StewartBoogertPhotometry20161021 < Public < RHUL Physics Department TWiki

-- LauraBevilacqua - 18 Oct 2016

To do by Friday:

Select star cluster for observations

Anisha:

Fix histrogram from last week
Plot median as a function of exposure time
Plot error as function of exposure time

Aaron:

Figure out how to save simulated images as FITS files.
Give Laura test fits file, with recorded star positions and intensities/counts.

Laura:

Convert Aaron's fits file to image
Test whether program counts accurately

Weekly Progress:

Anisha:

Corrected histrogram of number of photoelectrons for a 0.1s exposure in the dark frame with 500 bins - logarithmicly normalized:

The median intensity as a function of exposure time.:

Line of best fit: y = 917.43 + 0.08x

Error as a function of exposure time:

Line of best fit: y = 15.76 + 0.73x

$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 $\nu_0$.$

Aaron:

Implemented a true 2D Gaussian with correlation between x and y (with correlation coefficient P (rho)):

$\begin{equation} f\left ( x,y;x_0 ,y_0 ,\sigma _{x} ,\sigma _{y} ,\rho \right )= \frac{1}{2 \pi \sigma _{x} \sigma _{y} \sqrt{1-\rho ^{2}}} \exp {\left [ - \frac{1}{2\left ( 1-\rho ^{2} \right )}\left ( \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )^2 + \left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right )^2 -2\rho \left (\frac{ x-x_0 }{2{\sigma _{x}}^{2}} \right )\left (\frac{ y-y_0 }{2{\sigma _{y}}^{2}}\right ) \right )\right ]} \end{equation}$

(Note: normalisation factor is ignored so far for programming purposes; maximum pixel value is being used in its place)
Integration of 2D Gaussian in this form is done numerically.
Tested for P =0, P =0.5, P =0.999 (sigma_x=sigma_y=3 in each case)
(Note - image is rotated 90 degrees clockwise)
Also - found a way to save images as FITS files, similar to images gained from observations.
Simulated test images for Laura - all on 100x100 pixel grids, using calculated mean pixel values instead of randomised poisson values:
- 1 star at (50,50), peak=60000.
- 3 stars with decreasing intensities: (25.25), peak=10000; (50,50), peak=1000; (25,25), peak=100
- 8 stars with peak=60000, in pairs which are closely spaced: (45,20), (55,20); (44,40), (56,40); (43,60), (57,60); (42,80), (58,80)
- 8 stars with peak=60000, peaks are out of frame: (100,20), (102,40), (104,60), (106,80), (-8,20), (-10,40), (-12,60), (-14,80)

Laura:

Fits files from Aaron successfully converted to monochrome images
Images scanned for stars and correct star count is returned
Edge detection helps identify star position

The maximum pixel value was found to be 65195 from the fits file below, as opposed to Aaron's given value of 65535
Threshold of 100 set so if pixels are above this value they are set as white background, if below they are coloured black (remember reverse grayscale):
Edge detection:

Maximum pixel value found to be 62673, compared to Aaron's 60000:
Threshold set as 20 so that stars don't touch, achieves accurate count of 8:

Attachments

Topic attachments
I	Attachment	History	Action	Size	Date	Who	Comment
png	Error_as_a_function_of_exposure_time_with_best_fit.png	r1	manage	31.3 K	20 Oct 2016 - 18:01	AnishaVadher	Error as a function of exposure time
jpg	FinderTest1a.jpg	r1	manage	6.5 K	20 Oct 2016 - 18:07	AnishaVadher
png	FinderTest1a.png	r1	manage	14.5 K	21 Oct 2016 - 12:16	AaronAndrews	Finder test 1: 1 star
png	FinderTest1a_count.png	r1	manage	12.8 K	20 Oct 2016 - 18:07	AnishaVadher
jpg	FinderTest1a_mon.jpg	r1	manage	5.4 K	20 Oct 2016 - 18:07	AnishaVadher
png	FinderTest2.png	r1	manage	16.5 K	21 Oct 2016 - 12:17	AaronAndrews	Finder test 2: 3 stars, decreasing intensities
jpg	FinderTest3.jpg	r1	manage	14.1 K	20 Oct 2016 - 18:07	AnishaVadher
png	FinderTest3.png	r1	manage	35.9 K	21 Oct 2016 - 12:17	AaronAndrews	Finder test 3: 8 stars, closely spaced
png	FinderTest3_count.png	r1	manage	15.5 K	20 Oct 2016 - 18:07	AnishaVadher
jpg	FinderTest3_mon.jpg	r1	manage	6.2 K	20 Oct 2016 - 18:07	AnishaVadher
png	FinderTest4.png	r1	manage	17.0 K	21 Oct 2016 - 12:18	AaronAndrews	Finder test 4: 8 stars, out of frame
png	Histogram_of_number_of_pixel_values_for_0.1s_exposure_500_bins.png	r1	manage	18.4 K	20 Oct 2016 - 17:53	AnishaVadher	Corrected histrogram of number of photoelectrons for a 0.1s exposure in the dark frame with 500 bins - logarithmicly normalized
png	SkewTest2.png	r1	manage	18.6 K	18 Oct 2016 - 22:46	AaronAndrews	Testing x and y correlation (P) for P=0, P=0.5, P=0.999
png	The_median_intensity_as_a_function_of_exposure_time_with_best_fit.png	r1	manage	36.2 K	20 Oct 2016 - 17:55	AnishaVadher	The median intensity as a function of exposure time.

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Topic revision: r12 - 28 Feb 2022 - JoolsElliott

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