HANDBOOK OF THE MOIRE FRINGE TECHNIQUE

Transcription

1 k HANDBOOK OF THE MOIRE FRINGE TECHNIQUE K. PATORSKI Institute for Design of Precise and Optical Instruments Warsaw University of Technology Warsaw, Poland with a contribution by M. KUJAWINSKA Institute for Design of Precise and Optical Instruments Warsaw University of Technology Warsaw, Poland 1993 ELSEVIER Amsterdam - London - New York - Tokyo

2 XIV TABLE OF CONTENTS PREFACE References TABLE OF CONTENTS vii xi xiv 1. THEORETICAL INTERPRETATION OF FORMATION OF MOIRE FRINGES A Fourier Series Approach to the Description of Moir6 Patterns Derivation of the general equation Information display by moir fringes Profile of moir6 fringes The Parametric Equation Method Two families of equidistant straight lines Equidistant concentric circles superimposed on equidistant straight lines Two sets of equidistant concentric circles Zone grating superimposed on equispaced straight lines Zone grating superimposed on another zone grating Equiangular straight lines superimposed on equispaced straight lines Description of Moirö in Terms of Vectorial Sums in Fourier Space Moir6 as an Aliasing Phenomenon by Undersampling 24 References INCOHERENT METHODS OF SUPERIMPOSITION OF STRUCTURES Additive Type Moire Subtractive Type Moir Multiplicative Type Moire Examples of Two-structure Superimpositions Special Techniques - Use of Structures with Orthogonal Transmittances Coding by spectral filters 45

3 Table of Contents xv Coding by orthogonal polarization filters 47 References 50. COHERENT METHODS OF SUPERIMPOSITION Fringe Pattern Formation by Filtering of the Double Diffraction Orders Information content of diffraction Orders of deformed grating Double diffraction arrangement and coherent optical processor Fringe multiplication and sensitivity enhancement Contrast improvement of the additive type moir Fringe shifting and mismatch methods under coherent superimposition Separation of moirö fringe families Optical differentiation of grating encoded Information Overlapping Real Time Interference Fringes with a Recorded Pattern 66 References 67. INFLUENCE OF THE TYPE OF ILLUMINATION AND SEPARATION OF GRÄTINGS ON THE INTENSITY DISTRIBUTION IN MOIRE FRINGES The Case of Coherent Illumination The double diffraction System - general considerations Producing binary amplitude gratings in the double diffraction System The Case of Incoherent Illumination Introduction Multiple incoherent superimposition of self-imaging Utilization of gap effect with a focused Observation System onto a second grating plane The Case of Partially Coherent Illumination Self-imaging under partially coherent illumination Double-grating System with a defocused Observation plane 91 References 95

4 XVI Table of Contents 5. MOIRE DISPLACEMENT TRANSDUCERS Basic Concepts Gräting Reading Heads Transmission reading heads Reflection reading heads Projection reading heads Interference reading heads Accuracy of Moir6 Fringe Transducers Interpolation errors Error sources and correction methods Phase quadrature errors Amplitude errors Residual bias errors Waveform residual error Error considerations for angular measurement Interpolation methods - implementation Amplitude tracking Phase tracking Diffraction effects Theoretical formulation Use of binary amplitude gratings with various opening numbers Moire' fringe patterns generated by real nonmonochromatic light source Influence of axial defocus of photodetectors 132 References MOIRE FRINGE ALIGNMENT METHODS Optical Alignment by Whole-Field Detection of Moir6 Fringes In-plane alignment aids Alignment in Space Moir6 Patterns for Three Point Alignment Technique Introduction Derivation of component structures from moir6 patterns. Moir6 patterns by pure translation Submicron Alignment Methods for Lithography Coherent moir6 alignment for proximity printing Coherent moir6 alignment for optical projection printing 163 References 167

5 k Table of Contents xvu 7. MOIRE PHOTOGRAPHY Principles Implementation Camera Specimen gratings Fringe Pattern Recording and Processing Examples of Applications 180 References MOIRE METHODS IN INTERFEROMETRY Moir6 Methods in Two-beam Interferometry with a Reference Wavefront Subtraction of instrumental errors Reducing or eliminating the carrier fringes in an interferogram Whole-field differentiation offringe patterns Addition of phase functions Two-wavelength interferometry Moir6 Methods in the Two-beam Interferometry with Conjugate Wavefronts Determination of displacements Determination and processing of displacement derivatives Moir6 Methods in Gräting Shearing Interferometry Talbot interferometry Two-beam lateral shear interferometers 213 References SHADOW MOIRE TOPOGRAPHY Principles Theoretical Description Localization and Contrast of Moir6 Fringes Absolute Fringe Order Determination Relative Fringe Order Determination Techniques for ordinary moir6 fringes Techniques for moir6 fringes with asymmetrical profile Instrumental Considerations Shadow grids Light Sources Object Surface Preparation 241

6 xvm Table of Contents 9.7. Applications 241 References PROJECTION MOIRE TOPOGRAPHY Principles and Basic Configurations Configurations with a Single Projection System Projection and Observation Systems with axes parallel Projection and Observation Systems with axes intersecting Systems without Gräting in the Observation System Double Projection Moir6 Topography Off-line Demodulation Methods Contrast of Moir6 Fringes Absolute and Relative Fringe Ordering Absolute fringe ordering Relative fringe ordering - the case of processing of symmetrical profile moir6 fringes Relative fringe ordering - methods introducing asymmetric profile moir6 fringes Instrumental Considerations Projection and detection gratings Light sources and illumination optics Demodulation optics and pattern recording Applications 282 References REFLECTION MOIRE METHOD Ligtenberg and Rieder-Ritter Configurations Determination of the slope of elements in the surface Differentiation of Moir6 Patterns (Curvature Determination) Reflection Moire Arrangements for Studying Dynamic Events Slope angle determination Curvature determination Specific Experimental Arrangement for Studying the Flexure of Plates Applications 317 References 322

7 Table ofcontents xvc 12. MOIRE AS A GRAPHICAL SOLUTION TO PHYSICAL PROBLEMS Wave Physics Binary amplitude grating as an analog to electromagnetic wave Modeling of interference phenomena Field Physics Demonstration of Electric-Force Lines Solving potential field problems Demonstrating centrifugal spherical waves Interpretation of Images Formed in the Field-ion Microscope 337 References AUTOMATIC FRINGE PATTERN ANALYSIS Introduction Intensity methods Fringe pattern preprocessing Fringe recognition Fringe order assignment Phase measuring methods: general considerations Electronic phase-measuring methods Analytical phase-measuring methods Spatial-carrier fringe pattern analysis Fourier transform method Space-domain processing Computational complexities Phase-shifting method Phase-shifting algorithms Removal of phase ambiguities (Phase unwrapping) Temporal phase-shifting method Spatial phase-shifting techniques Spatial-carrier phase shifting technique Comparison of automatic fringe pattern analysis methods Future trends 400 References 401 SUBJECT INDEX 411