Difference: 20160211MSciPhototmetryAnalysisobs3part1 (1 vs. 4)

Revision 412 Feb 2016 - ElenaCukanovaite

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META TOPICPARENT	name="StewartBoogertPhotometry2015"

Comparison of fits

Before we fitted an unskewed Gaussian:

Line: 55 to 55

With a 150 images:

Therefore, the more images used the better the $\chi^$ follow the $\chi^2$ distribution.
Latex rendering error!! dvi file was not created.

Changed:

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Shall do 1000 images.

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600 images:

And $\chi^2_\rm{reduced}$ :

Looks more like a $\chi^2$ distribution. However, there is a small peak in the middle, maybe more images will fix. Will try a 1000.
Below are the differences in found and generated parameters for 600 images:

New errors on parameters:

	Error Now (600 images)	Errors before (150 images)
$\alpha$	$\pm$ 0.0009	$\pm$ 0.0008
$\beta_1$	$\pm$ 0.0131	$\pm$ 0.0122
$\beta_2$	$\pm$ 0.0201	$\pm$ 0.0165
$\rho$	$\pm$ 0.0080	$\pm$ 0.0062
$\sigma_x$	$\pm$ 0.0125	$\pm$ 0.0086
$\sigma_y$	$\pm$ 0.0316	$\pm$ 0.0254
	$\pm$ 0.0410	$\pm$ 0.0332
	$\pm$ 0.0268	$\pm$ 0.0227

An example with errors:

	Error Now (600 images)
$\alpha$	0.0014 $\pm$ 0.0009
$\beta_1$	0.087 $\pm$ 0.013
$\beta_2$	-1.160 $\pm$ 0.020
$\rho$	-0.0191 $\pm$ 0.0080
$\sigma_x$	4.28 $\pm$ 0.01
$\sigma_y$	5.38 $\pm$ 0.03
	29.2 $\pm$ 0.04

| 33.8 $\pm$ 0.03 |
Latex rendering error!! dvi file was not created.

Observation 3: Spiral Cluster

Took images of the spiral cluster.
Below is a map of our image locations:

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Revision 312 Feb 2016 - ElenaCukanovaite

Line: 1 to 1

META TOPICPARENT	name="StewartBoogertPhotometry2015"

Added:

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Comparison of fits

Before we fitted an unskewed Gaussian:

$\begin{equation} f_G(x,y,\mu_x,\mu_y,\sigma_x,\sigma_y,\rho, \beta_1, \beta_2) = \frac{1}{2\pi\sigma_x\sigma_y\sqrt{(1-\rho^2)}} \exp \Bigg\{-\frac{1}{2(1-\rho^2)}\Bigg[\bigg(\frac{x-\mu_x}{\sigma_x}\bigg)^2 + \bigg(\frac{y-\mu_y}{\sigma_y}\bigg)^2 -2\rho\bigg(\frac{x-\mu_x}{\sigma_x}\bigg)\bigg(\frac{y-\mu_y}{\sigma_y}\bigg)\Bigg]\Bigg\} \end{equation} \begin{equation} f_{bg}(N,M) = \frac{1}{N \times M} \end{equation} \begin{equation} f(\alpha) = \alpha f_G + (1 - \alpha) f_{bg} \end{equation}$

Now we fitted a skewed Gaussian:

$\begin{equation} f_G(x,y,\mu_x,\mu_y,\sigma_x,\sigma_y,\rho, \beta_1, \beta_2) = \frac{1}{2\pi\sigma_x\sigma_y\sqrt{(1-\rho^2)}} \exp \Bigg\{-\frac{1}{2(1-\rho^2)}\Bigg[\bigg(\frac{x-\mu_x}{\sigma_x}\bigg)^2 + \bigg(\frac{y-\mu_y}{\sigma_y}\bigg)^2 -2\rho\bigg(\frac{x-\mu_x}{\sigma_x}\bigg)\bigg(\frac{y-\mu_y}{\sigma_y}\bigg)\Bigg]\Bigg\} \times \Bigg[1 + \rm{erf} \frac{\beta_1 x + \beta_2 y}{\sqrt{2}}\Bigg] \end{equation} \begin{equation} f_{bg}(N,M) = \frac{1}{N \times M} \end{equation} \begin{equation} f(\alpha) = \alpha f_G + (1 - \alpha) f_{bg} \end{equation} <br />$

The fittings are shown below:

Parameters:

	Star (1124,513) unskewed	Star (1124,513) skewed	Star (180,591) unskewed	Star (180,591) skewed	Star (724,479) unskewed	Star (724,479) skewed
$\rho$	1.43e-01	-1.91e-01	1.74e-01	2.34e-01	0.11	-0.04
	3.07e+01	2.92e+01	2.98e+01	3.03e+01	30.1	29.4
	3.07e+01	3.38e+01	3.06e+01	3.55e+01	31.5	36.3
$\sigma_x$	3.86	4.28	4.18	4.30	4.29	4.37
$\sigma_y$	4.00	5.38	4.43	8.02	4.77	6.97
$\alpha$	1.41e-02	1.43e-02	1.42e-02	1.51e-02	0.80	0.80
$\beta_1$		8.65e-01		1.28e-01		0.40
$\beta_2$		-1.16		-2.62e+00		-1.51
$\chi^2$	3262	3229	3538	3412	895118	571302
Degrees of freedom	3952	3952	3952	3952	3952	3952

$\chi^2$ Monte Carlo distribution

With 40 images generated the $\chi^2$ histogram did not look promising:

With a 150 images:

Therefore, the more images used the better the $\chi^$ follow the $\chi^2$ distribution.
Shall do 1000 images.

Observation 3: Spiral Cluster

Took images of the spiral cluster.
Below is a map of our image locations:

Once realigned should look something like:

Images we took (lum):

Here is one of the images we captured, alognside its background (luminensce filter):

Ran through our finding algorithm, found 72 stars:

Some stars found are actually 2 stars.
Latex rendering error!! dvi file was not created.

Observation 2: Bias, dark and light frame evolution

The evolution before the cooling ring dissapeared:

Line: 11 to 80

Added:

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Decided to ignore first 20 images from the above plots to create the master bias.
On the left is master bias that takes all 100 bias frames, on the right is one ignoring first 20 bias frames:

All dark frames (30s):

Added:

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All flat frames (no filter):

Added:

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Kept all frames for master flat:
Unlike last week, removed the master bias frame from each flat frame before building a master flat frame.
On the left is last week's flat frame, on the right it is the one with master bias removed before averaging:

-- ElenaCukanovaite - 11 Feb 2016

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Revision 211 Feb 2016 - ElenaCukanovaite

Line: 1 to 1

META TOPICPARENT	name="StewartBoogertPhotometry2015"

Changed:

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Monte Carlo generated star fitting

>
>

Observation 2: Bias, dark and light frame evolution

The evolution before the cooling ring dissapeared:

All bias frames:

Changed:

<
<

>
>

Changed:

<
<

$\chi^2$ of Monte Carlo generated star

40 stars generated:

150 stars generated:

>
>

All dark frames (30s):

All flat frames (no filter):

-- ElenaCukanovaite - 11 Feb 2016

Line: 18 to 23

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Revision 111 Feb 2016 - ElenaCukanovaite

Line: 1 to 1

Added:

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META TOPICPARENT	name="StewartBoogertPhotometry2015"

Monte Carlo generated star fitting

$\chi^2$ of Monte Carlo generated star

40 stars generated:

150 stars generated:

-- ElenaCukanovaite - 11 Feb 2016

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