Difference: StewartBoogertPhotometry20161021 (10 vs. 11)

Revision 1121 Oct 2016 - AaronAndrews

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META TOPICPARENT name="StewartBoogertPhotometry2016"
-- LauraBevilacqua - 18 Oct 2016
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  • Error as a function of exposure time:
    Error_as_a_function_of_exposure_time_with_best_fit.png

  • Line of best fit: y = 15.76 + 0.73x
Changed:
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%BEGINLATEX% Mean number of effective photoelectrons : \begin{equation} \nu = \nu_0 + \mu t. \end{equation} Actual number of photoelectrons: \begin{equation} n = n_0 + m, \end{equation} where $n_0$ follows a Gaussian distribution and may come from electronic noise and $m$ follows a Poisson distribution as a function of $\mu t$. Error in $m \sigma_m$ come from $\sqrt{\mu t}$. Therefore the intercept of the $n_{peak}$ (the median) as a function of exposure time is $\mu$ and the intercept is $\nu_0$.
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%BEGINLATEX% Mean number of effective photoelectrons : \begin{equation} \nu = \nu_0 + \mu t. \end{equation} Actual number of photoelectrons: \begin{equation} n = n_0 + m, \end{equation} where $n_0$ follows a Gaussian distribution and may come from electronic noise and $m$ follows a Poisson distribution as a function of $\mu t$. Error in $m \sigma_m$ come from $\sqrt{\mu t}$. Therefore the intercept of the $n_{peak}$ (the median) as a function of exposure time is $\mu$ and the intercept is $\nu_0$.
 %ENDLATEX%

Aaron:

  • Implemented a true 2D Gaussian with correlation between x and y (with correlation coefficient P (rho)):
Changed:
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%BEGINLATEX% \begin{equation} f\left ( x,y;x_0 ,y_0 ,\sigma _{x} ,\sigma _{y} ,\rho \right )= \frac{1}{\pi \sigma _{x} \sigma _{y} \sqrt{1-\rho ^{2}}} \exp {\left [ - \frac{1}{2\left ( 1-\rho ^{2} \right )}\left ( \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )^2 + \left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right )^2 -2\rho \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )\left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right ) \right )\right ]}
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%BEGINLATEX% \begin{equation} f\left ( x,y;x_0 ,y_0 ,\sigma _{x} ,\sigma _{y} ,\rho \right )= \frac{1}{2 \pi \sigma _{x} \sigma _{y} \sqrt{1-\rho ^{2}}} \exp {\left [ - \frac{1}{2\left ( 1-\rho ^{2} \right )}\left ( \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )^2 + \left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right )^2 -2\rho \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )\left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right ) \right )\right ]}
  \end{equation} %ENDLATEX%
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