Sébastien Equis, and Pierre Jacquot EPFL, Nanophotonics and Metrology Laboratory, Lausanne, Switzerland

Transcription

1 Sébastien Equis, and Pierre Jacquot EPFL, Nanophotonics and Metrology Laboratory, Lausanne, Switzerland

2 Outline Conventional fringe projection and phase extraction Motivation of information multiplexing in fringe projection Color sensors Layers photo sensor from Foveon Color fringe projection and Foveon sensor: a processing road map Linearization and color transformation The Empirical Mode Decomposition for patterns normalizing Experimental assessment of the proposed solution Outlook: towards LED projector Summary 2

3 Fringe projection: principle In parallel projection and telecentric observation: 2 x, y x hx, ytan 0 p 3

4 Phase extraction in conventional fringe projection Fourier transform technique Single frame technique High measurement bandwidth - Sign ambiguity not resolved - Limited spatial resolution Phase shifting techniques - High spatial resolution - Sign ambiguity removed - High measurement accuracy Limited measurement bandwidth Total phase change below π between consecutive frames M. Takeda, H. Ina, and S. Kobayashi. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. JOSA, 72(1):156 60, X. Colonna De Lega and P. Jacquot. Deformation measurement with object induced dynamic phase shifting. AO, 35(25): ,

5 Motivation: How to make a technique working at camera frame-rate while keeping the advantages of the phase-shifting technique? Use color for phase-shifted frames multiplexing to achieve phase-shifting snap-shot profilometry P Red I P I Green P I Blue 1cos 2 x p 1cos 2 x p Projected patterns 1cos 2 x p G I 2 Red a b cos x p G I 2 Green a b cos x p G I 2 Blue a b cos x p Grabbed patterns 3-frames algorithm: G G 1cos I Red IBlue 2 arctan x G G G sin 2IGreen IRed IBlue p 5

6 Color sensor Excellent color separation Bayer matrix - Low spatial resolution - color aliasing Tri-CCD -Excellent color separation - A priori high spatial resolution - Complexity and cost - 3 frames registration Foveon X3 High spatial resolution Unambiguous relationship between image pixel and sensor pixel Spectral overlapping Color transformation 6

7 3-layer color sensor from Foveon: architecture Equis-Jacquot 7

8 Dedicated processing for 3-layer color sensor use: response linearization Non-linearities of video-projector and camera corrected by look-up tables 8

9 Dedicated processing for 3-layer color sensor use: color transformation 430 nm 550 nm 670 nm Grabbed image To 1 excitation X, the sensor gives the response R: At least 9 equations needed! In practice, Gretag MacBeth chart 1... \... S T R R X X 1 N T N R S X Spectral overlapping Large off-axis terms Linearized image Color transformed image 9

10 Fringe projection with the Foveon sensor Raw image Linearized image Color transformed image 10

11 The use of the Empirical Mode Decomposition for fringe patterns equalization Mandatory equalization of RGB signals for phase extraction The EMD algorithm: 11

12 The use of the Empirical Mode Decomposition for fringe patterns equalization 12

13 The use of the Empirical Mode Decomposition for fringe patterns equalization 13

14 The use of the Empirical Mode Decomposition for fringe patterns equalization 14

15 Experimental assessment of the proposed solution 15

16 Experimental assessment of the proposed solution Raw image Linearized image Color transformed image EMD processed image Raw phase Raw phase Filtered phase S. Equis, R. Schnabel and P. Jacquot. Snap-shot profilometry with the Empirical Mode Decomposition and a 3-layer color sensor. Opt. Ex. 19(2): ,

17 Experimental assessment of the proposed solution Availability and ease of use of video projector - pixelisation of the projected patterns - broad spectral bandwidth of pure colors S. Equis, R. Schnabel and P. Jacquot. Snap-shot profilometry with the Empirical Mode Decomposition and a 3-layer color sensor. Opt. Ex. 19(2): ,

18 Outlook: towards LED projector - Narrow spectral bandwidth of RGB components More accurate color transformation - No pixelisation - realization of grids - light intensity Houssem Ben Salem, Realization of a fringe projection system with LEDs and a layered CMOS sensor, semester project, NAM, EPFL. 18

19 Outlook: towards LED projector 19

20 Summary feasibility of carrying out snap-shot profilometry with the layered CMOS photo sensor from Foveon and a dedicated processing versatility of EMD to normalize the three layers responses accurately, efficiently and last but not least adaptively color objects can be measured as long as the object under analysis does not contain colors with one null RGB coordinate (information needed for each phase-shifted pattern after colortransformation) LED projector: promising preliminary results. Work in progress THANK YOU FOR YOUR ATTENTION This work is supported by the Swiss National Science Foundation 20