Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 4: Fringe projection Herbert Gross Winter term

2 2 Preliminary Schedule No Date Subject Detailed Content Introduction Introduction, optical measurements, shape measurements, errors, definition of the meter, sampling theorem Wave optics (ACP) Basics, polarization, wave aberrations, PSF, OTF Sensors Introduction, basic properties, CCDs, filtering, noise Fringe projection Moire principle, illumination coding, fringe projection, deflectometry Interferometry I (ACP) Introduction, interference, types of interferometers, miscellaneous Interferometry II Eamples, interferogram interpretation, fringe evaluation methods Wavefront sensors Hartmann-Shack WFS, Hartmann method, miscellaneous methods Geometrical methods Tactile measurement, photogrammetry, triangulation, time of flight, Scheimpflug setup Speckle methods Spatial and temporal coherence, speckle, properties, speckle metrology Holography Introduction, holographic interferometry, applications, miscellaneous Measurement of basic system properties Bssic properties, knife edge, slit scan, MTF measurement Phase retrieval Introduction, algorithms, practical aspects, accuracy Metrology of aspheres and freeforms Aspheres, null lens tests, CGH method, freeforms, metrology of freeforms OCT Principle of OCT, tissue optics, Fourier domain OCT, miscellaneous Confocal sensors Principle, resolution and PSF, microscopy, chromatical confocal method

3 3 Content Moire effect Illumination coding Fringe projection Deflectometry

4 4 Moire Effect Special pattern by using two identical but inclined gratings Sinusoidal grating Rotated grating Overlay: Moiré interference Ref: R. Kowarschik

5 5 Moire Effect Improved accuracy by two inclined gratings The new period is given by elementary period p o rotation angle p p0 sin( ) elementary period p 1 increased period p elementary period p 2 increased period p = p o /sin Improved accuracy by two gratings with slightly different periods p 1 / p 2 The new period is given by p pp p

6 6 Moire Point grating Moire Moire effect for two circular fringe systems

7 7 Shadow Moire Setup Ref: T. Yoshizawa Shadow Moire Illumination and observation propagated through the same grating (multiplicative Moire) Illumination: transmission at position A Observation: transmission at position B Total signal with geometry Finally gives and allows to reconstruct the height h(,y) High frequencies are filtered out: smoothed Moire signal A A p y t 2 cos 1 ), ( B B p y t 2 cos 1 ), ( B A p p y I 2 cos 1 2 cos 1 ), ( P P P B P P A h l l h s h l l, h l h s p y K y I 2 cos 1 ), ( ), (

8 8 Shadow Moire Typical formation of fringes Moire period quite longer then grating constant p grating period illumination Moire period observation Ref: R. Kowarschik/Wyant

9 9 Moire Shadow Moire for different viewing angles Shadow Moire filtering of the elementary period frequency Ref: R. Kowarschik

10 10 Shadow Moire Serat projection t (, ) t (, ) 1 y 2 y Ref: R. Kowarschik t1(, y) t2(, y) 128(1 cos2 (, y))

11 11 Shape Measurement by Structured Illumination Main idea: - light pattern projected onto the scene under investigation - deformation of the pattern due to 3D shape of the body - detection of the changed pattern by camera - analysis of the geometry to reconstruct the shape Physics: - incoherent illumination, light diffuse scattered into all directions - incoherent illumination, light specular reflected by polished surface (deflectometry) - coherent illumination, interferometry or holography Special coding/decoding strategies gives fast and unique shape reconstruction: coded structured light (CSL) Single shot: phase unwrapping is critical Classification of methods: - single/multiple shots - sparse/dense pattern (discretized, binary pattern/continuous grayscales) - spatial/time multipleing (binary encoding / phase shifting) - black/white vs colored pattern - number of cameras - ais codification: 1D vs 2D pattern

12 12 Measurement by Fringe Projection Projection of a light sheet onto a deformed surface Corresponds to one fringe in more complicated pattern projection

13 13 Linear Encoders Main idea: - linear scale as reference, linear pattern of fringes - reading head with similar linear scale - comparison of scales due to changes by movement or deformation Optical encoding techniques by: - Moire - grating fringe projection - interferometry - holography Quantitative evaluation of length by counting the periods/fringes Unique demodulation by phase shifting techniques Similar technique: angle encoding

14 14 Coded Illumination Time multipleing: - binary codes - n-ary codes - gray code with phase shift - hybrid methods Spatial codification: - non-formal codification - M-arrays - de Bruijn sequences Direct codification: - gray levels - color coding

15 15 Coded Illumination Comparison: binary graycode vs phase shift graycode phase shift Ref: R. Kowarschik

16 16 Coded Illumination Binary graycode projection of different pattern in a time series Ref: R. Kowarschik

17 17 Absolute Encoders Absolute decoding: simultaneously binary multi-track code Ref: R. Kowarschik

18 18 Coded Illumination Phase shift technique: projection of the same periodic pattern for different phases At least three phases are needed to guarantee a unique reconstruction To rela noise influence: 4 or 5 phase values measured (redundance) = 0 = 2 Ref: R. Kowarschik = = 3 2

19 19 Encoding with Moire Linear encoders: slightly different period in projection / observation

20 20 Wrapping Full surface height h: z(,y) Wrapped onto a limited height h Typical for recovery of angle/phase information onto the elementary interval 2 z(,y) h z(,y) h z(,y) wrapped

21 Fringe Projection Setup Shape measurement of a surface Projection of a fringe pattern onto the surface Observation of the fringe deformation by a camera, mostly by Scheimpflug geometry A shift corresponds to a change in depth Non-trivial image processing light source amplitude grating condenser collector surface under test sensor objective for detection

22 22 Pattern Projection Checkerboard projection pattern instead of simple linear fringes

23 23 Pattern Projection Setups General setup of a pattern projection

24 24 Fringe Projection Illumination: 1. telecentric / collimated z p surface z(,y) 2. central / source point z point source surface z(,y) p()

25 25 Fringe Projection Observation methods CCD sensor 1. structured detector z surface z(,y) 2. Moire projector CCD sensor z grating surface z(,y)

26 26 Fringe Projection Problems with shadowing Ref: R. Kowarschik

27 27 Measurement by Projection Visibility and unvisible regions in projection Here: measurement of a sphere

28 Signal Evaluation of Fringe Projection Fringe period in projection Lateral shift Corresponding depth value z p u z f ( ) p cos 1 cos1 cos u p z 2 cos cos z sin 1 p cos 1 2 p 1 cos 2 2 p u z P 1 p projected fringes P observation test surface z

29 29 Measurement by Central Projection Evaluation in only 2 dimensions for central projection Mapping transform ' ') ( d t c Z ' ') ( d t c d c X

30 30 Fringe Projection Systems 3D sensorhead Measuring of a seat with kolibrirobot Ref: R. Kowarschik

31 31 Eample Fringe projection Monochromatic illuminated technical surface

32 32 Fringe Projection Eamples Sheetmetal workpiece Measuring result; Comparision with CAD model Prepared stump, 4 different perspectives Ref: R. Kowarschik tooth Complete jaw

33 33 Shape Measurement Reverse engineering: from body to digital 3D data Ref: W. Osten

34 34 3D Shape Measurement for Biometry Colored biometric fringe projection Projection of a 2D triangular pattern

35 35 3D Shape Measurement for Biometry Biometric 3D mesh of a human face Error-free identification of people Ref: S. Zhang

36 36 Deflectometry Principle of deflectometry: measurement of the deflection of light rays for reflective polished surfaces under the specular direction nature of the light source is known measured object is a part of the imaging system observation of the light source over the object Ref: B. Fleck

37 37 Deflectometry General approach structured illumination of the object object phase image qualitative evidence of macroscopic defects gradient field Additional information from system calibration, system geometry quantitative 3D surface topography Ref: B. Fleck

38 Deflectometry 38 Principle: - an array of thin light pencils is incident on te surface under test - the ray positions are measured by a camera after reflection from teh surface under test - the nominal locations of the ray centroids must be calibrated - to ensure a unique interpretation, several z-positions of the screen are measured - only works for polished surfaces - the pattern can be a 2D array or a line pattern Accuracy: - strongly depends on the size of the surface - rough estimation: 1 mm for small pieces, 0.2 mm can be acchieved Problems: - ranges of large curvature: lateral resolution is poor - not usable before polishing - calibration and reconstruction algorithms complicated surface under test mask with pinhole array screen illumination projector camera moving camera position -38-

39 39 Deflectometry Setup for reflective sample Setup for refractive/transmissive sample

40 40 Deflectometry Calculation and evaluation p: stripe width d:distance focusing screen - surface 2 d tan(2 ) p camera screen Ref: B. Fleck bended surface