Simulation: ( Simulation_test10.py.txt)

• Made example star field with no background - used M103 data, 108 stars total. ( M103_Simtest_noBG.txt)
• Modified simulation to generate position-varying background. Mean and standard deviation can be changed independantly.
• For testing, generated means and standard deviations using following functions ('inclined planes'): ( M103_BG_1.txt)
  • Mean = 900 + (0.5)x + (0.005)y
  • S.D. = 5 + (0.01)x + (0.01)y
  • x,y = pixel positions
• Could also generate with more complicated functions - e.g. taylor expansion.
• Used mean and S.D. per pixel to generate random gaussian distributed value for background, added to example star field.
• Size of the median filter box as a function of the fitted mean:
• Used mean and S.D. per pixel to generate random gaussian distributed value for background, added to example star field:
• 

• Ran a median filter (i.e. finding median of a box, size n, centered on each pixel) for different box sizes, on the simulated background+stars.
• Subtracted the median image from original, to remove background. Then created histograms of resulting pixel values.
• Histograms assumed to be gaussian - found sigma and mean for each.
• Plotted sigmas and means in relation to box size.

• Median, sigma and mean plots on simulated M103 with background, 65 width box:
  

• Median, sigma and mean plots on simulated background, 65 width box:
  
• Histograms showing the simulated background minus the median filter of the background for box sizes 201 and 11
• For the 201 box size the fitted mean pixel value is 0.56057, the standard deviation is 15.992
• For the 11 box size the fitted mean pixel value is 0.40479, the standard deviation is 15.634

• Histograms showing the simulated background with stars minus the median filtered version for box sizes 301 and 15
• For the 201 box size the fitted mean pixel value is 0.15810, the standard deviation is 16.386
• For the 11 box size the fitted mean pixel value is 0.38595, the standard deviation is 15.972

• Size of the median filter box as a function of the fitted mean and the fitted standard deviation:
  

• Images showing the simulated background minus the median filter of the background for box sizes 201 and 11:

• Images showing the simulated background with stars minus the median filter of the background for box sizes 201 and 11: