Kevin Kelly
Mentor: Peter Revesz
Importance of Project: Beam stability is crucial in CHESS, down
to micron-level precision
 The beam position is measured using a video imaging system
by determining the intensity centroid.
 We measured how parameters like the image frame averaging
number and other acquisition settings affect the stability of the
measured centroid, modeling the X-ray luminescence with an
LED light source on an optical bench.
 We analyzed data measured with USBChameleon to calculate
the sigma of the centroid position, lower sigma relating to
higher precision.
 Noticed a trend – the
greater the frame average, the
lower the sigma.

Frame Averaging v. Sigma-Y: Normal Centroid at .183m
0.6
Sigma-Y Normal (um)
0.5
0.4
0.3
0.2
0.1
0.0
0
5
10
15
20
Frame Average
25
30
35
ROI
Profile of Image
Inputs
Outputs
Centroid Position Trace
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We have carried out our experiments using the
model light source (LED) mounted on a linear
precision slide on an optical bench for
maximum mechanical stability
To reduce any potential outside effects on the
experiment (airflow, external light, etc.), we
added a special shielding cover.
Using the USBChameleon program we
obtained statistical data about pixel intensities
and centroid position under various
experimental conditions.
CCD Camera, Mounted
to the Optics Bench
Chameleon by Point
Grey Research, pixel
size ~3.5 mm
Resolution:
640x480 (low), or,
1280x960 (high)
The LED Light source,
mounted and stabilized
Experimental setup, covered in
metal shield to reduce any airflow
from affecting the light source
Our next parameter to test was Shutter Time, or the length of exposure
for each image. Because longer exposure time means more light incident on the
CCD, the higher shutter time, the brighter the image.
• Tested 60 combinations of Frame Average and Shutter Time:
• Frame Average: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
• Shutter Time: 25ms, 40ms, 55ms, 70ms, 85ms, 100ms
We repeated this for Low Camera Resolution and High Camera Resolution
to have data for both settings as well.
Other parameters not adjusted include:
• Gain
• Camera Lens
• Light source symmetry
• Aperture
The instability of the centroid
comes from a variety of sources:
• Experimental Conditions:
X-Position of Centroid (microns)
2
2s
Mechanical instability of the light
source, vibrations, airflow in
experimental tunnel.
• Errors in CCD:
Read Noise, Photon Noise, Dark
Noise
• Experimental Paramters:
0
0
20
40
60
80
100
120
Time (s)
Adjusting Frame Average, Shutter,
Type of centroid calculation, etc.
A typical plot of the centroid position over time, static
LED position. After fitting a trend, we analyze the
residual and calculate a standard deviation from that
(s).
Instead of trying to separate and individually analyze
the sources of noise in experiments, we opted to just
measure the standard deviation experimentally and
attempt to look at the noise sources through different
means.
• Observed the same trend for
Shutter Time as for Frame
Average – inverse relationship.
After analyzing, the trend was
noticed to be an inverse-square-root.
The equation is this:
𝜎=
6.897
𝐹∗𝑆
Where F is the Frame Average
Value and S is the Shutter Time, in
milliseconds.
Some key measurements we needed to keep track of: Shutter Time, Frame
Average, Sigma (obviously), but also the ROI Size and the average FWHM of
the profile throughout each trial. These will be important later.
For static LED the best precision we measured ~0.07 mm !
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
Added a new functionality to
USBChameleon, PixelSave.
Used this on a slice of the
image for all the combinations
of frame average and shutter
time mentioned above.
The results were then analyzed
to see a trend between a given
pixel’s average intensity and
intensity distribution.
We repeated this measurement
a number of times (typically
200) to obtain statistics
ROI of Pixel Intensities being saved
60000
50000
40000
Pixel Intensity

30000
20000
10000
0
0
20
40
60
80
100
120
Pixel
Pixel Intensities across ROI
Typical plot of Standard Deviation of Pixel
Intensity v. Average Pixel Intensity with
trendline.
• Two important things to note:
• Each pixel’s histogram resembled a
Gaussian distribution.
• Increasing Average Intensity leads to
increasing Standard Deviation. – close
to a square root dependence.
We used the measured spix-int vs. intensity values
in the Monte Carlo Simulations
Histograms of single-pixel
statistics, one at low
intensity, one at high.
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Aliasing effect 1: The pixel intensity digitalization,
because it is to 12-bit accuracy, introduces
“rounding.”
Aliasing effect 2: Averaging the pixel intensity
over a finite pixel size results in a “jagged” image
profile
As a result, the image is slightly distorted, and the
distortion changes as the image moves.
The overall result of this is a (periodic) artifact in
the centroid position during image motion.
To verify this, we used the motor-controlled slide
that the LED is mounted on to perform our
experiments, taking steps of 5, 10, and 15 microns,
as well as a steady state to compare.
Beginning
Halfway
End
• Just looking at the trace of the
measured centroid, the position seems
perfect! But when we take a closer look
at the residual, we observe that there
are two frequencies of oscillation.
-2000
-4000
-6000
0
2000
4000
6000
8000
Distance moved by Slide (Microns)
Trace of Centroid, moving 10 micron steps
The easiest way to analyze this residual is
an FFT, Fast Fourier Transform. The result
of this is a plot of frequency v. magnitude.
The magnitude is related to the amplitude
of the oscillation at that given frequency.
4
Residual of X-Position of Centroid (microns)
Centroid Position (microns)
0
2
0
-2
-4
0
2000
4000
6000
Distance Moved by Slide (microns)
Residual of Above Graph
8000
0.75
Amplitude (microns)
Amplitude (microns)
1.58
0.79
0.00
0.50
0.25
0.00
-0.79
0.00
0.11
0.22
0.33
0.44
0.000
Spatial Frequency (1 / microns)
0.013
0.026
0.039
0.052
Spatial Frequency (1 / microns)
Control – Steady, unmoving, Normal Centroid
LED moving by10 micron steps, Low-Res, Normal Centroid
0.93
Amplitude (microns)
Amplitude (microns)
0.81
0.54
0.27
0.62
0.31
0.00
0.00
0.0000
0.0091
0.0182
0.0273
0.0364
Spatial Frequency (1 / microns)
LED moving by15 micron steps, High-Res, Normal Centroid
0.000
0.013
0.026
0.039
0.052
Spatial Frequency (1 / microns)
LED moving by10 micron steps, Low-Res, Squared Centroid
“Jigsaw”
Enlarge
45-Degree Tilt
Average
30000
20000
50
40
10000
30
0
20
10
20
30
X (Pix
els)
Y (Pix
els)
Pixel Intens
ity
40000
10
40
50
Ideal Gaussian
600
400
200
0
30
-400
20
10
20
30
X (Pix
els)
els)
50
40
-200
Y (Pix

Developed a Monte Carlo
simulation program to create
simulated 2D profiles with
randomized “noise” based
upon measured data and
calculate the centroid, similar to
what USBChameleon does.
For this I used the tables created
from the single-pixel intensity
statistic measurements.
Added Noise

50000
10
40
50
Noise added for Randomization
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After all of the code was written, I wrote a GUI for it for
appearance’s sake and ease of use.
It has all of the inputs necessary and displays the simulated
image over time,
with the 12-bit
greyscale
converted to RGB
(for visualization
purposes).
The code also enables the user to
move the Gaussian Profile with
added noise as the centroids are
calculated taking into account the
discrete levels of the grayscale
averaging over individual pixels.
0.4
Simulating the low
camera resolution
experiment, the results
had the same trend as the
experimental values, just
with a lower value,
roughly a quarter of the
measured sigma. The
equation was this:
Sigma (micro
ns)
0.3
0.2
0.1
𝜎=
Sh u
0.0
30
40
50
60
70
80
90
100
)
ms
(
tter
6
4
2
e Ave
Fram
8
rage
10
1.917
𝐹∗𝑆
0.0231
Amplitude (microns)
Amplitude (microns)
0.0165
0.0154
0.0110
0.0077
0.0055
0.0000
0.0000
0.000
0.013
0.026
0.039
0.052
Spatial Frequency (1 / microns)
FFT of Ideally Simulated Centroid moving 10mm
steps over 8mm, Low Resolution
0.000
0.013
0.026
0.039
0.052
Spatial Frequency (1 / microns)
FFT of Ideally Simulated Centroid moving 10mm
steps over 8mm, High Resolution
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Frame Average and Shutter both have a significant effect on the
stability of the centroid, at the tradeoff of measurement time.
The noise of the pixel intensity closely follows a square root
dependence on the intensity, as expected.
Analyzing the dynamic (moving) light source, we saw effects of
aliasing in the centroid position. We believe that this is a
combined effect from finite pixel sizes and the digitalization of the
pixel intensity.
To characterize the aliasing effect of the centroid position, we
utilized FFT techniques. This FFT analysis revealed oscillations
related to the pixel size and oscillation related to the imperfection
of the lead screw of the motor-controlled slide.
Monte Carlo simulation of the 2-Dimensional image profile with
added noise (using measured values) resulted in similar trends of
centroid stability as the experimental data for both static and
dynamic images.