### Comparing stars between different filters

• In order to compare the quality of our data, we looked at the data with the largest signal to noise ratio, in this case data taken with a green filter.
• For this, we found the largest and smallest stars, as determined by the amount of pixels which constituted them.
• The coordinates of the stars were recorded, so they can later be compared to the same stars in other filters.
• For the fitting the backgrounds were removed, therefore the error on the no background data is the following (assuming error is Poissonian):
• Below fits can be seen for the maximum and minimum size stars for all filters:

• The plots are projections (they are summed in rows and columns), so to plot the errors the errors were summed in the following way:
• where the is the error on the data point (pixel value).

### Introductory estimation

• Then set about finding for the above stars for all filters.

 Visual Brightest Star Visual Dimmest Star Green Filter Brightest Star Green Filter Dimmest Star Red Filter Brightest Star Red Filter Dimmest Star} Blue Filter Brightest Star Blue Filter Dimmest Star
• In general, a good should be around equal to the number of degrees of freedom,

• From the plots it is obvious that the Poisson errors are not correct as they are too small for the brightest star.

• Also the brightest stars are poorly fitted and therefore have high in comparison to dimmest stars.

### Testing curve_fit for better error estimation

• In order to better obtain errors from curve_fit (as it tends to give outlandish errors), we set out to create a Gaussian of known parameters, and then fit a general Gaussian curve to this.
 Fractional Error When Guessing Incorectly Fractional Error When Guessing Exactly Correlation Coefficient 0 Amplitude 0 X Centre 0 Y Centre 0 0 0 Offset 0

### Setting the threshold

• We decided to use our mode image to set the threshold.
• The mode image is shown below:
• We took the Poissonian error (the square root) of each section.
• We used the error as our threshold by setting the threshold:

### Standard deviation of the stars

• We previously tried to show that all stars in the image have the same standard deviations.
• To find our standard deviations we did the following:
• We cropped an area of 20x20 pixels around each star and found the standard deviations within the area.
• Histograms below are of the ratio of for Location 1 images:
• for Location 1 images:
• Ratio of for Location 2 images:
• for Location 2 images:
• Therefore for both locations we decided to set the requirement that an objects is only a star if its ratio:

### Monte Carlo simulation of a 2D star field

• We have done some prelimenary work on the simulation.
• To generate the positions of stars we uniformly generated x and y pixel positions.
• To create a background we generated Poisson distributed random variables around the mean of 160, which corresponded to a typical value for images of Location 1.
• For each position we wanted to create a Gaussian distribution that represents a star centered on the star's x,y position.
• As the standard deviations should be the same for each star we decided to generate only one value for for all stars. We also assumed that the standard deviations are the same in both directions so we generated only one for and .
• To experiment we uniformly generated values for and for each individual star.
• We then for each pixel in the image calculated the Gaussian value at that particular pixel for each star.
• Resulting image for 50 stars is shown below:

-- ElenaCukanovaite - 11 Jan 2016

Topic attachments
I Attachment History Action Size Date Who Comment
png 30_by_30.png r1 manage 52.9 K 13 Jan 2016 - 11:31 ElenaCukanovaite
png None_1_max.png r1 manage 113.1 K 13 Jan 2016 - 13:12 DavidHadden
png None_1_min.png r1 manage 109.8 K 13 Jan 2016 - 13:13 DavidHadden
png blue_1_max.png r1 manage 120.1 K 13 Jan 2016 - 13:11 DavidHadden
png blue_1_min.png r1 manage 115.9 K 13 Jan 2016 - 13:12 DavidHadden
png elena_b_b.png r1 manage 104.1 K 14 Jan 2016 - 19:51 ElenaCukanovaite
png elena_b_d.png r1 manage 104.0 K 14 Jan 2016 - 19:51 ElenaCukanovaite
png elena_g_b.png r1 manage 104.4 K 14 Jan 2016 - 19:40 ElenaCukanovaite
png elena_g_d.png r1 manage 98.1 K 14 Jan 2016 - 19:40 ElenaCukanovaite
png elena_no_br.png r1 manage 98.9 K 14 Jan 2016 - 19:12 ElenaCukanovaite
png elena_no_d.png r1 manage 100.1 K 14 Jan 2016 - 19:12 ElenaCukanovaite
png elena_r_b.png r1 manage 103.5 K 14 Jan 2016 - 19:57 ElenaCukanovaite
png elena_r_d.png r1 manage 105.1 K 14 Jan 2016 - 19:58 ElenaCukanovaite
png green_1_max.png r1 manage 121.4 K 13 Jan 2016 - 13:12 DavidHadden
png green_1_min.png r1 manage 107.0 K 13 Jan 2016 - 13:12 DavidHadden
png location_2.png r1 manage 50.5 K 14 Jan 2016 - 16:16 ElenaCukanovaite
png mode_sec.png r1 manage 46.3 K 13 Jan 2016 - 11:42 ElenaCukanovaite
png monte_carlo.png r1 manage 278.0 K 13 Jan 2016 - 13:38 ElenaCukanovaite
png red_1_max.png r1 manage 119.8 K 13 Jan 2016 - 13:12 DavidHadden
png red_1_min.png r1 manage 117.4 K 13 Jan 2016 - 13:12 DavidHadden
png sigma_x_loc_1.png r1 manage 66.3 K 14 Jan 2016 - 16:13 ElenaCukanovaite
png sigma_x_loc_2.png r1 manage 46.8 K 14 Jan 2016 - 16:17 ElenaCukanovaite
png stan_dev_n_t.png r1 manage 70.1 K 13 Jan 2016 - 16:13 ElenaCukanovaite
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Topic revision: r11 - 14 Jan 2016 - ElenaCukanovaite

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