optical interferometry and its applications in absolute distance measurements

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optical interferometryand its applications in
absolute distance measurements

• by KHALED ALZAHRANI
• Liverpool John Moores University
• GERI

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Outlines

• Interferometry Concepts
• Popular inteferometric configurations
• Absolute distance measurement (ADI)

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Interferometry Concepts

• Interference
• Intensity
• Visibility
• Optical Path Length OPL
• Optical Path Difference OPD
• Coherence
• Spatial coherence
• Temporal coherence

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General Concepts

• Optical Interfrometry is an optical measurement
  technique that provides extreme precise
  measurements of distance, displacement or shape
  and surface of objects.
• It exploits the phenomenon of light waves
  interference .
• Where under certain conditions a pattern of
  dark and light bars called interference fringes
  can be produced. Fringes can be analyzed to
  present accurate measurements in the range of
  nanometer.
• The recent developments in laser, fiber optics
  and digital processing techniques have supported
  optical interferometry .
• Applications ranging from the measurement of a
  molecule size to the diameters of stars.

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Light waves

• For many centuries, light was considered a stream
  of particles .
• Light wave exhibits various behaviours which can
  not interpreted through the particles theory of
  light such as, refraction, diffraction and
  interference.
• in19th century the particles concept was
  replaced by the wave theory .
• light waves are transverse waves with two
  components magnetic and electric field each one
  of them oscillating perpendicular to the other
  and to the propagation direction.
• The visible light is part of the electromagnetic
  spectrum it extends from 750nm for the red color
  to 380nm for the violet color.
• Light wave characteristics
• light speed in free space (c) C300k
  (km/s)
• C ?v
• V c/n
• ?n ? /n
• Where n is the refractive index of the medium
  in which the light travels.
• ?n is the wavelength in medium
  other than free space.

EM-wave propagation
Visible light spectrum
Refractive index
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Interference

• Interference is a light phenomenon .It can be
  seen in everyday life. e.g.. colures of oil film
  floating on water.
• In electromagnetic waves , interference between
  two or more waves is just an addition or
  superposition process. It results in a new wave
  pattern .

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Superposition of two waves

• When two waves with an equal amplitudes are
  superposed the output wave depends on the phase
  between the input waves.
• Y y1 y2
• Where y1A1 sin (wt ?1 )
• y2A2 sin (wt ?2)
• Since the energy in the light wave is intensity I
  ,which is proportional to the sum of square
  amplitudes A2
• where AA12A222A1A2 cos (?1 ?2)
• If A1A2A then
• A2A22A2 cos (?1 ?2)
• If y1y2 in phase ,cos(0)1 hence,
• Y 4A2 ,it gives a bright
  fringe.
• If y1y2 out of phase by (p)
  ,cos (p)-1 hence,
• Y 0 ,it gives a
  dark fringe

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Optical Path Length OPL

• When light beam travels in space from one point
  to another, the path length is the geometric
  length d multiplied by n (the air refractive
  index) which is one
• OPL d
• Light beam travels in different mediums will
  have different optical path, depending on the
  refractive index (n)of the medium or mediums.
• OPL n d

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Optical Path Difference OPD

• If two beams with the same wavelength i.e same
  frequency, travel from two different points
  towards the same destination ,taking different
  paths there will be a difference in their optical
  path this difference is called the optical path
  difference OPD.
• it is very important factor in determining
  fringes intensity.
• OPD m?
• Here, If m0 or any integer values there will be
  a bright fringe. Otherwise dark fringes (maximum
  darkness when )
• OPD (m-1/2) ?

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Intensity of Interference fringes

• Intensity of interference fringes depends on the
  phase between the recombined waves i.e.
• Intensity I is the complex amplitude of the
  interferer waves A given as IA2
• I lAl2 I1I22(I1I2) cos (??) 1/2
  
• When ?? 0
• I max I1 I2 2(I1I2)1/2
• if I1I2 then
• 
  I max4I
• When ?? p
• I min I1 I2 2(I1I2)1/2
• if I1I2 then
• 
  I min0

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Visibility of Interference fringes

• Visibility determines the ability to resolve
  interference fringes. It depends on the coherence
  degree between the recombined light waves.
• It is defined as
• V I max - I min / I max I min
• maximum if Imin 0 , V 1
• When Imin Imax , V 0
• 0 V1 .

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Coherence

• Coherence of light wave is defined as the
  correlation between the electric field values at
  different locations or times. The coherent light
  source is able to produce a coherent waves able
  to interfere with each other.
• Ideal coherent source is a source with one wave
  length only monochromatic which does not
  exist in practice.
• Practically, there is no fully coherent light or
  fully incoherent light, but there are light
  sources with deferent coherence degree .

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Spatial Temporal Coherence

• Spatial coherence
• The degree of correlation between
  different points on the same wave front at the
  same time.
• Spatial coherence is light source
  dependent, as the source size extends its spatial
  coherence degree deteriorate.
• Temporal coherence
• The correlation between the electric
  fields at the same point but at different times.
• Temporal coherence proportionate to the
  wave train length. Monochromatic sources such as
  laser have a high degree of temporal coherence,
  because of the long wave trains.
• Coherence Length ?S N ?.
• where N is the waves number
  contained in one wave train.
• Coherence time ?t ?S / C
• where C is the light speed in space
  .

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Interferometers configurations

• Interferometers classificationswave front
  division interferometers Amplitude division
  interferometer
• Popular configurations
• Michelson interferometer
• Twyman-Green interferometer
• Mach-Zehnder interferometer
• Fapry-Perot interferometer

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Interferometer

• Interferometer
• Is an optical instrument that can produced
  two beams interference or multiple beam
  interference.
• wave front division interferometers
• Two light beams from the same wave front
  are made to interfere to produce an interference
  fringe pattern.
• Amplitude-division interferometers
• A light beam from one source point is
  divided into two beams using a beam splitter.
• e.g. Michelsons interferometer

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Michelson interferometer

• Configuration
• Michelson interferometer consists of a
  coherent light source, a beam splitter BS a
  reference mirror ,a movable mirror and a screen .
  
• Applications
• There are many measurements that
  Michelson interferometer can be used for,
  absolute distance measurements, optical testing
  and measure gases refractive index.
• Work method
• The BS divides the incident beam into two
  parts one travel to the reference mirror and the
  other to the movable mirror .both parts are
  reflected back to BS recombined to form the
  interference fringes on the screen.

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Twyman-Green interferometer

• Configuration
• A modified configuration of Michelson
  interferometer ( rotatable mirror a
  monochromatic point source)
• Applications length measurements, optical
  testing e.g. lenses ,prisms, mirrors.
• Work method
• When the interferometer aligned properly,
  two images of the light source S from the two
  mirrors M1M2 will coincide. The superposed waves
  are parallel and have a constant phase
  difference. On the serene a uniform illumination
  can be seen with a constant intensity depends on
  the path difference.
• Mirror imperfections test
• There will be an interference fringes due
  to the path difference between W2 and the
  reference plan wave W1

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Mach-Zehnder interferometer

• Configuration
• consists of a light source, a detector,
  two mirrors to control the beams directions and
  two beam splitters to split and recombine the
  incident beam.
• Applications refractive index fluid flow ,heat
  transfer.
• Work method BS1 divides the incident beam into 2
  beams,mirrors M1M2 reflect beams to BS2 . BS2
  recombine the beams. interference fringes
  produced depending on the path difference .
• measure thickness at constant refractive index
• measure refractive index at constant thickness

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Fabry-Perot Interferometer FPI

• Configuration
• consisting of two parallel high reflecting
  glass plates separated several millimeters , a
  focusing lens and a display screen.
• Advantages disadvantages
• high sensitivity to wave length changes.
  (used in laser to select wave length)
• High resolution fringes (used in optical
  spectroscopy)
• Applications
• measure or control the light wave lengths e.g.
  in laser as a resonator to select a single wave
  length. optical spectroscopy.
• Work method
• the beam falls on L1, part of the beam is
  transmitted to L2, other part is reflected .the
  transmitted part partially reflected back to L1.
  Then again reflected to the L2 which partially
  reflects and transmit each incident light. The
  transmitted lights from L2 falls on the Focusing
  lens. beams are focused on the screen at point P
  .these beams interfere constructively or
  destructively according to the phase difference
  between them .
• .

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Absolute
Distance Measurements

• Developments in laser techniques and digital
  image processing have made distance measurement
  by optical techniques very attractive at variety
  of applications in industrial fields e.g. tool
  calibration, aircraft industry and robotics.
• Two measurement techniques
• Non-Coherent methods
• Triangulation techniques
• Time-of-flight systems
• Measurement accuracy larger than a
  1mm
• Coherent methods
• based on interferometry, enable high
  precision measurements of distances or
  displacements.

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Classical interferometry (i.e.
one-wavelength) commonly used for
high-resolution displacement measurements.
Resolution better than 100 nm .Drawback of
this technique is the incremental manner of
measuring, resulting from the counting of
optical fringes. ADI cannot be covered by
classical interferometry since the range of
non-ambiguity is limited to half the optical
wavelength multiple-wavelength
interferometry(MWI) offers great flexibility
in sensitivity by an appropriate choice of the
different wavelengths Example conceder two
optical wavelength ? 1?2 with PDL .the phases
f1 and f2 corresponding to the wavelengths ?1 and
?2 ?f1 (2p/ ?1) 2L ?f2(2p/ ? 2) 2L
?f12 (?f1 - ?f2) 2p/1/ ?1 - 1/ ?2 2L 2p/
?s2L ?s ?1?2/(?1- ?2) this synthetic
wavelength is much longer than ?1 or ?2. The
range of non-ambiguity of the phase difference
?f12, which is also known as the synthetic phase,
is therefore increased compared to the range of
non-ambiguity of classical interferometry.
Moreover, the sensitivity of the measurement is
reduced.
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ADI system module
Adjust laser to ?1
Calculate ?2
Adjust laser to ?2
d/2
ccd camera

FTA IDL
adjust ?s
dØ
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Practical example

• Iteration1
• Estimate distance manually e.g. L235 mm
• Estimate error range and ambiguity length.
• e.g. error 2 mm , 233mmL 237mm
• ?S gt 2 error range, to be say 5mm
• Adjust tunable laser source at arbitrary ? 1
  such as 682 nm and grab image-1
• Calculate ? 2 ? 2 ? 1 / (? 1/ ?S ) 1
  681.908 nm
• Adjust tunable laser source at ? 1 681.908 nm
  and grab image-2
• dØ calculated using FTA (it represents a fraction
  of a fringe)
• Divide ambiguity range by 2 so ? s 2.5mm

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Practical example

• Iteration2
• Adjust laser at ? 1 681.908 nm then Calculate
  ? 2 681.522nm grab image-3 .
• calculate dØ between image 23.
• Iteration3
• image-4 is for wavelengths 681.15 nm.
• calculate dØ between image34.
• This way ambiguity decreased and error decreased
  by 2 hence better accuracy. It is possible to
  converge in fewer steps if the confidence factor
  is higher.

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Thank youfor your attention Questions