1. Copyright © 2007-2008 Gregory Avady. All rights reserved. Electro-optical 3D Metrology Gregory Avady, Ph.D. Overview

2. Copyright © 2007-2008 Gregory Avady. All rights reserved. 3D Metrology Purpose: –Find target’s coordinates or orientation in 3D space Resources: –One or more optoelectronic sensors (cameras) –Some knowledge of the target, such as: geometry (shape), color, brightness, approximate location

3. Copyright © 2007-2008 Gregory Avady. All rights reserved. Control Device Typical Block-Diagram X Y Z O XOXO YOYO ZOZOO X1X1 Y1Y1 Z1Z1 O1O1 X2X2 Y2Y2 Z2Z2 O2O2 ZNZN XNXN YNYN ONON Sensor 1 Sensor 2 Sensor N Processor Acquisition Device Output Target Laser Designator (Optional)

4. Copyright © 2007-2008 Gregory Avady. All rights reserved. System Classifications Target Profile –Cooperative –Non-Cooperative Illumination Type –Active Systems (using laser designator) –Passive Systems Sensor Type –2D sensors (standard cameras) –1D sensors (linear CCD cameras) –Single element sensors (photodiodes) Metrology Objective –Range or angular position –3D measurement –Orientation measurement

5. Copyright © 2007-2008 Gregory Avady. All rights reserved. Cooperative Configuration Known target geometry (including distance between reference marks) Some reference marks under system control (each mark can be turned on or off in any time) Typical Procedure: –For each mark: Activate mark Acquire image Measure 3D mark’s coordinates –Calculate target orientation

6. Copyright © 2007-2008 Gregory Avady. All rights reserved. Non Cooperative Configuration Known target geometry (including distance between reference marks) The most difficult steps are: –Identification of reference marks by using: Mutual location of marks Previous target and / or marks location –Finding corresponding marks on all camera images

7. Copyright © 2007-2008 Gregory Avady. All rights reserved. Illumination Types Active System –External target illumination –If laser designator orientation is known then one 2D sensor (or two 1D sensors) may be removed Passive System –Only target’s features are used –System is not detectable from the target

8. Copyright © 2007-2008 Gregory Avady. All rights reserved. Sensors Types 2D scanning sensors (standard cameras) –Most flexible –Have more information than any other sensors 1D scanning sensors (linear CCD cameras) –Highest resolution in one direction and, as result, the highest measurement accuracy –Fastest (fewer total amount of pixels) –Required special cylindrical optics –High probability of “false parallax” in case of multiple reference marks Single element sensors (photodiodes) –Least expensive –Low accuracy

9. Copyright © 2007-2008 Gregory Avady. All rights reserved. F Individual Pixels … Z X Y 1D Scanning Sensors Cylindrical Optics

10. Copyright © 2007-2008 Gregory Avady. All rights reserved. Single Element Sensor Concept Half Mirror Mirror Object Active SensorReference Sensor Optics Variable Density Filter

11. Copyright © 2007-2008 Gregory Avady. All rights reserved. Active System Concept 2D Camera Laser Designator Target Surface Xc Yc Zc Oc Xd Yd Zd Od Reference Mark

12. Copyright © 2007-2008 Gregory Avady. All rights reserved. Analytical Description For sensor # i eleven calibration coefficients are required: a i1, a i2, …, a i11 Dependence between 2D coordinates on sensor # i and object’s 3D coordinates: Here: [X ai *, Y ai *, Z ai *] – point’s # a 2D coordinates on sensor # i (N is number of sensors)

13. Copyright © 2007-2008 Gregory Avady. All rights reserved. Analytical Description (Direct Task) The following system of linear equations is used for calculating 3D coordinates for selected point on the object: (N – number of sensors) Here: [X ai *, Y ai *, Z ai *] – point’s # a 2D coordinates on sensor # i

14. Copyright © 2007-2008 Gregory Avady. All rights reserved. Analytical Description (Inverse Task) The following equations are used for sensor # i calibration, i.e. for calculating coefficients a i1, a i2, …, a i11 : (N – number of sensors) (M – number of calibration data points) Here:[X ai *, Y ai *, Z ai *]– point’s # a 2D coordinates on sensor # i [X aj, Y aj, Z aj ]– point’s # a 3D coordinates

15. Copyright © 2007-2008 Gregory Avady. All rights reserved. Multi-Channel Processing Procedure For each channel: –Acquire image –Filter acquired image –Find center of gravity for all marks on the image –Identify each mark by using: Mutual location of reference marks Previous target / marks location (if known) Find corresponding marks on each camera image Calculate each mark’s 3D coordinates Calculate target’s orientation