SCALE FACTOR FOR FLUX CALIBRATION

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[edit] INTRODUCTION

1.Extract the pointsources from the image and determine their counts from the image doing photometry.

2.Compare these extracted point sources with sourses in Simbad or Hipparcos catalog.

3.calculate the flux of these sources using magnitude from catalog.

4.conver this flux to counts.

5.compare these counts with the counts that obtaines from image.

6.Determine the scale factor using least square fitting.

[edit] EXTRACTION OF POINT SOURCES

Extract point sources from the image using SExtractor.Sextractor is a software used for automated detection and photometry of sources in fits files.The Source Extractor package works in a series of steps. 1.Measure the background and its RMS noise.

2.Substract background.

3.Filter.

4.Find objects (Thresholding).

5.Deblend detection.(Break up detection in to defferent objects.).

6.Measure shape and positions.

7.Clean.

8.Perform photometry.

9.Seperate stars and galaxies.

10.Output catalog and check images.


USING SE ON ONE IMAGE

SE needs a series of parameters in order to run and these can be given at the command line or in a configuration file.So in order to run SE ,

sex image -c configuration file.txt

The parameter value can be given to SE on the command line

sex image -c configuration file.txt -PARAMETER1 value1 -PARAMETER2 value2

BACKGROUND ESTIMATION

SE estimate the background of the image and the RMS noise in that background.SE substracts the estimated background from the photometry and uses RMS to estimate errors.

FINDING AND SEPARATING OBJECTS

SE considers every pixel above a certain threshold to be a part of an object.The 'deblending' is the part where it figures out which pixels or parts of pixels belong to which objects.The threshold parameters indicate the level from which SE should start treating pixels as if they were part of objects,determining parameters from them.

FILTERING

Before the detection of pixels above the threshold,there is the option of applying a filter.This filter smooths the image.

DEBLENDING:sperating into different objects

PHOTOMETRY

After deblending the objects,SE performs astrometry,photometry and geometric parameters.The astrometry cannot be influenced by input parameters.The photometry is influenced by input parameters.There are five different approaches in SE's photometry,isophotal,isophotalcorrected,automatic,best estimate and aperture.

ISO:The pixels above the threshold constitute an isophotal area.The flux or magnitude determined from this is the isophot flux (counts in pixels above threshold minus the background).

ISOCOR:Corrected flux using Gaussian profile for the object.

AUTO:SE uses a flexible elliptical aperture around every detected object and measures all the flux inside that.

APERTURES

The aperture SE diameters are specified in pixels in the PHOT_APERTURES.These are user specified apertures.

Object classification

This section completely devoted to the CLASS_STAR parameter,SE's classification of the objects is on the basis of a Neural Network output.It can have value between 0 (galaxy) and 1 (star).


[edit] MAGNITUDE TO COUNT CONVERSION

After extracting the point sources from the image and doing the photometry ,next step is to find out these sources in simbad or Hipparcos catalog and find out their V magnitude and E(b-v).Use Kurucz model for finding the flux corresponding to the wavelength of interest.

If mv be the v magnitude of the star and F0 the flux of vega in v band ,then

flux of the star f=f_0\times 10^{-0.4 mv}

f=3.64\times 10^{-9} \times 10^{-0.4 mv}

Let Vflux be the Kurucz flux ,

4 \Pi R^{2} /4 \Pi D^{2} \times Vflux \times exp{-\tau_1}= 3.64\times 10^{-9} \times 10^{-0.4 mv}

Scale value for Kurucz flux

R^{2}/D^{2}=(3.64\times 10^{-9} \times 10^{-0.4 mv} ) \times exp{\tau_1} /Vflux

F_{star}=F_0 \times R^{2}/D^{2} \times exp{-\tau_2}

\tau_2= 5.8 \times 10^{21} \times \sigma \times E(b-v)

Fstar(ergs − 1cm − 2A − 1) the flux of star at the wavelength of interest recieved by the detector

count rate= \lambda /hc \times F_{star} \times A \times \Delta \lambda

A = Imaging effective area

Δλ =Effective bandwidth

[edit] Method of least squares

Let us consider the data points (xi,yi) where i = 1,2....n

We have to fit a straight line Y = mx + c

m= (n \sum (x_i \times y_i) - (\sum x_i) \times (\sum y_i))/( n\sum (x_i^{2}) - (\sum x_i)^{2} )

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