1 Single-Sided NMR ............................................. 1
Federico Casanova, Juan Perlo, and Bernhard Blümich
1.1 Development of Open NMR Sensors ......................... 2
1.1.1 Well-Logging Tools ............................... 2
1.1.2 Mobile Single-Sided Sensors ...................... 3
1.1.3 The NMR-MOUSE .................................... 4
1.2 Methods for Mobile NMR .................................. 6
References ................................................... 7
2 NMR in Inhomogeneous Fields ................................. 11
Federico Casanova and Juan Perlo
2.1 Introduction ........................................... 11
2.1.1 Evolution of the Magnetization During a Pulse
Sequence ........................................ 12
2.1.2 Separation of the Magnetization into Coherence
Pathways ........................................ 14
2.1.3 Numerical Calculation of the NMR Signal ......... 20
2.2 Pulse Sequence Analysis ................................ 21
2.2.1 Single rf Pulse ................................. 21
2.2.2 The Generation of Hahn Echoes ................... 23
2.2.3 The CPMG Sequence ............................... 28
2.2.4 Inversion and Saturation Recovery ............... 35
2.2.5 Diffusion Measurements .......................... 42
2.3 The SNR in Inhomogeneous Fields ........................ 47
2.3.1 The Reciprocity Principle ....................... 48
2.3.2 Numerical Calculations of the SNR ............... 49
2.3.3 An Analytical Solution for the SNR .............. 55
References .................................................. 55
3 Ex Situ Measurement of One- and Two-Dimensional
Distribution Functions ...................................... 57
Martin D. Hürlimann
3.1 Introduction ........................................... 57
3.1.1 Relaxation ...................................... 57
3.1.2 Diffusion ....................................... 58
3.1.3 Diffusion-Relaxation Distribution Functions ..... 58
3.2 Pulse Sequences and Spin Dynamics in Inhomogeneous
Fields ................................................. 59
3.2.1 Relaxation Measurement: Carr-Purcell-Meiboom-
Gill Sequence ................................... 59
3.2.2 Diffusion Measurements with Static Gradients .... 62
3.2.3 T1 Measurements in Inhomogeneous Fields ......... 64
3.3 One-Dimensional Distribution Functions ................. 64
3.3.1 Data Inversion .................................. 65
3.3.2 Regularization .................................. 67
3.3.3 Systematic Errors ............................... 68
3.3.4 Uncertainties ................................... 68
3.4 Two-Dimensional Diffusion-Relaxation Distribution
Functions .............................................. 69
3.4.1 Two-Dimensional Diffusion-Relaxation
Measurements .................................... 69
3.4.2 Data Analysis ................................... 71
3.4.3 Interpretation of Distribution Functions ........ 73
3.5 Applications of Two-Dimensional Distribution
Functions .............................................. 74
3.5.1 Two-Component Systems ........................... 75
3.5.2 Wettability ..................................... 76
3.5.3 Complex Miscible Fluid .......................... 77
3.5.4 Structured Fluid ................................ 78
3.5.5 Pore Geometry of Porous Media ................... 79
3.6 Conclusion ............................................. 81
References .................................................. 82
4 Magnets and Coils for Single-Sided NMR ...................... 87
Juan Perlo
4.1 Magnets ................................................ 88
4.1.1 B0 Perpendicular to the Sensor Surface, the
Bar Magnet Geometry ............................. 89
4.1.2 B0 Parallel to the Sensor Surface, the
U-Shaped Geometry ............................... 93
4.1.3 Magnets for Depth Profiling ..................... 95
4.1.4 Sweet-Spot Magnets .............................. 99
4.2 RF Coils .............................................. 102
4.2.1 Coils for Depth Profiling ...................... 103
4.2.2 Coils for Sweet-Spot Magnets ................... 105
4.3 Gradient Coils ........................................ 107
References ................................................. 108
5 Single-Sided Tomography .................................... 1ll
Federico Casanova
5.1 Depth Resolution Using the Static Field Gradient ...... 1ll
5.2 Spatial Encoding by Fourier Imaging ................... 113
5.3 Multi-Echo Acquisition Schemes ........................ 117
5.3.1 RARE-Like Imaging Sequence ..................... 117
5.3.2 CPMG-CP for Quadrature Detection ............... 121
5.4 Performance of the Multi-Echo Detection Scheme ........ 125
5.4.1 Sensitivity Improvement ........................ 125
5.4.2 Relaxation and Diffusion Contrast .............. 126
5.4.3 3D Imaging ..................................... 128
5.5 Displacement Encoding ................................. 129
5.5.1 PFG Methods in Inhomogeneous Fields ............ 130
5.5.2 Measurement of Velocity Distributions .......... 135
5.6 Spatially Resolved Velocity Distributions ............. 137
5.6.1 2D Velocity Maps ............................... 137
References ................................................. 140
6 High-Resolution NMR in Inhomogeneous Fields ................ 143
Vasiliki Demas, John M. Franck, Jeffrey A. Reimer, and
Alexander Pines
6.1 Introduction .......................................... 143
6.2 Approaches Based on Spin Interactions ................. 144
6.3 Ex Situ NMR: Spatially Dependent "z-Rotations" ........ 145
6.3.1 Ex Situ Matching: Compensating Static Field
Inhomogeneities via Spatially Matched rf ....... 147
6.3.2 Shim Pulses: Corrections Based on Gradient
Modulations During an Adiabatic Double
Passage ........................................ 157
6.3.3 Adjusted Chirp Shim Pulses ..................... 160
6.4 Summary ............................................... 162
References ................................................. 162
7 High-Resolution Spectroscopy in Highly Homogeneous Stray
Fields ..................................................... 165
Ernesto P. Danieli
7.1 Sensor Design ......................................... 166
7.1.1 Main Unit ...................................... 166
7.1.2 Shim Unit ...................................... 167
7.2 Shimming Magnetic Fields with Movable Permanent
Magnets ............................................... 170
7.2.1 Generation of Linear Terms Along у ............. 171
7.2.2 Generation of Linear Terms Along x and z ....... 172
7.2.3 Generation of Quadratic Terms x2 and z2 ........ 172
7.3 Experimental Results .................................. 175
7.4 Shimming the Magnet to Higher Order ................... 177
7.4.1 Improving Resolution and Working Volume Size ... 178
7.5 Temperature Compensation .............................. 181
7.6 Conclusions ........................................... 185
References ................................................. 185
8 Applications in Biology and Medicine ....................... 187
Bernhard Blümich
8.1 Skin .................................................. 188
8.2 Tendon ................................................ 192
8.3 Mummies and Bones ..................................... 194
8.4 Unilateral Imaging of Biological Matter ............... 196
8.5 Conclusions ........................................... 198
References ................................................. 199
9 Applications in Material Science and Cultural Heritage ..... 203
Jürgen Kolz
9.1 Elastomers ............................................ 204
9.1.1 Crosslink Density .............................. 204
9.1.2 Aging .......................................... 206
9.1.3 Imaging ........................................ 209
9.2 Hard Polymers ......................................... 212
9.2.1 Ingress of Solvents ............................ 215
9.3 Cultural Heritage ..................................... 217
References ................................................. 219
10 Spectrometer Hardware ...................................... 221
Jörg Felder
10.1 Single-Sided vs. Conventional: Systematic
Differences ........................................... 222
10.2 Frontend Design ....................................... 223
10.2.1 Matching and Balancing ......................... 223
10.2.2 Transmit-Receive Switching ..................... 226
10.3 Transmitter Design .................................... 228
10.3.1 Conventional Power Amplifiers .................. 229
10.3.2 Alternative Amplifier Designs .................. 230
10.4 Receiver Design ....................................... 233
10.4.1 Low-Noise Amplifier ............................ 234
10.4.2 Frequency Generation and Mixing ................ 235
10.5 Digital Hardware ...................................... 237
10.5.1 Frontend Signal Processor Selection ............ 237
10.5.2 Digital Phase Sensitive Detector ............... 239
References ................................................. 239
Index ......................................................... 241
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