Lecture 6 Cont’d - Encsusers.encs.concordia.ca/~nrskumar/Index_files/Mech6491... · 2015-05-26 · Lecture 6 Cont’d Instructor: N R Sivakumar. 2 ... When looking at the reconstruction

MECH 6491 Engineering Metrology

and Measurement Systems

Lecture 6 Cont’d

Instructor: N R Sivakumar

Interferometry Examples

Moire and Phase Shifting Interferometry

Theory

Types of measurement

Applications (form and stress measurement)

Theory of phase shifting

Types of phase shifting methods available,

Errors associated with phase shifting

Outline

Twyman Green InterferometerFlat Surfaces

Twyman Green InterferometerSpherical Surfaces

Mirau Interferometer

Diffraction

DiffractionTypes of diffraction

DiffractionDouble Slit

DiffractionTriple Slit

DiffractionMultiple Slit

dsin m m = 0,1,2,3..

d = w/N where w is the entire width of the grating

DiffractionGrating -- N slits or rulings

tan (ym y0) /D

Measure angles of diffracted lines with a spectroscope using

formula below. Then relate to wavelength

= dsin /m

Diffraction GratingsMeasure Wavelength of Light

R / Nm

Resolving power of grating.

Measure of the narrowness of lines

Diffraction GratingsResolving Power

Moire Interferometry

Dark fringe - when the dark lines are out of step one-half period

Bright fringe - when the dark lines from one fall on the dark lines

for of the other

If the between the two gratings is increased the separation

between the bright and dark fringes decreases

Moiré pattern formed

by two line gratings

rotated by small

M = 2y sin

Dark fringe - when the dark lines are out of step one-half period

If the gratings are not identical, the moiré pattern will not be

straight equi-spaced fringes

How are moiré patterns related to interferometry?

The grating shown in Fig. can be a “snapshot” of plane wave

traveling to the right, and the grating lines distance = of light.

M = 2y sin

It becomes like interfereing two plane waves at an angle 2

Where the two waves are in phase, bright fringes result, and

where they are out of phase, dark fringes result

The spacing of the fringes on the screen is given by previous

eqn. where is now the wavelength of light (M = 2y sin)

Thus, the moiré of two gratings correctly predicts the centers of

the interference fringes produced by interfering 2 plane waves

Since binary gratings are used, the moiré does not correctly

predict the sinusoidal intensity profile of the interference fringes.

Fig shows the moiré

produced by superimposing

two computer-generated

interferograms.

First interferogram (a) has

50 waves of tilt across the

radius

Second interferogram (b)

has 50 waves of tilt plus 4

waves of defocus.

If they are aligned such that

the tilt is same for both, tilt

cancels and the 4 waves of

defocus remain (c).

In (d), the two inferograms

are rotated wrt each other so

that the tilt will quite cancel.

These results can be

described mathematically

using two grating functions:

Gratings used in Moire measurements are usually

transparencies and if this is placed in contact with

object, the phase of this grating will be modulated

depending on the object displacement - np for maxima

and (n+1/2) P for minima

It there is a model grating as well, then the deformation

produces fringes, with which the displacement can be

computed

The model grating can be placed over the grating, or

imaged over the grating or imaged on

photographic film

Moire – In Plane Measurement

Out of plane displacements are

measured by using a single

grating and an interference with

the shadow of the grating itself

The most successful application

of shadow moire is in Medicine

Useful in coarse measurements

on large surfaces with complex

contours

Shadow Moire – Out of Plane

W = out of plane displacement

p = grating pitch; = light angle

= observation angle

Fringe Projection

Phase Shifting InterferometryParameters Fringe

skeletonizing

Phase stepping/

shifting

Fourier

transform

Temporal

heterodyning

No of interferograms to be

reconstructed

1 Minimum 3 1 (2) One per detection

Resolution () 1 to 1/10 1/10 to 1/100 1/10 1/30 1/100 to 1/1000

Evaluation between

intensity extremes

No Yes Yes Yes

Inherent noise suppression Partially Yes No (yes) Partially

Automatic sign detection No Yes No (yes) Yes

Necessary experimental

manipulation

No Phase shift No (phase

shift)

Frequency

Experimental effort Low High Low Extremely high

Sensitivity to external

influences

Low Moderate Low Extremely high

Interaction by the

operator

Possible Not possible Possible Not possible

Speed of evaluation Low High Low Extremely low

Cost Moderate High Moderate Very high

Comparison of phase evaluation methods

With CCDs, the intensity at multiple points can be recorded

and processed simultaneously at high speeds. Therefore,

the equation can be:

where I(x, y) is the intensity of the interference pattern at the

corresponding pixel of the CCD camera, (x, y) is the phase

difference at that particular pixel

3 unknowns in I0, V and . Therefore, a minimum of three

phase-shifted images is required to find out the phase

value of a particular point

Phase Shifting Interferometry

}]),(cos{1)[,(),( 0 ++ yxVyxIyxI

2 waves derived from a common source, the phase difference

between the two waves is given by

where is the phase difference, P is the path difference between

them and, the wavelength.

The phase difference could be introduced by introducing path

difference and vice versa

In most of the phase shifting interferometric techniques, changing

the path length of either the measurement, or the reference beam,

by a fraction of the wavelength provides the required phase shifts

Phase shifting with rotating glass plate.

Glass plate of thickness

't' rotated by an angle

))cos()cos(( 1 nk

t K =2/

n is refractive index of the plate

)cos(11

t Phase shift achieved by rotating

the glass plate by small angle

Phase shifting by moving grating and Bragg cell.

2 Where d is the period of the grating

and n is the order of diffraction

Phase shifting with laser feedback

the frequency of

the source is

changed by

injecting electrical

current to the

laser and using a

large optical path

difference

between the

measurement and

reference beams

Object

Reference

PZT to move

fraction

of a wavelength

Incident

Beam BS

Detector

Source

Interference Sensor

P is the path difference between the two beams

is the phase difference between them

the wavelength of the light source

‘I(x, y)’ is the intensity of the interference pattern,

‘(x, y)’ is the phase difference between object and

reference,

‘V’ is the modulation of the fringes

( )cos1),(),( 01 VyxIyxI +

Mirror with linear

transducer

Rotating glass

Moving diffraction

grating

Laser feedback

Polarization based phase shifting

Incident Beam Object Reference

Glass plate of thickness

't' rotated by angle

)cos(11

Where K =2/ and

‘n’ is the refractive index

Where d =grating period

‘n’ is the refractive index

2Where = phase shift

= angle of rotation

Where ‘phase shift’ is proportional to

path difference and ‘temporal frequency’

Where is wavelength

p is the path difference

Phase Shifting Techniques

Three step

method

Four step method

Carré

method

Five step

method

Other algorithms like ‘Integrated Bucket Technique’ for continuous

phase shifting and ‘multi-step techniques’ have been used

)]())][(()(3[

41324132

IIIIIIIITan

Phase Shifting Algorithms

Linear phase

Non linear phase

Light detector

anomalies

Vibration & air

turbulence

Other random

errors

All these are errors associated with

mechanical phase shifters

Phase Shifting Errors

MECH 6491 Engineering Metrology

and Measurement Systems

Lecture 7

Instructor: N R Sivakumar

Holography

Introduction and Background

Theory and types of Holography

Holographic Interferometry

Theory

Applications

Speckle Methods

Speckle Introduction

Speckle intensity and size

Speckle Interferometry

Theory

Applications

Outline

Holography Introduction

Reflection

hologram

Transmission

hologram

Holography Introduction

Holography History

Invented in 1948 by Dennis Gabor

Leith and Upatnieks (1962) applied laser to holography

Holography is the synthesis of interference and diffraction

In recording a hologram, two waves interfere to form an

interference pattern on the recording medium.

When reconstructing the hologram, the reconstructing

wave is diffracted by the hologram.

Holography History

When looking at the reconstruction of a 3-D object, it

is like looking at the real object

By means of holography an original wave field can

be reconstructed at a later time at a different location

This technique has many applications; we

concentrate on holographic interferometry

A photograph tells more than a thousand words and

a hologram tells more than a thousand photographs

Holography Advantages

Conventional Photography:

2-d version of a 3-d scene

Photograph lacks depth perception or parallax

Film sensitive only to radiant energy

Phase relation (i.e. interference) are lost

Holographic Photography:

Freezes the intricate wavefront of light that carries all

the visual information of the scene

To view a hologram, the wavefront is reconstructed

View what we would have seen if present at the

original scene through the hologram window

Provides depth perception and parallax

Holographic Photography:

Converts phase into amplitude information (in-phase

= max amp, out-of-phase = min amp)

Interfere wavefront of light from a scene with

reference wave

The hologram is a complex interference pattern of

microscopically spaced fringes

“holos” – Greek for whole message

Holography Recording

Laser beam is split in 2

1 wave illuminates the object

The object scatters the light

onto the hologram plate

(object wave)

The other wave is reflected directly onto the hologram

plate. (reference wave) constitutes a uniform illumination

of the hologram plate

The hologram plate must be a light-sensitive medium,

e.g. a silver halide film plate with high resolution

Let the object and

reference waves in the hologram

plane be described by the field

amplitudes uo and u.

These two waves will interfere

resulting in an intensity distribution

This intensity is allowed to blacken the hologram plate

Then it is removed and developed

This process is hologram recording

*uu u*u u u u u I oo

o ++++

This hologram has a

transmittance t proportional to

intensity distribution

*uu u*u u u I t oo

Replace the hologram back in the holder in

the same position

Block object wave and illuminate the hologram with the reference

wave (reconstruction wave) Ua which will be U multiplied by t

a uu (uu)*u u u u u u +++ t

Holography Reconstruction

The quantity IuI2 is constant –

uniform light and the last term thus

becomes (apart from a constant)

identical to the original object

wave uo.

We are able to reconstruct the

object wave, maintaining its

original phase and relative

amplitude distribution uo

by looking through the hologram, object can be seen in 3D

even though the physical object has been removed

Therefore this reconstructed wave is also called the virtual

Direct wave: corresponds to zeroth order grating

diffraction pattern

Object wave: gives virtual image of the object

(reconstructs object wavefront) – first order diffraction

Conjugate wave: conjugate point, real image (not

useful since image is inside-out) – negative first order

diffraction

In general, we wish to view only the object wave – the

other waves just confuse the issue

Hologram Reconstruction

Virtual image

Real image

Direct wave

Object

Conjugate

Reference wave

Virtual imageReal image

Direct wave

Object

Conjugate

Reference wave

Use an off-axis system to record the hologram, ensuring separation of the

three waves on reconstruction

Holography Reconstruction

Alternative method of recording

Fewer components hence more stable

Can you spot the difference …………..

Transmission hologram: reference and object waves

traverse the film from the same side

Reflection hologram: reference and object waves traverse

the emulsion from opposite sides

Hologram

View in Transmission View in reflection

Reflection vs. Transmission

Hologram - Transmission

Hologram - Reflection

Hologram: Wavelength

With a different color, the virtual image will appear at a

different angle – (i.e. as a grating, the hologram disperses

light of different wavelengths at different angles)

Volume hologram: emulsion thickness >> fringe spacing

Can be used to reproduce images in their original

color when illuminated by white light.

Use multiple exposures of scene in three primary

colors (R,G,B)

Volume Hologram

Reconstruction wave must be

a duplication of the reference

Reflection hologram can be

reconstructed in white light

giving images in their original

Hologram - Applications

Microscopy M = r/s

Increase magnification by viewing hologram with

longer wavelength

Produce hologram with x-ray laser, when viewed

with visible light M ~ 106

3-d images of microscopic objects – DNA, viruses

Hologram - Applications

Interferometry

Small changes in OPL can be measured by viewing

the direct image of the object and the holographic

image (interference pattern produce finges Δl)

E.g. stress points, wings of fruit fly in motion,

compression waves around a speeding bullet,

convection currents around a hot filament

Two waves reflected from two identical objects could

interfere

With the method of holography now at hand, we are

able to realize this by storing the wavefront scattered

from an object in a hologram.

We then can recreate this wavefront by hologram

reconstruction, where and when we choose.

For instance, we can let it interfere with the wave

scattered from the object in a deformed state.

This technique belongs to the field of holographic

interferometry

In the case of static deformations, the methods can be

grouped into two procedures, double-exposure and

real-time interferometry.

(Vest 1979; Erf 1974; Jones and Wykes 1989).

Double Exposure Interferometry

Two holograms of the object recorded in

same medium at different time instants

If conditions at the recordings different

→interference between the reconstructed

holographic images reveals deformations

simple to carry out

avoids the problem of

realignment

distortion minimized

compares only two time

instances

The observer sees any

deformation of the object

(in scale of λ) in real time

as interference between

the real object and the

holographic image of the

object at rest

Disadvantage is that the

hologram must be

replaced in its original

position with very high

accuracy

Real Time Interferometry

Holographic Interferograms

Deflection of a

rectangular plate

fastened with five

struts and subjected

to a uniform pressure

Detection of

debonded region of

a honeycomb

construction panel

A bullet in flight

observed through

a doubly-exposed

hologram

Make hologram of vibrating

object

Maximum vibration amplitude

should be limited to tens of

wavelengths

Illumination of hologram

yields image on which is

superimposed interference

fringes

Fringes are contour lines of

equal vibration amplitude

Holographic Vibration Analysis

When looking at the laser light

scattered from a rough surface, one

sees a granular pattern

This so-called speckle pattern can

be regarded as a multiple wave

interference with random phases

Speckle is considered a mere

nuisance

But from the beginning of 1970

there were several reports from

experiments in which speckle was

exploited as a measuring tool.

light is scattered from a

rough surface of height

variations greater than the .

In white light illumination,

this effect is scarcely

observable ???

Applying laser light,

however, gives the scattered

light a characteristic granular

appearance

The probability density

function P, for the intensity in

a speckle pattern is given as

Where I is the mean intensity.

The intensity of a speckle

pattern thus obeys negative

exponential statistics

From this plot we see that the

most probable intensity value

is zero, that is, black.

Speckle Size

Objective speckle size

(without lens) is given by

Subjective speckle size (with

lens) is given by

Objective speckle size

Subjective speckle size

Laser speckle methods can be utilized in many ways; Speckle-

shearing enables direct measurements of displacement derivatives

related to strains

(Hung and Taylor 1973; Leendertz and Butters 1973).

The principle of speckle-

shearing (shearography) is

to bring the rays scattered

from one point of the object

into interference with rays

from neighboring point

This can be obtained in a speckle-shearing interferometric camera

where one half of the camera lens is covered by a thin glass wedge

In that way, the two images focused by each half of the lens are

laterally sheared

If the wedge is oriented to shear in the x, the rays from a point P(x,

y) on the object will interfere in the image plane with those from a

neighbouring point P(x+x, y)

The shearing x is proportional to the wedge angle

When the object is deformed there is a relative displacement

between the two points that produces a relative optical phase

change

For small shear angles x the equation can be

approximated to (k= 2/)

For out of plane measurement normal angle (=0) is

enough and the equation becomes

For both in plane and out of plane measurement that is

both u and w, we need to use different angle

Electronic Speckle Interferometry

(a) Out-of-plane displacement fringes (w)

and slope fringes (w/x) for a aluminium

plate loaded at the centre. x is 6 mm,

and w = 2.5 µm and

(b) Out-of-plane displacement fringe

pattern (w) and slope pattern (w/y) for

the same object. The shear y is 7 mm.

Speckle and Holography

Electronic shearography (ES) used for non-destructive

testing of a ceramic material.

(a) A vertical crack is clearly visualized by ES as a

fringe in the centre of the sample and

(b) The crack is not detected using TV holography

ESPI for NDT

GOOD part BAD part

Digital Shearography

Able to detect surface/subsurface

defects effectively and efficiently

To develop a non-destructive In-line

subsurface defects detection system

READY FOR IC FABRICATION PROCESS

RECYCLE

Defect?yes no

New process

Unpolished Silicon Wafers

Defect?no

RECYCLE

yesSilicon wafers

Patterned Wafer

Unpolished Silicon Wafers

Polishing(whole batch)

Polishing(good wafers only)

Conventional process

Estimated cost

savings more than

S$1million/year

for ISP

ESPI for NDT Application

Lecture 6 Cont’d - Encsusers.encs.concordia.ca/~nrskumar/Index_files/Mech6491... · 2015-05-26 · Lecture 6 Cont’d Instructor: N R Sivakumar. 2 ... When looking at the reconstruction

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