Transcript Photorefractive Holography

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
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
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
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
Crystal
Signal Beam

Reference Beam
Charge distribution
Refractive Index distribution
Space – Charge Field
Absorption
Diffusion
Trapping
Spatial intensity gradients Magnitude of photorefractive grating
Overall intensity –
Speed of formation of grating
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
Signal Beam
Reference Beam
Transmitted
Reference Beam
Reference Beam
Reconstructed Signal
Beam
Conjugate Signal Beam
 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
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
Reconstruction Beam / Second Pump Beam
Signal Beam
Phase Conjugate
of the Signal Beam
Reference Beam
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 object’s 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
Surface Contouring by Rotation- Source Method
 Measurements of surface shape
 Difference between the phases before and after  of the object illumination beam
 2D Analysis : Object Phase before mirror tilt
b (i, j , k ) 
2

[ I sin   h(i, j ) cos  ]
 2D Analysis : Object Phase after mirror tilt
a (i, j , k ) 
2

[ I sin(   )  h(i, j ) cos(    )]
 Phase Map and height of the object
4
(i, j , k ) 
[sin( / 2)[I cos(   / 2)  h(i, j ) sin(   / 2)]]

[ I cos(   / 2)  (i, j , k ) / 4 [sin( / 2)]]
h(i, j ) 
sin(   / 2)
 Sensitivity of this method is given by
h(i, j ) 

2 sin( / 2) sin(   / 2)


 sin 
Tilt angle is sufficiently small
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
Phase-Shifting Interferometer
Interferogram obtained
from a plane Mirror
Interferogram
obtained
from a slightly
concave
And irregular surface
Four Frame Technique
 To determine the phase at each point (i,j), the intensity at each
point (i,j) is given by
I n (i, j )  I o (i, j ) cos[  (i, j ) 
(n  1)
], n  1,2,3,4
2
I (i, j )  I 2 (i, j )
(i, j )  arctan[ 4
]
I1 (i, j )  I 3 (i, j )
 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
Phase-Unwrapping Problem
 Relation between wrapped and unwrapped phase
(i, j )  (i, j )  2k (i, j )
- 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
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
Surface Contouring by RTHI
Experimental Setup
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
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
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
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
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