Download Optical Testing and Testing Instrumentation

Optical Testing and
Testing Instrumentation
James C. Wyant
College of Optical Sciences
University of Arizona
[email protected]
www.optics.arizona.edu
www.optics.arizona.edu/jcwyant
2007 - James C. Wyant
Outline
1.
n  2.
n  3.
n  4.
n  5.
n 
Basic Interferometers for Optical Testing
Phase-Shifting Interferometry
Testing of Aspheric Surfaces
Measurement of Surface Microstructure
Concluding Remarks
2015 – James C. Wyant
Page 2
Part 1 - Basic Interferometers
for Optical Testing
Two Beam Interference
n  Fizeau and Twyman-Green interferometers
n  Basic techniques for testing flat and
spherical surfaces
n  Scatterplate and Smartt Interferometers
n  Typical Interferograms
n 
2015 – James C. Wyant
Page 3
Two-Beam Interference Fringes
I = I1 + I 2 + 2 I1I 2 Cos (α1 − α 2 )
α1 − α 2 is the phase difference between
the two interfering beams
" 2π %
α1 − α 2 = $ ' ( optical path difference)
# λ &
2015 – James C. Wyant
Page 4
Sinusoidal Interference Fringes
1.01
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
1
2
2
4
3
64
58
6
I = I1 + I 2 + 2 I1I 2 cos (α1 − α 2 )
2015 – James C. Wyant
Page 5
Pioneer Fizeau Interferometer - 1862
Light
Source
Beamsplitter
Test
Surface
Eye
Lens
Reference
Surface
2015 – James C. Wyant
Page 6
Typical Interferogram Obtained
using Fizeau Interferometer
2015 – James C. Wyant
Page 7
Relationship between Surface
Height Error and Fringe Deviation
S
Δ (x,y)
! λ $! Δ $
Surface height error = # &# &
" 2 %" S %
2015 – James C. Wyant
Page 8
Fizeau Fringes
Valley
Bump
For a given fringe
the separation
between the two
surfaces is a
constant.
Top View
Reference
Test
1
4 5
2 3
6
7
Top View
Reference
Test
1
4 5
2 3
6
7
Height error = (λ/2)(Δ/S)
S
Δ
S
Interferogram
Δ
Interferogram
2015 – James C. Wyant
Page 9
Twyman-Green Interferometer
(Flat Surfaces)
Reference
Mirror
Test
Mirror
Laser
Beamsplitter
Imaging Lens
Interferogram
2015 – James C. Wyant
Page 10
Twyman-Green Interferometer
(Spherical Surfaces)
Reference
Mirror
Diverger
Lens
Laser
Beamsplitter
Imaging Lens
Test Mirror
Interferogram
Incorrect Spacing
Correct Spacing
2015 – James C. Wyant
Page 11
Typical Interferogram
2015 – James C. Wyant
Page 12
Fizeau Interferometer-Laser Source
(Flat Surfaces)
Beam
Expander
Reference
Surface
Laser
Test Surface
Imaging Lens
Interferogram
2015 – James C. Wyant
Page 13
Fizeau Interferometer-Laser Source
(Spherical Surfaces)
Beam
Expander
Reference
Surface
Laser
Imaging Lens
Diverger
Lens
Test Mirror
Interferogram
2015 – James C. Wyant
Page 14
Hill or Valley?
Beam
Expander
Reference Test Mirror
Surface
Push in
on mirror
Laser
Imaging Lens
Diverger
Lens
Fringe Motion
Interferogram
1
4 5
2 3
6
7
Hill
Interferogram
2015 – James C. Wyant
Page 15
Testing Windows in Transmission
Reference
Surface
Window
being
tested
Collimated
Beam
Return
Flat
Transmission
Flat
δt = window thickness variations
OPD measured = 2 (n-1) δt
2015 – James C. Wyant
Page 16
Measuring Window Wedge
Reference
Surface
Window
being
tested
Return
Flat
Transmission
Flat
Tilt difference between two interferograms
gives window wedge.
2015 – James C. Wyant
Page 17
Calculating Window Wedge
Tilt difference
between two
interferograms
gives window
wedge.
α = window wedge
tilt difference
α=
2(n-1)
2015 – James C. Wyant
Page 18
Calculation of Tilt
Fringes
y
d
dy
dx
θ
x
d = fringe spacing
d x = d / sin (θ )
λ
β = Tilt =
d
λ
βx =
dx
d y = d / cos (θ )
λ
βy =
dy
2015 – James C. Wyant
Page 19
Calculation of Tilt Difference
Tilt
1
Tilt
2
β x 2 , β y2
β x1, β y1
Tilt Difference =
2
( β x1 − β x 2 ) + ( β y1 − β y2 )
2
2015 – James C. Wyant
Page 20
Testing Prisms in Transmission
Reference
Surface
Prism
being
tested
Collimated
Beam
Return
Flat
Transmission
Flat
δt = error in prism thickness
OPD measured = 2 (n-1) δt
2015 – James C. Wyant
Page 21
Angle Accuracy of 90-Degree Prisms
ε = angle error
θ = beam
deviation
θ
ε=
2n
2015 – James C. Wyant
Page 22
Testing 90-Degree Prisms
(Double Pass)
Reference
Surface
90-Degree
Prism
Collimated
Beam
Beam
Block
Transmission
Flat
x tilt in interferogram
ε=
4n
ε = prism angle
error
Errors in collimated beam cancel.
2015 – James C. Wyant
Page 23
Testing Corner Cubes
(Double Pass)
Reference
Surface
Corner
Cube
Collimated
Beam
Beam
Block
Transmission
Flat
Errors in collimated beam cancel.
2015 – James C. Wyant
Page 24
Interferogram for Perfect
Corner Cube (Double Pass)
3 interferograms obtained
One fringe covers the entire
interferogram
2015 – James C. Wyant
Page 25
Analyzing Corner Cube
Interferograms (Double Pass)
3 interferograms obtained.
Tilt of each interferogram gives one angle
error in corner cube.
n is refractive index of corner cube.
Error = Tilt/(3.266 n)
2015 – James C. Wyant
Page 26
Scatterplate Interferometer
Test
Four Terms:
Scattered-Scattered
Scattered-Direct
Direct-Scattered
Direct-Direct
Source
High
magnification image
.
of a scatterplate
Reference
Scatterplate
Interferogram
n 
n 
n 
(Near center of curvature of
mirror being tested)
Mirror Being
Tested
Scatterplate has inversion symmetry
Scatterplate is located at center of curvature of test mirror
Direct-scattered and scattered-direct beams produce fringes
2015 – James C. Wyant
Page 27
Microscopic Image of Scatterplate
2015 – James C. Wyant
Page 28
Scatterplate Interferometer
2015 – James C. Wyant
Page 29
Scatterplate Interferograms
2015 – James C. Wyant
Page 30
Smartt Point Diffraction Interferometer
Lens under
Test
Reference &
Aberrated
Wavefronts
Source
PDI
Interferogram
2015 – James C. Wyant
Page 31
Interferograms
Spherical Aberration
2015 – James C. Wyant
Page 32
Interferograms
Small Astigmatism, Sagittal Focus
2015 – James C. Wyant
Page 33
Interferograms
Large Astigmatism, Sagittal Focus
2015 – James C. Wyant
Page 34
Interferograms
Large Astigmatism, Medial Focus
2015 – James C. Wyant
Page 35
Interferograms
Large Coma, Varying Tilt
2015 – James C. Wyant
Page 36
Interferograms
Changing Focus
2015 – James C. Wyant
Page 37
Interferograms
Combined Aberrations
2015 – James C. Wyant
Page 38
Part 2
Phase-Shifting Interferometry
n 
Basic algorithms
n 
Removing phase ambiguities
n 
Simultaneous Phase-Measurement
Interferometers
2015 – James C. Wyant
Page 39
Phase-Shifting Interferometry
TEST
1) MODULATE PHASE
SOURCE
2) RECORD MIN 3 FRAMES
REF
3) CALCULATE OPD
INTERFEROGRAM
0°
90°
180°
A
B
C
OPD =
λ
2π
TAN
-1
[ CA -- BB ]
2015 – James C. Wyant
Page 40
Advantages of Phase-Shifting
Interferometry
High measurement accuracy (>1/1000 fringe,
fringe following only 1/10 fringe)
n  Rapid measurement
n 
n 
n 
n 
n 
Good results with low contrast fringes
Results independent of intensity variations
across pupil
Phase obtained at fixed grid of points
Easy to use with large solid-state detector
arrays
2015 – James C. Wyant
Page 41
Phase-Shifting - Moving Mirror
Move λ/8
π/2
Phase
Shift
PZT
Pushing
Mirror
2015 – James C. Wyant
Page 42
Four-Step Method
phase shift
I(x,y) = Idc + Iac cos[φ(x,y)+ φ(t)]
measured object phase
I1(x,y) = Idc + Iac cos [φ(x,y)]
I2(x,y) = Idc - Iac sin [φ(x,y)]
I3(x,y) = Idc - Iac cos [φ(x,y)]
I4(x,y) = Idc + Iac sin [φ(x,y)]
φ(t) = 0
(0°)
= π/2 (90°)
= π (180°)
= 3π/2 (270°)
I 4 (x, y ) − I 2 (x, y )
Tan[φ (x, y )] =
I1 (x, y ) − I 3 (x, y )
2015 – James C. Wyant
Page 43
Relationship between Phase and Height
" I ( x, y) − I ( x, y) %
4
2
φ ( x, y) = Tan $
'
$# I1 ( x, y) − I 3 ( x, y) '&
λ
Height Error ( x, y) =
φ ( x, y)
4π
−1
2015 – James C. Wyant
Page 44
Phase-Measurement Algorithms
Three Measurements
" I3 − I 2 %
φ = ArcTan $
'
# I1 − I 2 &
Four Measurements
"I − I %
φ = ArcTan $ 4 2 '
# I1 − I 3 &
Schwider-Hariharan
Five Measurements
" 2 ( I4 − I2 ) %
φ = ArcTan $
'
# I1 − 2I 3 + I 5 &
Carré Equation
" "3 I − I − I − I $" I − I − I − I $ $
# ( 2 3 ) ( 1 4 )%#( 2 3 ) ( 1 4 )% '
φ = ArcTan &
&
'
( I 2 + I3 ) − ( I1 + I 4 )
#
%
2015 – James C. Wyant
Page 45
Typical Fringes
For Spherical Surfaces
Fringes
Phase map
2015 – James C. Wyant
Page 46
Phase Ambiguities - Before Unwrapping
2 π Phase Steps
2015 – James C. Wyant
Page 47
Removing Phase Ambiguities
• Arctan Mod 2π (Mod 1 wave)
• Require adjacent pixels less than π
difference (1/2 wave OPD)
• Trace path
• When phase jumps by >π
Add or subtract N2π
Adjust so <π
2015 – James C. Wyant
Page 48
Phase Ambiguities - After Unwrapping
Phase Steps Removed
2015 – James C. Wyant
Page 49
Simultaneous Phase-Measurement
Interferometer
•  Twyman-Green
–  Two beams have
orthogonal
polarization
•  4 Images formed
–  Holographic
element
Diverger
QWP
Test
Mirror
PBS
Laser
Optical Transfer
CCD
& HOE
•  Single Camera
–  1024 x 1024
–  2048 x 2048
•  Polarization used
to produce 90-deg
phase shifts
Holographic
Element
Phase Mask,
Polarizer &
Sensor Array
Four Phase Shifted
Interferograms on Detector
2015 – James C. Wyant
Page 50
Effects of vibration
Relative motion
between PhaseCam
and test object
Phase relationship is fixed
2015 – James C. Wyant
Page 51
Use polarizer as phase shifter
test ref
LHC RHC
Circ. Pol. Beams (Δφ) + linear polarizer
cos (Δφ + 2α)
Phase-shift depends on polarizer angle
Reference: S. Suja Helen, M.P. Kothiyal, and R.S. Sirohi,
"Achromatic phase-shifting by a rotating polarizer", Opt.
Comm. 154, 249 (1998).
2015 – James C. Wyant
Page 52
Array of Oriented Micropolarizers
α=45, φ=90
α=0, φ=0
Polarizer array
Matched to
detector array
pixels
Unit Cell
α=135, φ=270
α=90, φ=180
2015 – James C. Wyant
Page 53
System Configuration
Source
Test Mirror
PBS
Camera
QWP
A
B
A
B
A
B
C
D
C
D
C
D
A
B
A
B
A
B
C
D
C
D
C
D
A
B
A
B
A
B
C
D
C
D
C
D
Pixelated Mask
QWP
Reference
Mirror
Parsing
Sensor
Array
Phase-Shifted
Interferograms
2015 – James C. Wyant
Page 54
Measurement of 300 mm diameter,
2 meter ROC mirror
Mirror and interferometer on separate tables!
2015 – James C. Wyant
Page 55
Modal Movie - Disk Vibration
Al mirror, 408 Hz
2015 – James C. Wyant
Page 56
Conclusions – Single Shot Interferometer
•  Vibration insensitive, quantitative interferometer
•  Surface figure measurement (nm resolution)
•  Snap shot of surface height
•  Acquisition of “phase movies”
2015 – James C. Wyant
Page 57
Part 3
Testing of Aspheric Surfaces
n 
Description of aspheric surfaces
n 
Techniques for testing aspheric surfaces
n 
n 
Requirements for use of optical analysis
software in optical testing
Limitations of current aspheric testing
techniques
2015 – James C. Wyant
Page 58
Aspheric Surfaces
Aspheric surfaces are of much interest
because they can provide
• Improved performance
• Reduced number of optical
components
• Reduced weight
• Lower cost
2015 – James C. Wyant
Page 59
Sag for Asphere
2
s /r
4
6
z=
2 1/ 2 + A4 s + A6 s +. . .
1 + [1 - ( k +1)(s / r ) ]
2
2
s = x +y
2
k is the conic constant
r is the vertex radius of curvature
A's are aspheric coefficients
2015 – James C. Wyant
Page 60
Difficulty of Aspheric Test
Slope of aspheric departure
determines difficulty of test
2015 – James C. Wyant
Page 61
Wavefront Departure and Slope
versus Radius
500.00
400.00
300.00
200.00
100.00
0.00
-100.00
-200.00
-300.00
-400.00
-500.00
0.00
0.25
0.50
0.75
1.00
Radius
OPD (fringes)
Slope (fringes/radius)
2015 – James C. Wyant
Page 62
Aspheric Testing Techniques
n 
Null Tests - Perfect optics give straight
equally spaced fringes
Conventional null optics
Computer generated holograms
n 
Non-null Tests - Even perfect optics do not
give straight equally spaced fringes
Deflectometry (SCOTS)
Shack-Hartmann
Lateral shear interferometry
Radial shear interferometry
High-density detector arrays
Sub-Nyquist interferometry
Long-wavelength interferometry
Two-wavelength holography
Two-wavelength interferometry
Stitching Interferograms
2015 – James C. Wyant
Page 63
Conventional Null Optics
Beam
Expander
Diverger
Lens
Reference
Surface
Laser
Imaging Lens
Null Optics
Test Mirror
Interferogram
2015 – James C. Wyant
Page 64
Hubble Pictures
(Before and After the Fix)
2015 – James C. Wyant
Page 65
Null Tests for Conics
Hyperboloid (K<-1)
d1
Parabola (K=-1)
d2
d3
d1 = r / 2
d5
r
−K ±1
K +1
r
d 4 , d5 =
1± −K
K +1
d 2 , d3 =
d4
Ellipsoid (-1< K<0)
(
(
)
)
2015 – James C. Wyant
Page 66
CGH Interferometer
Reference
Mirror
Diverger and/or
Null Optics
Laser
CGH (image of
Spatial Filter
aspheric element)
Interferogram
Aspheric
Element
2015 – James C. Wyant
Page 67
Computer Generated Hologram
2015 – James C. Wyant
Page 68
Light in Spatial Filter Plane
2015 – James C. Wyant
Page 69
CGH Used as Null Lens
Reference
Surface
Laser
CGH
Test Mirror
Spatial Filter
Interferogram
n 
n 
n 
Can use existing commercial interferometer
Double pass through CGH, must be phase etched for
testing bare glass optics
Requires highly accurate substrate
2015 – James C. Wyant
Page 70
Error Source
Pattern distortion (Plotter errors)
n  Substrate surface figure
n  Alignment Errors
n 
2015 – James C. Wyant
Page 71
Pattern Distortion
The hologram used at mth order adds m waves per line;
n  CGH pattern distortions produce wavefront phase
error:
n 
ΔW ( x , y ) = - m λ
ε( x , y )
S( x , y )
ε(x,y) = grating position error in direction perpendicular to the fringes;
S(x,y) = localized fringe spacing;
For m = 1, phase error in waves = distortion/spacing
0.1 µm distortion / 20 µm spacing ->λ/200 wavefront
2015 – James C. Wyant
Page 72
Plotters
n 
E-beam
–  Critical dimension – 1 micron
–  Position accuracy – 50 nm
–  Max dimensions – 150 mm
n 
Laser scanner
–  Similar specs for circular holograms
2015 – James C. Wyant
Page 73
Calibration of Plotter Errors
n 
Put either orthogonal straight line gratings or circular
zone plates on CGH along with grating used to
produce the aspheric wavefront
Straight line gratings produce plane waves which can
be interfered with reference plane wave to determine
plotter errors
n  Circular zone plates produce spherical wave which
can be interfered with reference spherical wave to
determine plotter errors
n 
2015 – James C. Wyant
Page 74
Solving Substrate Distortion Problems
Use direct laser writing onto custom substrates
n  Use amplitude holograms, measure and back out
substrate
n  Use an optical test setup where reference and test
beams go through substrate
n 
2015 – James C. Wyant
Page 75
Alignment Errors
Lateral misalignment gives errors proportional to
slope of wavefront
n  Errors due to longitudinal misalignment less
sensitive if hologram placed in collimated light
n  Alignment marks (crosshairs) often placed on CGH
to aid in alignment
n  Additional holographic structures can be placed on
CGH to aid in alignment of CGH and optical system
under test
n 
2015 – James C. Wyant
Page 76
Use of CGH for Alignment
n 
Commonly CGH’s have
patterns that are used for
aligning the CGH to the
incident wavefront.
Using multiple patterns
outside the clear
aperture, many
degrees of freedom
can be constrained
using the CGH
2015 – James C. Wyant reference.
Page 77
Projection of Fiducial Marks
The positions of the crosshairs can be controlled
to micron accuracy
n  The patterns are well defined and can be found
using a CCD
n  Measured pattern at 15 meters from CGH. Central
lobe is only 100 µm FWHM
n 
2015 – James C. Wyant
Page 78
CGH Alignment for Testing
Off-Axis Parabola
2015 – James C. Wyant
Page 79
Holographic test of refractive element having 50
waves of third and fifth order spherical aberration
2015 – James C. Wyant
Page 80
Deflectometry (SCOTS Test)
Hartmann test in reverse
n  Measures slope
n  Accuracies in the range of 100 – 200 nrad (rms) have
been achieved
n 
• 
Ref: Su, Parks, Wang, Angel, and Burge, “Software configurable optical
test system: a computerized reverse Hartmann test”, Appl. Opt, 49(23),
4404-4412, (2010).
•  Ref: Su, Wang, Burge, Kaznatcheev, and Idir, “Non-null full field X-ray
mirror metrology using SCOTS: a reflection deflectometry approach”,
Opt. Express 20(11), 12393-12406 (2012).
•  Ref: Häusler, Faber, Olesch, and Ettl, “Deflectometry vs.
Interferometry”, Proc. SPIE. 8788, Optical Measurement Systems for
Industrial Inspection VIII 87881C (May 13, 2013) doi: 10.1117/12.2020578.
2015 – James C. Wyant
Page 81
SCOTS and Hartmann Test
Geometry of SCOTS Test
HartmannTest
Use line source to measure
either x-slope or y-slope.
Sinusoidal fringes can be
used instead of line and
phase-shifting techniques
can be used.
2015 – James C. Wyant
Page 82
Measurement of Off-Axis Parabola
Radians
Y-slope
X-slope
mm
Surface
Surface Departure
2015 – James C. Wyant
Page 83
8.4 m Giant Magellan Telescope
µm
Interferometry
SCOTS
2015 – James C. Wyant
Page 84
Stitching Interferograms
Perform sub-aperture test of aspheric and
stitch together interferograms.
n  Trade-off between overlap between
interferograms and number of interferograms
required.
n  Much easier to describe than to obtain
accurate results.
n 
2015 – James C. Wyant
Page 85
Subaperture Stitching Interferometry (SSI®)
n 
What is it?
–  6-axis motion system
–  “Standard” interferometer
–  Automatic collection of multiple
subaperture measurements
–  Magnified, locally nulled subapertures reduce “aspheric”
fringe density
–  Compensation of systematic
errors
n 
SSI extends standard
interferometry
–  Fast & Large parts
–  Aspheres (up to ~200 λ)
n 
And also can improve:
–  Accuracy & Resolution
2015 – James C. Wyant
Courtesy of QED
Page 86
Extending the SSI to ASI®
Variable Optical Null (VON) extends
aspheric departure capture range
n  Counter-rotating optical wedges
n 
–  Varying the wedge angle and tilt produces
astigmatism & coma
Plane-­‐parallel SSI Maximum wedge 650 μm departure asphere ASI (VON) 2015 – James C. Wyant
Courtesy of QED
Page 87
SSI/ASI: Summary
n 
What is it good for?
–  Flexible – no dedicated nulls
–  High departure
–  Large NA or CA
–  High vertical resolution
–  High lateral resolution
–  Compensation of systematic
errors
n 
Capability Summary What are its key
limitations?
Size –  Inflection points
–  High slope deviations
–  3rd order spherical uncertainty
2015 – James C. Wyant
Shape Lat Res Vert Res Courtesy of QED
Page 88
Zygo Verifire Multi-Zone Aspheric Tester
•  Measure 6 to 200 sub-measurements of concentric zones.
•  Measure distance of every zone from from center point of
spherical reference surface.
•  Measure distance to apex of part.
•  Stitching of overlapping apertures not required.
•  The results represents surface-deviation in normal direction.
2015 – James C. Wyant
Page 89
Verifire Asphere Spec (from Zygo brochure)
2015 – James C. Wyant
Page 90
Basic Limitations of Aspheric Testing
Must get light back into the test setup
n  Must be able to resolve the fringes
n  Must know precisely the optical test setup
n 
This is the most serious problem
2015 – James C. Wyant
Page 91
Part 4 - Measurement of Surface
Microstructure
n 
Non-Contact Optical Profilers
n 
White Light Interferometry
n 
Vertical Scanning Optical Profilers
2015 – James C. Wyant
Page 92
Non-Contact Optical Profilers for
Measurement of Surface Microstructure
§  Non-contact measurement
§  2D or 3D surface topography
§  Visual qualitative surface inspection
§  Vertical resolution suitable for superpolished optics
§  Fast measurement and analysis
2015 – James C. Wyant
Page 93
Advantages of White Light over Laser Light
§  Lower noise
§ No spurious fringes
§  Multiple wavelength operation
§ Measure large steps
§  Focus easy to determine
2015 – James C. Wyant
Page 94
Interference Microscope Diagram
Detector Array
Filters all but the red
light from white light
of halogen lamp
Digitized Intensity
Data
Magnification
Selector
Filter
Illuminator
Beamsplitter
Translator
Microscope
Objective
LightSource
Mirau
Interferometer
Sample
2015 – James C. Wyant
Page 95
Mirau Interferometer
(10X, 20X, 50X)
Microscope
Objective
Reference
Beamsplitter
Sample
2015 – James C. Wyant
Page 96
Michelson Interferometer
(1.5X, 2.5X, 5X)
Microscope
Objective
Reference
Mirror
Beamsplitter
Sample
2015 – James C. Wyant
Page 97
Linnik Interferometer
Reference
Mirror
(100 X, NA 0.95)
Beamsplitter
Microscope
Objectives
Sample
2015 – James C. Wyant
Page 98
Interference Objectives
n 
Mirau
–  Medium magnification
–  Central obscuration
–  Limited numerical aperture
n 
Michelson
–  Low magnification, large field-of-view
–  Beamsplitter limits working distance
–  No central obscuration
n 
Linnik
–  Large numerical aperture, large magnification
–  Beamsplitter does not limit working distance
–  Expensive, matched objectives
2015 – James C. Wyant
Page 99
Optical Profiler
2015 – James C. Wyant
Page 100
White Light Interferogram
2015 – James C. Wyant
Page 101
Profile of Diamond Turned Mirror
2015 – James C. Wyant
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Diamond Turned Mirror
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Grating
Ref: Bruker
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Diamond Film
Ref: Bruker
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How High is the Step?
Steps >λ/4 between adjacent detector pixels introduce
integer half-wavelength height ambiguities
Fringe Order ?
Step >λ/4
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White Light Interferometry
n 
n 
Eliminates ambiguities in heights present
with monochromatic interferometry
Techniques old, but use of modern
electronics and computers enhance
capabilities and applications
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Interferograms of Diffraction Grating
Quasi-Monochromatic Light
White Light
Profile
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White Light Interference Fringes
Fringes form bands of
contour of equal height
on the surface with
respect to the reference
surface.
n  Fringe contrast will be
greatest at point of
equal path length or
“best focus.”
n 
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Principles of Vertical Scanning
Interferometry
A difference between the reference and test
optical paths causes a difference in phase.
n  Best fringe contrast corresponds to zero optical
path difference.
n  Best focus corresponds to zero optical path
difference.
n 
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Interference Microscope Diagram
Digitized Intensity
Data
Detector Array
Magnification
Selector
Beamsplitter
Illuminator
Translator
Light Source
Microscope
Objective
Mirau
Interferometer
Sample
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Vertical Scanning Interference Microscope
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White Light Interferograms
Focus Position A
Focus Position B
As the scan moves different areas of the part being
measured come into focus (have zero OPD or maximum
contrast between fringes). A determination of the point of
maximum contrast and knowledge of the scan position
allows a reconstruction of the surface shape.
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Step Measurement
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Print Roller
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Print Roller Measurement
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Paper Measurement
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Micromachined Silicon Measurement
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Binary Optic Lens
Surface Stats:
RMS: 561.30 nm
PV: 2.37 um
493.7
um
um
1.189
400.0
0.500
300.0
0.000
200.0
-0.500
100.0
0.0
0.0
um
100.0 200.0
-1.185
375.5
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Heart Valve
X-Profile
um
469.3
384.24 nm
250.00
400.0
100.00
-50.00
300.0
-200.00
um
-343.18
0.00 50.00
200.0
150.00
250.00
350.00
419.90
Y-Profile
48.55 nm
100.0
0.00
um
0.0
0.0
100.0 200.0 300.0
419.9
-50.00
-100.00
-150.00
-219.10
0.00 50.00
um
150.00
Histogram
1849.79
Data Statistics
Rt: 1.419 um
Ra: 87.391 nm
Rq: 113.942 nm
250.00
350.00
469.34
Avg X PSD
Pts
86.76
1500.00
dB
80.00
1200.00
70.00
900.00
600.00
60.00
300.00
0.00
-69.39
nm
-30.00
10.00
69.39
52.46
0.00
1/mm
150.00
289.52
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Stitched Measurement - Fuel Cap
VSI
mode
Surface statistic
Ra=26.32 microns
Rq=32.72 microns
Rt=246.42 microns
array size 1251x1107
sampling 25.5 microns
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Sub-Region of Stitched - Fuel Cap
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Chatter on Camshaft
Ref:
Bruker
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Woven Cloth
Ref:
Bruker
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Part 5 –Concluding Remarks
•  Limitations of Direct Phase
Measurement Interferometers
•  Most Important to Remember
•  References
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Limitations of Direct Phase Measurement
Interferometers
n 
n 
n 
Accuracy generally limited by environment
– Vibration
– Turbulence
Measurement of surface roughness less limited
by environment because path differences small
Single-shot phase-measurement interferometers
greatly reduce the effects of vibration and
turbulence effects can be averaged out.
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Remember
n 
n 
n 
If you make optics you have to be able to
test the optics because you cannot make
optics any better than you can test.
If you purchase optics you need to test the
optics you buy to make sure the optics meet
the specs.
If you let the supplier know you are going to
test the optics when you receive them you
will get better optics.
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References
D. Malacara, Ed.
Optical Shop Testing
W. Smith
Modern Optical Engineering
Kingslake, Thompson, Shannon, and Wyant, Ed. Applied
Optics and Optical Engineering, Vols. 1-11
Goodwin and Wyant, Field Guide to Interferometric
Optical Testing
Optical Society of America
Optics Infobase
SPIE
Digital Library
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Field Guide to Interferometric Optical
Testing (Published by SPIE)
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Thank you for taking the short course!
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