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Students:Students:Paolo BellandiPaolo Bellandi Emanuele Ferrari Emanuele Ferrari

Course: Optical Measurements 2007Course: Optical Measurements 2007

Development of a laser slit systemin LabView

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• 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

Objectives

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P e C : exit and input pupils for the projector and the camera respectively

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.

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

(x,y,z) is the global reference system.

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.

System layout

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Similar triangles:

FW

LHf

FW

L

H

f

To calculate the value of FH:

f

LVFH

Layout in the x,z plane

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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.

Since the triangles are similar:

d

ZL

BO

Z PoPo

Consequently:

BOd

BOLZPo

Triangulation

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Laser line projector

Camera

d

L

f

The demonstrator

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The geometry is:

d

L

f

Laser

CCD

H

FW

z

y

x

This means :

d

Lf

Laser

CCDH

FW

FW

Ld

H

f 22

hence:

FW

LdHf

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Parameters evaluation 1

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Input values

D = 16 cm

L = 9.5 cm

H = 768 pixels

Evaluation of parameter f

mmFW

LdHf 6,18

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We have used an objective with f=12mm and a 5mm ring. The corresponding value for FW is 7 cm.

V = 576 pixels

Pixel Size = 8,48 um

FW = circa 6,5 cm

Parameters evaluation 2

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Ray tracing in the presence of an object

Triangulation again

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O’P is evaluated from the measure in pixels multiplied by the pixel size. Then:

Note that

And L

arctgd

ˆAOC

2 2OF d L 'O P OF

OAf

2 2AF OA OF

arcsinOF

AF

180 180 90 90

The vallues of angles and :

e

Triangulation equations

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Applying the sine theorem to we haveAOB

sin( ) sin(180 ) sin( )

OA OB OB

BOZ

F DZ

sin( )

OFOA

AFOB

OZ L OZ

dOB

L OBOZ

OB d

Sine triangles are similar andWe get:

This is the measurement information we want

then

Triangulation equations

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• The centre of gravity of the signal acquired along direction v, for each value of the coordinate u must be calculated.

• The algorithm is:

cc

cc

c l

clb

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.

Detection of the light pattern

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Filtering of the input image (preprocessing)

Image thresholding

Acquire image and calculate number of rows and number of columns.

Application of algorithm

Overlay of the centres on the image

This subVi outputs the vector of the centres of gravity and the

corresponding image

Labview subVi “Calcolo_Baricentri_Sub” (example)

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Live acquisition

Visualization window

Threshold to trim the detection algoritm

Freeze image

Front panel

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Freezed image

Gray level visulatization along a profile line

Front panel

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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

Front panel

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Deformed profile

Reference measurement (caliper used): 4.73 mm

Value measured by the system: 4.72 mm

Reference profile:

Threshold equal to 229.

Results

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Botton profiles Reference measure (mm)

System measure (mm)

threshold

3.13 3.23 229

4.29 4.40 9

5.76 5.77 39

3.26 3.23 39

3.91 4.08 21

Results

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botton Profiles Reference measure (mm)

System measure (mm)

threshold

2.88 2.80 21

3.10 3.12 21

3.26 3.23 51

3.18 3.12 72

Results

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botton Profiles Reference measure (mm)

System measure (mm)

threshold

5.11 4.61 112

5.15 3.98 47

4.46 4.61 216

12.89 12.99 213

Other results (influence of texture and of reflectivity

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•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

Conclusions