Diorico encallado
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Amanda D. Encallado, Fritz Randulf S. Diorico Department of Physics, University of San Carlos Talamban, Cebu City, Philippines 6000 [email protected], [email protected] Advisers: Albert James Licup and Claude Ceniza
Transcript of Diorico encallado
Amanda D. Encallado, Fritz Randulf S. DioricoDepartment of Physics, University of San CarlosTalamban, Cebu City, Philippines [email protected], [email protected]: Albert James Licup and Claude Ceniza
PRESENTATION OUTLINE
Introduction
Theory
Methodology
Results
Conclusions
INTRODUCTION
Fizeau interferometer
InSAR
INTRODUCTION
Michelson interferometer
Case 1: Flat Case 1: Flat surfacesurface
Case 2: Flat surface + round Case 2: Flat surface + round peripheryperiphery
Case 3: Convex surface + round Case 3: Convex surface + round peripheryperipheryCase 4: Concave surface + round Case 4: Concave surface + round peripheryperiphery
INTRODUCTION
INTERFEROGRAM CORRESPONDENCE OF LENS SURFACE
To construct a Fizeau interferometer
To be able to automate the three-dimensional reconstruction of the lens surface.
To obtain a three dimensional perspective of lenses
OBJECTIVES
INTRODUCTION
THEORY
4 ( , )( , ) airn d x yx y
1-D Interference
Fourier Transform
Inverse Fourier Transform
Phase Unwrapping
THEORY
*( , ) ( , ) ( , ) ( , )i x y a x y c x y c x y *( , ) ( , ) ( , ) ( , )I u v A u v C u v C u v
( , )1( , ) ( , )
2j x yc x y b x y e
1 Im ( , )( , ) tan
Re ( , )
c x yx y
c x y
THEORY
Phase Sign Ambiguity Correction
Interferogram Frequency Spectrum Wrapped Phase Distribution
Different possible orientations for filters for the Frequency Spectrum
Phase Sign Ambiguity Correction
Interferogram Frequency Spectrum Multi-regional filters
Resulting Phase Distributions Phase Masks
Phase Sign Ambiguity Correction
Phase Sign Ambiguity Correction
Sign corrected phase distribution
THEORY
Phase Unwrapping
4
1yx xy i
i
q
0.1 0.2 0.3
-0.1 -0.2 -0.4
-0.2 -0.2 -0.3
0.1 0.2 0.3
-0.1 -0.2 -0.4
-0.2 -0.2 -0.3
0.1 0.2 0.3
-0.1 -0.2 -0.4
-0.2 -0.2 -0.3
0.1 0.2 0.3
-0.1 -0.2 -0.4
-0.2 -0.2 -0.3
0.1 0.2 0.3
-0.1 -0.2 -0.4
-0.2 -0.2 -0.3
1234
THEORY
Phase Unwrapping
+
-
+
-
THEORY
Phase Unwrapping
Residue Distribution Branch Cuts
Phase Unwrapping
THEORY
Modified version of the Fizeau Interferometer
Beam Expander
Beam Splitter 50-50
Screen
Optical Flat or Reference FlatLens under
observation
Interferogram to be captured by
CCD camera and Analyze using
MATLAB®
Collimated Beam
C
CD
METHODOLOGY
If Complex
Multi-regional filtering
Fourier Transform
Pre-processed interferogram from LabVIEW
Phase-Unwrapping using Goldstein’s Branch Cut Algorithm
Pizza-slice masks append
View 3-D Lens Surface
Inverse FT
If Non-complex
Select best Phase Derivative Variance
METHODOLOGY
Information Flow Diagram
Interferogram
RESULTS
Log magnitude spectrum
RESULTS
( , ) *( , )C u v or C u v
Multi-regional filters
RESULTS
Filtered frequency domain
Wrapped
Phase
Distribution
Phase
Derivative
Variance
RESULTS
Wrapped Phase Distribution of highest quality
Phase residues
Branch cuts
RESULTS
Wrapped phase distribution
Unwrapped phase
RESULTS
Unwrapped Phase
Unwrapping Error
1, , ,( 1, ) xx i j i j i jx y
, 1 , ,( , 1) yy i j i j i jx y
x y (mean: 0.008, max: 12.57 radians)
RESULTS
RESULTS
Displacement plot
Displacement error(mean: 0.001,
max: 0.649 μm)
RESULTS
Interferogram
Wrapped Phase Distribution
RESULTS
Without mean filtering
Mean= 0.011 radians
With mean filteringMean=0.008
radians
RESULTS
Phase residues
Branch cuts
Unwrapped Phase
RESULTS
RESULTS
Displacement plot
Displacement errormean: 0.001, max: 1.343 μm)
RESULTS
Precision and Accuracy ±1.343 μm (accuracy based on unwrapping error) with mean =
0.001 μm Precision:
4 4precisiond z
2precision m
where m is the number of samples per fringe4 ( , )
( , ) airn d x yx y
0.1584
d m
RESULTS
2
4 4
Nd z
m
RESULTS
Conclusions Phase Measurement using the Fourier
transform method Multi-regional filtering for sign ambiguity
correction Goldstein’s branch cut algorithm,
obtained minimum PU error, 0.001 radians.
Displacement error through PU error Displacement resolution > 3-D Reconstruction process, successfully
implemented
0.158 m
References
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