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

Copyright © 2007-2008 Gregory Avady. All rights reserved.

Electro-optical 3D Metrology

Gregory Avady, Ph.D.

Overview


3D Metrology3D 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

Copyright © 2007-2008 Gregory Avady. All rights reserved.Control Device

Typical Block-DiagramTypical Block-Diagram

X

Y

Z

O

XO

YOZO

OO

X1

Y1

Z1

O1

X2

Y2

Z2

O2

ZN

XN

YN

ON

Sensor 1

Sensor 2 Sensor N

Processor

Acquisition Device

Output Target

Laser Designator(Optional)


System ClassificationsSystem 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


Cooperative ConfigurationCooperative 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


Non Cooperative ConfigurationNon 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


Illumination TypesIllumination 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


Sensors TypesSensors 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


F

Individual Pixels…

Z

X

Y

1D Scanning Sensors1D Scanning Sensors

Cylindrical Optics


Single Element Sensor ConceptSingle Element Sensor Concept

Half Mirror

Mirror

Object

Active Sensor

Reference Sensor

Optics

Variable Density Filter


Active System ConceptActive System Concept

2D Camera

Laser Designator

Target Surface

Xc

Yc

ZcOc

Xd

Yd

ZdOd

Reference Mark


Analytical DescriptionAnalytical Description

• For sensor # i eleven calibration coefficients are required: ai1, ai2, …, ai11

• Dependence between 2D coordinates on sensor # i and object’s 3D coordinates:

Here: [Xai*, Yai*, Zai*] – point’s # a 2D coordinates on sensor # i

1*11109

4321

aiaiai

iaiaiaiai ZaYaXa

aZaYaXaX

Ni ;1 (N is number of sensors)

1*11109

8765

aiaiai

iaiaiaiai ZaYaXa

aZaYaXaY


Analytical Description (Direct Task)Analytical Description (Direct Task)

• The following system of linear equations is used for calculating 3D coordinates for selected point on the object:

*)*()*()*( 431121019 aiiaiaiiaiaiiaiaii XaZaXaYaXaXaXa

Ni ;1 (N – number of sensors)

*)*()*()*( 871161059 aiiaiaiiaiaiiaiaii YaZaYaYaYaXaYa

Here: [Xai*, Yai*, Zai*] – point’s # a 2D coordinates on sensor # i


Analytical Description (Inverse Task)Analytical Description (Inverse Task)

• The following equations are used for sensor # i calibration, i.e. for calculating coefficients ai1, ai2, …, ai11:

**** 111098765 ajiajajiajajiajajiiajiajiaj YaYZaYYaYXaaZaYaX **** 111094321 ajiajajiajajiajajiiajiajiaj XaXZaXYaXXaaZaYaX

Ni ;1 (N – number of sensors)(M – number of calibration data points)Mj ;1

Here: [Xai*, Yai*, Zai*] – point’s # a 2D coordinates on sensor # i [Xaj, Yaj, Zaj] – point’s # a 3D coordinates


Multi-Channel Processing ProcedureMulti-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

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

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