ISBN: 3540678387
TITLE: Laser Doppler and Phase Doppler Measurement Techniques
AUTHOR: Albrecht/Borys/Damaschke/Tropea
TOC: 

1 Introduction I
1.1 Historical Perspective 1
1.2 Use of the Book 3
PART I: FUNDAMENTALS
2 Basic Measurement Principles 9
2.1 Laser Doppler Technique 12
2.2 Phase Doppler Technique 23
2.3 Time-Shift Technique 25
3 Fundamentals of Light Propagation and Optics 27
3.1 Electromagnetic Waves 27
3.1.1 Description of Electromagnetic Waves 27
3.1.2 Polarization 33
3.1.3 Boundary Conditions and Fresnel Coefficients 35
3.1.4 Laser Beams 37
3.1.5 Optical Mixing of Electromagnetic Waves 44
3.1.6 The Doppler Effect 45
3.2 Optical Components 47
3.2.1 Matrix Transformation for Imaging 47
3.2.2 Propagation of Laser Beams Through Lenses and Apertures 53
3.2.3 Optical Gratings and Bragg Cells 56
3.2.4 Optical Fibers 65
3.2.5 Photodetectors 70
4 Light Scattering from Small Particles 79
4.1 Scattering of a Plane Wave 81
4.1.1 Description using Geometrical Optics (GO) 85
4.1.2 Description using Lorenz-Mie Theory and Debye Series 96
4.1.3 Scattering Characteristics for a Plane Wave 100
4.2 Scattering of an Inhomogeneous Field 127
4.2.1 Extension to the Method of Geometrical Optics (EGO) 128
4.2.2 Description using Fourier Lorenz-Mie Theory (FLMT) 134
4.2.3 Scattering Characteristics of an Inhomogeneous Field 146
4.3 Characteristic Quantities of Light Scattered by Small Particles 162
PART II: MEASUREMENT PRINCIPLES
5 Signal Generation in Laser Doppler and Phase Doppler Systems 169
5.1 The Signal From an Arbitrarily Positioned Detector 169
5.1.1 Fundamental Relations 172
5.1.2 Signals from very Small Particles 177
5.1.3 Signals from Large Particles 199
5.1.4 Visibility of the Signal 214
5.1.5 Shift Frequency Influence 219
5.1.6 Measurement and Detection Volumes 221
5.1.7 Statistical Time Series of Particle Signals 227
5.2 Laser Doppler Technique 231
5.2.1 Dual-Beam Configuration 232
5.2.2 Reference-Beam Configuration 233
5.3 Particle Sizing with Phase Doppler and Time-Shift Technique 244
5.3.1 Determination of Incident and Glare Point Positions 247
5.3.2 Phase Doppler Technique 250
5.3.3 Reference Phase Doppler Technique 254
5.3.4 Time-Shift Technique 259
5.4 Refractive Index Determination 266
5.5 Moire Models 267
6 Signal Detection, Processing and Validation 273
6 1 Review of Some Fundamentals 275
6.1.1 Discrete Fourier Transform (DFT) 276
6.1.2 Correlation Function 281
6.1.3 Hilbert Transform 283
6.1.4 Signal Noise 287
6.1.5 Cramer-Rao Lower Bound (CRLB) 290
6.2 Signal Detection 300
6.3 Estimation of the Doppler Frequency 305
6.3.1 Spectral Analysis 307
6.3.2 Correlation Techniques 311
6.3.3 Period Timing Devices 313
6.3.4 Quadrature Demodulation 315
6.4 Determination of Signal Phase 317
6.4.1 Cross-Spectral Density 317
6.4.2 Covariance Methods 321
6.4.3 Quadrature Methods 322
6.5 Model-Based Signal Processing 323
6.5.1 Fundamentals 323
6.5.2 Example Applications 324
7 Laser Doppler Systems 337
7 1 Input Parameters from the Flow and Test Rig 338
7.1.1 Description of the Flow Field 338
7.1.2 Necessary Spatial and Temporal Resolution 351
7.1.3 Flow and Flow-Rig Parameters 358
7.2 Components and Layout of the Transmitting Optics 363
7.2.1 Collimators 363
7.2.2 Beamsplitters and Polarizers 369
7.2.3 Methods for Achieving Directional Sensitivity 371
7.2.4 Generation of the Measurement Volume 377
7 3 Layout of Receiving Optics 383
7.4 System Description 389
7.4.1 One-Velocity Component Systems 389
7.4.2 Two-Velocity Component Systems 392
7.4.3 Three-Velocity Component Systems 396
7.4.4 Multi-Point Systems 401
7.5 Laser Transit Velocimetry 405
8 Phase Doppler Systems 409
8 1 Selection of the Optical Configuration 411
8.2 Single-Point Phase Doppler Systems 417
8.2.1 Three-detector, Standard Phase Doppler System 417
8.2.2 Planar Phase Doppler System 425
8.2.3 Dual-Mode Phase Doppler 430
8.2.4 Dual-Burst Technique 436
8.2.5 Extended Phase Doppler Technique 446
8.2.6 Reference Phase Doppler Technique 449
8 3 Further Design Considerations for Phase Doppler Systems 454
8.3.1 Influence of the Gaussian Beam 454
8.3.2 Slit Effect 466
8.3.3 Non-Spherical and Inhomogeneous Particles 467
8.4 Multi-Dimensional Sizing Techniques 470
8.4.1 Interferometric Particle Imaging (IPI) 470
8.4.2 Global Phase Doppler (GPD) Technique 478
8.4.3 Concentration Limits 481
9 Further Particle Sizing Methods Based on the Laser Doppler Technique 491
9.11 Techniques Based on Signal Amplitude 491
9.1.1 Cross-sectional Area Difference Technique 491
9.1.2 Combined Laser Doppler and White Light Sizer 500
9.2 Time-Shift Technique 501
9.2.1 Time-Shift Technique in Forward Scatter 504
9.2.2 Time-Shift Technique in Backscatter 506
9.3 Rainbow Refractometry 517
9.4 Shadow Doppler Technique 523
PART III: DATA PROCESSING
10 Fundamentals of Data Processing 529
10.1 Statistical Principles 529
10.2 Stationary Random Processes 533
10.3 Estimator Expectation and Variance 535
10.3.1 Estimators for the Mean 535
10.3.2 Estimators for Higher Order Correlations 539
10.3.3 Estimators for Transient Processes 542
10.4 Propagation of Errors 543
11 Processing of Laser Doppler Data 545
11.1 Estimation of Moments 547
11.2 Estimation of Turbulent Velocity Spectra 552
11.2.1 The Slotting Technique 554
11.2.2 Reconstruction with FFT 558
11.2.3 Post-Processing Steps 561
11.3 Correlation Estimates from Multi-Point Systems 563
11.4 Measurements in Transient Processes 566
11.4.1 Effect of Window Size on Phase and Ensemble Statistics 567
11.4.2 Energy Partitioning in Transient flows 568
11.5 Data Simulation 569
12 Processing of Phase Doppler Data 573
12.1 Validation procedures 573
12.1.1 SNR Validation 573
12.1.2 Phase Difference Validation 574
12.1.3 Sphericity Validation 574
12.1.4 Amplitude Validation 574
12.1.5 Transit Time Validation 575
12.2 Particle Statistics 576
12.2.1 Flux Density Vectors and Concentration 576
12.2.2 Distribution of Particles 579
12.2.3 Geometry of the Detection Volume 582
12.2.4 Estimation of the Number of Particles 590
12.2.5 Summary and Examples 591
12.3 Post-Processing of phase Doppler Data 595
12.3.1 Particle Size Distributions 595
12.3.2 Mean Diameters 598
12.3.3 Non-Spherical and Inhomogeneous Particles 599
PART IV: APPLICATION ISSUES
13. Choice of Particles and Particle Generation 605
13.1 Particle Motion in Flows 606
13.2 Particle Generation 613
13.2.1 Droplet Generation 614
13.2.2 Solid Particle Generation 619
13.3 Introducing Particles into the Flow 621
13.3.1 Liquid mows 622
13.3.2 Gas Flows 622
13.3.3 Two-Phase Flows 623
13.3.4 Natural Seeding 624
14 System Design Considerations 627
14.1 System Design Guidelines 627
14.1.1 Laser Doppler Systems 628
14.1.2 Phase Doppler Systems 635
14.1.3 Alignment and Adjustment 638
14.2 System Design Examples 642
14.2.1 Velocity Measurements in a Narrow Channel Flow 642
14.2.2 Drop Size Measurements in a Diesel Injector Spray 647
14.3 Refractive Index Matching 655
14.3.1 Matching with Flow Containment 655
14.3.2 Matching for Variable Density 660
Appendix 661
List of Symbols and Acronyms 662
Derivation of Equations Describing a Laser Beam 681
Internal and Near Field Solution 686
Bibliography 689
References 690
Books (or parts thereof) on the Laser or Phase Doppler Techniques 718
Periodicals Dealing with the Laser or Phase Doppler Techniques 719
Conference Series devoted to Laser or Phase Doppler Techniques 720
Index 723
END
