Changeset 39815

Timestamp:

Nov 17, 2016, 11:01:53 AM (10 years ago)

Author:

eugene

Message:

updates

File:

• trunk/doc/release.2015/ps1.analysis/analysis.tex (modified) (6 diffs)

trunk/doc/release.2015/ps1.analysis/analysis.tex

@@ -1074 +1074 @@
 contour: 
 \[
-\rho = \sqrt{\frac{x^2}{S^2_{xx}} + \frac{y^2}{S^2_{yy}} + x y S_{xy} \\
+\rho = \sqrt{\frac{x^2}{S^2_{xx}} + \frac{y^2}{S^2_{yy}} + x y S_{xy}} \\
 \]
 
@@ -1100 +1100 @@
 galaxy distance.  
 
-In the classic definition, a reference radius, R90
-is specified as the radius at which the flux
-
 To measure the Petrosian radius and flux, we start by defining a
 series of radial apertures with power-law spacing: $r_{i + 1} = 1.25
@@ -1111 +1108 @@
 
 For any annulus $i$ spanning the radii $r_{\rm min}$ to $r_{\rm max} =
-\Beta r_{\rm min}$, the
+\beta r_{\rm min}$, the
 Petrosian Ratio for that annulus is defined as the ratio of the
 surface brightness in the annulus to the average surface brigthness
@@ -1146 +1143 @@
 In the galaxy model fittting stage, sources which meet certain
 criteria are fitted with analytical models for galaxies.  The
-available models for the PV3 analysis were:
+three models used for the PV3 analysis have similar form:
 \begin{itemize}
-\item Exponential profile : $f = I_0 e^{\frac{-r}{r_0}}$
-\item DeVaucouleur profile : $f = I_0 e^{\frac{-r^{1/4}}{r_0}}$
-\item Sersic : $f = I_0 e^{\frac{-r^{1/n}}{r_0}}$
+\item Exponential profile : $f = I_0 e^{-\rho}$
+\item DeVaucouleur profile : $f = I_0 e^{-\rho^{1/4}}$
+\item Sersic : $f = I_0 e^{-\rho^{1/n}}$
 \end{itemize}
+where $\rho$ is a normalized radial term: $\rho =
+\sqrt{\frac{x^2}{R^2_{xx}} + \frac{y^2}{R^2_{yy}} + x y R_{xx}}$.  The
+terms ($R_{xx}$, $R_{yy}$ , $R_{xy}$) describe the elliptical contour
+and the profile scale in all three models and the coordinates $x$ \&
+$y$ are determined relative to the centroids $x_0, y_0$.  Including
+the normalization ($I_0$) and a local sky value, the Exponential and
+DeVaucouleur profiles have 7 free parameters and the Sersic profile
+has the additional free parameter of the Sersic index $n$.
 
 In this stage, the galaxy model is convolved with our best guess for
@@ -1157 +1162 @@
 all sources detected in the 'bright source' analysis step (S/N > 20 ?)
 were fitted with all three galaxy models, unless (a) the morphological
-test identified the source as a likely cosmic ray (\ref{CR})
-or (b) the peak of the PSF profile was above the saturation limit
-\note{for the chip? cell?}.  Sources in the denser portions of the
-Galactic plane and bulge were not included in the analysis.  This
-restriction limited the total time spent on the galaxy modeling
-analysis at the expense of galaxy photometry in the plane (though Kron
-photometry is available for those objects).
+test identified the source as a likely cosmic ray (\ref{CR}) or (b)
+the peak of the PSF profile was above the saturation limit for the
+chip \note{link to the handling of saturation in detrend paper}.
+Sources in the denser portions of the Galactic plane and bulge were
+not included in the analysis.  This restriction limited the total time
+spent on the galaxy modeling analysis at the expense of galaxy
+photometry in the plane (though Kron photometry is available for those
+objects).
 
 The Galactic Plane region was defined by $|b| > b_{\rm min}$ where
@@ -1170 +1176 @@
 
 The galaxy models are fitted using the same Levenberg-Marquart
-minimization code use for the other non-linear fitting stages.  In the
+minimization code use for the other non-linear fitting stages.  
+
+Before the non-linear fitting may be performed, it is necessary to
+determine the initial values for the parameters to be fitted.  For
+each of the three model types, the position determined from the PSF
+fitting analysis is used as the initial centroid $x_0,y_0$.  A guess
+for the terms ($R_{xx}$, $R_{yy}$ , $R_{xy}$) is generated based on
+the second moments.  The guess does not attempt to use PSF model to
+adjust the ($R_{xx}$, $R_{yy}$ , $R_{xy}$) values; it was found that
+such a guess tended to be too small and resulted in more iterations
+rather than fewer. \note{more detail on that?}  The Kron flux is used
+to generate a guess for the normalization, applying an appropriate
+scale factor based on the ($R_{xx}$, $R_{yy}$ , $R_{xy}$) values.
+
+For the Sersic model, we do not fit the index in the
+Levenberg-Marquardt analysis.  Instead, we  
+
+% start with coarse grid search over the following index values:
+% n = 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0
+
+
+
+
+In the
 convolved galaxy fit, the galaxy model image and the model derivative
 images are convolved with the psf at each iteration. WRITE out the