional NMR experiment to said sample;
selecting m dimensions of said NMR experiment, wherein m≦N;
sampling a time domain modulation in a phase-sensitive manner in each selected dimension jε[1,2, . . . , m] arising from time evolution of chemical shift α j in both a forward and backward manner to obtain two interferograms for each time domain dimension t j defining the vector
C
j
,
ψ
j
(
t
j
)
:=
[
I
j
,
ψ
j
+
c
ψ
j
+
(
t
j
)
I
j
,
ψ
j
,
δ
j
-
c
ψ
j
,
δ
j
-
(
t
j
)
]
=
[
I
j
,
ψ
j
+
cos
(
ψ
j
+
α
j
t
j
+
Φ
j
,
ψ
j
+
)
I
j
,
ψ
j
,
δ
j
-
cos
(
ψ
j
+
δ
j
-
α
j
t
j
+
Φ
j
,
ψ
j
,
δ
j
-
)
]
,
wherein
I j,ψ j + and I j,ψ j ,δ j − are amplitudes, Ψ j and Ψ j +δ j are primary phase shifts with Ψ j , δ j ε[0,2π[and the cases {ψ j =nπ/2 and δ j =mπ} with n=0, 1, 2, 3 and m=0, 1 being omitted, and Φ j,ψ j + and Φ j,ψ j ,δ j − are secondary phase shifts;
multiplying each said vectors C j,ψ j t j ) with a D-matrix defined as
D
j
=
[
sin
(
ψ
j
+
δ
j
)
sin
(
ψ
j
)
-
cos
(
ψ
j
+
δ
j
)
cos
(
ψ
j
)
]
and a vector Q=[1 i], wherein i=√{square root over (−1)}, according to Q·D j ·C j,ψ j t j ) under conditions effective to create a complex time domain of said selected m dimensions according to
⊗
j
Q
·
D
j
·
C
j
,
ψ
j
(
t
j
)
;
and
transforming said complex time domain into frequency domain by use of an operator O under conditions effective to measure the values of I j,ψ j + , I j,ψ j ,δ j − , Φ j,ψ j + and Φ j,ψ j ,δ j − in said frequency domain in order to generate NMR spectra comprising frequency domain signals.
2. The method according to claim 1 , wherein said operator is a linear operator L.
3. The method according to claim 2 , wherein said linear operator is the Fourier transformation operator F.
4. The method according to claim 2 , wherein said vectors C j,ψ j (t j ) are transformed into frequency domain using said linear operator L under conditions effective to yield frequency domain vector L [C j,ψ j (t j )], and said multiplying comprises:
multiplying L [C j,ψ j (t j )] with said matrix D j and said vector Q according to Q·D j ·L[C j,ψ j (t j )] under conditions effective to generate said frequency domain according to
⊗
j
Q
·
D
j
·
L
[
C
j
,
ψ
j
(
t
j
)
]
.
5. The method according to claim 1 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =π/4 and δ j =0} or {Ψ j =3π/4 and δ j =0}.
6. The method according to claim 5 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive components.
7. The method according to claim 1 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =0 and δ j =π/2}, or {Ψ j =π/2 and δ j =3π/2}.
8. The method according to claim 7 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain located at (α 1 , α 2 , . . . α m ) are purely absorptive and devoid of dispersive components.
9. The method of claim 1 , wherein m′ dimensions of said selected m dimensions with m′≦m are jointly sampled according to t=t 1 /κ 1 =t 2 /κ 2 = . . . =t m ′/κ m ′, wherein κ m′ are scaling factors for time evolution in the jointly sampled dimensions, under conditions effective to conduct a G-matrix Fourier Transformation NMR experiment, wherein said multiplication with said vector Q is replaced for K=m′−1 of the m′ jointly sampled dimensions by multiplication with matrix G defined as
G
=
[
1
ⅈ
1
-
ⅈ
]
.
10. The method according to claim 9 , wherein for all j: I j,ψ j +=I j,ψ j ,δ j − , and {Ψ j =π/4 and δ j =0} or {Ψ j =3π/4 and δ j =0}.
11. The method according to claim 10 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive signal components.
12. The method according to claim 9 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =0 and δ j =π/2}, or {Ψ j =π/2 and δ j =3π/2}.
13. The method according to claim 12 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain located at linear combinations of (α 1 , α 2 , . . . α m ) for a given sub-spectrum of the G-matrix Fourier Transformation NMR experiment are purely absorptive and devoid of dispersive signal components.
14. The method according to claim 1 , wherein said secondary phase shifts Φ j,ψ j + , and Φ j,ψ j ,δ j − encode NMR parameters other than said chemical shifts α j .
15. The method according to claim 1 , wherein said sampling a time domain modulation is combined with preservation of equivalent pathways for sensitivity enhancement.
16. The method according to claim 1 , wherein said NMR experiment is a TROSY NMR experiment.
17. The method according to claim 1 , wherein said sampling a time domain modulation is accomplished by use of simultaneous phase cycled NMR.
18. The method according to claim 1 , wherein said interferograms are obtained by recording P- and N-type time domain by use of pulsed magnetic field gradients followed by linear combination effective to generate said interferograms.
19. A method of optimizing an N-dimensional nuclear magnetic resonance (NMR) experiment comprising:
measuring values of secondary phase shifts Φ j,ψ j + and Φ j,ψ j ,δ j − in a first N-dimensional NMR experiment according to the method of claim 1 ;
identifying an origin of the secondary phase shifts Φ j,ψ j + and Φ j,ψ j ,δ j − in the first N-dimensional NMR experiment; and
modifying a radio frequency pulse scheme of a second N-dimensional NMR experiment under conditions effective to at least partially eliminate the origin of the secondary phase shifts Φ j,ψ j + and Φ j,ψ j ,δ j − and at least partially eliminate said secondary phase shifts Φ j,ψ j + and Φ j,ψ j ,δ j − .
20. A method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by use of dual forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image signal components arising in a frequency domain from secondary phase shifts, said method comprising:
providing a sample;
applying radiofrequency pulses for an N-dimensional NMR experiment to said sample;
selecting m dimensions of said NMR experiment, wherein m≦N;
sampling a time domain modulation in a phase-sensitive manner in each said selected dimension j ε[1,2, . . . , m] arising from time evolution of chemical shift α j in both a forward and backward manner to obtain two interferograms for each time domain dimension t j defining the vector
C
j
,
ψ
j
(
t
j
)
:=
[
I
j
,
ψ
j
+
c
ψ
j
+
(
t
j
)
I
j
,
ψ
j
,
δ
j
-
c
ψ
j
,
δ
j
-
(
t
j
)
]
=
[
I
j
,
ψ
j
+
cos
(
ψ
j
+
α
j
t
j
+
Φ
j
,
ψ
j
+
)
I
j
,
ψ
j
,
δ
j
-
cos
(
ψ
j
+
δ
j
-
α
j
t
j
+
Φ
j
,
ψ
j
,
δ
j
-
)
]
,
wherein
I j,ψ j + and I j,ψ j ,δ j − are amplitudes, Ψ j and Ψ j +δ j are primary phase shifts with Ψ j , δ j ε[0,2π[and the cases {ψ j =nπ/2 and δ j =mπ} with n=0, 1, 2, 3 and m=0, 1 being omitted, and Φ j,ψ j + and Φ j,ψ j ,δ j − are secondary phase shifts;
multiplying each said vectors C j,ψ j (t j ) with a D-matrix defined as
D
j
=
[
sin
(
ψ
j
+
δ
j
)
sin
(
ψ
j
)
-
cos
(
ψ
j
+
δ
j
)
cos
(
ψ
j
)
]
and a vector Q=[1 i], wherein i=√{square root over (−1)}, according to Q·D j ·C j,ψ j (t j ) under conditions effective to create a complex time domain of said selected m dimensions according to
⊗
j
Q
·
D
j
·
C
j
,
ψ
j
(
t
j
)
;
repeating said selecting, said sampling and said multiplying (2 m −1)-times, thereby sampling the m dimensions with all 2 m possible permutations resulting from selecting for each dimension j either Ψ j or Ψ j +π/2, with δ j being incremented by either 0 or π, thereby yielding 2 m complex time domains;
linearly combining said 2 m complex time domains: and
transforming said linearly combined complex time domain into frequency domain by use of an operator O, under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image peak components arising from Φ j,ψ j + and Φ j,ψ j ,δ j − in said frequency domain in order to generate NMR spectra comprising frequency domain signals.
21. The method according to claim 20 , wherein said transforming comprises measuring the values of I j,ψ j + , I j,ψ j ,δ j − , Φ j,ψ j + and Φ j,ψ j ,δ j − in said frequency domain.
22. The method according to claim 20 , wherein said operator is a linear operator L.
23. The method according to claim 22 , wherein said linear operator is the Fourier transformation operator F.
24. The method according to claim 22 , wherein said vectors C j,ψ j (t j ) are transformed into frequency domain using said linear operator L under conditions effective to yield frequency domain vector L[C j,ψ j (t j )], and said multiplying comprises:
multiplying L[C j,ψ j (t j )] with said matrix D j and said vector Q according to Q·D j ·L[C j,ψ j (t j )] under conditions effective to generate said frequency domain according to
⊗
j
Q
·
D
j
·
L
[
C
j
,
ψ
j
(
t
j
)
]
.
25. The method according to claim 20 , wherein for all j: I j,ψ j + =I j,ψ j, δ j − , and {Ψ j =π/4 and δ j =0} or {Ψ j =3π/4 and δ j =0}.
26. The method according to claim 25 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive components.
27. The method according to claim 25 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive components, and quadrature image peaks in said frequency domain are cancelled.
28. The method according to claim 20 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =0 and δ j =π/2}, or {Ψ j =π/2 and δ j =3π/2}.
29. The method according to claim 28 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain located at (α 1 , α 2 , . . . α m ) are purely absorptive and devoid of dispersive components.
30. The method according to claim 28 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain located at (α 1 , α 2 , . . . , α m ) are purely absorptive and devoid of dispersive components, and quadrature image peaks in said frequency domain are cancelled.
31. The method according to claim 20 , wherein m′ dimensions of said selected m dimensions with m′≦m are jointly sampled according to t=t 1 /κ 1 =t 2 /κ 2 = . . . =t m ′/κ m ′, wherein κ m′ are scaling factors for the time evolution in the jointly sampled dimensions under conditions effective to conduct a G-matrix Fourier Transformation NMR experiment, wherein said multiplication with said vector Q is replaced for K=m′−1 of the m′ jointly sampled dimensions by multiplication with matrix G defined as
G
=
[
1
ⅈ
1
-
ⅈ
]
.
32. The method according to claim 31 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =π/4 and δ j =0} or {Ψ j =3π/4 and δ j =0}.
33. The method according to claim 32 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive signal components.
34. The method according to claim 32 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive signal components, and quadrature image and cross talk peaks in said frequency domain are cancelled.
35. The method according to claim 31 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j − , and {Ψ j =0 and δ j =π/2}, or {Ψ j =π/2 and δ j =3π/2}.
36. The method according to claim 35 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain located at linear combinations of (α 1 , α 2 , . . . α m ) for a given sub-spectrum of the GFT NMR experiment are purely absorptive and devoid of dispersive signal components.
37. The method according to claim 35 , wherein Φ j,ψ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain located at linear combinations of (α 1 , α 2 , . . . α m ) for a given sub-spectrum of the GFT NMR experiment are purely absorptive and devoid of dispersive signal components, and quadrature image and cross talk peaks in said frequency domain are cancelled.
38. The method according to claim 20 , wherein said permutation of said secondary phase shifts is concatenated with execution of a radio-frequency phase cycle.
39. The method according to claim 38 , wherein said NMR experiment is conducted under conditions of magic angle spinning of said sample.
40. The method according to claim 38 , wherein said phase cycle is executed to suppress signals arising from axial magnetization.
41. The method according to claim 38 , wherein said phase cycle is executed to reduce signal arising from solvent.
42. The method according to claim 20 , wherein said sampling a time domain modulation is combined with preservation of equivalent pathways for sensitivity enhancement.
43. The method according to claim 20 , wherein said NMR experiment is a TROSY NMR experiment.
44. The method according to claim 20 , wherein said sampling a time domain modulation is accomplished by use of simultaneous phase cycled NMR.
45. The method according to claim 20 , wherein said interferograms are obtained by recording P- and N-type time domain by use of pulsed magnetic field gradients followed by linear combination effective to generate said interferograms.
46. A method of conducting an N-dimensional nuclear magnetic resonance (NMR) experiment in a phase-sensitive manner by use of dual forward and backward sampling of time domain shifted by a primary phase shift under conditions effective to measure secondary phase shifts or at least partially cancel dispersive and quadrature image signal components arising in a frequency domain from secondary phase shifts, said method comprising:
providing a sample;
applying radiofrequency pulses for an N-dimensional NMR experiment to said sample;
selecting m dimensions of said NMR experiment, wherein m≦N;
sampling twice a time domain modulation in a phase-sensitive manner in each said selected dimension jε[1,2, . . . , m] arising from time evolution of chemical shift α j , once in a forward manner to obtain two interferograms for each time domain dimension
t j defining the vector
C
j
,
ψ
j
+
(
t
j
)
=
[
I
j
,
ψ
j
+
c
ψ
j
+
(
t
j
)
I
j
,
ψ
j
,
δ
j
+
c
ψ
j
,
δ
j
+
(
t
j
)
]
=
[
I
j
,
ψ
j
+
cos
(
ψ
j
+
α
j
t
j
+
Φ
j
,
ψ
j
+
)
I
j
,
ψ
j
,
δ
j
+
cos
(
ψ
j
+
δ
j
+
α
j
t
j
+
Φ
j
,
ψ
j
,
δ
j
+
)
]
,
and once in a backward manner to obtain two interferograms for each time domain dimension t j defining the vector
C
j
,
ψ
j
-
(
t
j
)
:=
[
I
j
,
ψ
j
-
c
ψ
j
-
(
t
j
)
I
j
,
ψ
j
,
δ
j
-
c
ψ
j
,
δ
j
-
(
t
j
)
]
=
[
I
j
,
ψ
j
-
cos
(
ψ
j
-
α
j
t
j
+
Φ
j
,
ψ
j
-
)
I
j
,
ψ
j
,
δ
j
-
cos
(
ψ
j
+
δ
j
-
α
j
t
j
+
Φ
j
,
ψ
j
,
δ
j
-
)
]
,
wherein I j,ψ j + , I j,ψ j, δ j + , I j,ψ j − and I j,ψ j, δ j − are amplitudes, Ψ j and Ψ j +δ j are primary phase shifts with Ψ j , δ j ε[0,2π[, and Φ j,ψ j + , Φ j,ψ j ,δ j + , Φ j,ψ j − and Φ j,ψ j ,δ j − are secondary phase shifts;
multiplying each said vector C j,ψ j + (t j ) with a D-matrix defined as
D
j
+
=
[
sin
(
ψ
j
+
δ
j
)
-
sin
(
ψ
j
)
cos
(
ψ
j
+
δ
j
)
-
cos
(
ψ
j
)
]
and each said vector C j,ψ j − (t j )with a D-matrix defined as
D
j
-
=
[
sin
(
ψ
j
+
δ
j
)
-
sin
(
ψ
j
)
-
cos
(
ψ
j
+
δ
j
)
cos
(
ψ
j
)
]
;
multiplying the said products D j + ·C j,ψ j + (t j ) and D j − ·C j,ψ j − (t j ) with a vector Q=[1 i], wherein i=√{square root over (−1)}, according to Q·D j + ·C j,ψ j + (t j ) and Q·D j − ·C j,ψ j − (t j )under conditions effective to create a complex time domain of said selected m dimensions according to
⊗
j
Q
·
D
j
+
·
C
j
,
ψ
j
+
(
t
j
)
and
⊗
j
Q
·
D
j
-
·
C
j
,
ψ
j
-
(
t
j
)
;
repeating said selecting, said phase-sensitive sampling twice and said multiplying (2 m −2)-times, thereby sampling said m dimensions with all 2 m possible permutations resulting from selecting for each dimension j either phase-sensitive forward or backward sampling according to C j,ψ j + (t j ) or C j,ψ j − (t j );
linearly combining said 2 m complex time domains; and
transforming said linearly combined complex time domain into frequency domain by use of an operator O, under conditions effective to measure secondary phase shift or at least partially cancel dispersive and quadrature image peak components arising from Φ j,ψ j + , Φ j,ψ j ,δ j + , Φ j,ψ j − and Φ j,ψ j ,δ j − in said frequency domain in order to generate NMR spectra comprising frequency domain signals.
47. The method according to claim 46 , wherein said sampling in a phase sensitive manner comprises excluding {ψ j =nπ/2 and δ j =mπ} with n=0, 1, 2, 3 and m=0, 1.
48. The method according to claim 46 , wherein said sampling in a phase sensitive manner for {ψ j =nπ/2 and δ j =mπ} with n=0, 1, 2, 3 and m=0, 1 comprises applying time-proportional phase incrementation of radio-frequency pulse or receiver phases.
49. The method according to claim 46 , wherein said transforming comprises measuring the values of I j,ψ j + , I j,ψ j ,δ j − , Φ j,ψ j + and Φ j,ψ j ,δ j − in said frequency domain.
50. The method according to claim 46 , wherein said operator is a linear operator L.
51. The method according to claim 50 , wherein said linear operator is the Fourier transformation operator F.
52. The method according to claim 50 , wherein said vectors C j,ψ j + (t j ) and C j,ψ j − (t j ) are transformed into frequency domain using said linear operator L under conditions effective to yield frequency domain vectors L[C j,ψ j + (t j )] and L[C j,ψ j − (t j )], and said multiplying comprises:
multiplying said vector L[C j,ψ j + (t j )] with said matrix D j + and said vector L [C j,ψ j − (t j )] with said matrix D j − ; and
multiplying said products D j + ·L [C j,ψ j + (t j )] and D j − ·L [C j,ψ j − (t j )] with said vector Q according to Q·D j + ·L[C j,ψ j + (t j )] and Q·D j − ·L[C j,ψ j − (t j )] under conditions effective to generate said frequency domain according to
⊗
j
Q
·
D
j
+
·
L
[
C
j
,
ψ
j
+
(
t
j
)
]
and
⊗
j
Q
·
D
j
-
·
L
[
C
j
,
ψ
j
-
(
t
j
)
]
.
53. The method according to claim 46 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j + =I j,ψ j − =I j,ψ j ,δ j − , and {ψ j =0 and δ j =π/2}.
54. The method according to claim 53 , wherein Φ j,ψ j + =Φ j,ψ j − =Φ j,ψ j and Φ j,ψ j ,δ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive components.
55. The method according to claim 53 , wherein Φ j,ψ j + =Φ j,ψ j − =Φ j,ψ j ,δ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive components, and quadrature image peaks in said frequency domain are entirely cancelled.
56. The method according to claim 46 , wherein m′ dimensions of said selected m dimensions with m′≦ m are jointly sampled according to t=t 1 /κ 1 =t 2 /κ 2 = . . . =t m ′/κ m ′, wherein κ m′ are the scaling factors for the time evolution in the jointly sampled dimensions, effective to conduct a G-matrix Fourier Transformation NMR experiment, wherein said multiplication with said vector Q is replaced for K=m′−1 of the m′ jointly sampled dimensions by multiplication with matrix G defined as
G
=
[
1
ⅈ
1
-
ⅈ
]
.
57. The method according to claim 56 , wherein for all j: I j,ψ j + =I j,ψ j ,δ j + =I j,ψ j − =I j,ψ j ,δ j − , and {ψ j =0 and δ j =π/2}.
58. The method according to claim 57 , wherein Φ j,ψ j + =Φ j,ψ j − =Φ j,ψ j and Φ j,ψ j ,δ j + =Φ j,ψ j ,δ j − =Φ j,ψ j ,δ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive signal components.
59. The method according to claim 57 , wherein Φ j,ψ j + =Φ j,ψ j − =Φ j,ψ j ,δ j + =Φ j,ψ j ,δ j − =Φ j , so that signals in said frequency domain are purely absorptive and devoid of dispersive signal components, and quadrature image and cross talk peaks in said frequency domain are entirely cancelled.
60. The method according to claim 46 , wherein said permutation of said secondary phase shifts is concatenated with execution of a radio-frequency phase cycle.
61. The method according to claim 60 , wherein said NMR experiment is conducted under conditions of magic angle spinning of said sample.
62. The method according to claim 60 , wherein said phase cycle is executed to suppress signals arising from axial magnetization.
63. The method according to claim 60 , wherein said phase cycle is executed to reduce signal arising from solvent.
64. The method according to claim 46 , wherein said sampling a time domain modulation is combined with preservation of equivalent pathways for sensitivity enhancement.
65. The method according to claim 46 , wherein said NMR experiment is a TROSY NMR experiment.
66. The method according to claim 46 , wherein said sampling a time domain modulation is accomplished by use of simultaneous phase cycled NMR.
67. The method according to claim 46 , wherein said interferograms are obtained by recording P- and N-type time domain by use of pulsed magnetic field gradients followed by linear combination effective to generate said interferograms.