1. Development of a laser slit system in 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. System layout
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.
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
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.

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

5. Triangulation Since the triangles are similar:
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.
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.
Consequently:

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

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

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

12. Detection of the light pattern
The centre of gravity of the signal acquired along direction v, for each value of the coordinate u must be calculated.
The algorithm is:
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. Labview subVi “Calcolo_Baricentri_Sub” (example)
Application of algorithm
Acquire image and calculate number of rows and number of columns.
Overlay of the centres on the image
Image thresholding
This subVi outputs the vector of the centres of gravity and the corresponding image
Filtering of the input image (preprocessing)

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

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

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

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

18. Results Botton profiles threshold 3.13 3.23 229 4.29 4.40 9 5.76 5.77
Reference measure (mm)
System measure (mm)
threshold
3.13
3.23
229
4.29
4.40 9
5.76
5.77 39
3.26
3.91
4.08 21

19. Results botton Profiles threshold 2.88 2.80 21 3.10 3.12 3.26 3.23 51
Reference measure (mm)
System measure (mm)
threshold
2.88
2.80 21
3.10
3.12
3.26
3.23 51
3.18 72

20. Other results (influence of texture and of reflectivity
botton
Profiles
Reference measure (mm)
System measure (mm)
threshold
5.11
4.61
112
5.15
3.98 47
4.46
216
12.89
12.99
213

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