1. Novel Techniques for the Position Calibration of FAUST
David Balaban
2014 Cyclotron REU Program
Dr. Sherry Yennello’s Group

2. Problem
The Forward Array Using Silicon Technology (FAUST) consists of 68 detectors
Detectors identify and measure the energy of charged particles
Recently upgraded to position-sensitive detectors
Structural tolerances may result in inaccurate relative positioning
Position must be accurately known for upcoming experiments

3. The Detectors Current induced by charged particle
Voltage determines position with:
X-Position = (Back2-Back1)/(Back1+Back2)
Y-Position = (Front2-Front1)/(Front1+Front2)
Left picture from: S.N Soisson, et al. "A dual-axis dual-lateral position-sensitive detector for charged particle detection." NIM A, 613, 2, 2010.

4. The FAUST aRRAY Mask
Mask blocks particles and creates striped pattern on detectors
Stripes on detectors will be misplaced by detector motion
Goal is to find how far detectors are from expected positions
2 phases to accomplish:
1.) Identify stripes on detector
2.) Find set of linear transformations applied to detector which will
reposition the stripes to the expected values

5. Phase 1 Process Noise Removal Rotation Projection onto y-axis
0. Collect Data
Noise Removal
Rotation
Projection onto y-axis
K-means algorithm
Data Selection and Linear Fit
Display Result

6. 1. Noise Removal Collected from 228Th Source
X-Position (cm)
Y-Position (cm)
Count
channel number
Collected from 228Th Source
Cut electrical noise at low energy
Stretch out data empirically
Trying to understand characteristics of compression

7. 2. Rotation Rotate data by expected angle of slope
Makes projecting and fitting easier.
X-Position (cm)
Y-Position (cm)

8. 3. Project Data onto y-axis
Y-Position (cm)
Count
After projecting onto y-axis, large peaks correspond to stripes.

9. Description of K-means:
1. Initialize k random points
2. Calculate average position of
data associated with each
point
3. Reset point to average
position
4. Repeat until convergence
Picture from:
Thomas, Philip. “Midterm Review.” Computer Science 383. University of Massachusetts Amherst, Amherst, MA. 25 Mar Lecture.

10. 4. Run K-means Algorithm Use K-means to identify location of stripes
Must select best K-value
Y-Position (cm)
Count
Black K=1
Red K=2
Green K=3

11. 5. Data Selection Approximate location of stripe Linear fit to data
X’-Position (cm)
Y’-Position (cm)

12. 6. Final Result Rotate lines back by 45 degrees
Fit line
Fit-data center
Rotate lines back by 45 degrees
Colors show which points were used in fit
Left shows plot from step 2
Right shows finished product.

13. Phase 2 Data collected with 228Th Source and 4He@15MeV/A+ natAu
beam
source
simulation
Data collected with 228Th Source and natAu
Want to get blue and red data points closer to orange

14. Geometry Simulation 228Th Source Geometry Simulation
“Perfect World” expectation
Alpha particle simulation perfect elastic scattering
Y-Position
X-Position
228Th Source
Can see stripes on ring C, not ring A
2-3 stripes on detectors
Y-Position
X-Position

15. Geometry Simulation 4He @15MeV/A+ natAu Geometry Simulation
“Perfect World” expectation
Alpha particle simulation perfect elastic scattering
Y-Position
X-Position
natAu
Y-Position
X-Position
Low stats on ring C
Similar stripes to source
Agrees with source for ring C

16. Description of Hill Climbing:
Define set of free parameters P
Define method eval(P) to evaluate parameters to a single value
HC tries to find the global maximum of eval(P) by changing P.
The picture to the left shows a successful Hill Climb with one free parameter. Local maxima causes difficulty for successful HC.
Picture from:
"Hill Climbing." Wikipedia. Wikimedia Foundation, 27 July Web. 03 Aug
eval(P) P

17. Preliminary testing of Hill Climbing algorithm.
Setup:
Two initially parallel lines are rotated randomly
Hill Climbing is told to make them parallel again through rotations
6 free parameters (3 per line)
Angle between Lines after Hill Climb (deg)
Count

18. .5˚
Setup:
Ring of detectors rotated by .5 degrees about beam-axis
Each detector is rotated randomly within a given range
Hill Climbing is told to rotate ring such that the set of stripes are as close to expected as possible

19. eval(P) at the end of Hill Climb θ in degrees (θ-.5)/.5
.5˚
eval(P) at the end of Hill Climb
θ in degrees
(θ-.5)/.5
Black min/max rotation: [-.05 ˚, .05 ˚]
Red min/max rotation: [-.1 ˚, .1 ˚]
Green min/max range: [-.2 ˚, .2 ˚]
Setup:
1 free parameter
Cutting on eval(P) allows better accuracy
As the range increases inaccuracy grows

20. Summary FAUST Detectors measure position but need to be calibrated
Mask allows for 2-phase process for calibration
Phase one identifies stripes with linear fits
Phase two needs to be tested more before implementation

21. Acknowledgements This work was supported by: Works Cited:
the Robert A. Welch Foundation under Grant No. A-1266
U. S. Department of Energy under Grant No. DE-FG03-93ER-40773
National Science Foundation under Grant No. PHY
Works Cited:
S.N Soisson, et al. "A dual-axis dual-lateral position-sensitive detector for charged particle detection." NIM A, (2010).
F. Gimeno-Nogues, et al. "FAUST: A new forward array detector." Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment 399.1 (1997).
Dabney, William. "Local Search." Computer Science Education Lab, UMASS, Amherst. N.p., n.d. Web. 7 Aug. 2014.
Thomas, Philip. "Unsupervised Learning." Computer Science Education Lab, UMASS, Amherst. N.p., n.d. Web. 7 Aug. 2014.