Students: Paolo Bellandi Emanuele Ferrari Course: Optical Measurements 2007

1. Development of a laser slit systemin LabView Students:Paolo Bellandi Emanuele Ferrari Course: Optical Measurements 2007

2. Objectives • Design of a laser slit system, using active triangulation • Implementation of the demonstrator • Laser line projector • CMOS camera • Triangulation geometry • Implementation of the measurement procedures in LabView • Metrological validation of the system

3. P e C : exit and input pupils for the projector and the camera respectively H and V: sensor size along u and v coordinates; N and M: sensor resolution along u and v The camera sensor is positioned at the image plane. The reference systems are (xc, yc, zc), and (u,v). The former is centered at point C; the latter is centered at point O’; it is the central point of the image plane. f: focal length od the camera lens Two geometrical parameters. Baseline d and standoff distance L. Their relation is: FW and FH represent the dimension of the Field of View (FOV). FW is the maximum length of the laser stripe. (x,y,z) is the global reference system. System layout

4. Similar triangles: To calculate the value of FH: Layout in the x,z plane

5. Since the triangles are similar: The height of object point Po is evaluated with respect to the reference plane. The deformation induced by the object shape is evaluated as the difference with respect to the undeformed line on the reference plane. In the presence of the object, ray PO is deviated at Po and impinges at position A on the image plane. Point B is the corresponding point on the reference plane. Consequently: Triangulation

6. Laser line projector f d  L Camera The demonstrator

7. This means : H CCD Laser f hence: L Laser H d d f CCD z L y FW FW x Parameters evaluation 1 The geometry is:

8. Parameters evaluation 2 Input values D = 16 cm L = 9.5 cm H = 768 pixels V = 576 pixels Pixel Size = 8,48 um FW = circa 6,5 cm Evaluation of parameter f We have used an objective with f=12mm and a 5mm ring. The corresponding value for FW is 7 cm.

9. Triangulation again Ray tracing in the presence of an object

10. Triangulation equations O’P is evaluated from the measure in pixels multiplied by the pixel size. Then: The vallues of angles b and g: e Note that And

11. Applying the sine theorem to we have Triangulation equations Sine triangles are similar and We get: then This is the measurement information we want

12. The centre of gravity of the signal acquired along direction v, for each value of the coordinate u must be calculated. The algorithm is: Detection of the light pattern • bc : position of the centre of gravity; lc : gray level of the c-element. • The method must be iterated for all the columns in the image.

13. Acquire image and calculate number of rows and number of columns. Overlay of the centres on the image This subVi outputs the vector of the centres of gravity and the corresponding image Image thresholding Filtering of the input image (preprocessing) Application of algorithm Labview subVi “Calcolo_Baricentri_Sub” (example)

14. Live acquisition Visualization window Threshold to trim the detection algoritm Freeze image Front panel

15. Freezed image Gray level visulatization along a profile line Front panel

16. New acquisition Save image Save the centres of gravity Evaluation of the measurement information. Triangulation is performed here. Front panel Error message if the results are not saved

17. Value measured by the system: 4.72 mm Results Deformed profile Reference profile: Threshold equal to 229. Reference measurement (caliper used): 4.73 mm

18. Results

19. Results

20. Other results (influence of texture and of reflectivity

21. Conclusions • For measurement ranges up to 10mm the measurement uncertainty is 0,1mm. • The performances can be increased if absolute calibration is performed • Camera model • Intrinsic and extrinsic parameters must be estimated • Projection model • The projection plane must be estimated • The front panel is user friendly