Spatial filtering velocimetry : fundamentals and applications

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The invention of lasers in the early 1960s enhanced the rapid development of optoelectronics which had introduced various optical measurement methods. A typical example of the methods is found in measurements of velocity. It is well recognized that optical velocity measuring methods have important advantages, such as noncontacting and nondisturbing operations, over c- ventional methods employed previously. These fundamental advantages are indicated by the enormous research e?ort which has gone into their devel- ment for many years. One of the optical methods proposed and studied to measure the velocity is laser Doppler velocimetry which was proposed in the early 1960s and extensively studied by many investigators and is at present applied to practical uses. Another is spatial ?ltering velocimetry which was also proposed in the early 1960s and studied by a number of investigators. In comparison with laser Doppler velocimetry, spatial ?ltering velocimetry had not received much attention from investigators but was studied steadily by several research groups mainly in Japan and is now practically used in various ?elds of engineering. Several important books on laser Doppler velocimetry have already been published, but there has been no book on spatial ?ltering velocimetry. This book is the ?rst contribution to spatial ?ltering velocimetry. Therefore, the Introduction of Chapter 1 provides in detail a historical review of spatial ?ltering velocimetry, relating it to other optical methods and discussing its practical relevance. In the book following Chap.

Author Notes

Yoshihisa Aizu received the B. Eng. in electronics from Musashi Institute of Technology in 1980, and Ms. Eng. and Dr. Eng. in electronics from Hokkaido University in 1982 and 1985, respectively. From 1985 to 1989, he was a leader of a research group in the Chofu Laboratory of Kowa Company Limited in Tokyo. In 1989, he joined the Research Institute of Applied Electricity, Hokkaido University, as a research associate. From 1990, he was an associate professor at Muroran Institute of Technology. From 1992 to 1993, he was a visiting researcher at the fluid mechanics institute of University Erlangen, Germany. His current research activities are in the fields of optical velocimetry, optical particle measurements, laser speckles and their applications to scientific, industrial, and medical fields, and biomedical application of visible to near infrared spectroscopy. He is a member of SPIE, OSA, the Japan Society of Applied Physics, Optical Society of Japan, the Japan Society of Mechanical Engineering, and the Society of Instrument and Control Engineers, Japan.

Toshimitsu Asakura received his M.A. in 1960 from Boston University and his Dr.Eng. in 1965 from the University of Tokyo. He was a research assistant at the Physical Research Laboratories, Boston University, from 1957 to 1958 and a member of the research staff at the Research Laboratory of Itek Corporation from 1958 to 1961. In 1971 he was promoted to professor at the Research Institute of Applied Electricity, Hokkaido University. He was also guest professor at the International Cooperation Center, Tokyo Institute of Technology, since 1980. In 1997, he retired from Hokkaido University and moved to Hokkai-Gakuen University. From 2005, he is a president of Hokkai-Gakuen University. His work has been in optics and its related fields particularly in relation to the properties and applications of laser light. His research interests include the properties and applications of speckles, the laser Doppler and transmission-grating velocimetries, light-propagation properties in optical fibers, apodization theory, optical information processing, and applications of lasers to medical fields. He has written many papers in technical journals and other publications. Dr. Asakura is a fellow of the Optical Society of America, and a member of the International Society for Optical Engineering (SPIE), the Physical Society of Japan, the Japan Society of Applied Physics, the Institute of Electronics and Communication Engineers of Japan, the Institute of Electrostatistics of Japan, The Japan Society for Laser Medicine, the Laser Society of Japan, and the Physics Education Society of Japan. He received an Optics Paper Award from the Japan Society of Applied Physics in 1962, the Hokkaido Science and Technology Award in 1986, and several other awards.

1 Introduction	p. 1
1.1 Survey of Optical Velocimetry	p. 1
1.2 Spatial Filtering Velocimetry	p. 5
1.3 The Book	p. 7
2 Principle and Properties of the Spatial Filtering Method	p. 9
2.1 Spatial Filtering Effect	p. 10
2.2 Transmittance Functions	p. 13
2.3 Power Spectra for Typical Spatial Filters	p. 18
2.4 Filtering Characteristics	p. 24
2.4.1 Spectral Bandwidth	p. 25
2.4.2 Central Frequency	p. 27
2.4.3 Direction of Grating Lines	p. 29
2.5 Parameters of the Spatial Filter	p. 31
2.5.1 Transmittance Function	p. 32
2.5.2 Filter Window	p. 32
2.5.3 Intervals of Grating Lines	p. 33
2.5.4 Number of Grating Lines	p. 33
2.6 Effects of Scattering Objects	p. 33
2.6.1 Deviation of the Central Frequency	p. 34
2.6.2 Visibility of Output Signals	p. 35
2.6.3 Light Scattering by Spherical Particles	p. 40
2.7 Requirements for Scattering Objects	p. 41
2.7.1 Small Particles	p. 42
2.7.2 Rough Surfaces	p. 44
2.7.3 Speckle Pattern	p. 45
3 Optical System	p. 47
3.1 Resolution of Imaging Systems	p. 47
3.1.1 Point Spread	p. 48
3.1.2 Transfer Function	p. 51
3.2 Lens Aberrations	p. 56
3.2.1 Primary Aberrations	p. 57
3.2.2 Chromatic Aberrations	p. 58
3.3 Focusing Depth and Probe Volume	p. 60
3.3.1 Depth of Focus	p. 60
3.3.2 Probe Volume	p. 61
3.4 Illumination	p. 63
3.4.1 Small Particles in a Fluid	p. 63
3.4.2 Rough Surfaces	p. 65
3.4.3 Coherent and Incoherent Illumination	p. 65
3.5 Image Modification	p. 66
3.5.1 Spatial Frequency Filtering	p. 66
3.5.2 Photographic Filters	p. 68
4 Signal Analysis	p. 69
4.1 Types of SFV Signals	p. 69
4.2 Spectral Analysis	p. 71
4.2.1 Frequency Scanning	p. 71
4.2.2 Filter Bank	p. 72
4.2.3 Fast Fourier Transform	p. 72
4.2.4 Maximum Entropy Method	p. 74
4.3 Frequency Tracking	p. 75
4.3.1 Frequency Tracker	p. 75
4.3.2 Autodyne	p. 76
4.4 Counting Techniques	p. 77
4.4.1 Frequency Counter	p. 77
4.4.2 Wave-Period Measurements	p. 78
4.5 Correlation Analysis	p. 80
4.5.1 Autocorrelation of Photocurrent Signals	p. 81
4.5.2 Fast Fourier Transform	p. 83
4.5.3 Photon Correlation Technique	p. 83
4.6 Choice of the Signal-Analyzing Technique	p. 85
5 Spatial Filtering Devices and Systems	p. 87
5.1 Transmission Grating	p. 87
5.1.1 Transmission Grating Velocimetry	p. 88
5.1.2 Differential Detection for Pedestal Removal	p. 89
5.1.3 Directional Discrimination - Frequency Shifting	p. 94
5.1.4 Directional Discrimination - Phase Shifting	p. 97
5.1.5 Two-Dimensional Measurements	p. 100
5.2 Prism Grating	p. 104
5.2.1 Two-Stage Type	p. 104
5.2.2 Three-Stage Type	p. 105
5.2.3 Mirror Grating	p. 107
5.3 Lenticular Grating	p. 107
5.3.1 Lenticular Grating Velocimeter	p. 108
5.3.2 Directional Discrimination	p. 110
5.3.3 Two-Dimensional Measurements	p. 112
5.4 Optical Fiber Array	p. 113
5.4.1 Optical Fiber Array SFV	p. 114
5.4.2 Directional Discrimination and Two-Dimensional Measurements	p. 116
5.5 Liquid Crystal Cell Array	p. 117
5.5.1 Liquid Crystal Spatial Filter	p. 118
5.5.2 Piled Construction for Velocity-Vector Measurements	p. 119
5.6 Integrated Solar Cell Array	p. 120
5.6.1 One-Dimensional Array	p. 120
5.6.2 Two-Dimensional Array	p. 123
5.7 Line Sensor	p. 124
5.7.1 Linear Photodiode Array	p. 124
5.7.2 CCD Line Sensor	p. 126
5.8 Area Sensor and Video Camera	p. 127
5.8.1 Image Sensor with Electronic Circuits	p. 127
5.8.2 Computer Image Processing	p. 133
5.9 Survey of Spatial Filtering Devices	p. 135
6 Applications	p. 139
6.1 Performance	p. 139
6.1.1 Accuracy	p. 140
6.1.2 Linearity	p. 142
6.1.3 Resolution	p. 142
6.2 Measurements of Flow Velocity	p. 143
6.2.1 Transmission Grating Velocimeter for a Microscopic Region	p. 143
6.2.2 Two-Dimensional Vector Velocimeter	p. 147
6.2.3 Blood Flow Velocity	p. 148
6.2.4 Applications to Fluid Mechanics	p. 149
6.2.5 Flow Velocity Gradient	p. 151
6.3 Measurements on Large Scales	p. 153
6.3.1 River Flows	p. 153
6.3.2 Debris Flows	p. 154
6.3.3 Aircraft	p. 154
6.3.4 Vehicle	p. 155
6.3.5 Common Objects	p. 158
6.4 Potential Applications and Speckle Velocimetry	p. 158
6.4.1 Production Process	p. 159
6.4.2 Rain and Snow	p. 160
6.4.3 Micromachines and Biological Samples	p. 160
6.4.4 Laser Speckle Velocimeter	p. 161
6.5 Derivative Measurements	p. 163
6.5.1 Particle Sizing	p. 163
6.5.2 Focus Detection	p. 164
6.5.3 Distance Measurement	p. 165
6.5.4 Displacement Sensing by Speckle	p. 167
6.6 Related Techniques	p. 167
6.6.1 Grating Illumination	p. 167
6.6.2 Double-Exposure Specklegram	p. 168
6.6.3 Diode Array Velocimetry	p. 169
6.6.4 Random Pattern Velocimetry	p. 170
6.7 Brief Comparison with Laser Doppler Velocimetry	p. 170
A Fourier Analysis	p. 173
A.1 Fourier Series	p. 173
A.2 Fourier Transform	p. 174
A.3 Two-Dimensional Expression	p. 175
A.4 Fourier Transform Theorems	p. 175
A.5 Examples of Fourier Transform Pairs	p. 177
B Power Spectral Density of the Signal	p. 179
C Derivation of (2.12)	p. 181
D Derivation of (2.20) and (2.21)	p. 183
E Power Spectra for Spatial Filters in Sect. 2.3	p. 185
E.1 Derivation of (2.24)	p. 185
E.2 Derivation of (2.30)	p. 186
E.3 Derivation of (2.34)	p. 188
F Derivation of (2.45)	p. 191
G One-Dimensional Power Spectrum of the Signal	p. 195
H Derivation of Output Signals for Visibility Analysis	p. 197
H.1 Derivation of (2.55)	p. 197
H.2 Derivation of (2.59)	p. 198
References	p. 201
Index	p. 207

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