Fun with the Shack-Hartmann - Space Nanotechnology Laboratory

Fun with the Shack-Hartmann
Shack Hartmann
Andrew Lapsa
Space Nanotechnology Laboratory
Massachusetts Institute of Technology
August 15, 2003
and the autocollimator…

User interfaces have
been developed
• Short-term Short term testing
Averages x number
of readings
• Long-term Long term testing
Takes data points for
x number of hours,
and saves data to a
spreadsheet file
Autocollimator

Objective
Shack-Hartmann
Shack Hartmann
• Increase the dynamic range of the
CLAS-2D CLAS 2D system
Understand details of CLAS-2D CLAS 2D
Develop own measurement routine
Integrate new routine and CLAS-2D CLAS 2D
Study results

CLAS-2D CLAS 2D Concept
Focal Plane
Lenslet Array
Optic

Lenslet Concept

Blobs out of range
Blobs often wander
out of the proper
AOI
Maximum angle
detectable ~350
microradians

Algorithm Concept
Use image processing techniques
identify blobs independent of AOIs
Calculate their centroids
Predict locations of centroids based
on knowledge of other centroids to
link centroids with AOI’s

Blob Detection Algorithms
Gaussian Mask – too complicated
Canny Edge Detector – too complicated
Papert’s Turtle – simple, but only good
for regions with 4-connectivity
4 connectivity
Inner Boundary Tracing – simple,
good for regions with 8-connectivity
8 connectivity

IBT – big picture
Subtract threshold from image
Scan for nonzero pixels from left to
right, top to bottom.
When nonzero pixel is hit, apply
Inner Boundary Tracing algorithm to
trace edge of blob
Record maximum and minimum
bounds of blob and move on

IBT – little picture
At first region pixel, look in 7+6 (mod 8) = 5
direction
Iterate direction until next region pixel is found
• If the new direction is odd, add 6
• If the new direction is even, add 7
Continue until you return to 1 st pixel, or until all
directions are determined to be non-region non region pixels
4
3
5
2
6
1
7
0
0
1
8
2
7
6
5
3 4

Centroid Calculation
Return to un-thresholded un thresholded image
Study expanded regions where dots
were found
Calculate centroid (ρ ( x,ρy) )
x
ρ
=
∑ ∑
cols rows
∑∑
cols rows
Return array of centroids
I
ij
I
x
ij
i
y
ρ
=
∑ ∑
cols rows
I
∑∑
cols rows
ij
I
y
ij
j

Keep in mind 3 file types:
Reference Centroids (.CLB)
Lenslet Centers and Indices (.XYB)
Test-Optic Test Optic Centroids (.PKB)

Prepare for Matching
Rearrange .XYB
• Place lenslet centers into matrix –
position of center in mtx corresponds to
position in physical lenslet array
Rearrange .CLB
• Place reference centroids into same type
of matrix – match each lenslet center
with closest reference centroid

Matching
Match center 5 reference and test-optic test optic
centroids by location in image
• Calculate size of search window, and record
the differences
• Link by location in matrix (lenslet assignment)
Match centroids along x & y axes
• Guess location of next centroid by difference in
previous centroid pair
• Link by location in matrix (lenslet assignment)
Match centroids row by row in quadrants
• Guess location: use x-error x error from neighboring
centroid in same column, y-error y error from
neighboring centroid in same row
• Link by location in matrix (lenslet assignment)

Comparison

Write .PKB file
Use test-optic test optic centroids’ indices
(lenslet assignment) to assign each
centroid to proper location in array
Save array as text file
Convert text file to .PKB
Use new .PKB with CLAS-2D, CLAS 2D, and
savor the results.

Results – Glass Wafer
Old .PKB New .PKB

.PKB Comparison
No significant error throughout entire range of
wafer
Best-fit Best fit Zernike polynomials almost identical
No practical difference in surface reconstruction
Frequency
100
90
80
70
60
50
40
30
20
10
0
HISTOGRAM
-0.31
-0.26
-0.21
-0.16
-0.11
-0.06
-0.02
0.03
0.08
0.13
0.18
0.23
0.28
0.33
0.37
0.42
Difference

Silicon Wafer
Max=2.0867 micron
Max=7.2488 micron
Max=9.1848 micron
Max=2.6774 micron
Max=15.4146 micron
Max=31.7745 micron

Silicon Wafer
Slope Field Matches Surface Reconstruction

Success
Understand CLAS-2D CLAS 2D – successful
Develop measurement routine –
successful
Integrate routine and CLAS-2D CLAS 2D –
successful, but could be prettier
Results – successful

Conclusions
Dynamic range has been increased
from 350 microradians to 350
microradians/224 microns
For 10 cm wafers, improvement is by
a factor of 450
Wafers with dynamic range between
5.8 and 100 microns have already
been measured