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ToshimitsuAsakura BoMonemar
Hokkai-GakuenUniversity DepartmentofPhysics
FacultyofEngineering andMeasurementTechnology
1-1,Minami-26,Nishi11,Chuo-ku MaterialsScienceDivision
Sapporo,Hokkaido064-0926,Japan Linko¨pingUniversity
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Y. Aizu T. Asakura
Spatial Filtering
Velocimetry
Fundamentals and Applications
With112Figures
123
ProfessorYoshihisaAizu
MuroranInstituteofTechnology,DepartmentofMechanicalSystemsEngineering
Mizumoto27-1,Muroran050-8585,Hokkaido,Japan
E-mail:[email protected]
ProfessorToshimitsuAsakura
President,Hokkai-GakuenUniversity
Asahi-Machi 4-1-40, Toyohira-Ku , Sapporo 062-8605, Hokkaido, Japan
E-mail: [email protected]
ISSN0342-4111
ISBN-103-540-28186-XSpringerBerlinHeidelbergNewYork
ISBN-13978-3-540-28186-3SpringerBerlinHeidelbergNewYork
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To our families
Preface
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 con-
ventional methods employed previously. These fundamental advantages are
indicated by the enormous research effort which has gone into their develop-
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 filtering velocimetry which was
also proposed in the early 1960s and studied by a number of investigators. In
comparison with laser Doppler velocimetry, spatial filtering velocimetry had
not received much attention from investigators but was studied steadily by
severalresearchgroupsmainlyinJapanandisnowpracticallyusedinvarious
fields of engineering.
Several important books on laser Doppler velocimetry have already been
published, but there has been no book on spatial filtering velocimetry. This
book is the first contribution to spatial filtering velocimetry. Therefore, the
Introduction of Chapter 1 provides in detail a historical review of spatial
filtering velocimetry, relating it to other optical methods and discussing its
practicalrelevance.InthebookfollowingChap.1,themostimportantresults
on the subject both from our own papers and from publications by other
authors have been collected together and presented in a concise and easily
readable form. Special emphasis has been placed on the fundamental content
ofspatialfilteringvelocimetryinageneralformandonawiderangeofsystems
and applications of this velocimetry. By following this emphasis, the contents
of this book consisting of six chapters may be divided into two main parts:
the fundamentals given in Chaps.2–4 and the systems and applications in
Chaps.5 and 6.
VIII Preface
Since the subject matter of this book is interdisciplinary, we have tried to
make the book self-contained and easily understandable to readers in various
fields. Considering the wide-ranging backgrounds of readers, we have also
attemptedtogiveacomprehensivelistofthemostpertinentreferencesatthe
end of the book.
TheauthorswishtoexpresstheirthankstoProf.A.Kobayashiformerlyat
the Tokyo Institute of Technology for kindly supplying reprints of his papers
on spatial filtering velocimetry, which were very helpful in the preparation of
fundamentalpartsinthisbook.Wearealsogratefultoseveralresearcherswho
provided us useful information on their works in spatial filtering velocimetry,
especiallyDr.K.MichelattheJena-OptronikGmbH,Prof.S.G.Hansonatthe
RisøNationalLaboratory,andProf.K.OkaatHokkaidoUniversity.Y.Aizuis
thankfultoProf.Y.ItakuraatShigaUniversityforkindcorrespondencewhich
began with discussions on spatial filtering velocimetry. Finally, we would like
to thank Mr. T. Ushizaka for his valuable cooperation in various studies on
spatial filtering velocimetry which were performed formerly by our group at
Hokkaido University.
Muroran and Sapporo, Hokkaido, Yoshihisa Aizu
May 2005 Toshimitsu Asakura
Contents
1 Introduction............................................... 1
1.1 Survey of Optical Velocimetry............................. 1
1.2 Spatial Filtering Velocimetry.............................. 5
1.3 The Book .............................................. 7
2 Principle and Properties of the Spatial Filtering Method .. 9
2.1 Spatial Filtering Effect ................................... 10
2.2 Transmittance Functions ................................. 13
2.3 Power Spectra for Typical Spatial Filters ................... 18
2.4 Filtering Characteristics.................................. 24
2.4.1 Spectral Bandwidth ............................... 25
2.4.2 Central Frequency................................. 27
2.4.3 Direction of Grating Lines.......................... 29
2.5 Parameters of the Spatial Filter ........................... 31
2.5.1 Transmittance Function ............................ 32
2.5.2 Filter Window .................................... 32
2.5.3 Intervals of Grating Lines .......................... 33
2.5.4 Number of Grating Lines........................... 33
2.6 Effects of Scattering Objects .............................. 33
2.6.1 Deviation of the Central Frequency .................. 34
2.6.2 Visibility of Output Signals......................... 35
2.6.3 Light Scattering by Spherical Particles ............... 40
2.7 Requirements for Scattering Objects ....................... 41
2.7.1 Small Particles.................................... 42
2.7.2 Rough Surfaces ................................... 44
2.7.3 Speckle Pattern ................................... 45
3 Optical System ............................................ 47
3.1 Resolution of Imaging Systems ............................ 47
3.1.1 Point Spread...................................... 48
3.1.2 Transfer Function ................................. 51
X Contents
3.2 Lens Aberrations ........................................ 56
3.2.1 Primary Aberrations............................... 57
3.2.2 Chromatic Aberrations............................. 58
3.3 Focusing Depth and Probe Volume ........................ 60
3.3.1 Depth of Focus.................................... 60
3.3.2 Probe Volume .................................... 61
3.4 Illumination ............................................ 63
3.4.1 Small Particles in a Fluid .......................... 63
3.4.2 Rough Surfaces ................................... 65
3.4.3 Coherent and Incoherent Illumination................ 65
3.5 Image Modification ...................................... 66
3.5.1 Spatial Frequency Filtering ......................... 66
3.5.2 Photographic Filters............................... 68
4 Signal Analysis ............................................ 69
4.1 Types of SFV Signals .................................... 69
4.2 Spectral Analysis........................................ 71
4.2.1 Frequency Scanning ............................... 71
4.2.2 Filter Bank....................................... 72
4.2.3 Fast Fourier Transform............................. 72
4.2.4 Maximum Entropy Method......................... 74
4.3 Frequency Tracking...................................... 75
4.3.1 Frequency Tracker................................. 75
4.3.2 Autodyne ........................................ 76
4.4 Counting Techniques..................................... 77
4.4.1 Frequency Counter ................................ 77
4.4.2 Wave-Period Measurements......................... 78
4.5 Correlation Analysis ..................................... 80
4.5.1 Autocorrelation of Photocurrent Signals.............. 81
4.5.2 Fast Fourier Transform............................. 83
4.5.3 Photon Correlation Technique ...................... 83
4.6 Choice of the Signal-Analyzing Technique .................. 85
5 Spatial Filtering Devices and Systems ..................... 87
5.1 Transmission Grating .................................... 87
5.1.1 Transmission Grating Velocimetry ................... 88
5.1.2 Differential Detection for Pedestal Removal........... 89
5.1.3 Directional Discrimination — Frequency Shifting ...... 94
5.1.4 Directional Discrimination — Phase Shifting.......... 97
5.1.5 Two-Dimensional Measurements ....................100
5.2 Prism Grating ..........................................104
5.2.1 Two-Stage Type ..................................104
5.2.2 Three-Stage Type .................................105
5.2.3 Mirror Grating....................................107
5.3 Lenticular Grating.......................................107
