Surface Contouring by phase-shifting real-time holography using photorefractive sillenite crystals

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Surface Contouring by phase-shifting real-time
holography using photorefractive sillenite
crystals

• M.R.R. Gesualdi ,D.Soga , M.Muramatsu
• Optics and Laser Technology
• Vol 39, pg 98-104 (2007)

Journal Club 9/10/2007 Presenter Ashwin
Kumar Advisors Prof. Todd Murray
Prof. Kamil Ekinci
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Contents

• Introduction to Holography
• Photorefractive Holography
• Photorefractive Effect
• Two-wave mixing
• Four-Wave Mixing
• Surface Contouring
• Rotation Source Method
• Phase shifting Technique
• Four-Frame Technique
• Cellular Automata Technique
• Experimental Setup
• Experimental Results
• Conclusions

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Holography

• Holography is technique by which a wavefront can
  be recorded and reconstructed at a later point in
  the absence of original wavefront
• Holographic interferometry Extension of
  interferometric technique in which atleast one of
  the waves which interfere is reconstruced by a
  hologram
• Advantages Storing a wavefront for
  reconstruction at later time
• Wavefronts separated
  in time or space can be compared
• Changes in shape of
  objects with rough surfaces can be studied

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Photorefractive Holography

• Photorefractive Materials Changes in index of
  refraction in accordance with variation in
  exposed light
• Photorefractive
• Effect Two beams interfere within the
  crystal to form a sinusoidal intensity pattern
• Generation of free carriers
  Bright region of the intensity pattern
• Carriers diffuse and/or drift
  leaving fixed charges behind
• Carriers are trapped in the
  dark regions due to introduction of point defects
• Results in the formation of a
  nonuniform charge distribution Space charge
  field (SCF)
• SCF modulates the refractive
  index of the crystal (electro-optic effect)
• Spatially nonuniform
  intensity pattern Charge distribution
  Refractive Index distribution

Crystal
Space Charge Field
Signal Beam
Spatial intensity gradients - Magnitude of
photorefractive grating Overall intensity
Speed of formation of grating
Absorption Diffusion Trapping
?
Reference Beam
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Photorefractive Holography

• Holography involves recording and reconstruction
  of optical waves (Two- Wave Mixing)
• PRC Dynamic hologram to record the information
  of
• optical (signal) beam
• Plane reference beam can be used
  to reconstruct the signal

• Recording and Reconstruction are done
  simultaneously
• Reference beam is diffracted into the path of
  the transmitted signal beam
• Reference beam matches with the wavefront of the
  signal beam
• Writing/Reading Process is reversible
• No chemical processing is required
• Short response time and lower noise levels in
  interferograms

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Photorefractive Holography

• Four Wave Mixing Technique
• Two strong pump beams are used to produce a
  phase conjugate
• of a weaker probe beam
• Four-wave mixing is useful in phase and adaptive
  amplitude correction and
• noise filtering

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Surface Contouring

• Shape determination of surfaces Real-time
  holographic interferometry
• Advantages Non-contact technique to analyze
  surfaces
• Provide good
  reliability, high accuracy and qualitative
  analysis through visual
• inspection
• Holographic contouring methods Rotation source
  method (Change in angle of illumination)
• Hologram of the object is first created
• The angle of illumination beam is slightly
  changed and a second hologram is superposed on
  the first
• Two sets of light waves reach the observer ,
  Reconstructed wave (Object wave before angle
  tilt) and
• wave from the objects present state
• Two wave amplitudes add at points where OPD is
  zero or n? and cancel at other points in between.
• A Reconstructed image covered with a pattern of
  interference fringes are observed
• Contour map of the surface of the object

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Surface Contouring by Rotation- Source Method

• Measurements of surface shape
• Difference between the phases before and after
  ?? of the object illumination beam

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Phase-Shifting Technique

• Spatial phase measurement technique
• Interferogram phase is calculated using
  holographic interferogram
• intensities
• Fringe pattern is complex due to irregularities
  and intricate shape
• of the object
• Four- Frame technique is used to determine the
  phase
• The PZT is moved over a distance of ?/8
  inducing a phase shift of ?/2 to the reference
  beam
• Four interference patterns are acquired after
  stepwise phase shifts of the reference beam

Interferogram obtained from a slightly
concave And irregular surface
Phase-Shifting Interferometer
Interferogram obtained from a plane Mirror
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Four Frame Technique

• To determine the phase at each point (i,j), the
  intensity at each point (i,j) is given by

• 2D graphic is obtained by representing
• each phase value by a gray shade intensity
• Black corresponding to -? and white to ?
• 8 bit imaging system 256 different gray
  intensities
• Phase wrapping occurs
• Noise is filtered using anisotropic sin/cos
  filter
• Phase unwrapping Cellular-automata technique

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Phase-Unwrapping Problem

• Relation between wrapped and unwrapped phase

• - unwrapped phase
• - wrapped phase
• k wrap count integer field
• Phase unwrapping problem consists of singling out
  the correct k value

• Reconstruction of unwrapped phase is obtained by
  direct integration
• in absence of noise and correctly sampled
  data
• In presence of noise or under sampling, wrapped
  phase is rotational in nature
• Result of the integration depends on the path
  followed
• Presence of rotational components (residues and
  dipoles)
• make the solution non-unique
• Removal of noise is important in the phase
  unwrapping problem

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Cellular Automata Technique

• By repeating these steps, phase progressively
• unwrapped
• Each cycle removes one fringe as the local
• iteration moves the discontinuities to the
• boundary of the phase field
• Removed slowly owing to global iteration

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Surface Contouring by RTHI
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Experimental Setup
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Experimental Results

• All objects were painted with retro-reflector
  ink to increase the
• intensity of the scattered laser beam
• Angle between the recording beams was 45 degs
• Recording time 30 secs
• ? 0.36 radians
• Four Frame Technique (?? 0,?/2, ?,3 ?/2)
• Intensity ratio of Reference Object Beam 6.0

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Experimental Results

• Specimen Bulb of length 30.0 mm and 10.0 mm
  diameter
• Change in incidence angle ?? 0.0001 rad
• Surface contouring difference between the max.
  and min.
• height is 5.0 mm

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Experimental Results

• Specimen Chess of length 30.0 mm and 10.0 mm
  diameter
• Change in incidence angle ?? 0.0002 rad
• Surface contouring difference between the max.
  and min.
• height is 6.0 mm

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Experimental Results

• Specimen Plug of height 10.0 mm and 20.0 mm
  diameter
• Change in incidence angle ?? 0.00006 rad
• Surface contouring Internal border of the piece

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Conclusion

• Phase shifting (RTHI) presents new possibilities
  of surface topograph
• BSO crystal in diffusive regimen with
  configuration exhibiting diffraction
• anisotropy
• Height at each point of surface is proportional
  to the difference of phases
• due to tilt of the object illuminating beam
• Results of good quality were obtained and can be
  improved by fringe
• analysis
• Surface height of large objects were determined
• Errors in measurements
• 1.
  Miscalibration of the phase shifter
• 2.
  Spurious reflections and diffractions
• 3.
  Quality limitations of the optical elements
• 4.
  Nonlinearities and resolution of CCD
• 5.
  Air turbulence and vibrations
• 6.
  Photorefractive Errors Temporal modulation of
• 
  holographic interferograms and temporal
• 
  fluctuations of thermal dependence on the
• 
  photorefractive effect