
META TOPICPARENT 
name="StewartBoogertPhotometry2016" 
Part One 

 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.


> >  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" 
