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Cover image for Laser doppler and phase doppler measurement techniques
Title:
Laser doppler and phase doppler measurement techniques
Publication Information:
Berlin : Springer, 2003
ISBN:
9783540678380
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30000010029723 TA357.5.M43 L38 2003 Open Access Book Book
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Summary

Summary

Providing the first comprehensive treatment, this book covers all aspects of the laser Doppler and phase Doppler measurement techniques, including light scattering from small particles, fundamental optics, system design, signal and data processing, tracer particle generation, and applications in single and two-phase flows. The book is intended as both a reference book for more experienced users as well as an instructional book for students. It provides ample material as a basis for a lecture course on the subject and represents one of the most comprehensive treatments of the phase Doppler technique to date. The book will serve as a valuable reference book in any fluid mechanics laboratory where the laser Doppler or phase Doppler techniques are used. This work reflects the authors' long practical experience in the development of the techniques and equipment, as the many examples confirm.


Table of Contents

1 Introductionp. 1
1.1 Historical Perspectivep. 1
1.2 Use of the Bookp. 3
Part I Fundamentals
2 Basic Measurement Principlesp. 9
2.1 Laser Doppler Techniquep. 12
2.2 Phase Doppler Techniquep. 23
2.3 Time-Shift Techniquep. 25
3 Fundamentals of Light Propagation and Opticsp. 27
3.1 Electromagnetic Wavesp. 27
3.1.1 Description of Electromagnetic Wavesp. 27
3.1.2 Polarizationp. 33
3.1.3 Boundary Conditions and Fresnel Coefficientsp. 35
3.1.4 Laser Beamsp. 37
3.1.5 Optical Mixing of Electromagnetic Wavesp. 44
3.1.6 The Doppler Effectp. 45
3.2 Optical Componentsp. 47
3.2.1 Matrix Transformation for Imagingp. 47
3.2.2 Propagation of Laser Beams Through Lenses and Aperturesp. 53
3.2.3 Optical Gratings and Bragg Cellsp. 56
3.2.4 Optical Fibersp. 65
3.2.5 Photodetectorsp. 70
4 Light Scattering from Small Particlesp. 79
4.1 Scattering of a Plane Wavep. 81
4.1.1 Description using Geometrical Optics (GO)p. 85
4.1.2 Description using Lorenz-Mie Theory and Debye Seriesp. 96
4.1.3 Scattering Characteristics for a Plane Wavep. 100
4.2 Scattering of an Inhomogeneous Fieldp. 127
4.2.1 Extension to the Method of Geometrical Optics (EGO)p. 128
4.2.2 Description using Fourier Lorenz-Mie Theory (FLMT)p. 134
4.2.3 Scattering Characteristics of an Inhomogeneous Fieldp. 146
4.3 Characteristic Quantities of Light Scattered by Small Particlesp. 162
Part II Measurement Principles
5 Signal Generation in Laser Doppler and Phase Doppler Systemsp. 169
5.1 The Signal From an Arbitrarily Positioned Detectorp. 169
5.1.1 Fundamental Relationsp. 172
5.1.2 Signals from very Small Particlesp. 177
5.1.3 Signals from Large Particlesp. 199
5.1.4 Visibility of the Signalp. 214
5.1.5 Shift Frequency Influencep. 219
5.1.6 Measurement and Detection Volumesp. 221
5.1.7 Statistical Time Series of Particle Signalsp. 227
5.2 Laser Doppler Techniquep. 231
5.2.1 Dual-Beam Configurationp. 232
5.2.2 Reference-Beam Configurationp. 233
5.3 Particle Sizing with Phase Doppler and Time-Shift Techniquep. 244
5.3.1 Determination of Incident and Glare Point Positionsp. 247
5.3.2 Phase Doppler Techniquep. 250
5.3.3 Reference Phase Doppler Techniquep. 254
5.3.4 Time-Shift Techniquep. 259
5.4 Refractive Index Determinationp. 266
5.5 Moiré Modelsp. 267
6 Signal Detection, Processing and Validationp. 273
6.1 Review of Some Fundamentalsp. 275
6.1.1 Discrete Fourier Transform (DFT)p. 276
6.1.2 Correlation Functionp. 281
6.1.3 Hilbert Transformp. 283
6.1.4 Signal Noisep. 287
6.1.5 Cramèr-Rao Lower Bound (CRLB)p. 290
6.2 Signal Detectionp. 300
6.3 Estimation of the Doppler Frequencyp. 305
6.3.1 Spectral Analysisp. 307
6.3.2 Correlation Techniquesp. 311
6.3.3 Period Timing Devicesp. 313
6.3.4 Quadrature Demodulationp. 315
6.4 Determination of Signal Phasep. 317
6.4.1 Cross-Spectral Densityp. 317
6.4.2 Covariance Methodsp. 321
6.4.3 Quadrature Methodsp. 322
6.5 Model-Based Signal Processingp. 323
6.5.1 Fundamentalsp. 323
6.5.2 Example Applicationsp. 324
7 Laser Doppler Systemsp. 337
7.1 Input Parameters from the Flow and Test Rigp. 338
7.1.1 Description of the Flow Fieldp. 338
7.1.2 Necessary Spatial and Temporal Resolutionp. 351
7.1.3 Flow and Flow-Rig Parametersp. 358
7.2 Components and Layout of the Transmitting Opticsp. 363
7.2.1 Collimatorsp. 363
7.2.2 Beamsplitters and Polarizersp. 369
7.2.3 Methods for Achieving Directional Sensitivityp. 371
7.2.4 Generation of the Measurement Volumep. 377
7.3 Layout of Receiving Opticsp. 383
7.4 System Descriptionp. 389
7.4.1 One-Velocity Component Systemsp. 389
7.4.2 Two-Velocity Component Systemsp. 392
7.4.3 Three-Velocity Component Systemsp. 396
7.4.4 Multi-Point Systemsp. 401
7.5 Laser Transit Velocimetryp. 405
8 Phase Doppler Systemsp. 409
8.1 Selection of the Optical Configurationp. 411
8.2 Single-Point Phase Doppler Systemsp. 417
8.2.1 Three-detector, Standard Phase Doppler Systemp. 417
8.2.2 Planar Phase Doppler Systemp. 425
8.2.3 Dual-Mode Phase Dopplerp. 430
8.2.4 Dual-Burst Techniquep. 436
8.2.5 Extended Phase Doppler Techniquep. 446
8.2.6 Reference Phase Doppler Techniquep. 449
8.3 Further Design Considerations for Phase Doppler Systemsp. 454
8.3.1 Influence of the Gaussian Beamp. 454
8.3.2 Slit Effectp. 466
8.3.3 Non-Spherical and Inhomogeneous Particlesp. 467
8.4 Multi-Dimensional Sizing Techniquesp. 470
8.4.1 Interferometric Particle Imaging (IPI)p. 470
8.4.2 Global Phase Doppler (GPD) Techniquep. 478
8.4.3 Concentration Limitsp. 481
9 Further Particle Sizing Methods Based on the Laser Doppler Techniquep. 491
9.1 Techniques B ased o n Signal Amplitudep. 491
9.1.1 Cross-sectional Area Difference Techniquep. 491
9.1.2 Combined Laser Doppler and White Light Sizerp. 500
9.2 Time-Shift Techniquep. 501
9.2.1 Time-Shift Technique in Forward Scatterp. 504
9.2.2 Time-Shift Technique in Backscatterp. 506
9.3 Rainbow Refractometryp. 517
9.4 Shadow Doppler Techniquep. 523
Part III Data Processing
10 Fundamentals of Data Processingp. 529
10.1 Statistical Principlesp. 529
10.2 Stationary Random Processesp. 533
10.3 Estimator Expectation and Variancep. 535
10.3.1 Estimators for the Meanp. 535
10.3.2 Estimators for Higher Order Correlationsp. 539
10.3.3 Estimators for Transient Processesp. 542
10.4 Propagation of Errorsp. 543
11 Processing of Laser Doppler Datap. 545
11.1 Estimation of Momentsp. 547
11.2 Estimation of Turbulent Velocity Spectrap. 552
11.2.1 The Slotting Techniquep. 554
11.2.2 Reconstruction with FFTp. 558
11.2.3 Post-Processing Stepsp. 561
11.3 Correlation Estimates from Multi-Point Systemsp. 563
11.4 Measurements in Transient Processesp. 566
11.4.1 Effect of Window Size on Phase and Ensemble Statisticsp. 567
11.4.2 Energy Partitioning in Transient Flowsp. 568
11.5 Data Simulationp. 569
12 Processing of Phase Doppler Datap. 573
12.1 Validation Proceduresp. 573
12.1.1 SNR Validationp. 573
12.1.2 Phase Difference Validationp. 574
12.1.3 Sphericity Validationp. 574
12.1.4 Amplitude Validationp. 574
12.1.5 Transit Time Validationp. 575
12.2 Particle Statisticsp. 576
12.2.1 Flux Density Vectors and Concentrationp. 576
12.2.2 Distribution of Particlesp. 579
12.2.3 Geometry of the Detection Volumep. 582
12.2.4 Estimation of the Number of Particlesp. 590
12.2.5 Summary and Examplesp. 591
12.3 Post-Processing of Phase Doppler Datap. 595
12.3.1 Particle Size Distributionsp. 595
12.3.2 Mean Diametersp. 598
12.3.3 Non-Spherical and Inhomogeneous Particlesp. 599
Part IV Application Issues
13 Choice of Particles and Particle Generationp. 605
13.1 Particle Motion in Flowsp. 606
13.2 Particle Generationp. 613
13.2.1 Droplet Generationp. 614
13.2.2 Solid Particle Generationp. 619
13.3 Introducing Particles into the Flowp. 621
13.3.1 Liquid Flowsp. 622
13.3.2 Gas Flowsp. 622
13.3.3 Two-Phase Flowsp. 623
13.3.4 Natural Seedingp. 624
14 System Design Considerationsp. 627
14.1 System Design Guidelinesp. 627
14.1.1 Laser Doppler Systemsp. 628
14.1.2 Phase Doppler Systemsp. 635
14.1.3 Alignment and Adjustmentp. 638
14.2 System Design Examplesp. 642
14.2.1 Velocity Measurements in a Narrow Channel Flowp. 642
14.2.2 Drop Size Measurements in a Diesel Injector Sprayp. 647
14.3 Refractive Index Matchingp. 655
14.3.1 Matching with Flow Containmentp. 655
14.3.2 Matching for Variable Densityp. 660
Appendixp. 661
List of Symbols and Acronymsp. 662
Derivation of Equations Describing a Laser Beamp. 681
Internal and Near Field Solutionp. 686
Bibliographyp. 689
Referencesp. 690
Books (or parts thereof) on the Laser or Phase Doppler Techniquesp. 718
Periodicals Dealing with the Laser or Phase Doppler Techniquesp. 719
Conference Series devoted to Laser or Phase Doppler Techniquesp. 720
Indexp. 723
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