Experimentation of Centroid Stability and Simulated Noise, statics and Dynamics

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Experimentation of Centroid Stability and
Simulated Noise, statics and Dynamics

• Kevin Kelly
• Mentor Peter Revesz

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Brief Introduction

• 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.

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Chameleon GUI
Inputs
ROI
Profile of Image
Outputs
Centroid Position Trace
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Experimental Setup

• 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.

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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
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Parameters to Test
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

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• The instability of the centroid comes from a
  variety of sources
• Experimental Conditions Mechanical instability
  of the light source, vibrations, airflow in
  experimental tunnel.
• Errors in CCD Read Noise, Photon
  Noise, Dark Noise
• Experimental Paramters Adjusting
  Frame Average, Shutter, Type of centroid
  calculation, etc.

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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.
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Results

• 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
 
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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Analysis of Pixel NoiseStatic Image

• 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 pixels average intensity and
  intensity distribution.
• We repeated this measurement a number of times
  (typically 200) to obtain statistics

ROI of Pixel Intensities being saved
Pixel Intensities across ROI
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Typical plot of Standard Deviation of Pixel
Intensity v. Average Pixel Intensity with
trendline.

• Two important things to note
• Each pixels 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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Moving from Static to Dynamic

• 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.

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Aliasing Pictures
Beginning
Halfway
End
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• 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.

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.
Residual of Above Graph
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FFTs
LED moving by10 micron steps, Low-Res, Normal
Centroid
Control Steady, unmoving, Normal Centroid
LED moving by10 micron steps, Low-Res, Squared
Centroid
LED moving by15 micron steps, High-Res, Normal
Centroid
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Methods to Reduce Aliasing
Jigsaw
Enlarge
45-Degree Tilt
Average
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Simulation

• 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.

Ideal Gaussian
Noise added for Randomization
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Simulation GUI

• After all of the code was written, I wrote a GUI
  for it for appearances 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.
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Simulation ResultsStatic Image
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
 
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Simulation ResultsDynamic Image
FFT of Ideally Simulated Centroid moving 10mm
steps over 8mm, Low Resolution
FFT of Ideally Simulated Centroid moving 10mm
steps over 8mm, High Resolution
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Conclusion

• 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.

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Questions?