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Metrology and Sensing

Lecture 8: Geometrical methods

2017-12-07

Herbert Gross

Winter term 2017

2

Preliminary Schedule

No Date Subject Detailed Content

1 19.10. Introduction Introduction, optical measurements, shape measurements, errors,

definition of the meter, sampling theorem

2 26.10. Wave optics Basics, polarization, wave aberrations, PSF, OTF

3 02.11. Sensors Introduction, basic properties, CCDs, filtering, noise

4 09.11. Fringe projection Moire principle, illumination coding, fringe projection, deflectometry

5 16.11. Interferometry I Introduction, interference, types of interferometers, miscellaneous

6 23.11. Interferometry II Examples, interferogram interpretation, fringe evaluation methods

7 30.11. Wavefront sensors Hartmann-Shack WFS, Hartmann method, miscellaneous methods

8 07.12. Geometrical methods Tactile measurement, photogrammetry, triangulation, time of flight,

Scheimpflug setup

9 14.12. Speckle methods Spatial and temporal coherence, speckle, properties, speckle metrology

10 21.12. Holography Introduction, holographic interferometry, applications, miscellaneous

11 11.01. Measurement of basic

system properties Bssic properties, knife edge, slit scan, MTF measurement

12 18.01. Phase retrieval Introduction, algorithms, practical aspects, accuracy

13 25.01. Metrology of aspheres

and freeforms Aspheres, null lens tests, CGH method, freeforms, metrology of freeforms

14 01.02. OCT Principle of OCT, tissue optics, Fourier domain OCT, miscellaneous

15 08.02. Confocal sensors Principle, resolution and PSF, microscopy, chromatical confocal method

3

Content

Tactile measurement

Triangulation

Scheimpflug setup

Stereo-Photogrammetry

Time of flight

4

Overview: Resolution vs Working distance

Comparison of various methods for 3D-shape measurement

Conflict: large working distance and high resolution

WLI = white light interferometry

FM-CW = frequency modulated continuous wave radar

AM-TOF = amplitude modulated time of flight

OCT = optical coherence tomography

5

Tactile Measurement

Measuring head is touching the test surface,

measurement by contact

Coordinate measuring machine with large weight andf high precision is necessary

Punctual scanning measurement

All surface types are possible: flexible method

- independent of color, structure, material

- damage of labile surfaces possible

Precision is sub µm

Ref: B. Fleck

6

Tactile Measurement Principle

Ref: B. Fleck

test piece is fixed in a workpiece holder and scanned by contacting displacement

sensors

- workpiece is fixed and scanned point by point

- workpiece can be moved and scanned by fixed sensors

based on mechanically moving switching or measuring probes, which are pressed

against the measuring surface

switching probes solve of a switching pulse at probing the target surface, which

interrogates the current position of the probe

measuring probes measure the movement of a movable resiliently storing probe, which

is continuously pressed against the surface, whereby the surface can be scanned

the coordinates of the individual measuring points can be used as coordinate data to

calculate the actual shape of the workpiece surface

in practice non-contact pneumatic or optical sensors with tactile buttons

7

Tactile Measurement

Ref: B. Fleck

Applications:

- used for geometric control of coarse or fine shape deviations of workpieces:

- quality control by sampling or complete testing

- statistical process control

- determination of geometric models

Used in the measuring room or in the manufacturing environment

Suitable for the measurement of sufficiently solid surfaces, independent of color,

material and lighting conditions

Systems for coordinate metrology, form metrology and surface and contour

measurement technology are basically universally

Tested products for example:

metal parts, gears or complete vehicle bodies

8

Tactile Measurement

Used for:

1. Dimensional measuring:

allows the detection of deviations

2. 3D-Shape measurement:

determined shape deviations in form and position

3. Surface measurement:

Waviness and roughness measurement

Ref: B. Fleck

9

Tactile Measurement

Example maschines

Complicated geometries measurable

Tactile Measurement

Ref: H. Hage / R.Börret

Scanning method

- Sapphire sphere probes shape

- slow

- only some traces are measured

Universal coordinate measuring machine

(CMM) as basic engine

Contact can damage the surface

Accuracy 0.2 mm in best case

10

Influence of the taste sphere:

filtering of higher spatial frequencies due to finite size

Gradient of skew touching geometry can be calibrated and corrected

Periods of same size as the sphere: error in amplitude

High frequencies: not detected

Tactile Measurement

A

high accuracy

v

gradient

correction

amplitude

reduced

period not

resolved

calibration

according to

contact slope

12

Tactile Measurement

Ref: B. Fleck

Working principle of a coordinate measuring machine:

- capturing of spatial coordinates on a workpiece surface

these measuring points are processed by a computer and the values of the selected

assigned, geometric quantities (e.g. length, distance, angle) calculated

Basic designs:

- cantilever design

- bridge construction

- portal design

- stand construction

cantilever design portal design

bridge construction stand construction

13

Coordinate Measurement Machine

Ref: B. Fleck

Working principle of a coordinate measuring machine:

- touch on with sensors

- mechanical probing with tactile sensors

- non-contact probing with optical, electrical or X-ray tomography sensors possible

14

Triangulation

Triangulation principle

Active triangulation:

scanning and tracking of reflected scattered light

Projection of a line instead of a single point

Active triangulation: structured illumination

Ref: W. Osten

object

detector

lens

illumination

15

Triangulation

Geometry of reconstruction

Analysis of the triangles:

Elimination of the angles:

reconstruction of z from

Setup data: a,f,zo

camera spot centroid:Dx

camera

zo

z

a

P

P’

sample

illumination

direction

ODx

q qo

f

0 tan

( ) tan

f tan( )

o o

o

a z

a z z

x

q

q

q q

D

Projection of a narrow beam onto a surface

Backscattering of light

Observation under an oblique angle:

Lateral shift of image point corresponds to depth

Dz

Scattered light amplitude depends strongly on material

properties:

poor SNR for polished surfaces

u

Cz

sinsin2

D

q

Triangulation

q

test piece

u

sensor

illumination

observation

Dx

Dz

laser

17

Triangulation

Example of triangulation:

digital monument of

Michelangelo

(Levoy et al. )

Ref: R. Kowarschik

18

Triangulation

Ref: B. Fleck

Single Point Measurement Profile Measurement Surface Measurement

Projection Projection Projection Detection Detection Detection

Principles with active triangulation with structured illumination

Depending on the dimension of the used illumination source, a distinction is made:

19

Triangulation

Modified version:

light sheet illumination

Ref: R. Kowarschik

Camera

Object

Laser

(x,y)

20

Applications of Triangulation

21

Triangulation in Ophthalmology

Measurement of the human eye

by a slit lamp and triangulation

Scheimpflug imaging setup

Ref: M. Kaschke

Scheimpflug Imaging

Example for oblique imaging with

Scheimpflug condition

Sharp image

Strong distortion:

example: keystone distortion

Ref: W. Osten

detector

22

ideal

real

General :

1. Image plane is tilted

2. Magnification is anamorphic

Example :

Scheimpflug-Imaging

Scheimpflug System

object plane

lens

image plane

q q'

s

s'

'sin

sin2

q

q oy mm

q

q

tan

'tan'

s

smm ox

More general case of finite loactions of the principal planes

Derivation of Scheimpflug imaging

condition with depth magnification

Scheimpflug Imaging

yo

z

z'

P P'

F'

s's

q q'

d

y'o y'

y

2

22 ''

y

ym

z

zo

24

Imaging with tilted object plane

If principal plane, object and image plane meet in a common point:

Scheimpflug condition,

sharp imaging possible

Scheimpflug equation

q

q

tan'tan

tantan

'

s

s

Scheimpflug Imaging

q q'

y

s

s'

h

y'

h'

tilted

object

tilted

image

system

optical axis

principal

plane

25

Scheimpflug imaging setup:

changes of performance due to skew

geometry

Intensity variation: SNR affected

1. NA changes

2. incidence angle changes

Imaging performance changes:

resolution affected

different object distances causes

change of aberrations

Scheimpflug Imaging

26

Scheimpflug imaging setup:

changes of performance due

to aberrations:

1. spot

2. coma

3. rms diameter

Scheimpflug Imaging

27

Scheimpflug systems

Scheimpflug Imaging

28

29

Photogrammetry

Traditional recording of the earth

Modern recording

with drones for

google earth

30


Basic principle:

recording a scene by two cameras under different angles

Ref: R. Kowarschik

31


Two images from:

1. a stereo setup with two cameras and simultaneous recording

or

2. a single camera, which acquires the two images sequentially (moved)

Both scenarios are geometrically equivalent

Ref: R. Kowarschik

32


Examples:

recording of two images

Ref: R. Kowarschik

33


Determination of the position and the orientation of the cameras

Comparison of two reference points

Ref: R. Kowarschik

34


Computing the projection matrix

Reconstruction

Compute textured triangles

Ref: R. Kowarschik

35


Image rectification:

x: point of interest in the scene

OL, OR: centers of the camera lenses

xL, xR: projections of the point x onto the two camera planes

eL, eR: images of the camera centers on the other camera respectively:

epipolar points

blue planes: camera images

central projection of 3D scene onto 2D geometry

OL, OR, eL, eR are on one straight line

points OL, X, X1,... are seen by the left camera as one point

for the right camera they are located on one line:

epipolar line (red)

the lines OL, X and eR, XR must be parallel

(property of projection)

OL, OL, X are in the epipolar plane (green)

this geometry allows for a reconstruction

of the geometry out of the two planes by

using the epipolar constraint to find the

corresponding point in the other camera

36


Given an image point in one view

Find: corresponding point in the other view

A point in one view generates an epipolar line in the other view

The corresponding line must lie on this line

Ref: R. Kowarschik

Epipolar line

?

Baseline

Epipole C' C

37


In the epipolar plane necessarily lie:

1. camera centre

2. corresponding points

3. scene point

Epipolar geometry:

consequence of the coplanarity of the camera centres and the scene point

Ref: R. Kowarschik

x x /

X

C C'

38


Dimensions:

1. one dimensional

- collinear

- one point

2. three-dimensional - 2 planes - stereo

- same object point on two planes

- identification of corresponding

points on the two images

3. three-dimensional - multi-planes

- redundant information

- fit of transform parameters

- calibration of cameras

39

Photogrammetry

Central projection

Camera centre, image point and scene point are collinear

Image point back projects to a ray in 3D-space

Depth of the scene point is unknown

Ref: R. Kowarschik

Camera centre Image plane

Image

point

Scene

point

?

40


Image gathering point search

Ref: R. Kowarschik

41


Given: two images of a scene acquired by known cameras

Goal: 3D structure of the scene

Principle: triangulation from corresponding image points

Determination of a 3D point at the intersection of two back-projected rays

Ref: R. Kowarschik

42


Corresponding points are images of the same object point

The back-projected points generate rays which

intersect at the 3D object point

Complete process of reconstruction:

1. for each point in the first image find

the corresponding point in the second

image

2. for each pair of corresponding points

determine the 3D point by triangulation

Ref: R. Kowarschik

Triangulation

43


Setup

Ref: R. Kowarschik

Standard XGA-Projector

Fire-Wire cameras (1.3

MPixel)

Lateral resolution 0.3 mm

Longitudinal resolution: 0.4 –

0.8 mm

44

Time of Flight

Principle of TOF:

direct measuring the propagation time of a light wave by detecting the phase (radar)

Direct method:

measurement in the time domain

Indirect method:

Modulation of the signal and observation of the phase shift in frequency space

Estimation:

Speed of light: c = 3 108 m/s

detectable time period: 10 ps

corresponds to a distance of: 1.5 mm

Ref: R. Kowarschik

tcd D2

1

45

Time of Flight: Properties

The success of TOF is strongly related to the electronic capabilities of fast detection:

gating, calibration, charge transfer, time to digital converter,...

Continuous light waves instead of short light pulses possible

Modulation in terms of frequency of sinusoidal waves

Detected wave after reflection has shifted phase

Advantages:

- Large variety of light sources available

- Applicable to different modulation techniques

- Simultaneous range and amplitude images

- Large volume of measurement (up to 100 m)

- Fast

Disadvantages:

- Integration over time required to reduce noise

- Frame rates limited by integration time

- Motion blur caused by long integration time

- Relative low accuracy (> ~ 1...5 mm)

- Exact triggering ~10 ps ...30 ps

- No scaling with volume

Applications: buildings, rooms, security, archeology

Ref: R. Kowarschik

46

Time of Flight:

System configuration:

1. single point, 2D scanner

2. 1D array, 1D scanner

3. 2D array, no scanner

Example 1:

- point detector

- 2D scanner in both transverse directions

- Laser pulses synchronized with scan mirror

position

- additional stop reduces sensitivity for background light

Example 3:

- area detector

- no scanner necessary

47

Time of Flight

Example:

scene and depth map

Laser radar = ladar

Ref: R. Kowarschik

48

Time of Flight

Example: PMDVision CamCube

Typical systems

Ref: R. Kowarschik

Near-infrared light (700-1400 nm)

Continuous wave modulation

Sinusoidal signal

Resolution: 204x204 pixels

Standard lens, standard calibration

Frame rate: 20 fps

Multiple camera operation by using

different modulation frequencies

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