# Difference: Photometry2016_Simulation (4 vs. 5)

#### Revision 513 Oct 2016 - AaronAndrews

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 META TOPICPARENT name="StewartBoogertPhotometry2016"

### Part One

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• Important things to note: This is a projection for the 2d gaussian at y=0 (green line shows the 'maximum' profile on the x axis). Bin values are calculated using integration over both x and y axis, resulting in decreased bin heights, particularly near the peak.
• Near the peak, measured values from integration is less than value of gaussian.
• Position of integrated peak bin offset from actual gaussian peak position - could estimate position using relative heights of adjacent bins.
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Poisson Distribution of pixel values: Simulation_test4.py.txt

• Each pixel value consists of a summation of n random variables (e.g. y=x1+...+xn). Each random variable corresponds to the contribution of a particular star (out of n stars in the image).
• Each random variable follows a Poisson distribution, with a mean value (E[x]) equal to the integrated value of a star's gaussian profile over the pixel area.
• We can assume that these random variables are not correlated (correlation coefficient P=0), therefore the total mean value will be the sum of individual mean values (E[y]=E[x1]+...+E[xn]).
• We can also assume that the summed pixel values (from star contributions only) also follow a Poisson distribution.
• Therefore, we can simulate te 'counting' of photons in each pixel by using the total intgrated pixel value as the mean to gain a random poisson distributed value.
• Example: projection (y=0) of a 16x1 pixel grid with a star generated at x=7.75 (A=100, sigma=2):
• -- AaronAndrews - 09 Oct 2016

 META FILEATTACHMENT attachment="PositionSimTest2.png" attr="" comment="random position test (100x100, 50 stars)" date="1476004481" name="PositionSimTest2.png" path="PositionSimTest2.png" size="19417" user="zyva010" version="1"

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