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Commit e901a648 authored by Kevin Lüdemann's avatar Kevin Lüdemann
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Error correction done

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......@@ -716,7 +716,7 @@ In addition to that the errors are smaller es well which means they were highly
\includegraphics[width=0.48\textwidth]{MF_G_res.pdf}
\includegraphics[width=0.48\textwidth]{MF_B.pdf}
\includegraphics[width=0.48\textwidth]{MF_B_res.pdf}
\caption{Master Flat for filter R (top), filter G (center) and filter B (bottom). The right image is always intensity rescaled to better see structures. The colour bars show the intensities if the left images.}
\caption{Master Flat for filter R (top), filter G (center) and filter B (bottom). The right image is always intensity rescaled to better see structures. The colour bars show the intensities of the left images.}
\label{fig:MF}
\end{figure}
Prior to taking scientifically valuable images with a CCD the bias, ron and dark current correction has to be done again at final temperature which was $T_\text{final}=(-15.1\pm0.3)\si{\celsius}$
......@@ -735,17 +735,17 @@ Some pixels are shown as black pixels, which suggest that the are hot or not fun
These need to be avoided while analysing the final images because they do not contain any information.
The other pixels show a distribution of warmer and colder pixels which was expected.\\
With these correction images the dome flat images can be corrected.
For the Observation three filter are useful “R” for red, “G” for green and “B” for blue.
For the observation three filter are useful “R” for red, “G” for green and “B” for blue.
For all those filters dome flat image needs to be taken.
They are shown in figure \ref{fig:MF} where R is on top, G in the center and B in the bottom.
Left are the fields without contrast enhancement and right with.
These image show similar feature which is the donut shadow slightly up end left from the center.
This suggests that it originates from the telescope and might be a dust particle on the mirror.
Also some distortions appear on the top of every frame which is biggest for the R filter.
These seem to be filter dependent and do only show up on images takes on that evening which suggest that the CCD was not correctly attached.
These seem to be filter dependent and do only show up on images taken on that evening which suggest that the CCD was not correctly attached.
Fortunately they only appear on the top and can later be ignored.\\
In Addition to those every filter shows some donut shadows on its own, which suggests that they are dust particles on the filter itself.
Also the shading and vignetting is slightly different for different filter but not majorly different in intensity in the normalized field as the left side images show.
Also the shading and vignetting is slightly different for different filters but not majorly different in intensity in the normalized field as the left side images show.
These will be corrected in the later images with this master flat field but to avoid amplifying noise stars should be mostly taken from the center region.
......@@ -756,7 +756,7 @@ These will be corrected in the later images with this master flat field but to a
\centering
\includegraphics[width=0.48\textwidth]{boxes.pdf}
\includegraphics[width=0.48\textwidth]{gain_length.pdf}
\caption{Positions in the bias subtracted raw flat image with filter R that were used for the gain calculation (left). Resulting curve showing gain as a function of the side length of the boxes (right).}
\caption{Position in the bias subtracted raw flat image with filter R that was used for the gain calculation (left). Resulting curve showing gain as a function of the side length of the boxes (right).}
\label{fig:boxes}
\end{figure}
In order to calculate the gain factor the equation \eqref{eq:gain} is used on a small region in a bias subtracted flat image.
......@@ -818,18 +818,18 @@ In order to make the transit visible a time series of images is needed.
We choose to only use the “R” filter due to a time constraint and the still blue sky.
The images taken are bias and dark current corrected and rescaled with the master flat field.
The resulting images are in units ADU and can be analysed.
All shown images are intensity rescaled and darker images mean higher intensities.\\
All shown images are intensity rescaled and darker pixels mean higher intensities.\\
Due to the rotation of the earth the stars seem to be moving in the images which needs to be corrected.
Afterwards the photon flux in ADU can be calculated by summing the pixel values in a small region around the star.
For minimizing the background in the sum a circular aperture should be used but a square was all that could be done in time.
For minimizing the background in the sum a circular aperture should be used but a square one was all that could be done in time.
In order to correct the brightness of the star for fluctuations in the atmosphere more stars are averaged in to a flattening value per time point.
For comparing all the stars their intensity is calculated per pixel that were used in the sum which is an average resulting in units ADU/pixel.
A summary of all stars used can be seen in figure \ref{fig:sky} (right) where every other star which was used for correction is marked with a red box.
Only stars which have at least $\nicefrac{1}{4}$ of the brightness of WASP-48-a where used for the calculation and are shown on the bottom image of figure \ref{fig:sky}.
A summary of all stars used can be seen in figure \ref{fig:sky} (left) where every other star which was used for correction is marked with a red box.
Only stars which have at least $\nicefrac{1}{4}$ of the brightness of WASP-48-a where used for the calculation and are shown in the right image of figure \ref{fig:sky}.
This is because smaller intensities have a smaller signal to noise ration which will not make the average flattening value better.
Additionally all stars are subtracted by the median background signal due to the large changes over time.
The median background intensity is show on the right in figure \ref{fig:intensities}.\\
The resulting curves are shown in figure \ref{fig:intensities} where WASP-48-a is the blue and mean values of the stars used for correction the black curve on the left axis.
The resulting curves are shown on the left in figure \ref{fig:intensities} where WASP-48-a is the blue and mean values of the stars used for correction the black curve on the left axis.
The resulting intensity curve after flattening is shown in red on the right axis.
The dashed vertical line shows the time when the transit should start.
Two different levels of intensity seem to appear in the plot.
......@@ -867,10 +867,10 @@ With this in mind these areas have to be avoided if possible during the measurem
Looking at the ron it is clear that this type of noise is very small.
It's error resulting from a standard deviation is in the same order of magnitude as the value but the value of the ron itself is very low.
This can be seen by comparing to the intensities of WASP-48-a per pixel, which are two orders of magnitude larger.
Therefore the ron is seen as an source of error but its error is neglected in further calculations.\\
Therefore the ron is seen as a source of error but its error is neglected in further calculations.\\
The dome flat images show the gradients towards the sides which are quite large but can be corrected in the measurements.
But this also means by correcting the sides, the errors are also amplified.
The best way is to only use stars in the center of the image, where the gradients are not to large.
The best way is to only use stars in the center of the image, where the gradients are not to large which we did not have much of.
This can also be seen in the calculation of the gain.
There the larger the box for calculating the standard deviation gets the larger the gain is.
In order to compensate for that some box sizes where averaged in a regime where the gain is almost constant leading to an error an order of magnitude smaller than the value itself which means a good estimate.\\
......@@ -884,12 +884,12 @@ There a plain flew through the area of observation and caused an overflow in som
This persisted for some of the following exposures.
Some time later a few bright and fast objects like a satellite or meteoroid also flew through the area of observation and caused hot pixels.
These images either need to be taken out of analyses or no star should be selected in those areas.
Due to the time constraint with the transit happening we could not take out the plane because the transit happened time wise to close the plane flying over.
Due to the time constraint with the transit happening we could not take out the plane because the transit happened time wise to close to the plane flying over.
Fortunately the largest part of the plane is exposed to the part of the CCD where we had the unexplained errors, which meant ignoring this area was not an issue.\\
Regarding the transit itself we found that no clear transit is visible.
Our assumption is that the background was still to strong because it has almost the same brightness per pixel as the WASP-48-a star has.\\
This is emphasized by the values for $noise^2$ which we calculated for two different set of stars with different brightness.
They have an offset because on set of stars is less bright but they follow qualitatively the curve of the background.
They have an offset because one set of stars is less bright but they follow qualitatively the curve of the background.
Additionally the signal to noise ratio gets as low as $3.5$ in the beginning of the measurement which is very small.\\
This may be a problem with the summer time, because it does not get as dark as it gets during winter time.
In addition to that the city of Göttingen and the almost full moon were quite bright as well.
......
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